Loading image file :/home/twolf/lisp/psl/linux/red/reduce.img *** Function `!%compactheap' has been redefined ("/home/twolf/para/" "" "$reduce/lisp/psl/linux/red/" "$reduce/lisp/psl/linux/psl/") REDUCE 3.7, 15-Apr-1999, patched to 15-May-2003 ... 1: The name of this new session is: "bu498-3-Oct-" 2: If this file is loaded just for printing then in addition do: in drvlist$ depend {f,b},t,s,x$ lisp <>$ 3: ####### This is the case N2f1b0t6s10w3. ####### The equation: f =D f *f*p1 + D f*D D f*p3 + D f*f *p5 + D D f *p7 + D D f*D f*p4 + D f *f*p2 t 2 x 2 1 2 2 x 1 2 2x 1 2 1 1 x + D f*f *p6 + f *p8 1 x 3x It's symmetry: f =D f *f*q1 + D f *D D f*q11 + D f *f *q16 + D f *D f*f*q5 + D f *D D f *q18 s 2 3x 2 2x 1 2 2 2x x 2 x 2 2 x 1 2 x 2 2 + D f *D f*f*q6 + D f *f *q20 + (D f) *D D f*q7 + (D f) *f *q12 2 x 1 2 x 2x 2 1 2 2 x + D f*D D f *q23 + D f*D D f*D f*q8 + D f*D f *f*q3 + D f*D f*f *q13 2 1 2 2x 2 1 2 1 2 1 x 2 1 x + D f*f *q21 + D D f *q26 + D D f *D f*q24 + D D f *D f *q17 2 3x 1 2 4x 1 2 2x 1 1 2 x 1 x 2 + D D f*D f *q10 + D D f*(D f) *q9 - D D f*f *f*q25 + D f *f*q2 1 2 1 2x 1 2 1 1 2 x 1 3x 2 + D f *f *q15 + D f *D f*f*q4 + D f *f *q19 + (D f) *f *q14 + D f*f *q22 1 2x x 1 x 1 1 x 2x 1 x 1 3x + f *q27 5x {q26,q25,q24,q23,q21,q20,q18,q17,q16,q13,q12,q11,q10,q9,q8,q7,q6,q5,q3,q1,p7,p5, p4,p3,p1} {q26,q25,q24,q23,q22,q19,q18,q17,q15,q14,q13,q11,q10,q9,q8,q7,q6,q4,q3,q2,p7,p6, p4,p3,p2} {q25,q24,q23,q22,q21,q20,q19,q18,q17,q16,q15,q14,q13,q12,q11,q10,q9,q8,q7,q6,q5, q4,q3,q2,q1,p6,p5,p4,p3,p2,p1} {q27,q26,q25,q24,q23,q22,q21,q20,q19,q18,q17,q16,q15,q14,q13,q12,q11,q10,q9,q8, q7,q6,q5,q4,q3,q2,q1} {p8,p7,p6,p5,p4,p3,p2,p1} Generating all terms of total degree 2 Pairing now degree 1 terms from the system with degree 1 terms from the symmetry df(f,t)=D D f *p7 + f *p8 1 2 2x 3x df(f,s)=D D f *q26 + f *q27 1 2 4x 5x Generating all terms of total degree 3 Pairing now degree 1 terms from the system with degree 2 terms from the symmetry df(f,t)=D D f *p7 + f *p8 1 2 2x 3x df(f,s)=D f *f*q1 + D f *D D f*q11 + D f *f *q16 + D f *D D f *q18 2 3x 2 2x 1 2 2 2x x 2 x 1 2 x + D f *f *q20 + D f*D D f *q23 + D f*f *q21 + D D f *D f*q24 2 x 2x 2 1 2 2x 2 3x 1 2 2x 1 + D D f *D f *q17 + D D f*D f *q10 + D f *f*q2 + D f *f *q15 1 2 x 1 x 1 2 1 2x 1 3x 1 2x x + D f *f *q19 + D f*f *q22 1 x 2x 1 3x Pairing now degree 2 terms from the system with degree 1 terms from the symmetry df(f,t)=D f *f*p1 + D f*D D f*p3 + D f*f *p5 + D D f*D f*p4 + D f *f*p2 2 x 2 1 2 2 x 1 2 1 1 x + D f*f *p6 1 x df(f,s)=D D f *q26 + f *q27 1 2 4x 5x *** Garbage collection starting *** GC 1 3-Oct-2003 04:49:41, 30 ms (0%), 990052 occupied, 24009900 free Generating all terms of total degree 4 Pairing now degree 1 terms from the system with degree 3 terms from the symmetry df(f,t)=D D f *p7 + f *p8 1 2 2x 3x 2 2 df(f,s)=D f *D f*f*q5 + D f *D f*f*q6 + (D f) *D D f*q7 + (D f) *f *q12 2 x 2 2 x 1 2 1 2 2 x 2 + D f*D D f*D f*q8 + D f*D f *f*q3 + D f*D f*f *q13 + D D f*(D f) *q9 2 1 2 1 2 1 x 2 1 x 1 2 1 2 - D D f*f *f*q25 + D f *D f*f*q4 + (D f) *f *q14 1 2 x 1 x 1 1 x *** Garbage collection starting *** GC 2 3-Oct-2003 04:50:17, 40 ms (0%), 1088558 occupied, 23911393 free *** Garbage collection starting *** GC 3 3-Oct-2003 04:51:49, 60 ms (0%), 1317980 occupied, 23681972 free Pairing now degree 2 terms from the system with degree 2 terms from the symmetry df(f,t)=D f *f*p1 + D f*D D f*p3 + D f*f *p5 + D D f*D f*p4 + D f *f*p2 2 x 2 1 2 2 x 1 2 1 1 x + D f*f *p6 1 x df(f,s)=D f *f*q1 + D f *D D f*q11 + D f *f *q16 + D f *D D f *q18 2 3x 2 2x 1 2 2 2x x 2 x 1 2 x + D f *f *q20 + D f*D D f *q23 + D f*f *q21 + D D f *D f*q24 2 x 2x 2 1 2 2x 2 3x 1 2 2x 1 + D D f *D f *q17 + D D f*D f *q10 + D f *f*q2 + D f *f *q15 1 2 x 1 x 1 2 1 2x 1 3x 1 2x x + D f *f *q19 + D f*f *q22 1 x 2x 1 3x *** Garbage collection starting *** GC 4 3-Oct-2003 04:53:26, 40 ms (0%), 1186104 occupied, 23813848 free Generating all terms of total degree 5 Pairing now degree 2 terms from the system with degree 3 terms from the symmetry df(f,t)=D f *f*p1 + D f*D D f*p3 + D f*f *p5 + D D f*D f*p4 + D f *f*p2 2 x 2 1 2 2 x 1 2 1 1 x + D f*f *p6 1 x 2 2 df(f,s)=D f *D f*f*q5 + D f *D f*f*q6 + (D f) *D D f*q7 + (D f) *f *q12 2 x 2 2 x 1 2 1 2 2 x 2 + D f*D D f*D f*q8 + D f*D f *f*q3 + D f*D f*f *q13 + D D f*(D f) *q9 2 1 2 1 2 1 x 2 1 x 1 2 1 2 - D D f*f *f*q25 + D f *D f*f*q4 + (D f) *f *q14 1 2 x 1 x 1 1 x *** Garbage collection starting *** GC 5 3-Oct-2003 04:54:21, 30 ms (0%), 1089804 occupied, 23910147 free Now crack is called. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This is CRACK - a solver for overdetermined partial differential equations Enter `h' for help. The list of inequalities got extended by: An expression with 25 terms The list of inequalities got extended by: An expression with 25 terms The list of inequalities got extended by: An expression with 31 terms The list of inequalities got extended by: An expression with 27 terms The list of inequalities got extended by: An expression with 8 terms *** Garbage collection starting *** GC 6 3-Oct-2003 04:54:42, 30 ms (0%), 987059 occupied, 24012893 free *** Garbage collection starting *** GC 7 3-Oct-2003 04:54:49, 30 ms (0%), 1019363 occupied, 23980588 free *** Garbage collection starting *** GC 8 3-Oct-2003 04:55:06, 40 ms (0%), 1019653 occupied, 23980299 free *** Garbage collection starting *** GC 9 3-Oct-2003 04:55:30, 40 ms (0%), 1081061 occupied, 23918890 free *** Garbage collection starting *** GC 10 3-Oct-2003 04:55:54, 40 ms (0%), 1144111 occupied, 23855841 free *** Garbage collection starting *** GC 11 3-Oct-2003 04:56:21, 40 ms (0%), 1200555 occupied, 23799397 free old input: l Select a method by its number that is to be executed repeatedly: old input: 2 To repeat this method as often as possible, enter `;' To repeat this method as often as possible, but at most a number of n times, enter n : old input: ; Step 1: separation w.r.t. x linear independent expressions : f*D f 2 6x D D f*D f 1 2 2 5x f *D f x 2 5x D D f *D f 1 2 x 2 4x f *D f 2x 2 4x D D f *D f 1 2 2x 2 3x f *D f 3x 2 3x D D f *D f 1 2 3x 2 2x f *D f 4x 2 2x D D f *D f 1 2 4x 2 x f *D f 5x 2 x D D f *D f 1 2 5x 2 f *D f 6x 2 D f*D D f 1 1 2 5x D f *D D f 1 x 1 2 4x D f *D D f 1 2x 1 2 3x D f *D D f 1 3x 1 2 2x D f *D D f 1 4x 1 2 x D f *D D f 1 5x 1 2 f*D f 1 6x f *D f x 1 5x f *D f 2x 1 4x f *D f 3x 1 3x f *D f 4x 1 2x f *D f 5x 1 x f *D f 6x 1 *** Garbage collection starting *** GC 12 3-Oct-2003 04:56:41, 30 ms (0%), 1048937 occupied, 23951014 free Separation of e_3 yields (e_26 e_15 e_25 e_10 e_24 e_21 e_20 e_17 e_16 e_14 e_12 e_9 e_7 e_5 e_23 e_19 e_13 e_11 e_18 e_6 e_22 e_8) Step 2: separation w.r.t. x linear independent expressions : 2 f*(D f) *D f 2 2 2x f*D f*D f*D f 1 2 2 2x 2 f*(D f) *D f 1 2 2x 2 f*D f*(D f ) 2 2 x 2 f*D f*(D f ) 1 2 x 2 D D f*(D f) *D f 1 2 2 2 x 2 f *(D f) *D f x 2 2 x D f*D D f*D f*D f 1 1 2 2 2 x f*D f *D f*D f 1 x 2 2 x f *D f*D f*D f x 1 2 2 x 2 (D f) *D D f*D f 1 1 2 2 x f*f *D D f*D f x 1 2 2 x f*D f*D f *D f 1 1 x 2 x 2 f *(D f) *D f x 1 2 x 3 D D f *(D f) 1 2 x 2 3 f *(D f) 2x 2 2 D f*D D f *(D f) 1 1 2 x 2 2 D f *D D f*(D f) 1 x 1 2 2 2 f*D f *(D f) 1 2x 2 2 f *D f *(D f) x 1 x 2 2 f *D f*(D f) 2x 1 2 f*D D f*D D f *D f 1 2 1 2 x 2 2 (D f) *D D f *D f 1 1 2 x 2 f*f *D D f *D f x 1 2 x 2 D f*D f *D D f*D f 1 1 x 1 2 2 f*f *D D f*D f 2x 1 2 2 f*D f*D f *D f 1 1 2x 2 2 f*(D f ) *D f 1 x 2 f *D f*D f *D f x 1 1 x 2 2 f *(D f) *D f 2x 1 2 f*f *f *D f x 2x 2 f*D f*D D f*D D f 1 1 2 1 2 x 3 (D f) *D D f 1 1 2 x f*f *D f*D D f x 1 1 2 x 2 (D f) *D f *D D f 1 1 x 1 2 f*f *D f *D D f x 1 x 1 2 f*f *D f*D D f 2x 1 1 2 2 f*(D f) *D f 1 1 2x 2 f*D f*(D f ) 1 1 x 2 f *(D f) *D f x 1 1 x 3 f *(D f) 2x 1 f*f *f *D f x 2x 1 *** Garbage collection starting *** GC 13 3-Oct-2003 04:56:46, 30 ms (0%), 1017747 occupied, 23982205 free *** Garbage collection starting *** GC 14 3-Oct-2003 04:56:54, 30 ms (0%), 1006365 occupied, 23993586 free Separation of e_1 yields (e_66 e_52 e_35 e_30 e_64 e_49 e_65 e_51 e_47 e_46 e_45 e_41 e_38 e_36 e_63 e_61 e_56 e_50 e_33 e_29 e_60 e_53 e_48 e_44 e_37 e_34 e_28 e_27 e_62 e_59 e_43 e_40 e_57 e_42 e_39 e_31 e_58 e_55 e_54 e_32) Step 3: separation w.r.t. x linear independent expressions : f*D f*D f 2 2 4x f*D f*D f 1 2 4x f*D f *D f 2 x 2 3x D D f*D f*D f 1 2 2 2 3x f *D f*D f x 2 2 3x D f*D D f*D f 1 1 2 2 3x f*D f *D f 1 x 2 3x f *D f*D f x 1 2 3x 2 f*(D f ) 2 2x D D f*D f *D f 1 2 2 x 2 2x f *D f *D f x 2 x 2 2x D D f *D f*D f 1 2 x 2 2 2x f *D f*D f 2x 2 2 2x D f*D D f *D f 1 1 2 x 2 2x D f *D D f*D f 1 x 1 2 2 2x f*D f *D f 1 2x 2 2x f *D f *D f x 1 x 2 2x f *D f*D f 2x 1 2 2x 2 D D f *(D f ) 1 2 x 2 x 2 f *(D f ) 2x 2 x D D f *D f*D f 1 2 2x 2 2 x f *D f*D f 3x 2 2 x D f*D D f *D f 1 1 2 2x 2 x D f *D D f *D f 1 x 1 2 x 2 x D f *D D f*D f 1 2x 1 2 2 x f*D f *D f 1 3x 2 x f *D f *D f x 1 2x 2 x f *D f *D f 2x 1 x 2 x f *D f*D f 3x 1 2 x 2 D D f *(D f) 1 2 3x 2 2 f *(D f) 4x 2 D f*D D f *D f 1 1 2 3x 2 D f *D D f *D f 1 x 1 2 2x 2 D f *D D f *D f 1 2x 1 2 x 2 D f *D D f*D f 1 3x 1 2 2 f*D f *D f 1 4x 2 f *D f *D f x 1 3x 2 f *D f *D f 2x 1 2x 2 f *D f *D f 3x 1 x 2 f *D f*D f 4x 1 2 f*D D f*D D f 1 2 1 2 3x 2 (D f) *D D f 1 1 2 3x f*f *D D f x 1 2 3x f*D D f *D D f 1 2 x 1 2 2x f *D D f*D D f x 1 2 1 2 2x D f*D f *D D f 1 1 x 1 2 2x f*f *D D f 2x 1 2 2x f *D D f*D D f 2x 1 2 1 2 x D f*D f *D D f 1 1 2x 1 2 x 2 (D f ) *D D f 1 x 1 2 x f*f *D D f 3x 1 2 x f *f *D D f x 2x 1 2 x D f*D f *D D f 1 1 3x 1 2 D f *D f *D D f 1 x 1 2x 1 2 f*f *D D f 4x 1 2 f *f *D D f x 3x 1 2 f*D f*D f 1 1 4x f*D f *D f 1 x 1 3x f *D f*D f x 1 1 3x 2 f*(D f ) 1 2x f *D f *D f x 1 x 1 2x f *D f*D f 2x 1 1 2x 2 f *(D f ) 2x 1 x f *D f*D f 3x 1 1 x 2 f *(D f) 4x 1 f*f *f x 4x f*f *f 2x 3x *** Garbage collection starting *** GC 15 3-Oct-2003 04:56:59, 40 ms (0%), 1086131 occupied, 23913821 free *** Garbage collection starting *** GC 16 3-Oct-2003 04:57:48, 40 ms (0%), 1209097 occupied, 23790855 free *** Garbage collection starting *** GC 17 3-Oct-2003 04:59:24, 50 ms (0%), 1302203 occupied, 23697748 free *** Garbage collection starting *** GC 18 3-Oct-2003 05:00:13, 30 ms (0%), 1020235 occupied, 23979716 free *** Garbage collection starting *** GC 19 3-Oct-2003 05:00:15, 30 ms (0%), 1035139 occupied, 23964813 free Separation of e_2 yields (e_131 e_102 e_91 e_76 e_130 e_97 e_101 e_93 e_92 e_113 e_89 e_83 e_90 e_123 e_122 e_120 e_111 e_87 e_84 e_79 e_78 e_73 e_68 e_128 e_126 e_114 e_112 e_98 e_95 e_88 e_80 e_70 e_67 e_129 e_118 e_109 e_108 e_103 e_100 e_99 e_94 e_75 e_127 e_125 e_119 e_117 e_110 e_107 e_106 e_77 e_74 e_71 e_69 e_124 e_96 e_121 e_86 e_85 e_82 e_72 e_116 e_104 e_115 e_105 e_81) Step 4: old input: cp Please type in a list of the numbers 1 .. 60, like 1,2,5,4,..,15; which will be the new priority list of procedures done by CRACK. Numbers stand for the following actions: 1 : Hot list of urgent steps 2 : Direct separation 3 : Substitution of <=2 terms, only fcts. of less vars., no cases 4 : Substitution of <=2 terms, alg. expressions, no cases 5 : Substitution of <=1000 terms, alg. expressions, no cases 6 : Substitution, minimal growth, with max 100 add. terms, no cases 7 : Integration of a first order de with at most two terms. 8 : Factorization to subcases leading to substitutions 9 : Substitution of derivatives by new functions 10 : Indirect separation of <6 or >300 terms 11 : Algebraic length reduction of equations 12 : Find and drop linear dependent general equations 13 : Find a linear dependent equation with only 1 term 14 : Triangularize a linear algebraic system 15 : Substitution of <=8 terms in <=1000 terms, fcts. of less vars. 16 : Substitution of <=20 terms in <=1000 terms 17 : Substitution of <=1000 terms, minimal growth 18 : Substitution of <=1000 terms, fcts. of less vars., no cases 19 : Substitution of <=1000 terms only linear expressions, f-indep. coeff. 20 : Substitution of <=1000 terms, no cases 21 : Substitution of <=1000 terms 22 : The parametric solution of underdetermined ODE 23 : The parametric solution of underdetermined PDE 24 : Integration of a pde such that a function can be subst. 25 : Any integration 26 : Indirect separation of equations of any size 27 : Length reducing decoupling steps 28 : Delete redundant equations 29 : Integrate an identity 30 : Do one decoupling step 31 : Differentiate pdes with nonlinear leading derivs 32 : Differentiate indirectly separable equations 33 : Find an integrating factor for a set of pde's 34 : Solving an algebraic equation. 35 : Solving equations for fnct.s or deriv.s algebraically 36 : Undo Substitutions of derivatives by new functions 37 : Changing the list of priorities 38 : Stop batch mode 39 : Find a transformation to integrate a 1st order PDE 40 : Drop redundant functions and constants 41 : Solve a subset of equations first 42 : Find and drop linear dependent bi-linear equations 43 : Find factorizable bi-linear equations 44 : Consider a given expression to be zero and non-zero 45 : Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases 46 : Find symmetries and then first integrals for an ODE 47 : Any factorization 48 : Alternative indirect separation of non-lin equations 49 : Find sub-systems with 2 non-flin_ functions 50 : Find sub-systems with 3 non-flin_ functions 51 : Find sub-systems with 4 non-flin_ functions 52 : Find sub-systems with 5 non-flin_ functions 53 : Find sub-systems with 2 flin_ functions 54 : Find sub-systems with 3 flin_ functions 55 : Find sub-systems with 4 flin_ functions 56 : Find sub-systems with 5 flin_ functions 57 : Do one high priority decoupling step 58 : user_defined 59 : Computation of the algebraic Groebner basis 60 : Check whether a given solution is contained The list so far was: 1,2,3,4,7,8,47,9,15,16,18,19,20,21,24,26,27,30,25,22,32, 34,36; old input: (*comma* 1 3 45 11 27 8 20 30 47 21 38) old input: s number of equations : 127 total no of terms : 1182 total no of factors : 2364 127 equations in 0 variables: e_115(17),e_105(17),e_81(17),e_116(16),e_104(16),e_121(15),e_86(15), e_85(15),e_82(15),e_72(15),e_124(14),e_96(14),e_22(13),e_8(13), e_127(13),e_125(13),e_119(13),e_117(13),e_110(13),e_107(13),e_106(13), e_77(13),e_74(13),e_71(13),e_69(13),e_18(12),e_6(12),e_129(12), e_118(12),e_109(12),e_108(12),e_103(12),e_100(12),e_99(12),e_94(12), e_75(12),e_23(11),e_19(11),e_13(11),e_11(11),e_58(11),e_55(11), e_54(11),e_32(11),e_128(11),e_126(11),e_114(11),e_112(11),e_98(11), e_95(11),e_88(11),e_80(11),e_70(11),e_67(11),e_57(10),e_42(10), e_39(10),e_31(10),e_123(10),e_122(10),e_120(10),e_111(10),e_87(10), e_84(10),e_79(10),e_78(10),e_73(10),e_68(10),e_24(9),e_21(9),e_20(9), e_17(9),e_16(9),e_14(9),e_12(9),e_9(9),e_7(9),e_5(9),e_62(8),e_59(8), e_43(8),e_40(8),e_90(8),e_25(7),e_10(7),e_60(7),e_53(7),e_48(7), e_44(7),e_37(7),e_34(7),e_28(7),e_27(7),e_113(7),e_89(7),e_83(7), e_63(6),e_61(6),e_56(6),e_50(6),e_33(6),e_29(6),e_101(6),e_93(6), e_92(6),e_65(5),e_51(5),e_47(5),e_46(5),e_45(5),e_41(5),e_38(5), e_36(5),e_130(5),e_97(5),e_64(4),e_49(4),e_131(3),e_102(3),e_91(3), e_76(3),e_26(2),e_15(2),e_66(2),e_52(2),e_35(2),e_30(2) 35 constants : p1,p2,p3,p4,p5,p6,p7,p8,q1,q2, q3,q4,q5,q6,q7,q8,q9,q10,q11,q12,q13, q14,q15,q16,q17,q18,q19,q20,q21,q22,q23,q24, q25,q26,q27 old input: w Enter a list of equations, like e2,e5,e35; from: e_30,e_35,e_52,e_66,e_15,e_26,e_76,e_91,e_102,e_131,e_49,e_64,e_97,e_130,e_36, e_38,e_41,e_45,e_46,e_47,e_51,e_65,e_92,e_93,e_101,e_29,e_33,e_50,e_56,e_61,e_63 ,e_83,e_89,e_113,e_27,e_28,e_34,e_37,e_44,e_48,e_53,e_60,e_10,e_25,e_90,e_40, e_43,e_59,e_62,e_5,e_7,e_9,e_12,e_14,e_16,e_17,e_20,e_21,e_24,e_68,e_73,e_78, e_79,e_84,e_87,e_111,e_120,e_122,e_123,e_31,e_39,e_42,e_57,e_67,e_70,e_80,e_88, e_95,e_98,e_112,e_114,e_126,e_128,e_32,e_54,e_55,e_58,e_11,e_13,e_19,e_23,e_75, e_94,e_99,e_100,e_103,e_108,e_109,e_118,e_129,e_6,e_18,e_69,e_71,e_74,e_77,e_106 ,e_107,e_110,e_117,e_119,e_125,e_127,e_8,e_22,e_96,e_124,e_72,e_82,e_85,e_86, e_121,e_104,e_116,e_81,e_105,e_115 To write all equations just enter ; old input: nil Shall the name of the equation be written? (y/n) old input: n Please give the name of the file in double quotes without `;' : old input: w old input: cr These are all the user defined rules: {} You can either - give the number of a rule above to be dropped, or - give the name of a rule list activated before the call of CRACK which should be disabled: old input: ssrules Rule list ssrules has been disabled. old input: dp old input: sb Please give the name of the file in double quotes without `;' : old input: 0 next: next: next: Please type in a list of the numbers 1 .. 60, like 1,2,5,4,..,15; which will be the new priority list of procedures done by CRACK. Numbers stand for the following actions: 1 : Hot list of urgent steps 2 : Direct separation 3 : Substitution of <=2 terms, only fcts. of less vars., no cases 4 : Substitution of <=2 terms, alg. expressions, no cases 5 : Substitution of <=1000 terms, alg. expressions, no cases 6 : Substitution, minimal growth, with max 100 add. terms, no cases 7 : Integration of a first order de with at most two terms. 8 : Factorization to subcases leading to substitutions 9 : Substitution of derivatives by new functions 10 : Indirect separation of <6 or >300 terms 11 : Algebraic length reduction of equations 12 : Find and drop linear dependent general equations 13 : Find a linear dependent equation with only 1 term 14 : Triangularize a linear algebraic system 15 : Substitution of <=8 terms in <=1000 terms, fcts. of less vars. 16 : Substitution of <=20 terms in <=1000 terms 17 : Substitution of <=1000 terms, minimal growth 18 : Substitution of <=1000 terms, fcts. of less vars., no cases 19 : Substitution of <=1000 terms only linear expressions, f-indep. coeff. 20 : Substitution of <=1000 terms, no cases 21 : Substitution of <=1000 terms 22 : The parametric solution of underdetermined ODE 23 : The parametric solution of underdetermined PDE 24 : Integration of a pde such that a function can be subst. 25 : Any integration 26 : Indirect separation of equations of any size 27 : Length reducing decoupling steps 28 : Delete redundant equations 29 : Integrate an identity 30 : Do one decoupling step 31 : Differentiate pdes with nonlinear leading derivs 32 : Differentiate indirectly separable equations 33 : Find an integrating factor for a set of pde's 34 : Solving an algebraic equation. 35 : Solving equations for fnct.s or deriv.s algebraically 36 : Undo Substitutions of derivatives by new functions 37 : Changing the list of priorities 38 : Stop batch mode 39 : Find a transformation to integrate a 1st order PDE 40 : Drop redundant functions and constants 41 : Solve a subset of equations first 42 : Find and drop linear dependent bi-linear equations 43 : Find factorizable bi-linear equations 44 : Consider a given expression to be zero and non-zero 45 : Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases 46 : Find symmetries and then first integrals for an ODE 47 : Any factorization 48 : Alternative indirect separation of non-lin equations 49 : Find sub-systems with 2 non-flin_ functions 50 : Find sub-systems with 3 non-flin_ functions 51 : Find sub-systems with 4 non-flin_ functions 52 : Find sub-systems with 5 non-flin_ functions 53 : Find sub-systems with 2 flin_ functions 54 : Find sub-systems with 3 flin_ functions 55 : Find sub-systems with 4 flin_ functions 56 : Find sub-systems with 5 flin_ functions 57 : Do one high priority decoupling step 58 : user_defined 59 : Computation of the algebraic Groebner basis 60 : Check whether a given solution is contained The list so far was: 1,3,45,11,27,8,20,30,47,21,38; The new list: next: There is no time-limit set currently. After time has expired, shall CRACK go into interactive mode (1) or shall CRACK terminate with error (2) ? How many hours? How many minutes? next: Step 5: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 6: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms e_2 is a consequence of e_208. Step 7: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 8: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 9: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 10: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 11: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 12: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms e_155 is a consequence of e_145. Step 13: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms e_156 is a consequence of e_145. Step 14: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 15: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 16: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 17: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 18: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 19: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms e_167 is a consequence of e_208. Step 20: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 21: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms e_174 is a consequence of e_208. Step 22: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms e_175 is a consequence of e_208. Step 23: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 24: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 20 3-Oct-2003 05:00:17, 40 ms (0%), 1016663 occupied, 23983288 free shortening by 1 term Step 25: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 26: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 27: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms e_183 is a consequence of e_145. Step 28: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms e_184 is a consequence of e_145. Step 29: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 30: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 31: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 32: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 33: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 34: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 35: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 36: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 37: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 38: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 39: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 40: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 41: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 42: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 43: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 44: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 45: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 46: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 47: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 48: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 49: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 50: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 51: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 52: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 53: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms e_34 is a consequence of e_131. Step 54: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms e_150 is a consequence of e_131. Step 55: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 56: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 57: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 58: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms e_155 is a consequence of e_102. Step 59: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 60: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 61: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 62: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 63: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms e_159 is a consequence of e_102. Step 64: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms e_160 is a consequence of e_102. Step 65: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 66: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 67: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 68: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 69: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 70: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 71: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 72: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 73: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 4 terms Step 74: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 75: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 76: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 77: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 78: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 79: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 4 terms Step 80: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 81: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 82: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 83: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 4 terms Step 84: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 85: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 21 3-Oct-2003 05:00:20, 30 ms (0%), 1014605 occupied, 23985347 free shortening by 3 terms Step 86: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 4 terms e_23 is a consequence of e_133. Step 87: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 4 terms Step 88: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 89: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 90: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 91: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 4 terms e_18 is a consequence of e_141. Step 92: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 93: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 94: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 95: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 96: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 6 terms Step 97: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 5 terms Step 98: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 5 terms Step 99: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 6 terms Step 100: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 101: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 102: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 22 3-Oct-2003 05:00:22, 30 ms (0%), 1011777 occupied, 23988174 free *** Garbage collection starting *** GC 23 3-Oct-2003 05:00:23, 30 ms (0%), 1012803 occupied, 23987149 free *** Garbage collection starting *** GC 24 3-Oct-2003 05:00:25, 30 ms (0%), 1013879 occupied, 23986072 free *** Garbage collection starting *** GC 25 3-Oct-2003 05:00:26, 30 ms (0%), 1014047 occupied, 23985905 free *** Garbage collection starting *** GC 26 3-Oct-2003 05:00:28, 30 ms (0%), 1014187 occupied, 23985764 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : *** Garbage collection starting *** GC 27 3-Oct-2003 05:00:30, 30 ms (0%), 1016228 occupied, 23983723 free *** Garbage collection starting *** GC 28 3-Oct-2003 05:00:33, 30 ms (0%), 1027420 occupied, 23972530 free *** Garbage collection starting *** GC 29 3-Oct-2003 05:00:36, 40 ms (0%), 1044090 occupied, 23955862 free Eliminate q5 from e_164 and e_13. e_13: 7 terms, 14 factors, with derivatives of functions of all variables: (q25,q8,q6,q5,q4,p4,p3,p2,p1) is replaced by e_86: 7 terms, 14 factors, with derivatives of functions of all variables: (q25,q8,q6,q4,q3,p4,p3,p2,p1) Step 103: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 104: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 30 3-Oct-2003 05:00:38, 30 ms (0%), 1013071 occupied, 23986881 free *** Garbage collection starting *** GC 31 3-Oct-2003 05:00:40, 30 ms (0%), 1013919 occupied, 23986033 free *** Garbage collection starting *** GC 32 3-Oct-2003 05:00:41, 30 ms (0%), 1014393 occupied, 23985559 free *** Garbage collection starting *** GC 33 3-Oct-2003 05:00:43, 30 ms (0%), 1014691 occupied, 23985261 free *** Garbage collection starting *** GC 34 3-Oct-2003 05:00:44, 30 ms (0%), 1014933 occupied, 23985019 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q8 from e_145 and e_178. e_178: 7 terms, 14 factors, with derivatives of functions of all variables: (q25,q8,q5,q4,q3,p4,p3,p2,p1) is replaced by e_160: 6 terms, 12 factors, with derivatives of functions of all variables: (q25,q6,q4,q3,p3,p2,p1) Step 105: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 35 3-Oct-2003 05:00:46, 30 ms (0%), 1014391 occupied, 23985561 free *** Garbage collection starting *** GC 36 3-Oct-2003 05:00:47, 40 ms (0%), 1015629 occupied, 23984322 free *** Garbage collection starting *** GC 37 3-Oct-2003 05:00:49, 40 ms (0%), 1016399 occupied, 23983553 free *** Garbage collection starting *** GC 38 3-Oct-2003 05:00:50, 40 ms (0%), 1016783 occupied, 23983168 free *** Garbage collection starting *** GC 39 3-Oct-2003 05:00:51, 40 ms (0%), 1016993 occupied, 23982959 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q13 from e_5 and e_196. e_196: 4 terms, 8 factors, with derivatives of functions of all variables: (q25,q13,q4,p5,p4,p2) is replaced by e_80: 0=p1*q4 - p2*q25 - p2*q3 Step 106: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms e_128 is a consequence of e_172. Step 107: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 108: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 109: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 110: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 40 3-Oct-2003 05:00:53, 40 ms (0%), 1013349 occupied, 23986601 free *** Garbage collection starting *** GC 41 3-Oct-2003 05:00:55, 30 ms (0%), 1014475 occupied, 23985476 free shortening by 1 term Step 111: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 42 3-Oct-2003 05:00:56, 30 ms (0%), 1012395 occupied, 23987556 free shortening by 1 term Step 112: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 113: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 114: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 43 3-Oct-2003 05:00:58, 30 ms (0%), 1012309 occupied, 23987643 free shortening by 1 term Step 115: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 116: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 117: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 44 3-Oct-2003 05:00:59, 30 ms (0%), 1013665 occupied, 23986286 free shortening by 1 term Step 118: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 119: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 120: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 121: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 122: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 45 3-Oct-2003 05:01:01, 30 ms (0%), 1012921 occupied, 23987031 free shortening by 1 term Step 123: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 124: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 46 3-Oct-2003 05:01:02, 30 ms (0%), 1013715 occupied, 23986236 free shortening by 2 terms Step 125: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 126: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 127: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 47 3-Oct-2003 05:01:04, 30 ms (0%), 1012999 occupied, 23986953 free *** Garbage collection starting *** GC 48 3-Oct-2003 05:01:05, 30 ms (0%), 1014103 occupied, 23985848 free shortening by 1 term Step 128: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 129: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 49 3-Oct-2003 05:01:07, 40 ms (0%), 1012275 occupied, 23987677 free shortening by 1 term Step 130: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 4 terms Step 131: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 132: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 133: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 4 terms Step 134: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 135: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 50 3-Oct-2003 05:01:08, 30 ms (0%), 1012279 occupied, 23987672 free shortening by 2 terms Step 136: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 137: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 138: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 51 3-Oct-2003 05:01:10, 30 ms (0%), 1011319 occupied, 23988632 free shortening by 1 term Step 139: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 4 terms Step 140: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 4 terms Step 141: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 142: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 52 3-Oct-2003 05:01:11, 30 ms (0%), 1011515 occupied, 23988435 free shortening by 2 terms Step 143: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 144: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 53 3-Oct-2003 05:01:12, 30 ms (0%), 1012465 occupied, 23987486 free *** Garbage collection starting *** GC 54 3-Oct-2003 05:01:14, 40 ms (0%), 1014021 occupied, 23985929 free *** Garbage collection starting *** GC 55 3-Oct-2003 05:01:15, 40 ms (0%), 1014651 occupied, 23985300 free *** Garbage collection starting *** GC 56 3-Oct-2003 05:01:17, 40 ms (0%), 1014879 occupied, 23985071 free *** Garbage collection starting *** GC 57 3-Oct-2003 05:01:18, 30 ms (0%), 1014971 occupied, 23984980 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q5 from e_164 and e_46. e_46: 0=p1*q25 - p1*q6 + p2*q5 is replaced by e_42: 0=(q25 + q3 - q6)*p1 Step 145: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 58 3-Oct-2003 05:01:20, 40 ms (0%), 1013959 occupied, 23985991 free *** Garbage collection starting *** GC 59 3-Oct-2003 05:01:21, 30 ms (0%), 1014451 occupied, 23985500 free *** Garbage collection starting *** GC 60 3-Oct-2003 05:01:23, 40 ms (0%), 1014895 occupied, 23985055 free *** Garbage collection starting *** GC 61 3-Oct-2003 05:01:24, 30 ms (0%), 1015025 occupied, 23984926 free *** Garbage collection starting *** GC 62 3-Oct-2003 05:01:26, 30 ms (0%), 1015951 occupied, 23983999 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : *** Garbage collection starting *** GC 63 3-Oct-2003 05:01:29, 30 ms (0%), 1049453 occupied, 23950494 free *** Garbage collection starting *** GC 64 3-Oct-2003 05:01:32, 30 ms (0%), 1021674 occupied, 23978275 free *** Garbage collection starting *** GC 65 3-Oct-2003 05:01:35, 30 ms (0%), 1061408 occupied, 23938540 free *** Garbage collection starting *** GC 66 3-Oct-2003 05:01:38, 30 ms (0%), 1050630 occupied, 23949319 free *** Garbage collection starting *** GC 67 3-Oct-2003 05:01:41, 40 ms (0%), 1048804 occupied, 23951145 free Stop of a subroutine. Number of garbage collections exceeds max_gc_red_len. --- Factorization to subcases leading to substitutions : factorizing e_42 we get the alternative equations : 0=p1 0=q25 + q3 - q6 New level : 1. CRACK is now called with the new equation e_215 : 0=p1 Step 146: Hot list of urgent steps : The list of inequalities got extended by: An expression with 24 terms The list of inequalities got extended by: An expression with 30 terms The list of inequalities got extended by: An expression with 7 terms e_181 is a consequence of e_209. Substitution of p1 found in e_215 : p1=0 Step 147: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 148: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 149: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 150: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 151: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 152: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 153: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 154: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 155: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 156: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 157: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 158: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 159: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 160: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 5 terms Step 161: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 68 3-Oct-2003 05:01:44, 30 ms (0%), 1032470 occupied, 23967482 free *** Garbage collection starting *** GC 69 3-Oct-2003 05:01:45, 30 ms (0%), 1033692 occupied, 23966260 free *** Garbage collection starting *** GC 70 3-Oct-2003 05:01:47, 30 ms (0%), 1034562 occupied, 23965390 free *** Garbage collection starting *** GC 71 3-Oct-2003 05:01:48, 40 ms (0%), 1034916 occupied, 23965036 free *** Garbage collection starting *** GC 72 3-Oct-2003 05:01:50, 40 ms (0%), 1035114 occupied, 23964837 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q6 from e_62 and e_209. e_209: 0=(q25 + q3 - q6)*p4 is replaced by e_107: 0=(q25 + q3)*p4 Step 162: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 73 3-Oct-2003 05:01:52, 30 ms (0%), 1033368 occupied, 23966584 free *** Garbage collection starting *** GC 74 3-Oct-2003 05:01:54, 30 ms (0%), 1034592 occupied, 23965359 free *** Garbage collection starting *** GC 75 3-Oct-2003 05:01:55, 30 ms (0%), 1034808 occupied, 23965144 free *** Garbage collection starting *** GC 76 3-Oct-2003 05:01:57, 40 ms (0%), 1034982 occupied, 23964969 free *** Garbage collection starting *** GC 77 3-Oct-2003 05:01:58, 40 ms (0%), 1035156 occupied, 23964796 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q25 from e_84 and e_47. e_47: 4 terms, 8 factors, with derivatives of functions of all variables: (q25,q13,q3,p6,p3,p2) is replaced by e_69: 4 terms, 8 factors, with derivatives of functions of all variables: (q13,q3,p6,p3,p2) Step 163: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 78 3-Oct-2003 05:02:00, 30 ms (0%), 1034444 occupied, 23965507 free *** Garbage collection starting *** GC 79 3-Oct-2003 05:02:02, 30 ms (0%), 1035306 occupied, 23964646 free *** Garbage collection starting *** GC 80 3-Oct-2003 05:02:03, 30 ms (0%), 1035694 occupied, 23964258 free *** Garbage collection starting *** GC 81 3-Oct-2003 05:02:05, 40 ms (0%), 1035984 occupied, 23963967 free *** Garbage collection starting *** GC 82 3-Oct-2003 05:02:06, 30 ms (0%), 1036144 occupied, 23963808 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : *** Garbage collection starting *** GC 83 3-Oct-2003 05:02:10, 40 ms (0%), 1068767 occupied, 23931179 free Eliminate q6 from e_2 and e_120. e_120: 0=p3*q6 + p5*q5 is replaced by e_162: 0=q5*(p4 - p5) Step 164: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 84 3-Oct-2003 05:02:11, 30 ms (0%), 1035722 occupied, 23964229 free *** Garbage collection starting *** GC 85 3-Oct-2003 05:02:13, 40 ms (0%), 1036558 occupied, 23963392 free *** Garbage collection starting *** GC 86 3-Oct-2003 05:02:15, 30 ms (0%), 1036936 occupied, 23963014 free *** Garbage collection starting *** GC 87 3-Oct-2003 05:02:16, 30 ms (0%), 1037314 occupied, 23962635 free shortening by 1 term Step 165: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 88 3-Oct-2003 05:02:18, 30 ms (0%), 1034304 occupied, 23965647 free shortening by 1 term Step 166: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 167: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 89 3-Oct-2003 05:02:19, 40 ms (0%), 1034018 occupied, 23965932 free shortening by 1 term Step 168: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 169: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 170: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 90 3-Oct-2003 05:02:21, 30 ms (0%), 1035522 occupied, 23964429 free shortening by 1 term Step 171: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 172: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 173: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 174: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 175: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 176: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 91 3-Oct-2003 05:02:23, 40 ms (0%), 1033710 occupied, 23966240 free shortening by 1 term Step 177: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 178: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 179: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 92 3-Oct-2003 05:02:25, 30 ms (0%), 1035804 occupied, 23964148 free *** Garbage collection starting *** GC 93 3-Oct-2003 05:02:26, 30 ms (0%), 1036782 occupied, 23963169 free *** Garbage collection starting *** GC 94 3-Oct-2003 05:02:28, 40 ms (0%), 1037216 occupied, 23962736 free *** Garbage collection starting *** GC 95 3-Oct-2003 05:02:29, 30 ms (0%), 1037434 occupied, 23962517 free *** Garbage collection starting *** GC 96 3-Oct-2003 05:02:31, 40 ms (0%), 1037752 occupied, 23962200 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q25 from e_107 and e_138. e_138: 4 terms, 8 factors, with derivatives of functions of all variables: (q25,q13,q9,p5,p4) is replaced by e_187: 4 terms, 8 factors, with derivatives of functions of all variables: (q13,q9,q3,p5,p4) Step 180: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 97 3-Oct-2003 05:02:33, 30 ms (0%), 1035600 occupied, 23964351 free *** Garbage collection starting *** GC 98 3-Oct-2003 05:02:35, 40 ms (0%), 1036894 occupied, 23963058 free *** Garbage collection starting *** GC 99 3-Oct-2003 05:02:36, 30 ms (0%), 1037396 occupied, 23962555 free *** Garbage collection starting *** GC 100 3-Oct-2003 05:02:38, 30 ms (0%), 1037714 occupied, 23962238 free *** Garbage collection starting *** GC 101 3-Oct-2003 05:02:40, 40 ms (0%), 1037930 occupied, 23962021 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q25 from e_84 and e_129. e_129: 4 terms, 8 factors, with derivatives of functions of all variables: (q25,q13,q4,p5,p4,p2) is replaced by e_125: 4 terms, 8 factors, with derivatives of functions of all variables: (q13,q4,q3,p5,p4,p2) Step 181: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 102 3-Oct-2003 05:02:42, 30 ms (0%), 1036766 occupied, 23963186 free *** Garbage collection starting *** GC 103 3-Oct-2003 05:02:43, 30 ms (0%), 1037630 occupied, 23962321 free *** Garbage collection starting *** GC 104 3-Oct-2003 05:02:45, 40 ms (0%), 1038254 occupied, 23961698 free *** Garbage collection starting *** GC 105 3-Oct-2003 05:02:47, 40 ms (0%), 1038512 occupied, 23961439 free *** Garbage collection starting *** GC 106 3-Oct-2003 05:02:49, 30 ms (0%), 1039152 occupied, 23960800 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q6 from e_137 and e_143. e_143: 4 terms, 8 factors, with derivatives of functions of all variables: (q18,q11,q6,q1,p7,p5,p2) is replaced by e_13: 4 terms, 8 factors, with derivatives of functions of all variables: (q18,q11,q1,p5,p4,p2) Step 182: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 107 3-Oct-2003 05:02:51, 30 ms (0%), 1037476 occupied, 23962475 free *** Garbage collection starting *** GC 108 3-Oct-2003 05:02:53, 30 ms (0%), 1038800 occupied, 23961152 free *** Garbage collection starting *** GC 109 3-Oct-2003 05:02:55, 40 ms (0%), 1039654 occupied, 23960297 free *** Garbage collection starting *** GC 110 3-Oct-2003 05:02:57, 30 ms (0%), 1040470 occupied, 23959482 free *** Garbage collection starting *** GC 111 3-Oct-2003 05:02:58, 40 ms (0%), 1041096 occupied, 23958855 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : *** Garbage collection starting *** GC 112 3-Oct-2003 05:03:02, 40 ms (0%), 1050588 occupied, 23949361 free Eliminate q25 from e_107 and e_141. e_141: 5 terms, 10 factors, with derivatives of functions of all variables: (q25,q14,q13,q8,q7,p6,p4,p3) is replaced by e_206: 5 terms, 10 factors, with derivatives of functions of all variables: (q14,q13,q8,q7,q3,p6,p4,p3) Step 183: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 113 3-Oct-2003 05:03:04, 40 ms (0%), 1039262 occupied, 23960689 free shortening by 1 term Step 184: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 114 3-Oct-2003 05:03:06, 40 ms (0%), 1039336 occupied, 23960616 free *** Garbage collection starting *** GC 115 3-Oct-2003 05:03:08, 30 ms (0%), 1041920 occupied, 23958030 free shortening by 1 term Step 185: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 186: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 116 3-Oct-2003 05:03:10, 30 ms (0%), 1038110 occupied, 23961842 free shortening by 1 term Step 187: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 117 3-Oct-2003 05:03:12, 30 ms (0%), 1037394 occupied, 23962557 free shortening by 1 term Step 188: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 118 3-Oct-2003 05:03:14, 40 ms (0%), 1038676 occupied, 23961276 free shortening by 1 term Step 189: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 190: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 191: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 192: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 119 3-Oct-2003 05:03:16, 40 ms (0%), 1037028 occupied, 23962923 free shortening by 3 terms Step 193: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 194: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 120 3-Oct-2003 05:03:18, 30 ms (0%), 1036960 occupied, 23962992 free shortening by 2 terms Step 195: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 196: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 121 3-Oct-2003 05:03:20, 40 ms (0%), 1038326 occupied, 23961625 free *** Garbage collection starting *** GC 122 3-Oct-2003 05:03:22, 40 ms (0%), 1040928 occupied, 23959024 free *** Garbage collection starting *** GC 123 3-Oct-2003 05:03:24, 30 ms (0%), 1041468 occupied, 23958483 free *** Garbage collection starting *** GC 124 3-Oct-2003 05:03:26, 40 ms (0%), 1041774 occupied, 23958178 free *** Garbage collection starting *** GC 125 3-Oct-2003 05:03:28, 30 ms (0%), 1041958 occupied, 23957993 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : *** Garbage collection starting *** GC 126 3-Oct-2003 05:03:32, 30 ms (0%), 1047880 occupied, 23952070 free Eliminate q6 from e_137 and e_8. e_8: 6 terms, 12 factors, with derivatives of functions of all variables: (q22,q19,q15,q6,q2,q1,p7,p5,p2) is replaced by e_211: 6 terms, 12 factors, with derivatives of functions of all variables: (q22,q19,q15,q2,q1,p5,p4,p2) Step 197: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 127 3-Oct-2003 05:03:34, 40 ms (0%), 1040528 occupied, 23959422 free *** Garbage collection starting *** GC 128 3-Oct-2003 05:03:36, 40 ms (0%), 1041530 occupied, 23958421 free *** Garbage collection starting *** GC 129 3-Oct-2003 05:03:38, 30 ms (0%), 1041966 occupied, 23957984 free *** Garbage collection starting *** GC 130 3-Oct-2003 05:03:41, 30 ms (0%), 1042260 occupied, 23957691 free *** Garbage collection starting *** GC 131 3-Oct-2003 05:03:43, 30 ms (0%), 1042540 occupied, 23957410 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : *** Garbage collection starting *** GC 132 3-Oct-2003 05:03:47, 40 ms (0%), 1070773 occupied, 23929176 free Eliminate q5 from e_56 and e_203. e_203: 6 terms, 12 factors, with derivatives of functions of all variables: (q20,q18,q17,q12,q7,q5,p8,p7,p5,p3) is replaced by e_14: 6 terms, 12 factors, with derivatives of functions of all variables: (q20,q18,q17,q12,q7,q1,p8,p7,p5,p3) Step 198: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 133 3-Oct-2003 05:03:49, 40 ms (0%), 1041690 occupied, 23958260 free *** Garbage collection starting *** GC 134 3-Oct-2003 05:03:51, 30 ms (0%), 1042840 occupied, 23957111 free *** Garbage collection starting *** GC 135 3-Oct-2003 05:03:54, 40 ms (0%), 1043430 occupied, 23956520 free *** Garbage collection starting *** GC 136 3-Oct-2003 05:03:56, 30 ms (0%), 1043658 occupied, 23956293 free *** Garbage collection starting *** GC 137 3-Oct-2003 05:03:59, 40 ms (0%), 1044282 occupied, 23955668 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q6 from e_137 and e_126. e_126: 8 terms, 16 factors, with derivatives of functions of all variables: (q25,q24,q21,q13,q10,q9,q6,p7,p5,p4) is replaced by e_27: 8 terms, 16 factors, with derivatives of functions of all variables: (q25,q24,q21,q13,q10,q9,q1,p7,p5,p4) Step 199: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 200: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 138 3-Oct-2003 05:04:02, 40 ms (0%), 1040094 occupied, 23959857 free *** Garbage collection starting *** GC 139 3-Oct-2003 05:04:04, 40 ms (0%), 1042730 occupied, 23957220 free *** Garbage collection starting *** GC 140 3-Oct-2003 05:04:07, 40 ms (0%), 1043538 occupied, 23956413 free *** Garbage collection starting *** GC 141 3-Oct-2003 05:04:09, 40 ms (0%), 1043968 occupied, 23955982 free *** Garbage collection starting *** GC 142 3-Oct-2003 05:04:12, 40 ms (0%), 1045026 occupied, 23954925 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q6 from e_137 and e_180. e_180: 5 terms, 10 factors, with derivatives of functions of all variables: (q25,q18,q11,q6,q3,p7,p2) is replaced by e_4: 5 terms, 10 factors, with derivatives of functions of all variables: (q25,q18,q11,q3,q1,p7,p4,p2) Step 201: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 202: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 143 3-Oct-2003 05:04:15, 40 ms (0%), 1042292 occupied, 23957658 free *** Garbage collection starting *** GC 144 3-Oct-2003 05:04:18, 40 ms (0%), 1044242 occupied, 23955709 free *** Garbage collection starting *** GC 145 3-Oct-2003 05:04:21, 40 ms (0%), 1045670 occupied, 23954281 free *** Garbage collection starting *** GC 146 3-Oct-2003 05:04:24, 40 ms (0%), 1047262 occupied, 23952687 free *** Garbage collection starting *** GC 147 3-Oct-2003 05:04:27, 40 ms (0%), 1049810 occupied, 23950139 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q5 from e_56 and e_7. e_7: 7 terms, 14 factors, with derivatives of functions of all variables: (q21,q10,q5,q4,q2,q1,p7,p6,p5,p4,p2) is replaced by e_224: 7 terms, 14 factors, with derivatives of functions of all variables: (q21,q10,q4,q2,q1,p7,p6,p5,p4,p3,p2) Step 203: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 148 3-Oct-2003 05:04:30, 30 ms (0%), 1040970 occupied, 23958980 free *** Garbage collection starting *** GC 149 3-Oct-2003 05:04:32, 40 ms (0%), 1045590 occupied, 23954361 free shortening by 2 terms Step 204: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 150 3-Oct-2003 05:04:34, 40 ms (0%), 1047328 occupied, 23952621 free shortening by 2 terms Step 205: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 151 3-Oct-2003 05:04:36, 30 ms (0%), 1042748 occupied, 23957203 free *** Garbage collection starting *** GC 152 3-Oct-2003 05:04:38, 30 ms (0%), 1044886 occupied, 23955064 free *** Garbage collection starting *** GC 153 3-Oct-2003 05:04:40, 40 ms (0%), 1045314 occupied, 23954637 free *** Garbage collection starting *** GC 154 3-Oct-2003 05:04:42, 40 ms (0%), 1045782 occupied, 23954167 free *** Garbage collection starting *** GC 155 3-Oct-2003 05:04:44, 30 ms (0%), 1046100 occupied, 23953850 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q5 from e_56 and e_101. e_101: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q23,q21,q12,q10,q8,q5,p7,p5,p4,p3) is replaced by e_200: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q23,q21,q12,q10,q8,q1,p7,p5,p4,p3) Step 206: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 156 3-Oct-2003 05:04:47, 40 ms (0%), 1043264 occupied, 23956687 free *** Garbage collection starting *** GC 157 3-Oct-2003 05:04:50, 30 ms (0%), 1046300 occupied, 23953650 free *** Garbage collection starting *** GC 158 3-Oct-2003 05:04:52, 30 ms (0%), 1046702 occupied, 23953249 free *** Garbage collection starting *** GC 159 3-Oct-2003 05:04:54, 30 ms (0%), 1047130 occupied, 23952820 free *** Garbage collection starting *** GC 160 3-Oct-2003 05:04:57, 30 ms (0%), 1047926 occupied, 23952025 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q5 from e_56 and e_103. e_103: 11 terms, 22 factors, with derivatives of functions of all variables: (q24,q23,q22,q15,q14,q8,q6,q5,q2,q1,p8,p7,p6,p4,p3) is replaced by e_194: 11 terms, 22 factors, with derivatives of functions of all variables: (q24,q23,q22,q15,q14,q8,q6,q2,q1,p8,p7,p6,p4,p3) Step 207: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 161 3-Oct-2003 05:05:00, 40 ms (0%), 1044714 occupied, 23955236 free *** Garbage collection starting *** GC 162 3-Oct-2003 05:05:03, 30 ms (0%), 1046916 occupied, 23953035 free *** Garbage collection starting *** GC 163 3-Oct-2003 05:05:06, 30 ms (0%), 1048478 occupied, 23951472 free *** Garbage collection starting *** GC 164 3-Oct-2003 05:05:08, 40 ms (0%), 1049304 occupied, 23950647 free *** Garbage collection starting *** GC 165 3-Oct-2003 05:05:11, 40 ms (0%), 1050938 occupied, 23949012 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q6 from e_137 and e_28. e_28: 6 terms, 12 factors, with derivatives of functions of all variables: (q25,q22,q19,q6,q2,p7,p6,p2) is replaced by e_186: 6 terms, 12 factors, with derivatives of functions of all variables: (q25,q22,q19,q2,q1,p7,p6,p4,p2) Step 208: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 166 3-Oct-2003 05:05:15, 40 ms (0%), 1046262 occupied, 23953689 free *** Garbage collection starting *** GC 167 3-Oct-2003 05:05:18, 40 ms (0%), 1049948 occupied, 23950002 free shortening by 1 term Step 209: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 168 3-Oct-2003 05:05:21, 30 ms (0%), 1044312 occupied, 23955639 free shortening by 1 term Step 210: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 169 3-Oct-2003 05:05:25, 40 ms (0%), 1046090 occupied, 23953860 free *** Garbage collection starting *** GC 170 3-Oct-2003 05:05:28, 40 ms (0%), 1050324 occupied, 23949626 free *** Garbage collection starting *** GC 171 3-Oct-2003 05:05:32, 30 ms (0%), 1050906 occupied, 23949043 free *** Garbage collection starting *** GC 172 3-Oct-2003 05:05:36, 30 ms (0%), 1051230 occupied, 23948720 free *** Garbage collection starting *** GC 173 3-Oct-2003 05:05:40, 40 ms (0%), 1051490 occupied, 23948459 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : *** Garbage collection starting *** GC 174 3-Oct-2003 05:05:44, 40 ms (0%), 1082986 occupied, 23916961 free Eliminate q5 from e_56 and e_50. e_50: 7 terms, 14 factors, with derivatives of functions of all variables: (q24,q21,q10,q5,q3,q2,q1,p8,p7,p6,p5,p2) is replaced by e_183: 7 terms, 14 factors, with derivatives of functions of all variables: (q24,q21,q10,q3,q2,q1,p8,p6,p5,p3,p2) Step 211: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 175 3-Oct-2003 05:05:48, 40 ms (0%), 1049700 occupied, 23950245 free *** Garbage collection starting *** GC 176 3-Oct-2003 05:05:52, 40 ms (0%), 1050532 occupied, 23949414 free *** Garbage collection starting *** GC 177 3-Oct-2003 05:05:57, 30 ms (0%), 1051440 occupied, 23948505 free *** Garbage collection starting *** GC 178 3-Oct-2003 05:06:02, 40 ms (0%), 1052000 occupied, 23947946 free *** Garbage collection starting *** GC 179 3-Oct-2003 05:06:07, 40 ms (0%), 1053120 occupied, 23946825 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q6 from e_137 and e_3. e_3: 7 terms, 14 factors, with derivatives of functions of all variables: (q25,q18,q6,q5,q3,q2,q1,p8,p7,p5,p3,p2) is replaced by e_147: 7 terms, 14 factors, with derivatives of functions of all variables: (q25,q18,q5,q3,q2,q1,p8,p7,p5,p4,p3,p2) Step 212: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 213: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 214: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 180 3-Oct-2003 05:06:13, 40 ms (0%), 1050216 occupied, 23949734 free *** Garbage collection starting *** GC 181 3-Oct-2003 05:06:19, 40 ms (0%), 1051888 occupied, 23948061 free *** Garbage collection starting *** GC 182 3-Oct-2003 05:06:25, 40 ms (0%), 1055512 occupied, 23944437 free *** Garbage collection starting *** GC 183 3-Oct-2003 05:06:33, 40 ms (0%), 1058244 occupied, 23941703 free *** Garbage collection starting *** GC 184 3-Oct-2003 05:06:41, 40 ms (0%), 1058802 occupied, 23941146 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q18 from e_13 and e_130. e_130: 4 terms, 8 factors, with derivatives of functions of all variables: (q23,q18,q5,q1,p8,p5,p2) is replaced by e_209: 4 terms, 8 factors, with derivatives of functions of all variables: (q23,q11,q5,q1,p8,p4,p2) Step 215: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 185 3-Oct-2003 05:06:49, 40 ms (0%), 1052182 occupied, 23947767 free *** Garbage collection starting *** GC 186 3-Oct-2003 05:06:58, 40 ms (0%), 1054236 occupied, 23945714 free *** Garbage collection starting *** GC 187 3-Oct-2003 05:07:10, 40 ms (0%), 1057864 occupied, 23942083 free *** Garbage collection starting *** GC 188 3-Oct-2003 05:07:26, 40 ms (0%), 1059288 occupied, 23940660 free --- Length reducing decoupling steps : *** Garbage collection starting *** GC 189 3-Oct-2003 05:07:54, 40 ms (0%), 1092350 occupied, 23907597 free Eliminate q5 from e_56 and e_71. e_71: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q23,q21,q16,q12,q10,q7,q5,p8,p7,p5,p3) is replaced by e_175: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q23,q21,q16,q12,q10,q7,q1,p8,p7,p5,p3) Step 216: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q6 from e_137 and e_128. e_128: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q22,q21,q19,q16,q10,q6,q4,p8,p7,p4,p2) is replaced by e_119: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q22,q21,q19,q16,q10,q4,q1,p8,p4,p2) Step 217: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 190 3-Oct-2003 05:08:15, 40 ms (0%), 1084776 occupied, 23915171 free Eliminate q18 from e_13 and e_152. e_152: 7 terms, 14 factors, with derivatives of functions of all variables: (q24,q22,q19,q18,q17,q11,p6,p4,p2) is replaced by e_79: 7 terms, 14 factors, with derivatives of functions of all variables: (q24,q22,q19,q17,q1,p6,p5,p4,p2) Step 218: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 191 3-Oct-2003 05:08:26, 30 ms (0%), 1057200 occupied, 23942749 free --- Length reducing decoupling steps : Eliminate q27 from e_127 and e_225. e_225: 6 terms, 12 factors, with derivatives of functions of all variables: (q27,q24,q21,q16,q10,q2,p8,p7,p2) is replaced by e_158: 6 terms, 12 factors, with derivatives of functions of all variables: (q24,q22,q21,q15,q10,q2,p8,p7) Step 219: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q5 from e_56 and e_106. e_106: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q22,q19,q18,q13,q8,q6,q5,p8,p7,p5,p4,p3) is replaced by e_10: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q22,q19,q18,q13,q8,q6,q1,p8,p7,p5,p4,p3) Step 220: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 192 3-Oct-2003 05:08:48, 40 ms (0%), 1092201 occupied, 23907744 free Eliminate q5 from e_56 and e_149. e_149: 10 terms, 20 factors, with derivatives of functions of all variables: (q24,q21,q16,q10,q5,q4,q3,q2,p8,p7,p5,p3,p2) is replaced by e_179: 10 terms, 20 factors, with derivatives of functions of all variables: (q24,q21,q16,q10,q4,q3,q2,q1,p8,p7,p5,p3,p2) Step 221: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 193 3-Oct-2003 05:09:01, 40 ms (0%), 1063915 occupied, 23936030 free Eliminate q6 from e_137 and e_5. e_5: 9 terms, 18 factors, with derivatives of functions of all variables: (q22,q21,q19,q17,q16,q14,q10,q9,q6,p8,p7,p6,p4,p2) is replaced by e_39: 9 terms, 18 factors, with derivatives of functions of all variables: (q22,q21,q19,q17,q16,q14,q10,q9,q1,p8,p7,p6,p4,p2) Step 222: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q23 from e_43 and e_42. e_42: 6 terms, 12 factors, with derivatives of functions of all variables: (q27,q26,q23,q21,q2,q1,p8,p7,p5,p3) is replaced by e_32: 6 terms, 12 factors, with derivatives of functions of all variables: (q27,q26,q20,q18,q2,q1,p8,p7,p5,p3) Step 223: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 194 3-Oct-2003 05:09:22, 40 ms (0%), 1058000 occupied, 23941948 free --- Length reducing decoupling steps : Eliminate q6 from e_137 and e_160. e_160: 10 terms, 20 factors, with derivatives of functions of all variables: (q25,q20,q19,q17,q14,q9,q6,q4,q3,p8,p7,p6,p4,p2) is replaced by e_60: 10 terms, 20 factors, with derivatives of functions of all variables: (q25,q20,q19,q17,q14,q9,q4,q3,q1,p8,p7,p6,p4,p2) Step 224: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 225: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q6 from e_137 and e_93. e_93: 10 terms, 20 factors, with derivatives of functions of all variables: (q25,q23,q21,q15,q13,q11,q8,q6,q2,p8,p7,p6,p4,p3) is replaced by e_109: 10 terms, 20 factors, with derivatives of functions of all variables: (q25,q23,q21,q15,q13,q11,q8,q2,q1,p8,p7,p6,p4,p3) Step 226: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 195 3-Oct-2003 05:09:49, 40 ms (0%), 1066690 occupied, 23933258 free Eliminate q6 from e_137 and e_38. e_38: 10 terms, 20 factors, with derivatives of functions of all variables: (q18,q17,q13,q11,q10,q8,q6,q3,p8,p7,p6,p5,p4,p2) is replaced by e_124: 10 terms, 20 factors, with derivatives of functions of all variables: (q18,q17,q13,q11,q10,q8,q3,q1,p8,p7,p6,p5,p4,p2) Step 227: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q24 from e_64 and e_216. e_216: 6 terms, 12 factors, with derivatives of functions of all variables: (q27,q26,q24,q22,q2,q1,p8,p7,p6,p4) is replaced by e_8: 6 terms, 12 factors, with derivatives of functions of all variables: (q27,q26,q19,q17,q2,q1,p8,p7,p6,p4) Step 228: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 196 3-Oct-2003 05:10:13, 40 ms (0%), 1061403 occupied, 23938545 free Eliminate q6 from e_137 and e_169. e_169: 10 terms, 20 factors, with derivatives of functions of all variables: (q25,q23,q22,q15,q13,q7,q6,q5,q2,q1,p8,p7,p6,p5,p3) is replaced by e_203: 10 terms, 20 factors, with derivatives of functions of all variables: (q25,q23,q22,q15,q13,q7,q5,q2,q1,p8,p7,p6,p5,p4,p3) Step 229: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 230: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 197 3-Oct-2003 05:10:28, 40 ms (0%), 1090530 occupied, 23909414 free Eliminate q6 from e_137 and e_170. e_170: 11 terms, 22 factors, with derivatives of functions of all variables: (q25,q23,q21,q19,q18,q13,q8,q6,q3,p8,p7,p6,p4,p3,p2) is replaced by e_171: 11 terms, 22 factors, with derivatives of functions of all variables: (q25,q23,q21,q19,q18,q13,q8,q3,q1,p8,p7,p6,p4,p3,p2) Step 231: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q25 from e_221 and e_171. e_171: 11 terms, 22 factors, with derivatives of functions of all variables: (q25,q23,q21,q19,q18,q13,q8,q3,q1,p8,p7,p6,p4,p3,p2) is replaced by e_180: 11 terms, 22 factors, with derivatives of functions of all variables: (q23,q21,q19,q18,q13,q8,q3,q1,p8,p7,p6,p5,p4,p3,p2) Step 232: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 233: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 198 3-Oct-2003 05:10:46, 40 ms (0%), 1055950 occupied, 23944000 free shortening by 1 term Step 234: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q25 from e_221 and e_215. e_215: 9 terms, 18 factors, with derivatives of functions of all variables: (q25,q23,q19,q18,q15,q11,q1,p7,p5,p4,p3,p2) is replaced by e_218: 9 terms, 18 factors, with derivatives of functions of all variables: (q23,q19,q18,q15,q11,q3,q1,p7,p5,p4,p3,p2) Step 235: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 236: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 199 3-Oct-2003 05:11:21, 50 ms (0%), 1086543 occupied, 23913402 free Eliminate q20 from e_189 and e_17. e_17: 13 terms, 26 factors, with derivatives of functions of all variables: (q20,q19,q17,q16,q15,q14,q10,q9,q4,p8,p7,p6,p5,p4,p2) is replaced by e_182: 13 terms, 26 factors, with derivatives of functions of all variables: (q19,q17,q16,q15,q14,q10,q9,q4,q1,p8,p7,p6,p5,p4,p2) Step 237: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q6 from e_137 and e_74. e_74: 10 terms, 20 factors, with derivatives of functions of all variables: (q25,q24,q22,q20,q17,q13,q11,q8,q6,q3,p8,p7,p5,p4,p3,p2) is replaced by e_4: 10 terms, 20 factors, with derivatives of functions of all variables: (q25,q24,q22,q20,q17,q13,q11,q8,q3,q1,p8,p7,p5,p4,p3,p2) Step 238: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 200 3-Oct-2003 05:11:48, 40 ms (0%), 1077369 occupied, 23922576 free Eliminate q25 from e_221 and e_4. e_4: 10 terms, 20 factors, with derivatives of functions of all variables: (q25,q24,q22,q20,q17,q13,q11,q8,q3,q1,p8,p7,p5,p4,p3,p2) is replaced by e_222: 10 terms, 20 factors, with derivatives of functions of all variables: (q24,q22,q20,q17,q13,q11,q8,q3,q1,p8,p7,p5,p4,p3,p2) Step 239: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q5 from e_56 and e_156. e_156: 12 terms, 24 factors, with derivatives of functions of all variables: (q25,q22,q21,q16,q15,q11,q10,q5,q4,p8,p7,p6,p5,p4,p3,p2) is replaced by e_121: 12 terms, 24 factors, with derivatives of functions of all variables: (q25,q22,q21,q16,q15,q11,q10,q4,q1,p8,p7,p6,p5,p4,p3,p2) Step 240: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 201 3-Oct-2003 05:12:16, 40 ms (0%), 1066817 occupied, 23933130 free Eliminate q5 from e_56 and e_174. e_174: 14 terms, 28 factors, with derivatives of functions of all variables: (q25,q20,q19,q18,q17,q16,q15,q5,q4,p8,p7,p6,p5,p4,p3,p2) is replaced by e_96: 14 terms, 28 factors, with derivatives of functions of all variables: (q25,q20,q19,q18,q17,q16,q15,q4,q1,p8,p7,p6,p5,p4,p3,p2) Step 241: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 202 3-Oct-2003 05:12:32, 40 ms (0%), 1075504 occupied, 23924442 free Eliminate q23 from e_146 and e_175. e_175: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q23,q21,q16,q12,q10,q7,q1,p8,p7,p5,p3) is replaced by e_7: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q20,q18,q16,q12,q10,q7,q1,p8,p7,p5,p3) Step 242: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 243: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q23 from e_219 and e_23. e_23: 9 terms, 18 factors, with derivatives of functions of all variables: (q25,q24,q23,q18,q16,q15,q11,q10,p7,p4,p3,p2) is replaced by e_50: 9 terms, 18 factors, with derivatives of functions of all variables: (q25,q24,q19,q18,q16,q11,q10,q3,p7,p4,p3,p2) Step 244: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 203 3-Oct-2003 05:12:39, 30 ms (0%), 1072434 occupied, 23927517 free Eliminate q25 from e_221 and e_50. e_50: 9 terms, 18 factors, with derivatives of functions of all variables: (q25,q24,q19,q18,q16,q11,q10,q3,p7,p4,p3,p2) is replaced by e_3: 9 terms, 18 factors, with derivatives of functions of all variables: (q24,q19,q18,q16,q11,q10,q1,p5,p4,p3,p2) Step 245: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 246: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q5 from e_56 and e_54. e_54: 15 terms, 30 factors, with derivatives of functions of all variables: (q20,q18,q16,q15,q13,q10,q8,q6,q5,q3,p8,p7,p6,p5,p4,p3,p2) is replaced by e_129: 15 terms, 30 factors, with derivatives of functions of all variables: (q20,q18,q16,q15,q13,q10,q8,q6,q3,q1,p8,p7,p6,p5,p4,p3,p2) Step 247: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 204 3-Oct-2003 05:12:48, 30 ms (0%), 1076238 occupied, 23923712 free Eliminate q6 from e_137 and e_159. e_159: 10 terms, 20 factors, with derivatives of functions of all variables: (q18,q13,q11,q10,q8,q6,q3,p8,p7,p6,p5,p3,p2) is replaced by e_22: 10 terms, 20 factors, with derivatives of functions of all variables: (q18,q13,q11,q10,q8,q3,q1,p8,p7,p6,p5,p4,p3,p2) Step 248: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 205 3-Oct-2003 05:12:55, 40 ms (0%), 1083831 occupied, 23916119 free Eliminate q27 from e_8 and e_12. e_12: 9 terms, 18 factors, with derivatives of functions of all variables: (q27,q26,q23,q22,q19,q17,q15,q10,p8,p7,p6,p4,p2) is replaced by e_155: 9 terms, 18 factors, with derivatives of functions of all variables: (q26,q23,q22,q19,q17,q15,q10,q2,q1,p8,p7,p2) Step 249: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 250: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 251: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 252: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 206 3-Oct-2003 05:13:01, 40 ms (0%), 1082496 occupied, 23917455 free Eliminate q24 from e_59 and e_87. e_87: 10 terms, 20 factors, with derivatives of functions of all variables: (q24,q23,q22,q17,q15,q14,q11,q9,q4,p8,p7,p6,p4,p2) is replaced by e_1: 10 terms, 20 factors, with derivatives of functions of all variables: (q23,q19,q17,q15,q14,q11,q10,q9,q4,p8,p7,p6,p4,p2) Step 253: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 254: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 7 terms Step 255: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 207 3-Oct-2003 05:13:09, 30 ms (0%), 1055682 occupied, 23944269 free --- Length reducing decoupling steps : Eliminate q1 from e_141 and e_183. e_183: 7 terms, 14 factors, with derivatives of functions of all variables: (q24,q21,q10,q3,q2,q1,p8,p6,p5,p3,p2) is replaced by e_130: 5 terms, 10 factors, with derivatives of functions of all variables: (q24,q21,q10,q3,q2,p8,p5,p2) Step 256: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q1 from e_141 and e_224. e_224: 7 terms, 14 factors, with derivatives of functions of all variables: (q21,q10,q4,q2,q1,p7,p6,p5,p4,p3,p2) is replaced by e_128: 5 terms, 10 factors, with derivatives of functions of all variables: (q21,q10,q4,q2,p7,p5,p4,p2) Step 257: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 208 3-Oct-2003 05:13:21, 30 ms (0%), 1078011 occupied, 23921939 free *** Garbage collection starting *** GC 209 3-Oct-2003 05:13:26, 30 ms (0%), 1071395 occupied, 23928557 free Eliminate q25 from e_221 and e_214. e_214: 10 terms, 20 factors, with derivatives of functions of all variables: (q25,q24,q22,q21,q18,q16,q10,q9,q8,q3,p8,p7,p4,p3,p2) is replaced by e_5: 10 terms, 20 factors, with derivatives of functions of all variables: (q24,q22,q21,q18,q16,q10,q9,q8,q1,p8,p7,p5,p4,p3,p2) Step 258: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q18 from e_13 and e_5. e_5: 10 terms, 20 factors, with derivatives of functions of all variables: (q24,q22,q21,q18,q16,q10,q9,q8,q1,p8,p7,p5,p4,p3,p2) is replaced by e_42: 10 terms, 20 factors, with derivatives of functions of all variables: (q24,q22,q21,q16,q11,q10,q9,q8,q1,p8,p7,p5,p4,p3,p2) Step 259: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 210 3-Oct-2003 05:13:35, 30 ms (0%), 1055018 occupied, 23944933 free --- Length reducing decoupling steps : *** Garbage collection starting *** GC 211 3-Oct-2003 05:13:43, 30 ms (0%), 1065193 occupied, 23934758 free Eliminate q23 from e_40 and e_95. e_95: 11 terms, 22 factors, with derivatives of functions of all variables: (q23,q21,q20,q17,q13,q10,q8,q4,q3,p8,p7,p6,p4,p3,p2) is replaced by e_160: 11 terms, 22 factors, with derivatives of functions of all variables: (q21,q20,q17,q16,q10,q3,q1,p8,p3,p2) Step 260: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q25 from e_221 and e_65. e_65: 9 terms, 18 factors, with derivatives of functions of all variables: (q25,q23,q22,q13,q11,q7,q3,p7,p6,p3,p2) is replaced by e_60: 9 terms, 18 factors, with derivatives of functions of all variables: (q23,q22,q13,q11,q7,q1,p7,p6,p5,p4,p3,p2) Step 261: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 212 3-Oct-2003 05:13:55, 40 ms (0%), 1063492 occupied, 23936457 free Eliminate q19 from e_83 and e_96. e_96: 14 terms, 28 factors, with derivatives of functions of all variables: (q25,q20,q19,q18,q17,q16,q15,q4,q1,p8,p7,p6,p5,p4,p3,p2) is replaced by e_93: 14 terms, 28 factors, with derivatives of functions of all variables: (q25,q20,q18,q17,q16,q15,q14,q9,q1,p8,p7,p6,p5,p4,p3,p2) Step 262: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 213 3-Oct-2003 05:14:05, 40 ms (0%), 1064922 occupied, 23935026 free *** Garbage collection starting *** GC 214 3-Oct-2003 05:14:10, 40 ms (0%), 1076031 occupied, 23923919 free *** Garbage collection starting *** GC 215 3-Oct-2003 05:14:15, 30 ms (0%), 1068304 occupied, 23931645 free *** Garbage collection starting *** GC 216 3-Oct-2003 05:14:21, 30 ms (0%), 1056165 occupied, 23943786 free *** Garbage collection starting *** GC 217 3-Oct-2003 05:14:27, 30 ms (0%), 1063233 occupied, 23936717 free Stop of a subroutine. Number of garbage collections exceeds max_gc_red_len. --- Factorization to subcases leading to substitutions : factorizing e_16 we get the alternative equations : 0=p2 0=q1 New level : 1.1. CRACK is now called with the new equation e_242 : 0=p2 e_132,e_84,e_24,e_11 are consequences of e_242 Step 263: Hot list of urgent steps : The list of inequalities got extended by: An expression with 24 terms The list of inequalities got extended by: An expression with 29 terms The list of inequalities got extended by: An expression with 6 terms e_138 is a consequence of e_3. Substitution of p2 found in e_242 : p2=0 Step 264: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 265: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 266: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 267: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 268: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 269: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 270: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 271: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 272: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 273: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 274: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 275: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 276: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 277: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 278: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 279: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 218 3-Oct-2003 05:14:29, 40 ms (0%), 1048589 occupied, 23951361 free *** Garbage collection starting *** GC 219 3-Oct-2003 05:14:31, 40 ms (0%), 1050413 occupied, 23949538 free *** Garbage collection starting *** GC 220 3-Oct-2003 05:14:33, 40 ms (0%), 1050955 occupied, 23948995 free *** Garbage collection starting *** GC 221 3-Oct-2003 05:14:35, 40 ms (0%), 1051197 occupied, 23948754 free *** Garbage collection starting *** GC 222 3-Oct-2003 05:14:37, 40 ms (0%), 1051471 occupied, 23948479 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q3 from e_205 and e_172. e_172: 0=(q25 + q3 - q6)*p3 is replaced by e_268: 0=(q25 - q6)*p3 Step 280: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 223 3-Oct-2003 05:14:39, 40 ms (0%), 1050881 occupied, 23949070 free *** Garbage collection starting *** GC 224 3-Oct-2003 05:14:41, 30 ms (0%), 1051329 occupied, 23948621 free *** Garbage collection starting *** GC 225 3-Oct-2003 05:14:43, 30 ms (0%), 1052393 occupied, 23947558 free *** Garbage collection starting *** GC 226 3-Oct-2003 05:14:45, 40 ms (0%), 1053263 occupied, 23946687 free *** Garbage collection starting *** GC 227 3-Oct-2003 05:14:47, 40 ms (0%), 1054281 occupied, 23945670 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q4 from e_256 and e_148. e_256: 0=p5*q2 + p7*q4 is replaced by e_271: 0=q2*(p4 - p5) Step 281: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 228 3-Oct-2003 05:14:52, 40 ms (0%), 1050525 occupied, 23949425 free shortening by 1 term Step 282: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 283: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 284: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 285: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 286: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 4 terms Step 287: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 229 3-Oct-2003 05:14:54, 40 ms (0%), 1049093 occupied, 23950858 free shortening by 1 term Step 288: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 230 3-Oct-2003 05:14:56, 40 ms (0%), 1051429 occupied, 23948521 free *** Garbage collection starting *** GC 231 3-Oct-2003 05:14:58, 40 ms (0%), 1052433 occupied, 23947518 free *** Garbage collection starting *** GC 232 3-Oct-2003 05:15:00, 40 ms (0%), 1053003 occupied, 23946947 free *** Garbage collection starting *** GC 233 3-Oct-2003 05:15:02, 30 ms (0%), 1053297 occupied, 23946654 free *** Garbage collection starting *** GC 234 3-Oct-2003 05:15:04, 30 ms (0%), 1053601 occupied, 23946349 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q3 from e_143 and e_23. e_143: 0=p6*q2 - p7*q3 is replaced by e_234: 0=q2*(p3 + p6) Step 289: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 235 3-Oct-2003 05:15:06, 30 ms (0%), 1053251 occupied, 23946700 free *** Garbage collection starting *** GC 236 3-Oct-2003 05:15:08, 40 ms (0%), 1053955 occupied, 23945995 free *** Garbage collection starting *** GC 237 3-Oct-2003 05:15:11, 30 ms (0%), 1054755 occupied, 23945196 free *** Garbage collection starting *** GC 238 3-Oct-2003 05:15:13, 40 ms (0%), 1055323 occupied, 23944627 free *** Garbage collection starting *** GC 239 3-Oct-2003 05:15:16, 40 ms (0%), 1055693 occupied, 23944258 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q4 from e_194 and e_28. e_28: 0=p3*q4 + p5*q3 is replaced by e_32: 0=q3*(p4 - p5) Step 290: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 240 3-Oct-2003 05:15:18, 40 ms (0%), 1054747 occupied, 23945203 free shortening by 1 term Step 291: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 241 3-Oct-2003 05:15:21, 30 ms (0%), 1052507 occupied, 23947444 free *** Garbage collection starting *** GC 242 3-Oct-2003 05:15:24, 40 ms (0%), 1055835 occupied, 23944115 free *** Garbage collection starting *** GC 243 3-Oct-2003 05:15:27, 40 ms (0%), 1058391 occupied, 23941560 free shortening by 1 term Step 292: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 244 3-Oct-2003 05:15:30, 30 ms (0%), 1056743 occupied, 23943207 free *** Garbage collection starting *** GC 245 3-Oct-2003 05:15:33, 30 ms (0%), 1059143 occupied, 23940808 free *** Garbage collection starting *** GC 246 3-Oct-2003 05:15:36, 40 ms (0%), 1059547 occupied, 23940404 free *** Garbage collection starting *** GC 247 3-Oct-2003 05:15:40, 40 ms (0%), 1059907 occupied, 23940043 free *** Garbage collection starting *** GC 248 3-Oct-2003 05:15:43, 40 ms (0%), 1060261 occupied, 23939690 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q25 from e_268 and e_185. e_185: 4 terms, 8 factors, with derivatives of functions of all variables: (q25,q13,q7,p6,p3) is replaced by e_240: 4 terms, 8 factors, with derivatives of functions of all variables: (q13,q7,q6,p6,p3) Step 293: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 249 3-Oct-2003 05:15:47, 40 ms (0%), 1056881 occupied, 23943069 free *** Garbage collection starting *** GC 250 3-Oct-2003 05:15:51, 40 ms (0%), 1057861 occupied, 23942090 free *** Garbage collection starting *** GC 251 3-Oct-2003 05:15:56, 40 ms (0%), 1059541 occupied, 23940409 free *** Garbage collection starting *** GC 252 3-Oct-2003 05:16:00, 30 ms (0%), 1060773 occupied, 23939178 free *** Garbage collection starting *** GC 253 3-Oct-2003 05:16:05, 40 ms (0%), 1062585 occupied, 23937365 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q1 from e_3 and e_71. e_71: 6 terms, 12 factors, with derivatives of functions of all variables: (q24,q22,q19,q17,q1,p6,p5,p4) is replaced by e_24: 4 terms, 8 factors, with derivatives of functions of all variables: (q24,q22,q19,q17,p6,p4) Step 294: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 254 3-Oct-2003 05:16:10, 30 ms (0%), 1060735 occupied, 23939215 free shortening by 1 term Step 295: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 255 3-Oct-2003 05:16:16, 40 ms (0%), 1062631 occupied, 23937319 free *** Garbage collection starting *** GC 256 3-Oct-2003 05:16:22, 40 ms (0%), 1063247 occupied, 23936704 free *** Garbage collection starting *** GC 257 3-Oct-2003 05:16:28, 40 ms (0%), 1063881 occupied, 23936069 free *** Garbage collection starting *** GC 258 3-Oct-2003 05:16:35, 40 ms (0%), 1065377 occupied, 23934573 free *** Garbage collection starting *** GC 259 3-Oct-2003 05:16:44, 40 ms (0%), 1068183 occupied, 23931766 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q3 from e_23 and e_246. e_246: 0=p7*q3 - p8*q4 is replaced by e_117: 0=p3*q2 + p8*q4 Step 296: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 260 3-Oct-2003 05:16:49, 40 ms (0%), 1059871 occupied, 23940080 free *** Garbage collection starting *** GC 261 3-Oct-2003 05:16:58, 40 ms (0%), 1062965 occupied, 23936986 free *** Garbage collection starting *** GC 262 3-Oct-2003 05:17:09, 40 ms (0%), 1063785 occupied, 23936166 free *** Garbage collection starting *** GC 263 3-Oct-2003 05:17:22, 40 ms (0%), 1068553 occupied, 23931398 free *** Garbage collection starting *** GC 264 3-Oct-2003 05:17:43, 40 ms (0%), 1070755 occupied, 23929196 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q6 from e_2 and e_240. e_240: 4 terms, 8 factors, with derivatives of functions of all variables: (q13,q7,q6,p6,p3) is replaced by e_224: 4 terms, 8 factors, with derivatives of functions of all variables: (q13,q7,q5,p6,p4,p3) Step 297: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 265 3-Oct-2003 05:18:03, 40 ms (0%), 1066708 occupied, 23933243 free Eliminate q25 from e_268 and e_133. e_133: 5 terms, 10 factors, with derivatives of functions of all variables: (q25,q13,q12,q9,q8,p5,p4,p3) is replaced by e_215: 5 terms, 10 factors, with derivatives of functions of all variables: (q13,q12,q9,q8,q6,p5,p4,p3) Step 298: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q6 from e_2 and e_215. e_215: 5 terms, 10 factors, with derivatives of functions of all variables: (q13,q12,q9,q8,q6,p5,p4,p3) is replaced by e_225: 5 terms, 10 factors, with derivatives of functions of all variables: (q13,q12,q9,q8,q5,p5,p4,p3) Step 299: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_23 and e_154. e_154: 6 terms, 12 factors, with derivatives of functions of all variables: (q23,q19,q18,q15,q11,q3,p7,p3) is replaced by e_265: (#) 6 terms, 7 factors, with derivatives of functions of all variables: (q23,q19,q18,q15,q11,q2,p3) Step 300: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 266 3-Oct-2003 05:18:27, 40 ms (0%), 1076217 occupied, 23923732 free Eliminate q4 from e_148 and e_47. e_47: 6 terms, 12 factors, with derivatives of functions of all variables: (q23,q19,q18,q15,q11,q4,p7,p4) is replaced by e_272: (#) 6 terms, 7 factors, with derivatives of functions of all variables: (q23,q19,q18,q15,q11,q2,p4) Step 301: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_23 and e_221. e_221: 4 terms, 8 factors, with derivatives of functions of all variables: (q25,q3,q1,p7,p5,p4) is replaced by e_158: 4 terms, 8 factors, with derivatives of functions of all variables: (q25,q2,q1,p7,p5,p4,p3) Step 302: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 267 3-Oct-2003 05:18:45, 40 ms (0%), 1067427 occupied, 23932523 free --- Length reducing decoupling steps : Eliminate q4 from e_148 and e_149. e_149: 6 terms, 12 factors, with derivatives of functions of all variables: (q19,q18,q17,q14,q9,q4,p8,p7,p6,p4) is replaced by e_283: 6 terms, 12 factors, with derivatives of functions of all variables: (q19,q18,q17,q14,q9,q2,p8,p7,p6,p4) Step 303: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 268 3-Oct-2003 05:18:51, 40 ms (0%), 1064871 occupied, 23935080 free --- Length reducing decoupling steps : Eliminate q3 from e_23 and e_255. e_255: 7 terms, 14 factors, with derivatives of functions of all variables: (q23,q22,q15,q13,q7,q5,q3,p8,p7,p6,p3) is replaced by e_284: 7 terms, 14 factors, with derivatives of functions of all variables: (q23,q22,q15,q13,q7,q5,q2,p8,p7,p6,p3) Step 304: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_23 and e_216. e_216: 7 terms, 14 factors, with derivatives of functions of all variables: (q20,q19,q18,q12,q7,q5,q3,p8,p7,p5,p3) is replaced by e_166: 7 terms, 14 factors, with derivatives of functions of all variables: (q20,q19,q18,q12,q7,q5,q2,p8,p7,p5,p3) *** Garbage collection starting *** GC 269 3-Oct-2003 05:19:10, 40 ms (0%), 1063372 occupied, 23936579 free Step 305: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q4 from e_148 and e_169. e_169: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q23,q22,q14,q11,q8,q4,p7,p6,p4,p3) is replaced by e_170: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q23,q22,q14,q11,q8,q2,p7,p6,p4,p3) Step 306: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 270 3-Oct-2003 05:19:17, 40 ms (0%), 1083002 occupied, 23916941 free Eliminate q6 from e_264 and e_226. e_226: 13 terms, 26 factors, with derivatives of functions of all variables: (q18,q16,q15,q13,q10,q8,q6,q3,q1,p8,p7,p6,p5,p4,p3) is replaced by e_218: 13 terms, 26 factors, with derivatives of functions of all variables: (q18,q16,q15,q13,q10,q8,q3,q1,p8,p7,p6,p5,p4,p3) Step 307: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q4 from e_117 and e_5. e_5: 6 terms, 12 factors, with derivatives of functions of all variables: (q24,q21,q16,q10,q4,q1,p8,p4) is replaced by e_267: 6 terms, 12 factors, with derivatives of functions of all variables: (q24,q21,q16,q10,q2,q1,p4,p3) Step 308: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 271 3-Oct-2003 05:19:25, 40 ms (0%), 1066162 occupied, 23933788 free Eliminate q6 from e_264 and e_193. e_193: 7 terms, 14 factors, with derivatives of functions of all variables: (q22,q19,q18,q15,q11,q6,q2,p8,p4) is replaced by e_229: 7 terms, 14 factors, with derivatives of functions of all variables: (q22,q19,q18,q15,q11,q2,q1,p6,p4) Step 309: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_155 and e_17. e_17: 7 terms, 14 factors, with derivatives of functions of all variables: (q21,q20,q17,q16,q10,q3,q1,p8,p3) is replaced by e_8: 7 terms, 14 factors, with derivatives of functions of all variables: (q21,q20,q17,q16,q10,q2,q1,p5,p3) Step 310: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q5 from e_50 and e_20. e_20: 7 terms, 14 factors, with derivatives of functions of all variables: (q22,q19,q18,q15,q11,q5,q2,p8,p3) is replaced by e_231: 7 terms, 14 factors, with derivatives of functions of all variables: (q22,q19,q18,q15,q11,q2,q1,p4,p3) Step 311: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q24 from e_87 and e_204. e_204: 5 terms, 10 factors, with derivatives of functions of all variables: (q27,q26,q24,q22,q2,p8,p7,p6,p4) is replaced by e_232: 5 terms, 10 factors, with derivatives of functions of all variables: (q27,q26,q19,q17,q2,p8,p7,p6,p4) Step 312: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 272 3-Oct-2003 05:19:36, 40 ms (0%), 1064027 occupied, 23935924 free --- Length reducing decoupling steps : Eliminate q6 from e_264 and e_10. e_10: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q22,q19,q18,q13,q8,q6,q1,p8,p7,p5,p4,p3) is replaced by e_27: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q22,q19,q18,q13,q8,q1,p8,p7,p6,p5,p4,p3) Step 313: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q1 from e_141 and e_27. e_27: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q22,q19,q18,q13,q8,q1,p8,p7,p6,p5,p4,p3) is replaced by e_175: 6 terms, 12 factors, with derivatives of functions of all variables: (q24,q22,q19,q18,q13,q8,p8,p7,p5,p4,p3) Step 314: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q4 from e_148 and e_57. e_57: 8 terms, 16 factors, with derivatives of functions of all variables: (q23,q21,q20,q17,q13,q8,q4,q3,p8,p7,p6,p4,p3) is replaced by e_185: 8 terms, 16 factors, with derivatives of functions of all variables: (q23,q21,q20,q17,q13,q8,q3,q2,p8,p7,p6,p4,p3) Step 315: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 273 3-Oct-2003 05:19:51, 40 ms (0%), 1087244 occupied, 23912697 free Eliminate q3 from e_155 and e_185. e_185: 8 terms, 16 factors, with derivatives of functions of all variables: (q23,q21,q20,q17,q13,q8,q3,q2,p8,p7,p6,p4,p3) is replaced by e_241: 8 terms, 16 factors, with derivatives of functions of all variables: (q23,q21,q20,q17,q13,q8,q2,p8,p7,p6,p5,p4,p3) Step 316: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q2 from e_271 and e_241. e_241: 8 terms, 16 factors, with derivatives of functions of all variables: (q23,q21,q20,q17,q13,q8,q2,p8,p7,p6,p5,p4,p3) is replaced by e_41: 6 terms, 12 factors, with derivatives of functions of all variables: (q23,q21,q20,q17,q13,q8,p8,p7,p6,p4,p3) Step 317: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_23 and e_171. e_171: 9 terms, 18 factors, with derivatives of functions of all variables: (q24,q22,q20,q17,q13,q8,q3,q1,p8,p7,p5,p4,p3) is replaced by e_11: 9 terms, 18 factors, with derivatives of functions of all variables: (q24,q22,q20,q17,q13,q8,q2,q1,p8,p7,p5,p4,p3) Step 318: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_23 and e_64. e_64: 10 terms, 20 factors, with derivatives of functions of all variables: (q18,q16,q15,q12,q11,q7,q5,q3,p8,p7,p6,p5,p3) is replaced by e_71: 10 terms, 20 factors, with derivatives of functions of all variables: (q18,q16,q15,q12,q11,q7,q5,q2,p8,p7,p6,p5,p3) Step 319: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 274 3-Oct-2003 05:20:08, 30 ms (0%), 1068337 occupied, 23931614 free --- Length reducing decoupling steps : Eliminate q24 from e_267 and e_203. e_203: 9 terms, 18 factors, with derivatives of functions of all variables: (q24,q22,q21,q16,q10,q9,q8,q1,p8,p7,p5,p4,p3) is replaced by e_84: 9 terms, 18 factors, with derivatives of functions of all variables: (q22,q21,q16,q10,q9,q8,q2,q1,p8,p7,p5,p4,p3) Step 320: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_155 and e_253. e_253: 7 terms, 14 factors, with derivatives of functions of all variables: (q24,q21,q16,q10,q4,q3,q1,p8,p7,p3) is replaced by e_132: 7 terms, 14 factors, with derivatives of functions of all variables: (q24,q21,q16,q10,q4,q2,q1,p7,p5,p3) Step 321: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 275 3-Oct-2003 05:20:22, 40 ms (0%), 1085338 occupied, 23914609 free Eliminate q4 from e_148 and e_132. e_132: 7 terms, 14 factors, with derivatives of functions of all variables: (q24,q21,q16,q10,q4,q2,q1,p7,p5,p3) is replaced by e_243: 7 terms, 14 factors, with derivatives of functions of all variables: (q24,q21,q16,q10,q2,q1,p5,p4,p3) Step 322: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q27 from e_232 and e_152. e_152: 6 terms, 12 factors, with derivatives of functions of all variables: (q27,q26,q20,q17,q15,q10,p8,p7,p6,p4) is replaced by e_92: 6 terms, 12 factors, with derivatives of functions of all variables: (q20,q19,q17,q15,q10,q2,p8,p7) Step 323: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_155 and e_218. e_218: 13 terms, 26 factors, with derivatives of functions of all variables: (q18,q16,q15,q13,q10,q8,q3,q1,p8,p7,p6,p5,p4,p3) is replaced by e_4: 13 terms, 26 factors, with derivatives of functions of all variables: (q18,q16,q15,q13,q10,q8,q2,q1,p8,p7,p6,p5,p4,p3) Step 324: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 276 3-Oct-2003 05:20:39, 40 ms (0%), 1070567 occupied, 23929383 free Eliminate q24 from e_279 and e_195. e_195: 5 terms, 10 factors, with derivatives of functions of all variables: (q26,q24,q21,q10,p7,p5,p4) is replaced by e_246: 5 terms, 10 factors, with derivatives of functions of all variables: (q26,q16,q10,q2,p8,p7,p5,p4) Step 325: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q23 from e_16 and e_207. e_207: 5 terms, 10 factors, with derivatives of functions of all variables: (q26,q23,q22,q11,p7,p6,p3) is replaced by e_251: 5 terms, 10 factors, with derivatives of functions of all variables: (q26,q15,q11,q1,p8,p7,p6,p3) Step 326: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 327: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 328: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q4 from e_148 and e_239. e_239: 11 terms, 22 factors, with derivatives of functions of all variables: (q25,q20,q19,q18,q17,q16,q15,q4,q1,p8,p7,p6,p5,p4,p3) is replaced by e_258: 11 terms, 22 factors, with derivatives of functions of all variables: (q25,q20,q19,q18,q17,q16,q15,q2,q1,p8,p6,p5,p4,p3) Step 329: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 277 3-Oct-2003 05:20:59, 40 ms (0%), 1069867 occupied, 23930082 free --- Length reducing decoupling steps : Eliminate q4 from e_148 and e_156. e_156: 11 terms, 22 factors, with derivatives of functions of all variables: (q25,q22,q21,q16,q15,q11,q10,q4,q1,p8,p7,p6,p5,p4,p3) is replaced by e_215: 11 terms, 22 factors, with derivatives of functions of all variables: (q25,q22,q21,q16,q15,q11,q10,q2,q1,p8,p6,p5,p4,p3) Step 330: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q5 from e_50 and e_166. e_166: 7 terms, 14 factors, with derivatives of functions of all variables: (q20,q19,q18,q12,q7,q5,q2,p8,p7,p5,p3) is replaced by e_260: 7 terms, 14 factors, with derivatives of functions of all variables: (q20,q19,q18,q12,q7,q2,q1,p8,p7,p5,p4,p3) Step 331: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 278 3-Oct-2003 05:21:17, 40 ms (0%), 1068574 occupied, 23931376 free Eliminate q5 from e_50 and e_284. e_284: 7 terms, 14 factors, with derivatives of functions of all variables: (q23,q22,q15,q13,q7,q5,q2,p8,p7,p6,p3) is replaced by e_261: 7 terms, 14 factors, with derivatives of functions of all variables: (q23,q22,q15,q13,q7,q2,q1,p7,p6,p4,p3) Step 332: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 333: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 334: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q25 from e_1 and e_263. e_263: 6 terms, 12 factors, with derivatives of functions of all variables: (q25,q23,q22,q15,q11,q1,p7,p4,p3) is replaced by e_259: 6 terms, 12 factors, with derivatives of functions of all variables: (q23,q22,q15,q11,q2,q1,p6,p4,p3) Step 335: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 279 3-Oct-2003 05:21:40, 40 ms (0%), 1081335 occupied, 23918609 free Eliminate q6 from e_264 and e_227. e_227: 13 terms, 26 factors, with derivatives of functions of all variables: (q17,q16,q15,q13,q11,q8,q6,q4,q3,p8,p7,p6,p5,p4,p3) is replaced by e_154: 13 terms, 26 factors, with derivatives of functions of all variables: (q17,q16,q15,q13,q11,q8,q4,q3,q1,p8,p7,p6,p5,p4,p3) Step 336: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_155 and e_154. e_154: 13 terms, 26 factors, with derivatives of functions of all variables: (q17,q16,q15,q13,q11,q8,q4,q3,q1,p8,p7,p6,p5,p4,p3) is replaced by e_266: 13 terms, 26 factors, with derivatives of functions of all variables: (q17,q16,q15,q13,q11,q8,q4,q2,q1,p8,p7,p6,p5,p4,p3) Step 337: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q4 from e_148 and e_266. e_266: 13 terms, 26 factors, with derivatives of functions of all variables: (q17,q16,q15,q13,q11,q8,q4,q2,q1,p8,p7,p6,p5,p4,p3) is replaced by e_196: 13 terms, 26 factors, with derivatives of functions of all variables: (q17,q16,q15,q13,q11,q8,q2,q1,p8,p7,p6,p5,p4,p3) Step 338: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 280 3-Oct-2003 05:22:02, 40 ms (0%), 1071080 occupied, 23928870 free Eliminate q27 from e_244 and e_34. e_34: 7 terms, 14 factors, with derivatives of functions of all variables: (q27,q26,q23,q22,q21,q16,q11,p8,p7,p5,p3) is replaced by e_172: 7 terms, 14 factors, with derivatives of functions of all variables: (q23,q22,q21,q19,q18,q16,q11,p8,p7) Step 339: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q23 from e_43 and e_172. e_172: 7 terms, 14 factors, with derivatives of functions of all variables: (q23,q22,q21,q19,q18,q16,q11,p8,p7) is replaced by e_269: 7 terms, 14 factors, with derivatives of functions of all variables: (q22,q21,q20,q19,q18,q16,q11,p8,p7) Step 340: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q4 from e_117 and e_65. e_65: 8 terms, 16 factors, with derivatives of functions of all variables: (q20,q19,q17,q14,q9,q4,q1,p8,p7,p6,p5,p4) is replaced by e_270: 8 terms, 16 factors, with derivatives of functions of all variables: (q20,q19,q17,q14,q9,q2,q1,p8,p7,p6,p5,p4,p3) Step 341: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_23 and e_109. e_109: 9 terms, 18 factors, with derivatives of functions of all variables: (q17,q13,q11,q10,q8,q3,q1,p8,p7,p6,p5,p4) is replaced by e_256: 9 terms, 18 factors, with derivatives of functions of all variables: (q17,q13,q11,q10,q8,q2,q1,p8,p7,p6,p5,p4,p3) Step 342: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 281 3-Oct-2003 05:22:30, 40 ms (0%), 1073747 occupied, 23926201 free --- Length reducing decoupling steps : Eliminate q5 from e_50 and e_71. e_71: 10 terms, 20 factors, with derivatives of functions of all variables: (q18,q16,q15,q12,q11,q7,q5,q2,p8,p7,p6,p5,p3) is replaced by e_47: 10 terms, 20 factors, with derivatives of functions of all variables: (q18,q16,q15,q12,q11,q7,q2,q1,p8,p7,p6,p5,p4,p3) Step 343: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q4 from e_117 and e_174. e_174: 11 terms, 22 factors, with derivatives of functions of all variables: (q17,q16,q15,q14,q10,q9,q4,q1,p8,p7,p6,p5,p4) is replaced by e_86: 11 terms, 22 factors, with derivatives of functions of all variables: (q17,q16,q15,q14,q10,q9,q2,q1,p8,p7,p6,p5,p4,p3) Step 344: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 282 3-Oct-2003 05:22:50, 40 ms (0%), 1084129 occupied, 23915814 free Eliminate q20 from e_228 and e_11. e_11: 9 terms, 18 factors, with derivatives of functions of all variables: (q24,q22,q20,q17,q13,q8,q2,q1,p8,p7,p5,p4,p3) is replaced by e_274: 9 terms, 18 factors, with derivatives of functions of all variables: (q24,q22,q19,q18,q13,q8,q2,q1,p8,p7,p5,p4,p3) Step 345: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 3 terms Step 346: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q1 from e_3 and e_275. e_275: 6 terms, 12 factors, with derivatives of functions of all variables: (q24,q23,q22,q21,q1,p6,p5,p4,p3) is replaced by e_276: 4 terms, 8 factors, with derivatives of functions of all variables: (q24,q23,q22,q21,p6,p5,p4,p3) Step 347: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q22 from e_231 and e_274. e_274: 9 terms, 18 factors, with derivatives of functions of all variables: (q24,q22,q19,q18,q13,q8,q2,q1,p8,p7,p5,p4,p3) is replaced by e_281: 9 terms, 18 factors, with derivatives of functions of all variables: (q24,q19,q18,q15,q13,q11,q8,q1,p8,p7,p5,p4,p3) Step 348: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 283 3-Oct-2003 05:23:20, 40 ms (0%), 1072679 occupied, 23927268 free --- Length reducing decoupling steps : *** Garbage collection starting *** GC 284 3-Oct-2003 05:23:30, 40 ms (0%), 1084279 occupied, 23915664 free Eliminate q17 from e_256 and e_86. e_86: 11 terms, 22 factors, with derivatives of functions of all variables: (q17,q16,q15,q14,q10,q9,q2,q1,p8,p7,p6,p5,p4,p3) is replaced by e_282: 11 terms, 22 factors, with derivatives of functions of all variables: (q16,q15,q14,q13,q11,q10,q9,q8,q2,q1,p8,p7,p6,p5,p4,p3) Step 349: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 350: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 285 3-Oct-2003 05:23:41, 50 ms (0%), 1071291 occupied, 23928657 free --- Length reducing decoupling steps : *** Garbage collection starting *** GC 286 3-Oct-2003 05:23:54, 40 ms (0%), 1071992 occupied, 23927957 free *** Garbage collection starting *** GC 287 3-Oct-2003 05:24:03, 40 ms (0%), 1075609 occupied, 23924340 free --- Factorization to subcases leading to substitutions : factorizing e_18 we get the alternative equations : 0=p7 0=q1 New level : 1.1.1. CRACK is now called with the new equation e_310 : 0=p7 e_53,e_101 are consequences of e_310 Step 351: Hot list of urgent steps : The list of inequalities got extended by: An expression with 23 terms The list of inequalities got extended by: An expression with 23 terms The list of inequalities got extended by: An expression with 5 terms *** Garbage collection starting *** GC 288 3-Oct-2003 05:24:18, 30 ms (0%), 1063849 occupied, 23936102 free Substitution of p7 found in e_310 : p7=0 Step 352: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 353: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 354: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 355: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 356: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 357: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 358: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 359: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 360: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 361: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 362: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 363: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 364: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 365: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 366: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 367: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 368: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 369: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 370: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 371: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 372: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 373: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 374: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 375: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 376: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 377: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 378: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 379: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 380: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 381: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 382: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 383: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 384: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 385: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 386: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 387: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 388: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 389: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 390: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 391: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 392: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 393: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 394: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 395: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 396: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 397: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 398: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 399: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 400: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 401: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 402: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 403: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 289 3-Oct-2003 05:24:21, 40 ms (0%), 1058947 occupied, 23941003 free *** Garbage collection starting *** GC 290 3-Oct-2003 05:24:24, 40 ms (0%), 1060687 occupied, 23939263 free *** Garbage collection starting *** GC 291 3-Oct-2003 05:24:26, 40 ms (0%), 1061369 occupied, 23938581 free *** Garbage collection starting *** GC 292 3-Oct-2003 05:24:29, 40 ms (0%), 1061937 occupied, 23938013 free *** Garbage collection starting *** GC 293 3-Oct-2003 05:24:32, 40 ms (0%), 1062493 occupied, 23937457 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q1 from e_185 and e_253. e_253: (#) 3 terms, 4 factors, with derivatives of functions of all variables: (q17,q10,q1,p8) is replaced by e_323: 0=(q10 - q17)*p8 Step 404: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 294 3-Oct-2003 05:24:36, 40 ms (0%), 1062913 occupied, 23937037 free *** Garbage collection starting *** GC 295 3-Oct-2003 05:24:39, 40 ms (0%), 1063541 occupied, 23936409 free shortening by 1 term Step 405: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 406: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 407: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 408: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 296 3-Oct-2003 05:24:43, 30 ms (0%), 1063309 occupied, 23936641 free *** Garbage collection starting *** GC 297 3-Oct-2003 05:24:47, 40 ms (0%), 1064967 occupied, 23934983 free *** Garbage collection starting *** GC 298 3-Oct-2003 05:24:51, 40 ms (0%), 1065635 occupied, 23934315 free *** Garbage collection starting *** GC 299 3-Oct-2003 05:24:56, 40 ms (0%), 1066639 occupied, 23933311 free *** Garbage collection starting *** GC 300 3-Oct-2003 05:25:02, 40 ms (0%), 1067595 occupied, 23932355 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q2 from e_27 and e_132. e_132: 0=(2*q15 - 2*q19 - q2)*p8 is replaced by e_215: 0=(q15 - q19)*p8 Step 409: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 410: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 411: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 301 3-Oct-2003 05:25:08, 40 ms (0%), 1065995 occupied, 23933955 free *** Garbage collection starting *** GC 302 3-Oct-2003 05:25:15, 50 ms (0%), 1069871 occupied, 23930079 free *** Garbage collection starting *** GC 303 3-Oct-2003 05:25:24, 40 ms (0%), 1071903 occupied, 23928047 free *** Garbage collection starting *** GC 304 3-Oct-2003 05:25:36, 40 ms (0%), 1073945 occupied, 23926005 free *** Garbage collection starting *** GC 305 3-Oct-2003 05:25:55, 40 ms (0%), 1075665 occupied, 23924285 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q20 from e_166 and e_250. e_250: 0=(3*q16 - 4*q20 + q21)*p8 is replaced by e_28: 0=(q16 - q21)*p8 Step 412: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q19 from e_215 and e_180. e_180: 3 terms, 6 factors, with derivatives of functions of all variables: (q27,q26,q19,p8,p6,p4) is replaced by e_340: 3 terms, 6 factors, with derivatives of functions of all variables: (q27,q26,q15,p8,p6,p4) Step 413: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 306 3-Oct-2003 05:26:09, 40 ms (0%), 1069733 occupied, 23930217 free --- Length reducing decoupling steps : Eliminate q20 from e_166 and e_172. e_172: 3 terms, 6 factors, with derivatives of functions of all variables: (q27,q26,q20,p8,p5,p3) is replaced by e_266: 3 terms, 6 factors, with derivatives of functions of all variables: (q27,q26,q16,p8,p5,p3) Step 414: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q17 from e_323 and e_227. e_227: 3 terms, 6 factors, with derivatives of functions of all variables: (q27,q26,q17,p8,p6,p4) is replaced by e_109: 3 terms, 6 factors, with derivatives of functions of all variables: (q27,q26,q10,p8,p6,p4) Step 415: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 307 3-Oct-2003 05:26:18, 40 ms (0%), 1075310 occupied, 23924639 free Eliminate q23 from e_297 and e_276. e_276: 4 terms, 8 factors, with derivatives of functions of all variables: (q24,q23,q22,q21,p6,p5,p4,p3) is replaced by e_343: 4 terms, 8 factors, with derivatives of functions of all variables: (q24,q22,q21,q15,p5,p4,p3) Step 416: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 308 3-Oct-2003 05:26:27, 40 ms (0%), 1073136 occupied, 23926813 free Eliminate q24 from e_350 and e_335. e_335: 5 terms, 10 factors, with derivatives of functions of all variables: (q24,q23,q21,q10,p5,p4,p3) is replaced by e_325: 5 terms, 10 factors, with derivatives of functions of all variables: (q23,q16,q10,q2,p5,p4,p3) Step 417: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q24 from e_218 and e_74. e_74: 8 terms, 16 factors, with derivatives of functions of all variables: (q24,q23,q22,q21,q20,q19,q18,q17,p6,p5,p4,p3) is replaced by e_259: 8 terms, 16 factors, with derivatives of functions of all variables: (q23,q21,q20,q19,q18,q17,q13,p8,p6,p5,p4,p3) Step 418: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 419: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 309 3-Oct-2003 05:26:37, 40 ms (0%), 1071813 occupied, 23928137 free --- Length reducing decoupling steps : --- Factorization to subcases leading to substitutions : *** Garbage collection starting *** GC 310 3-Oct-2003 05:26:50, 40 ms (0%), 1072258 occupied, 23927691 free factorizing e_226 we get the alternative equations : 0=p4 0=q2 New level : 1.1.1.1. CRACK is now called with the new equation e_339 : 0=p4 e_272,e_95,e_252,e_107,e_62,e_7,e_193 are consequences of e_339 Step 420: Hot list of urgent steps : The list of inequalities got extended by: An expression with 28 terms The list of inequalities got extended by: An expression with 22 terms The list of inequalities got extended by: An expression with 22 terms The list of inequalities got extended by: An expression with 4 terms e_263 is a consequence of e_278. e_367 is a consequence of e_360. Substitution of p4 found in e_339 : p4=0 Step 421: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 422: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 423: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 424: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 425: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 426: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 427: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 428: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 429: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 430: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 431: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 432: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 433: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 434: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 435: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 436: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 437: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 438: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 2 terms Step 439: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 311 3-Oct-2003 05:26:53, 40 ms (0%), 1065809 occupied, 23934140 free *** Garbage collection starting *** GC 312 3-Oct-2003 05:26:56, 40 ms (0%), 1067449 occupied, 23932500 free *** Garbage collection starting *** GC 313 3-Oct-2003 05:27:00, 40 ms (0%), 1068577 occupied, 23931372 free *** Garbage collection starting *** GC 314 3-Oct-2003 05:27:04, 40 ms (0%), 1070619 occupied, 23929328 free *** Garbage collection starting *** GC 315 3-Oct-2003 05:27:10, 40 ms (0%), 1072425 occupied, 23927522 free Stop of a subroutine. Number of garbage collections exceeds max_gc_short. --- Length reducing decoupling steps : Eliminate q6 from e_349 and e_268. e_268: 0=(q25 - q6)*p3 is replaced by e_309: 0=p3*q25 Step 440: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 441: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 316 3-Oct-2003 05:27:20, 40 ms (0%), 1072641 occupied, 23927307 free --- Length reducing decoupling steps : Eliminate q6 from e_120 and e_353. e_353: 0=(q25 - q6)*p5 is replaced by e_267: 0=p5*q25 Step 442: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_293 and e_249. e_249: 0=(q25 + q3 - q6)*p8 is replaced by e_312: 0=(q25 - q6)*p8 Step 443: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q25 from e_229 and e_312. e_312: 0=(q25 - q6)*p8 is replaced by e_315: 0=p8*q6 e_315 is a consequence of e_252. Step 444: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : *** Garbage collection starting *** GC 317 3-Oct-2003 05:27:37, 40 ms (0%), 1076537 occupied, 23923411 free Eliminate q22 from e_171 and e_296. e_296: 0=(q11 - q15 + q22 - q23)*p3 is replaced by e_245: 0=(q11 - q23)*p3 Step 445: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q22 from e_171 and e_297. e_297: 3 terms, 6 factors, with derivatives of functions of all variables: (q23,q22,q15,p6,p3) is replaced by e_319: 0=p3*q15 - p6*q23 Step 446: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q19 from e_360 and e_101. e_101: 4 terms, 8 factors, with derivatives of functions of all variables: (q20,q19,q18,q12,p8,p5,p3) is replaced by e_329: 3 terms, 6 factors, with derivatives of functions of all variables: (q20,q18,q12,p8,p5,p3) Step 447: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 448: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q19 from e_360 and e_34. e_34: 5 terms, 10 factors, with derivatives of functions of all variables: (q19,q18,q15,q11,q8,p8,p3) is replaced by e_248: 3 terms, 6 factors, with derivatives of functions of all variables: (q15,q11,q8,p8,p3) Step 449: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q23 from e_245 and e_247. e_247: 3 terms, 6 factors, with derivatives of functions of all variables: (q23,q21,q12,p8,p5,p3) is replaced by e_334: 3 terms, 6 factors, with derivatives of functions of all variables: (q21,q12,q11,p8,p5,p3) Step 450: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q17 from e_356 and e_306. e_306: 6 terms, 12 factors, with derivatives of functions of all variables: (q20,q17,q16,q13,q10,p8,p6,p3) is replaced by e_338: 6 terms, 12 factors, with derivatives of functions of all variables: (q20,q16,q13,q10,q9,p8,p6,p3) Step 451: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 318 3-Oct-2003 05:27:58, 40 ms (0%), 1074875 occupied, 23925075 free --- Length reducing decoupling steps : Eliminate q17 from e_356 and e_342. e_342: 6 terms, 12 factors, with derivatives of functions of all variables: (q20,q18,q17,q16,q15,p6,p5,p3) is replaced by e_226: 6 terms, 12 factors, with derivatives of functions of all variables: (q20,q18,q16,q15,q9,p8,p6,p5,p3) Step 452: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : --- Factorization to subcases leading to substitutions : factorizing e_169 we get the alternative equations : 0=p3 0=q2 New level : 1.1.1.1.1. CRACK is now called with the new equation e_429 : 0=p3 e_33,e_265,e_318,e_255,e_289,e_360,e_171,e_245,e_191,e_205,e_5,e_250,e_349,e_309 are consequences of e_429 Step 453: Hot list of urgent steps : The list of inequalities got extended by: An expression with 27 terms The list of inequalities got extended by: An expression with 21 terms The list of inequalities got extended by: An expression with 21 terms The list of inequalities got extended by: g0111*p8 + g0113*p6 + g0114*p5 e_172 is a consequence of e_221. e_254 is a consequence of e_377. e_381 is a consequence of e_272. Substitution of p3 found in e_429 : p3=0 Step 454: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 455: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 456: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 457: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 458: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 459: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 319 3-Oct-2003 05:28:09, 40 ms (0%), 1067592 occupied, 23932358 free shortening by 1 term Step 460: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 461: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 462: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term e_422 is a consequence of e_356. Step 463: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : *** Garbage collection starting *** GC 320 3-Oct-2003 05:28:14, 30 ms (0%), 1069858 occupied, 23930092 free --- Length reducing decoupling steps : Eliminate q10 from e_400 and e_323. e_323: 0=(q10 - q17)*p8 is replaced by e_423: 0=p8*q17 Step 464: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q17 from e_423 and e_204. e_204: 0=(q17 - q24)*p8 is replaced by e_425: 0=p8*q24 Step 465: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q24 from e_425 and e_57. e_57: 0=(q10 - q24)*p8 is replaced by e_427: 0=p8*q10 e_427 is a consequence of e_400. Step 466: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q23 from e_17 and e_50. e_50: 0=(q18 - q23)*p5 is replaced by e_428: 0=p5*q18 Step 467: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 468: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 469: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 470: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 471: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q11 from e_71 and e_203. e_203: 0=(q11 - q23)*p8 is replaced by e_318: 0=p8*q23 Step 472: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q23 from e_318 and e_143. e_143: 0=(q18 - q23)*p8 is replaced by e_33: 0=p8*q18 Step 473: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q3 from e_292 and e_276. e_276: 0=(q25 + q3)*p6 is replaced by e_254: 0=p6*q25 Step 474: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q24 from e_383 and e_361. e_361: 0=(q17 - q24)*p6 is replaced by e_429: 0=p6*q17 Step 475: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 476: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 477: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 478: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : shortening by 1 term Step 479: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q17 from e_287 and e_392. e_392: 3 terms, 6 factors, with derivatives of functions of all variables: (q17,q11,q10,p6,p5) is replaced by e_268: 0=p5*q10 + p6*q11 Step 480: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q18 from e_259 and e_328. e_328: 4 terms, 8 factors, with derivatives of functions of all variables: (q18,q16,q12,q11,p8,p6,p5) is replaced by e_353: 3 terms, 6 factors, with derivatives of functions of all variables: (q16,q12,q11,p8,p6,p5) Step 481: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q11 from e_268 and e_353. e_353: 3 terms, 6 factors, with derivatives of functions of all variables: (q16,q12,q11,p8,p6,p5) is replaced by e_20: 3 terms, 6 factors, with derivatives of functions of all variables: (q16,q12,q10,p8,p5) Step 482: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q16 from e_53 and e_322. e_322: 0=p5*q15 - p6*q16 is replaced by e_126: 0=p5*q15 - p8*q13 e_126 is a consequence of e_360. Step 483: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q11 from e_268 and e_396. e_396: 3 terms, 6 factors, with derivatives of functions of all variables: (q15,q14,q11,p8,p6) is replaced by e_231: 3 terms, 6 factors, with derivatives of functions of all variables: (q15,q14,q10,p8,p6,p5) Step 484: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : --- Factorization to subcases leading to substitutions : factorizing e_400 we get the alternative equations : 0=p8 0=q10 New level : 1.1.1.1.1.1. CRACK is now called with the new equation e_411 : 0=p8 e_138,e_235,e_64,e_166,e_215,e_28,e_27,e_185,e_291,e_295,e_252,e_229,e_293,e_71, e_272,e_423,e_425,e_309,e_318,e_33,e_374 are consequences of e_411 Step 485: Hot list of urgent steps : The list of inequalities got extended by: g0113*p6 + g0114*p5 *** Garbage collection starting *** GC 321 3-Oct-2003 05:28:24, 40 ms (0%), 1066243 occupied, 23933706 free Substitution of p8 found in e_411 : p8=0 Step 486: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : Eliminate q19 from e_419 and e_359. e_359: 0=(q19 - q22)*p6 is replaced by e_171: 0=p6*q22 Step 487: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : --- Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : --- Algebraic length reduction of equations : --- Length reducing decoupling steps : --- Factorization to subcases leading to substitutions : factorizing e_286 we get the alternative equations : 0=p6 0=q10 New level : 1.1.1.1.1.1.1. CRACK is now called with the new equation e_447 : 0=p6 e_259,e_221,e_348,e_180,e_377,e_383,e_354,e_154,e_292,e_65,e_227,e_237,e_282, e_254,e_429,e_412,e_414,e_419,e_420,e_171 are consequences of e_447 Step 488: Hot list of urgent steps : The list of inequalities got extended by: An expression with 20 terms The list of inequalities got extended by: An expression with 26 terms The list of inequalities got extended by: p5 e_381 is a consequence of e_276. Substitution of p6 found in e_447 : p6=0 Step 489: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 26 terms The list of inequalities got extended by: An expression with 20 terms The list of inequalities got extended by: An expression with 25 terms Substitution of q1 found in e_278 : q1=0 Step 490: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 19 terms The list of inequalities got extended by: An expression with 25 terms The list of inequalities got extended by: An expression with 19 terms Substitution of q26 found in e_243 : q26=0 Step 491: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 24 terms The list of inequalities got extended by: An expression with 18 terms The list of inequalities got extended by: An expression with 24 terms The list of inequalities got extended by: An expression with 18 terms Substitution of q3 found in e_8 : q3=0 Step 492: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 23 terms The list of inequalities got extended by: An expression with 17 terms The list of inequalities got extended by: An expression with 23 terms Substitution of q2 found in e_132 : q2=0 Step 493: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 22 terms The list of inequalities got extended by: An expression with 16 terms The list of inequalities got extended by: An expression with 22 terms Substitution of q4 found in e_258 : q4=0 Step 494: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 17 terms The list of inequalities got extended by: An expression with 21 terms The list of inequalities got extended by: An expression with 21 terms Substitution of q5 found in e_38 : q5=0 Step 495: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 15 terms The list of inequalities got extended by: An expression with 16 terms The list of inequalities got extended by: An expression with 20 terms The list of inequalities got extended by: An expression with 20 terms Substitution of q6 found in e_120 : q6=0 Step 496: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 14 terms The list of inequalities got extended by: An expression with 15 terms The list of inequalities got extended by: An expression with 19 terms The list of inequalities got extended by: An expression with 19 terms Substitution of q24 found in e_357 : q24=0 Step 497: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 13 terms The list of inequalities got extended by: An expression with 14 terms The list of inequalities got extended by: An expression with 18 terms The list of inequalities got extended by: An expression with 18 terms Substitution of q9 found in e_362 : q9=0 Step 498: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 12 terms The list of inequalities got extended by: An expression with 13 terms The list of inequalities got extended by: An expression with 17 terms The list of inequalities got extended by: An expression with 17 terms Substitution of q25 found in e_267 : q25=0 Step 499: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 11 terms The list of inequalities got extended by: An expression with 12 terms The list of inequalities got extended by: An expression with 16 terms The list of inequalities got extended by: An expression with 16 terms Substitution of q23 found in e_17 : q23=0 Step 500: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 10 terms The list of inequalities got extended by: An expression with 11 terms The list of inequalities got extended by: An expression with 15 terms The list of inequalities got extended by: An expression with 15 terms Substitution of q8 found in e_365 : q8=0 Step 501: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 9 terms The list of inequalities got extended by: An expression with 10 terms The list of inequalities got extended by: An expression with 14 terms The list of inequalities got extended by: An expression with 14 terms Substitution of q7 found in e_86 : q7=0 Step 502: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 8 terms The list of inequalities got extended by: An expression with 9 terms The list of inequalities got extended by: An expression with 13 terms The list of inequalities got extended by: An expression with 13 terms Substitution of q18 found in e_428 : q18=0 Step 503: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 7 terms The list of inequalities got extended by: An expression with 8 terms The list of inequalities got extended by: An expression with 12 terms The list of inequalities got extended by: An expression with 12 terms Substitution of q11 found in e_250 : q11=0 Step 504: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 6 terms The list of inequalities got extended by: An expression with 11 terms The list of inequalities got extended by: An expression with 11 terms Substitution of q15 found in e_301 : q15=0 Step 505: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 10 terms Substitution of q27 found in e_415 : q27=0 Step 506: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 10 terms The list of inequalities got extended by: An expression with 5 terms The list of inequalities got extended by: An expression with 9 terms Substitution of q22 found in e_416 : q22=0 Step 507: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 7 terms The list of inequalities got extended by: An expression with 9 terms The list of inequalities got extended by: An expression with 8 terms Substitution of q20 found in e_417 : q20=0 Step 508: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 6 terms The list of inequalities got extended by: An expression with 8 terms The list of inequalities got extended by: An expression with 7 terms Substitution of q21 found in e_413 : q21=0 Step 509: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 4 terms The list of inequalities got extended by: An expression with 7 terms The list of inequalities got extended by: An expression with 6 terms Substitution of q19 found in e_172 : q19=0 Step 510: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 5 terms The list of inequalities got extended by: g0035*q17 + g0037*q14 + g0038*q13 The list of inequalities got extended by: An expression with 6 terms The list of inequalities got extended by: An expression with 5 terms Substitution of q10 found in e_276 : q10=0 Step 511: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: An expression with 4 terms The list of inequalities got extended by: An expression with 5 terms The list of inequalities got extended by: An expression with 4 terms Substitution of q16 found in e_418 : q16=0 Step 512: Hot list of urgent steps : --- Substitution of <=2 terms, only fcts. of less vars., no cases : The list of inequalities got extended by: g0037*q14 + g0038*q13 The list of inequalities got extended by: g0012*q13 + g0013*q12 + g0024*p5 The list of inequalities got extended by: An expression with 4 terms The list of inequalities got extended by: g0097*q14 + g0098*q13 + g0099*q12 Substitution of q17 found in e_287 : q17=0 >>>>>>>>> Solution of level 1.1.1.1.1.1.1. : no equations Non-vanishing expressions: p5 g0097*q14 + g0098*q13 + g0099*q12 g0064*q14 + g0065*q13 + g0066*q12 + g0079*p5 g0012*q13 + g0013*q12 + g0024*p5 g0037*q14 + g0038*q13 functions : q27=0 q26=0 q25=0 q24=0 q23=0 q22=0 q21=0 q20=0 q19=0 q18=0 q17=0 q16=0 q15=0 q14, q13, q12, q11=0 q10=0 q9=0 q8=0 q7=0 q6=0 q5=0 q4=0 q3=0 q2=0 q1=0 p8=0 p7=0 p6=0 p5, p4=0 p3=0 p2=0 p1=0 with 35 terms no equations 4 constants : p5,q12,q13,q14 The equation: 

f =D f*f *p5
 t  2   x
The symmetry: 
        2                                2
f =(D f) *f *q12 + D f*D f*f *q13 + (D f) *f *q14
 s   2     x        2   1   x         1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*df(f(1),x)*p5$
The symmetry: 
df(f(1),s)=d(2,f(1))**2*df(f(1),x)*q12 + d(2,f(1))*d(1,f(1))*df(f(1),x)*q13 + d(
1,f(1))**2*df(f(1),x)*q14$

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q27,q26,q25,q24,q23,q22,q21,q20,q19,q18,q17,q16,q15,q14,q13,q12,
q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1,p6,p5
New ordering: q27,q26,q25,q24,q23,q22,q21,q20,q19,q18,q17,q16,q15,q14,q13,q12,
q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1,p5,p6

New level : 1.1.1.1.1.1.2.
CRACK is now called with the new equation e_447 : 
0=q10


Step 513: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 26 terms

e_172 is a consequence of e_412.
e_276 is a consequence of e_429.e_301 is a consequence of e_381
e_250 is a consequence of e_361

Substitution of q10 found in e_447 : 
q10=0


Step 514: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 25 terms

Substitution of q2 found in e_221 : 
q2=0


Step 515: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 24 terms

Substitution of q4 found in e_348 : 
q4=0


Step 516: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 23 terms

Substitution of q6 found in e_180 : 
q6=0


Step 517: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 22 terms

Substitution of q1 found in e_377 : 
q1=0


Step 518: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 21 terms

Substitution of q24 found in e_383 : 
q24=0


Step 519: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 20 terms

Substitution of q9 found in e_354 : 
q9=0


Step 520: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 19 terms

Substitution of q26 found in e_154 : 
q26=0


Step 521: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 18 terms

Substitution of q3 found in e_292 : 
q3=0


Step 522: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 17 terms

Substitution of q5 found in e_65 : 
q5=0


Step 523: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 16 terms

Substitution of q23 found in e_227 : 
q23=0


Step 524: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 15 terms

Substitution of q8 found in e_237 : 
q8=0


Step 525: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 14 terms

Substitution of q7 found in e_282 : 
q7=0


Step 526: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 13 terms

Substitution of q25 found in e_254 : 
q25=0


Step 527: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 12 terms

Substitution of q17 found in e_429 : 
q17=0


Step 528: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 11 terms

Substitution of q16 found in e_412 : 
q16=0


Step 529: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 10 terms

Substitution of q21 found in e_414 : 
q21=0


Step 530: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 9 terms
e_417 is a consequence of e_422

Substitution of q19 found in e_419 : 
q19=0


Step 531: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 8 terms

Substitution of q27 found in e_420 : 
q27=0


Step 532: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 7 terms

Substitution of q22 found in e_171 : 
q22=0


Step 533: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 6 terms

Substitution of q15 found in e_381 : 
q15=0


Step 534: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 5 terms
e_428 is a consequence of e_117

Substitution of q11 found in e_361 : 
q11=0


Step 535: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 4 terms

Substitution of q20 found in e_422 : 
q20=0


Step 536: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 

g0037*q14 + g0038*q13 + g0049*p6


The list of inequalities got extended by: 

g0012*q13 + g0013*q12 + g0024*p5


The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 

g0097*q14 + g0098*q13 + g0099*q12


Substitution of q18 found in e_117 : 
q18=0



>>>>>>>>> Solution of level 1.1.1.1.1.1.2. : 
no equations


Non-vanishing expressions: p6

g0097*q14 + g0098*q13 + g0099*q12


g0064*q14 + g0065*q13 + g0066*q12 + g0078*p6 + g0079*p5


g0012*q13 + g0013*q12 + g0024*p5


g0037*q14 + g0038*q13 + g0049*p6


g0113*p6 + g0114*p5


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0

q14, q13, q12, 
q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0

p6, p5, 
p4=0


p3=0


p2=0


p1=0


with 35 terms
no equations
5 constants : p5,p6,q12,q13,q14
The equation: 

f =D f*f *p5 + D f*f *p6
 t  2   x       1   x
The symmetry: 
        2                                2
f =(D f) *f *q12 + D f*D f*f *q13 + (D f) *f *q14
 s   2     x        2   1   x         1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*df(f(1),x)*p5 + d(1,f(1))*df(f(1),x)*p6$
The symmetry: 
df(f(1),s)=d(2,f(1))**2*df(f(1),x)*q12 + d(2,f(1))*d(1,f(1))*df(f(1),x)*q13 + d(
1,f(1))**2*df(f(1),x)*q14$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p8

The lexicographical ordering of unknowns is changed
because p8 has to be non-zero, giving p8 a low priority.
Old ordering: q27,q26,q25,q24,q23,q22,q21,q20,q19,q18,q17,q16,q15,q14,q13,q12,
q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1,p8,p6,p5
New ordering: q27,q26,q25,q24,q23,q22,q21,q20,q19,q18,q17,q16,q15,q14,q13,q12,
q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1,p6,p5,p8

New level : 1.1.1.1.1.2.
CRACK is now called with the new equation e_411 : 
0=q10

e_286 is a consequence of e_411

Step 537: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 20 terms

e_412 is a consequence of e_423.
e_301 is a consequence of e_71.
Substitution of q10 found in e_411 : 
q10=0


Step 538: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 19 terms

Substitution of q2 found in e_27 : 
q2=0


Step 539: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 24 terms

Substitution of q1 found in e_185 : 
q1=0


Step 540: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 23 terms

Substitution of q5 found in e_291 : 
q5=0


Step 541: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 22 terms

Substitution of q4 found in e_295 : 
q4=0


Step 542: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 21 terms

Substitution of q6 found in e_252 : 
q6=0


Step 543: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 20 terms

Substitution of q25 found in e_229 : 
q25=0


Step 544: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 19 terms

Substitution of q3 found in e_293 : 
q3=0


Step 545: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 18 terms

e_259 is a consequence of e_33.
Substitution of q11 found in e_71 : 
q11=0


Step 546: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 17 terms

Substitution of q8 found in e_272 : 
q8=0


Step 547: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 16 terms

Substitution of q17 found in e_423 : 
q17=0


Step 548: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 15 terms

Substitution of q24 found in e_425 : 
q24=0


Step 549: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 14 terms

Substitution of q7 found in e_309 : 
q7=0


Step 550: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 13 terms

Substitution of q23 found in e_318 : 
q23=0


Step 551: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 12 terms

Substitution of q18 found in e_33 : 
q18=0


Step 552: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

Substitution of q9 found in e_374 : 
q9=0


Step 553: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

e_64 is a consequence of e_215.
Substitution of q22 by an expression in 
q19 found in e_138 : 
q22=q19


Step 554: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

e_28 is a consequence of e_166.
e_382 is a consequence of e_155.
Substitution of q21 by an expression in 
q20 found in e_235 : 
q21=q20


Step 555: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

e_350 is a consequence of e_53.
e_155 is a consequence of e_415.
Substitution of q20 by an expression in 
q16 found in e_166 : 
q20=q16


Step 556: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

e_133 is a consequence of e_360.
e_50 is a consequence of e_414.
Substitution of q19 by an expression in 
q15 found in e_215 : 
q19=q15


Step 557: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

Substitution of q15 by an expression in 
q27, p6, p8 found in e_352 : 
      5
     ---*p6*q27
      3
q15=------------
         p8


Step 558: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
*** Garbage collection starting 
*** GC 322  3-Oct-2003 05:28:26, 40 ms (0%), 1000761 occupied, 23999191 free

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

Substitution of q14 by an expression in 
q27, p6, p8 found in e_169 : 
      5    2
     ---*p6 *q27
      6
q14=-------------
           2
         p8


Step 559: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

e_402 is a consequence of e_336.
e_349 is a consequence of e_336.
Substitution of q13 by an expression in 
q27, p6, p5, p8 found in e_290 : 7 factors in 2 terms

Step 560: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

Substitution of q16 by an expression in 
q27, p5, p8 found in e_336 : 
      5
     ---*p5*q27
      3
q16=------------
         p8


Step 561: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

Substitution of q12 by an expression in 
q27, p5, p8 found in e_5 : 
      5    2
     ---*p5 *q27
      6
q12=-------------
           2
         p8


Step 562: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_243 we get the alternative equations : 
0=q26


0=p5


New level : 1.1.1.1.1.2.1.
CRACK is now called with the new equation e_240 : 
0=q26

e_154 is a consequence of e_240

Step 563: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 6 terms

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q27,q26,p6,p5,p8
New ordering: q27,q26,p5,p6,p8

The list of inequalities got extended by: 
An expression with 6 terms

p5


The list of inequalities got extended by: 
An expression with 10 terms

q27

The lexicographical ordering of unknowns is changed
because q27 has to be non-zero, giving q27 a low priority.
Old ordering: q27,q26,p5,p6,p8
New ordering: q26,q27,p5,p6,p8

Substitution of q26 found in e_240 : 
q26=0



>>>>>>>>> Solution of level 1.1.1.1.1.2.1. : 
no equations


Non-vanishing expressions: q27,p5,p6,p8

          2
6*g0084*p8  + 10*g0089*p6*p8 + 10*g0090*p5*p8 + 10*g0091*p5*p8 + 10*g0092*p6*p8

                                               2                              2
 + 10*g0095*p5*p8 + 10*g0096*p6*p8 + 5*g0097*p6  + 10*g0098*p5*p6 + 5*g0099*p5


10*g0007*p8*q27 + 10*g0008*p8*q27 + 10*g0011*p8*q27 + 10*g0012*p6*q27

                              2
 + 5*g0013*p5*q27 + 6*g0024*p8


10*g0032*p8*q27 + 10*g0033*p8*q27 + 10*g0036*p8*q27 + 5*g0037*p6*q27

                               2
 + 10*g0038*p5*q27 + 6*g0049*p8


g0111*p8 + g0113*p6 + g0114*p5


10*g0056*p6*p8*q27 + 10*g0057*p5*p8*q27 + 10*g0058*p5*p8*q27

 + 10*g0059*p6*p8*q27 + 10*g0062*p5*p8*q27 + 10*g0063*p6*p8*q27

             2                                      2                    2
 + 5*g0064*p6 *q27 + 10*g0065*p5*p6*q27 + 5*g0066*p5 *q27 + 6*g0078*p6*p8

                2
 + 6*g0079*p5*p8


functions : q27, 
q26=0


q25=0


q24=0


q23=0


      5
     ---*p6*q27
      3
q22=------------
         p8


      5
     ---*p5*q27
      3
q21=------------
         p8


      5
     ---*p5*q27
      3
q20=------------
         p8


      5
     ---*p6*q27
      3
q19=------------
         p8


q18=0


q17=0


      5
     ---*p5*q27
      3
q16=------------
         p8


      5
     ---*p6*q27
      3
q15=------------
         p8


      5    2
     ---*p6 *q27
      6
q14=-------------
           2
         p8


      5
     ---*p5*p6*q27
      3
q13=---------------
            2
          p8


      5    2
     ---*p5 *q27
      6
q12=-------------
           2
         p8


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, 
p7=0

p6, p5, 
p4=0


p3=0


p2=0


p1=0


with 44 terms
no equations
4 constants : p5,p6,p8,q27
The equation: 

f =D f*f *p5 + D f*f *p6 + f  *p8
 t  2   x       1   x       3x
The symmetry: 
     5                        5                        5       2      2
f =(---*D f  *f *p5*p8*q27 + ---*D f *f  *p5*p8*q27 + ---*(D f) *f *p5 *q27
 s   3   2 2x  x              3   2 x  2x              6    2     x

        5                          5                       5
     + ---*D f*D f*f *p5*p6*q27 + ---*D f*f  *p5*p8*q27 + ---*D f  *f *p6*p8*q27
        3   2   1   x              3   2   3x              3   1 2x  x

        5                        5       2      2        5
     + ---*D f *f  *p6*p8*q27 + ---*(D f) *f *p6 *q27 + ---*D f*f  *p6*p8*q27
        3   1 x  2x              6    1     x            3   1   3x

             2        2
     + f  *p8 *q27)/p8
        5x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*df(f(1),x)*p5 + d(1,f(1))*df(f(1),x)*p6 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=(5/3*d(2,df(f(1),x,2))*df(f(1),x)*p5*p8*q27 + 5/3*d(2,df(f(1),x))*df(
f(1),x,2)*p5*p8*q27 + 5/6*d(2,f(1))**2*df(f(1),x)*p5**2*q27 + 5/3*d(2,f(1))*d(1,
f(1))*df(f(1),x)*p5*p6*q27 + 5/3*d(2,f(1))*df(f(1),x,3)*p5*p8*q27 + 5/3*d(1,df(f
(1),x,2))*df(f(1),x)*p6*p8*q27 + 5/3*d(1,df(f(1),x))*df(f(1),x,2)*p6*p8*q27 + 5/
6*d(1,f(1))**2*df(f(1),x)*p6**2*q27 + 5/3*d(1,f(1))*df(f(1),x,3)*p6*p8*q27 + df(
f(1),x,5)*p8**2*q27)/p8**2$

Time: 0 ms

Time: 0 ms

Time: 0 ms

The list of inequalities got extended by: 

q26


New level : 1.1.1.1.1.2.2.
CRACK is now called with the new equation e_240 : 
0=p5


Step 564: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

g0111*p8 + g0113*p6


The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 5 terms

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q27,q26,p6,p5,p8
New ordering: q27,q26,p5,p6,p8

Substitution of p5 found in e_240 : 
p5=0


Step 565: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
contradiction from the substitution:
p6=0

because of the non-vanishing expression:
p6


The list of inequalities got extended by: 
An expression with 4 terms

p8


This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 40 ms

The list of inequalities got extended by: 

p3


New level : 1.1.1.1.2.
CRACK is now called with the new equation e_429 : 
0=q2

e_234,e_27,e_221,e_132 are consequences of e_429

Step 566: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 21 terms

Substitution of q2 found in e_429 : 
q2=0


Step 567: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 26 terms

Substitution of q5 found in e_191 : 
q5=0


Step 568: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 25 terms

e_254 is a consequence of e_309.
Substitution of q3 found in e_205 : 
q3=0


Step 569: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 24 terms

Substitution of q1 found in e_5 : 
q1=0


Step 570: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 23 terms

Substitution of q4 found in e_250 : 
q4=0


Step 571: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 22 terms

Substitution of q6 found in e_349 : 
q6=0


Step 572: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 21 terms

Substitution of q25 found in e_309 : 
q25=0


Step 573: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 21 terms

e_276 is a consequence of e_215.
Substitution of q22 by an expression in 
q15 found in e_171 : 
q22=q15


Step 574: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 21 terms

e_17 is a consequence of e_382.
Substitution of q23 by an expression in 
q11 found in e_245 : 
q23=q11


Step 575: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 21 terms

Substitution of q19 by an expression in 
q18 found in e_360 : 
q19= - q18


Step 576: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 21 terms

e_74 is a consequence of e_155.
e_248 is a consequence of e_366.
Substitution of q15 by an expression in 
q11 found in e_382 : 
q15= - q11


Step 577: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 23 terms

e_328 is a consequence of e_235.
e_33 is a consequence of e_289.
Substitution of q24 by an expression in 
q21, q20, q17 found in e_255 : 
q24=q17 - q20 + q21


Step 578: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 27 terms

e_50 is a consequence of e_298.
Substitution of q21 by an expression in 
q20, q17, q16, q10 found in e_289 : 13 factors in 5 terms

Step 579: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 27 terms

Substitution of q14 by an expression in 
q8, p6, p3 found in e_372 : 
      1
     ---*p6*q8
      2
q14=-----------
        p3


Step 580: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 26 terms

e_352 is a consequence of e_319.
Substitution of q27 by an expression in 
q11, p8, p3 found in e_216 : 
      3
     ---*p8*q11
      5
q27=------------
         p3


Step 581: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 26 terms

e_359 is a consequence of e_355.
e_375 is a consequence of e_319.
Substitution of q11 by an expression in 
q8, p8, p3 found in e_366 : 
      - p8*q8
q11=----------
        p3


Step 582: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 27 terms

Substitution of q16 by an expression in 
q10, q8, p8, p5, p3 found in e_335 : 7 factors in 3 terms

Step 583: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 27 terms

e_351 is a consequence of e_324.
Substitution of q26 by an expression in 
q10, p8, p3 found in e_300 : 
         3
      - ---*p8*q10
         5
q26=---------------
          p3


Step 584: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 28 terms

Substitution of q13 by an expression in 
q7, p6, p3 found in e_358 : 
      - p3*q7 + p6*q7
q13=------------------
            p3


Step 585: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 29 terms

Substitution of q12 by an expression in 
q8, q7, p5, p3 found in e_363 : 10 factors in 3 terms

Step 586: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 33 terms

Substitution of q20 by an expression in 
q18, q17, q7, p8, p5, p3 found in e_330 : 13 factors in 4 terms

Step 587: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 39 terms

Substitution of q17 by an expression in 
q10, q9, p8, p6, p3 found in e_299 : 10 factors in 4 terms

Step 588: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 45 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 44 terms

Substitution of q9 by an expression in 
q8, q7, p6, p5, p3 found in e_371 : 14 factors in 4 terms

Step 589: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 590: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 323  3-Oct-2003 05:28:29, 30 ms (0%), 1037237 occupied, 23962715 free
Eliminate 
q18

from e_355 and e_303. e_303: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

                        2      2
 (q18,q10,q8,q7,p8,p6,p5 ,p5,p3 ,p3)

is replaced by e_400: 
(#) 3 terms, 10 factors, with derivatives of functions of all variables: 

                 2      2
 (q10,q8,q7,p8,p5 ,p5,p3 ,p3)


Step 591: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_373 and e_388. e_388: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                           2
 (q18,q10,q8,q7,p8,p6,p5,p3 ,p3)

is replaced by e_404: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                 2
 (q10,q7,p8,p6,p3 ,p3)


Step 592: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_373 and e_264. e_264: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                           2
 (q18,q10,q8,q7,p8,p6,p5,p3 ,p3)

is replaced by e_405: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

                       2
 (q10,q8,q7,p8,p6,p5,p3 ,p3)


Step 593: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_373 and e_392. e_392: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

                           3   2
 (q18,q10,q8,q7,p8,p6,p5,p3 ,p3 ,p3)

is replaced by e_406: 

0=q8*p8*p5*(p3 + p6)


e_406 is a consequence of e_319.
Step 594: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_110 and e_263. e_110: 
(#) 6 terms, 19 factors, with derivatives of functions of all variables: 

                        2      2
 (q18,q10,q8,q7,p8,p6,p5 ,p5,p3 ,p3)

is replaced by e_407: 
(#) 3 terms, 10 factors, with derivatives of functions of all variables: 

                 2      2
 (q10,q8,q7,p8,p5 ,p5,p3 ,p3)


Step 595: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_407 and e_400. e_407: 
(#) 3 terms, 10 factors, with derivatives of functions of all variables: 

                 2      2
 (q10,q8,q7,p8,p5 ,p5,p3 ,p3)

is replaced by e_411: 

0=p8*p5*(p3*q7 + p5*q8)


Step 596: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q8

from e_411 and e_400. e_400: 
(#) 3 terms, 10 factors, with derivatives of functions of all variables: 

                 2      2
 (q10,q8,q7,p8,p5 ,p5,p3 ,p3)

is replaced by e_414: 

0=p5*q10

e_243 is a consequence of e_414

Step 597: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 598: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 599: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 600: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 601: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q8

from e_411 and e_416. e_416: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

                    2
 (q18,q8,q7,p8,p6,p5 ,p5,p3)

is replaced by e_420: 
(#) 3 terms, 10 factors, with derivatives of functions of all variables: 

                 2
 (q18,q7,p8,p6,p5 ,p5,p3)


Step 602: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q8

from e_411 and e_362. e_411: 

0=p8*p5*(p3*q7 + p5*q8)

is replaced by e_423: 

0=p5*p6*p8*q7


Step 603: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_373 and e_389. e_389: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                           3   2
 (q18,q10,q8,q7,p8,p6,p5,p3 ,p3 ,p3)

is replaced by e_425: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                       3   2
 (q10,q8,q7,p8,p6,p5,p3 ,p3 ,p3)


Step 604: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 324  3-Oct-2003 05:28:32, 30 ms (0%), 1038121 occupied, 23961830 free
Eliminate 
q8

from e_319 and e_387. e_387: 
 10 terms, 40 factors, with derivatives of functions of all variables: 

                     2         3   2
 (q18,q10,q8,q7,p8,p6 ,p6,p5,p3 ,p3 ,p3)

is replaced by e_426: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                  2         3   2
 (q18,q10,q7,p8,p6 ,p6,p5,p3 ,p3 ,p3)


Step 605: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_373 and e_390. e_390: 
 10 terms, 40 factors, with derivatives of functions of all variables: 

                     2         3   2
 (q18,q10,q8,q7,p8,p6 ,p6,p5,p3 ,p3 ,p3)

is replaced by e_427: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                 2         3   2
 (q10,q8,q7,p8,p6 ,p6,p5,p3 ,p3 ,p3)


Step 606: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_414 we get the alternative equations : 
0=p5


0=q10


New level : 1.1.1.1.2.1.
CRACK is now called with the new equation e_453 : 
0=p5

e_420,e_362,e_423 are consequences of e_453

Step 607: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

g0111*p8 + g0113*p6 + g0116*p3


The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 34 terms

e_191 is a consequence of e_319.e_355,e_155 are consequences of e_377

e_71 is a consequence of e_377.
Substitution of p5 found in e_453 : 
p5=0


Step 608: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 30 terms

e_250 is a consequence of e_38.
e_227 is a consequence of e_38.
e_154 is a consequence of e_38.
e_172 is a consequence of e_38.
e_252 is a consequence of e_38.
e_205 is a consequence of e_38.
e_205 is a consequence of e_429.
e_254 is a consequence of e_38.
e_8 is a consequence of e_38.
e_293 is a consequence of e_38.
e_237 is a consequence of e_38.
e_65 is a consequence of e_38.
e_348 is a consequence of e_38.
e_5 is a consequence of e_38.
e_258 is a consequence of e_38.
Substitution of q10 by an expression in 
q7, p8, p6, p3 found in e_292 : 
      - 2*p6*p8*q7
q10=---------------
            2
          p3


Step 609: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 30 terms

e_120 is a consequence of e_319.
Substitution of q18 by an expression in 
q8, p8, p3 found in e_377 : 
      - p8*q8
q18=----------
        p3


Step 610: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_38 we get the alternative equations : 
0=p8


0=q7


0=p3 + p6


New level : 1.1.1.1.2.1.1.
CRACK is now called with the new equation e_381 : 
0=p8

e_319 is a consequence of e_381

Step 611: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

g0113*p6 + g0116*p3


The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 8 terms

Substitution of p8 found in e_381 : 
p8=0


Step 612: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_429 we get the alternative equations : 
0=q7


0=p3 - p6


0=p3 + p6


New level : 1.1.1.1.2.1.1.1.
CRACK is now called with the new equation e_17 : 
0=q7


Step 613: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 3 terms

The list of inequalities got extended by: 
An expression with 3 terms

q8

The lexicographical ordering of unknowns is changed
because q8 has to be non-zero, giving q8 a low priority.
Old ordering: q8,q7,p6,p3
New ordering: q7,q8,p6,p3

Substitution of q7 found in e_17 : 
q7=0



>>>>>>>>> Solution of level 1.1.1.1.2.1.1.1. : 
no equations


Non-vanishing expressions: q8,p3

g0097*p6 + g0099*p3 + 2*g0103*p3


g0013*q8 + 2*g0017*q8 + 2*g0026*p3


                                                                      2
g0064*p6*q8 + g0066*p3*q8 + 2*g0070*p3*q8 + 2*g0078*p3*p6 + 2*g0081*p3


                                                        2
g0037*p6*q8 + 2*g0042*p3*q8 + 2*g0049*p3*p6 + 2*g0051*p3


g0113*p6 + g0116*p3


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


      1
     ---*p6*q8
      2
q14=-----------
        p3


q13=0


     1
q12=---*q8
     2


q11=0


q10=0


q9=0

q8, 
q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0

p6, 
p5=0


p4=0

p3, 
p2=0


p1=0


with 37 terms
no equations
3 constants : p3,p6,q8
The equation: 

f =D f*D D f*p3 + D f*f *p6
 t  2   1 2        1   x
The symmetry: 
     1       2                                   1       2
    ---*(D f) *f *p3*q8 + D f*D D f*D f*p3*q8 + ---*(D f) *f *p6*q8
     2    2     x          2   1 2   1           2    1     x
f =-----------------------------------------------------------------
 s                                p3
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(1,f(1))*df(f(1),x)*p6$
The symmetry: 
df(f(1),s)=(1/2*d(2,f(1))**2*df(f(1),x)*p3*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1
))*p3*q8 + 1/2*d(1,f(1))**2*df(f(1),x)*p6*q8)/p3$

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

q7


The list of inequalities got extended by: 

p6


New level : 1.1.1.1.2.1.1.2.
CRACK is now called with the new equation e_17 : 
0=p3 - p6


Step 614: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 4 terms

Substitution of p6 by an expression in 
p3 found in e_17 : 
p6=p3



>>>>>>>>> Solution of level 1.1.1.1.2.1.1.2. : 
no equations


Non-vanishing expressions: p6,p3,q7

g0097*q8 + g0099*q8 + 2*g0103*q8 + 2*g0104*q7


g0013*q8 + 2*g0017*q8 + 2*g0018*q7 + 2*g0026*p3


g0064*q8 + g0066*q8 + 2*g0070*q8 + 2*g0071*q7 + 2*g0078*p3 + 2*g0081*p3


g0037*q8 + 2*g0042*q8 + 2*g0043*q7 + 2*g0049*p3 + 2*g0051*p3


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


     1
q14=---*q8
     2


q13=0


     1
q12=---*q8
     2


q11=0


q10=0


q9=0

q8, q7, 
q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


p6=p3


p5=0


p4=0

p3, 
p2=0


p1=0


with 38 terms
no equations
3 constants : p3,q7,q8
The equation: 

f =D f*D D f*p3 + D f*f *p3
 t  2   1 2        1   x
The symmetry: 
        2             1       2                             1       2
f =(D f) *D D f*q7 + ---*(D f) *f *q8 + D f*D D f*D f*q8 + ---*(D f) *f *q8
 s   2     1 2        2    2     x       2   1 2   1        2    1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(1,f(1))*df(f(1),x)*p3$
The symmetry: 
df(f(1),s)=d(2,f(1))**2*d(1,d(2,f(1)))*q7 + 1/2*d(2,f(1))**2*df(f(1),x)*q8 + d(2
,f(1))*d(1,d(2,f(1)))*d(1,f(1))*q8 + 1/2*d(1,f(1))**2*df(f(1),x)*q8$

Time: 0 ms

Time: 0 ms

Time: 0 ms

The list of inequalities got extended by: 

q7


The list of inequalities got extended by: 

p3 - p6


The list of inequalities got extended by: 

p6


New level : 1.1.1.1.2.1.1.3.
CRACK is now called with the new equation e_17 : 
0=p3 + p6


Step 615: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 6 terms

Substitution of p6 by an expression in 
p3 found in e_17 : 
p6= - p3



>>>>>>>>> Solution of level 1.1.1.1.2.1.1.3. : 
no equations


Non-vanishing expressions: p6,p3,q7

g0097*q8 + 4*g0098*q7 - g0099*q8 + 2*g0102*q7 - 2*g0103*q8 - 2*g0104*q7


4*g0012*q7 - g0013*q8 + 2*g0016*q7 - 2*g0017*q8 - 2*g0018*q7 - 2*g0026*p3


g0064*q8 + 4*g0065*q7 - g0066*q8 + 2*g0069*q7 - 2*g0070*q8 - 2*g0071*q7

 + 2*g0078*p3 - 2*g0081*p3


g0037*q8 + 4*g0038*q7 + 2*g0041*q7 - 2*g0042*q8 - 2*g0043*q7 + 2*g0049*p3

 - 2*g0051*p3


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


        1
q14= - ---*q8
        2


q13= - 2*q7


     1
q12=---*q8
     2


q11=0


q10=0


q9= - q7

q8, q7, 
q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


p6= - p3


p5=0


p4=0

p3, 
p2=0


p1=0


with 40 terms
no equations
3 constants : p3,q7,q8
The equation: 

f =D f*D D f*p3 - D f*f *p3
 t  2   1 2        1   x
The symmetry: 
        2             1       2
f =(D f) *D D f*q7 + ---*(D f) *f *q8 + D f*D D f*D f*q8 - 2*D f*D f*f *q7
 s   2     1 2        2    2     x       2   1 2   1          2   1   x

              2       1       2
 - D D f*(D f) *q7 - ---*(D f) *f *q8
    1 2    1          2    1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 - d(1,f(1))*df(f(1),x)*p3$
The symmetry: 
df(f(1),s)=d(2,f(1))**2*d(1,d(2,f(1)))*q7 + 1/2*d(2,f(1))**2*df(f(1),x)*q8 + d(2
,f(1))*d(1,d(2,f(1)))*d(1,f(1))*q8 - 2*d(2,f(1))*d(1,f(1))*df(f(1),x)*q7 - d(1,d
(2,f(1)))*d(1,f(1))**2*q7 - 1/2*d(1,f(1))**2*df(f(1),x)*q8$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p8

The lexicographical ordering of unknowns is changed
because p8 has to be non-zero, giving p8 a low priority.
Old ordering: q8,q7,p8,p6,p3
New ordering: q8,q7,p6,p8,p3

New level : 1.1.1.1.2.1.2.
CRACK is now called with the new equation e_381 : 
0=q7

e_429 is a consequence of e_381

Step 616: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 10 terms

q8

The lexicographical ordering of unknowns is changed
because q8 has to be non-zero, giving q8 a low priority.
Old ordering: q8,q7,p6,p8,p3
New ordering: q7,q8,p6,p8,p3

The list of inequalities got extended by: 

p6


Substitution of q7 found in e_381 : 
q7=0


Step 617: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 

g0111*p8 - g0113*p3 + g0116*p3


The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 10 terms

Substitution of p6 by an expression in 
p3 found in e_319 : 
p6= - p3



>>>>>>>>> Solution of level 1.1.1.1.2.1.2. : 
no equations


Non-vanishing expressions: p6,p8,p3,q8

          2
6*g0084*p8  + 10*g0088*p3*p8 - 10*g0089*p3*p8 - 10*g0092*p3*p8 + 10*g0093*p3*p8

                              2             2                               2
 - 10*g0096*p3*p8 + 5*g0097*p3  - 5*g0099*p3  + 10*g0100*p3*p8 - 10*g0103*p3


2*g0055*p8*q8 - 2*g0056*p8*q8 - 2*g0059*p8*q8 + 2*g0060*p8*q8 - 2*g0063*p8*q8

                                                                         2
 + g0064*p3*q8 - g0066*p3*q8 + 2*g0067*p8*q8 - 2*g0070*p3*q8 + 2*g0078*p3

             2
 - 2*g0081*p3


2*g0031*p8*q8 - 2*g0032*p8*q8 - 2*g0033*p8*q8 + 2*g0034*p8*q8 - 2*g0036*p8*q8

                                                           2             2
 + g0037*p3*q8 + 2*g0039*p8*q8 - 2*g0042*p3*q8 + 2*g0049*p3  - 2*g0051*p3


g0111*p8 - g0113*p3 + g0116*p3


2*g0006*p8*q8 + 2*g0009*p8*q8 - g0013*p3*q8 + 2*g0014*p8*q8 - 2*g0017*p3*q8

             2
 - 2*g0026*p3


functions : 
         3    2
      - ---*p8 *q8
         5
q27=---------------
            2
          p3


q26=0


q25=0


q24=0


      - p8*q8
q23=----------
        p3


     p8*q8
q22=-------
      p3


q21=0


q20=0


     p8*q8
q19=-------
      p3


      - p8*q8
q18=----------
        p3


q17=0


q16=0


     p8*q8
q15=-------
      p3


        1
q14= - ---*q8
        2


q13=0


     1
q12=---*q8
     2


      - p8*q8
q11=----------
        p3


q10=0


q9=0

q8, 
q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, 
p7=0


p6= - p3


p5=0


p4=0

p3, 
p2=0


p1=0


with 45 terms
no equations
3 constants : p3,p8,q8
The equation: 

f =D f*D D f*p3 - D f*f *p3 + f  *p8
 t  2   1 2        1   x       3x
The symmetry: 
                                                      1       2      2
f =( - D f  *D D f*p3*p8*q8 - D f *D D f *p3*p8*q8 + ---*(D f) *f *p3 *q8
 s      2 2x  1 2              2 x  1 2 x             2    2     x

                                              2
     - D f*D D f  *p3*p8*q8 + D f*D D f*D f*p3 *q8 + D f  *f *p3*p8*q8
        2   1 2 2x             2   1 2   1            1 2x  x

                            1       2      2
     + D f *f  *p3*p8*q8 - ---*(D f) *f *p3 *q8 + D f*f  *p3*p8*q8
        1 x  2x             2    1     x           1   3x

        3        2       2
     - ---*f  *p8 *q8)/p3
        5   5x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 - d(1,f(1))*df(f(1),x)*p3 + df(f(1),x,3)*
p8$
The symmetry: 
df(f(1),s)=( - d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p3*p8*q8 - d(2,df(f(1),x))*d(1,d
(2,df(f(1),x)))*p3*p8*q8 + 1/2*d(2,f(1))**2*df(f(1),x)*p3**2*q8 - d(2,f(1))*d(1,
d(2,df(f(1),x,2)))*p3*p8*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3**2*q8 + d(1,
df(f(1),x,2))*df(f(1),x)*p3*p8*q8 + d(1,df(f(1),x))*df(f(1),x,2)*p3*p8*q8 - 1/2*
d(1,f(1))**2*df(f(1),x)*p3**2*q8 + d(1,f(1))*df(f(1),x,3)*p3*p8*q8 - 3/5*df(f(1)
,x,5)*p8**2*q8)/p3**2$

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p8

The lexicographical ordering of unknowns is changed
because p8 has to be non-zero, giving p8 a low priority.
Old ordering: q8,q7,p8,p6,p3
New ordering: q8,q7,p6,p8,p3

The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 

q7


New level : 1.1.1.1.2.1.3.
CRACK is now called with the new equation e_381 : 
0=p3 + p6

e_429,e_319 are consequences of e_381

Step 618: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

g0111*p8 - g0113*p3 + g0116*p3


The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 20 terms

Substitution of p6 by an expression in 
p3 found in e_381 : 
p6= - p3



>>>>>>>>> Solution of level 1.1.1.1.2.1.3. : 
no equations


Non-vanishing expressions: p6,p3,p8,q7

          2                 2
6*g0084*p8 *q8 + 12*g0085*p8 *q7 - 20*g0087*p3*p8*q7 + 10*g0088*p3*p8*q8

 - 10*g0089*p3*p8*q8 - 20*g0090*p3*p8*q7 - 20*g0091*p3*p8*q7 - 10*g0092*p3*p8*q8

 + 10*g0093*p3*p8*q8 - 20*g0094*p3*p8*q7 - 20*g0095*p3*p8*q7 - 10*g0096*p3*p8*q8

             2                 2                2
 + 5*g0097*p3 *q8 + 20*g0098*p3 *q7 - 5*g0099*p3 *q8 + 10*g0100*p3*p8*q8

                                  2                 2                 2
 - 20*g0101*p3*p8*q7 + 10*g0102*p3 *q7 - 10*g0103*p3 *q8 - 10*g0104*p3 *q7


           2
12*g0003*p8 *q7 - 20*g0005*p3*p8*q7 + 10*g0006*p3*p8*q8 - 20*g0007*p3*p8*q7

 - 20*g0008*p3*p8*q7 + 10*g0009*p3*p8*q8 - 20*g0010*p3*p8*q7 - 20*g0011*p3*p8*q7

              2                2
 + 20*g0012*p3 *q7 - 5*g0013*p3 *q8 + 10*g0014*p3*p8*q8 - 20*g0015*p3*p8*q7

              2                 2                 2                 3
 + 10*g0016*p3 *q7 - 10*g0017*p3 *q8 - 10*g0018*p3 *q7 - 10*g0026*p3


4*g0054*p8*q7 - 2*g0055*p8*q8 + 2*g0056*p8*q8 + 4*g0057*p8*q7 + 4*g0058*p8*q7

 + 2*g0059*p8*q8 - 2*g0060*p8*q8 + 4*g0061*p8*q7 + 4*g0062*p8*q7 + 2*g0063*p8*q8

 - g0064*p3*q8 - 4*g0065*p3*q7 + g0066*p3*q8 - 2*g0067*p8*q8 + 4*g0068*p8*q7

                                                             2             2
 - 2*g0069*p3*q7 + 2*g0070*p3*q8 + 2*g0071*p3*q7 - 2*g0078*p3  + 2*g0081*p3


           2
12*g0028*p8 *q7 - 20*g0030*p3*p8*q7 + 10*g0031*p3*p8*q8 - 10*g0032*p3*p8*q8

 - 10*g0033*p3*p8*q8 + 10*g0034*p3*p8*q8 - 20*g0035*p3*p8*q7 - 10*g0036*p3*p8*q8

             2                 2
 + 5*g0037*p3 *q8 + 20*g0038*p3 *q7 + 10*g0039*p3*p8*q8 - 20*g0040*p3*p8*q7

              2                 2                 2                 3
 + 10*g0041*p3 *q7 - 10*g0042*p3 *q8 - 10*g0043*p3 *q7 + 10*g0049*p3

              3
 - 10*g0051*p3


g0111*p8 - g0113*p3 + g0116*p3


functions : 
         3    2
      - ---*p8 *q8
         5
q27=---------------
            2
          p3


         6    2
      - ---*p8 *q7
         5
q26=---------------
            2
          p3


q25=0


     2*p8*q7
q24=---------
       p3


      - p8*q8
q23=----------
        p3


     p8*q8
q22=-------
      p3


     2*p8*q7
q21=---------
       p3


     2*p8*q7
q20=---------
       p3


     p8*q8
q19=-------
      p3


      - p8*q8
q18=----------
        p3


     2*p8*q7
q17=---------
       p3


     2*p8*q7
q16=---------
       p3


     p8*q8
q15=-------
      p3


        1
q14= - ---*q8
        2


q13= - 2*q7


     1
q12=---*q8
     2


      - p8*q8
q11=----------
        p3


     2*p8*q7
q10=---------
       p3


q9= - q7

q8, q7, 
q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, 
p7=0


p6= - p3


p5=0


p4=0

p3, 
p2=0


p1=0


with 54 terms
no equations
4 constants : p3,p8,q7,q8
The equation: 

f =D f*D D f*p3 - D f*f *p3 + f  *p8
 t  2   1 2        1   x       3x
The symmetry: 
f =( - D f  *D D f*p3*p8*q8 + 2*D f  *f *p3*p8*q7 - D f *D D f *p3*p8*q8
 s      2 2x  1 2                2 2x  x             2 x  1 2 x

                                  2         2       1       2      2
     + 2*D f *f  *p3*p8*q7 + (D f) *D D f*p3 *q7 + ---*(D f) *f *p3 *q8
          2 x  2x              2     1 2            2    2     x

                                              2                     2
     - D f*D D f  *p3*p8*q8 + D f*D D f*D f*p3 *q8 - 2*D f*D f*f *p3 *q7
        2   1 2 2x             2   1 2   1              2   1   x

                             6            2
     + 2*D f*f  *p3*p8*q7 - ---*D D f  *p8 *q7 + 2*D D f  *D f*p3*p8*q7
          2   3x             5   1 2 4x             1 2 2x  1

                                                                    2   2
     + 2*D D f *D f *p3*p8*q7 + 2*D D f*D f  *p3*p8*q7 - D D f*(D f) *p3 *q7
          1 2 x  1 x               1 2   1 2x             1 2    1

                                                1       2      2
     + D f  *f *p3*p8*q8 + D f *f  *p3*p8*q8 - ---*(D f) *f *p3 *q8
        1 2x  x             1 x  2x             2    1     x

                           3        2       2
     + D f*f  *p3*p8*q8 - ---*f  *p8 *q8)/p3
        1   3x             5   5x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 - d(1,f(1))*df(f(1),x)*p3 + df(f(1),x,3)*
p8$
The symmetry: 
df(f(1),s)=( - d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p3*p8*q8 + 2*d(2,df(f(1),x,2))*
df(f(1),x)*p3*p8*q7 - d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p3*p8*q8 + 2*d(2,df(f
(1),x))*df(f(1),x,2)*p3*p8*q7 + d(2,f(1))**2*d(1,d(2,f(1)))*p3**2*q7 + 1/2*d(2,f
(1))**2*df(f(1),x)*p3**2*q8 - d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p3*p8*q8 + d(2,f(
1))*d(1,d(2,f(1)))*d(1,f(1))*p3**2*q8 - 2*d(2,f(1))*d(1,f(1))*df(f(1),x)*p3**2*
q7 + 2*d(2,f(1))*df(f(1),x,3)*p3*p8*q7 - 6/5*d(1,d(2,df(f(1),x,4)))*p8**2*q7 + 2
*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p3*p8*q7 + 2*d(1,d(2,df(f(1),x)))*d(1,df(f(1),
x))*p3*p8*q7 + 2*d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p3*p8*q7 - d(1,d(2,f(1)))*d(1,
f(1))**2*p3**2*q7 + d(1,df(f(1),x,2))*df(f(1),x)*p3*p8*q8 + d(1,df(f(1),x))*df(f
(1),x,2)*p3*p8*q8 - 1/2*d(1,f(1))**2*df(f(1),x)*p3**2*q8 + d(1,f(1))*df(f(1),x,3
)*p3*p8*q8 - 3/5*df(f(1),x,5)*p8**2*q8)/p3**2$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p5


New level : 1.1.1.1.2.2.
CRACK is now called with the new equation e_453 : 
0=q10

e_324 is a consequence of e_453

Step 619: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 33 terms

e_293 is a consequence of e_362.
e_227 is a consequence of e_362.
Substitution of q10 found in e_453 : 
q10=0


Step 620: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 30 terms

e_250 is a consequence of e_237.
e_180 is a consequence of e_423.
e_120 is a consequence of e_423.
e_272 is a consequence of e_309.
Substitution of q18 by an expression in 
q7, p8, p6, p5, p3 found in e_420 : 12 factors in 3 terms

Step 621: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 31 terms

q7


e_309 is a consequence of e_423.
e_229 is a consequence of e_423.
e_133 is a consequence of e_429.
e_282 is a consequence of e_245.
e_417 is a consequence of e_245.
e_418 is a consequence of e_237.
Substitution of q8 by an expression in 
q7, p6, p5, p3 found in e_362 : 
     - p3*q7 + p6*q7
q8=------------------
           p5


Step 622: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_423 we get the alternative equations : 
0=p8


0=p6


New level : 1.1.1.1.2.2.1.
CRACK is now called with the new equation e_231 : 
0=p8

e_419,e_349,e_336,e_360,e_276,e_245,e_429,e_252,e_237,e_267 are consequences of 
e_231

Step 623: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

g0113*p6 + g0114*p5 + g0116*p3


The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 10 terms

Substitution of p8 found in e_231 : 
p8=0



>>>>>>>>> Solution of level 1.1.1.1.2.2.1. : 
no equations


Non-vanishing expressions: p5,p3,q7

                      2                                           2
g0097*p3*p6 - g0097*p6  + 2*g0098*p3*p5 - 2*g0098*p5*p6 + g0099*p3

                         2             2
 - g0099*p3*p6 - g0099*p5  + 2*g0103*p3  - 2*g0103*p3*p6 - 2*g0104*p3*p5


                                              2
2*g0012*p3*p5*q7 - 2*g0012*p5*p6*q7 + g0013*p3 *q7 - g0013*p3*p6*q7

           2                2
 - g0013*p5 *q7 + 2*g0017*p3 *q7 - 2*g0017*p3*p6*q7 - 2*g0018*p3*p5*q7

                2             2
 - 2*g0024*p3*p5  - 2*g0026*p3 *p5


                         2
g0064*p3*p6*q7 - g0064*p6 *q7 + 2*g0065*p3*p5*q7 - 2*g0065*p5*p6*q7

           2                               2                2
 + g0066*p3 *q7 - g0066*p3*p6*q7 - g0066*p5 *q7 + 2*g0070*p3 *q7

                                                                         2
 - 2*g0070*p3*p6*q7 - 2*g0071*p3*p5*q7 - 2*g0078*p3*p5*p6 - 2*g0079*p3*p5

             2
 - 2*g0081*p3 *p5


                         2
g0037*p3*p6*q7 - g0037*p6 *q7 + 2*g0038*p3*p5*q7 - 2*g0038*p5*p6*q7

             2
 + 2*g0042*p3 *q7 - 2*g0042*p3*p6*q7 - 2*g0043*p3*p5*q7 - 2*g0049*p3*p5*p6

             2
 - 2*g0051*p3 *p5


g0113*p6 + g0114*p5 + g0116*p3


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


         1              1    2
      - ---*p3*p6*q7 + ---*p6 *q7
         2              2
q14=------------------------------
                p3*p5


      - p3*q7 + p6*q7
q13=------------------
            p3


         1    2       1              1    2
      - ---*p3 *q7 + ---*p3*p6*q7 + ---*p5 *q7
         2            2              2
q12=-------------------------------------------
                       p3*p5


q11=0


q10=0


q9=0


     - p3*q7 + p6*q7
q8=------------------
           p5

q7, 
q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0

p6, p5, 
p4=0

p3, 
p2=0


p1=0


with 44 terms
no equations
4 constants : p3,p5,p6,q7
The equation: 

f =D f*D D f*p3 + D f*f *p5 + D f*f *p6
 t  2   1 2        2   x       1   x
The symmetry: 
         2                   1       2      2       1       2
f =((D f) *D D f*p3*p5*q7 - ---*(D f) *f *p3 *q7 + ---*(D f) *f *p3*p6*q7
 s    2     1 2              2    2     x           2    2     x

        1       2      2                      2
     + ---*(D f) *f *p5 *q7 - D f*D D f*D f*p3 *q7 + D f*D D f*D f*p3*p6*q7
        2    2     x           2   1 2   1            2   1 2   1

                                                    1       2
     - D f*D f*f *p3*p5*q7 + D f*D f*f *p5*p6*q7 - ---*(D f) *f *p3*p6*q7
        2   1   x             2   1   x             2    1     x

        1       2      2
     + ---*(D f) *f *p6 *q7)/(p3*p5)
        2    1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(2,f(1))*df(f(1),x)*p5 + d(1,f(1))*df(
f(1),x)*p6$
The symmetry: 
df(f(1),s)=(d(2,f(1))**2*d(1,d(2,f(1)))*p3*p5*q7 - 1/2*d(2,f(1))**2*df(f(1),x)*
p3**2*q7 + 1/2*d(2,f(1))**2*df(f(1),x)*p3*p6*q7 + 1/2*d(2,f(1))**2*df(f(1),x)*p5
**2*q7 - d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3**2*q7 + d(2,f(1))*d(1,d(2,f(1)))*
d(1,f(1))*p3*p6*q7 - d(2,f(1))*d(1,f(1))*df(f(1),x)*p3*p5*q7 + d(2,f(1))*d(1,f(1
))*df(f(1),x)*p5*p6*q7 - 1/2*d(1,f(1))**2*df(f(1),x)*p3*p6*q7 + 1/2*d(1,f(1))**2
*df(f(1),x)*p6**2*q7)/(p3*p5)$

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 

p8


This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 60 ms

The list of inequalities got extended by: 

p4

The lexicographical ordering of unknowns is changed
because p4 has to be non-zero, giving p4 a low priority.
Old ordering: q27,q26,q25,q24,q23,q22,q21,q20,q19,q18,q17,q16,q15,q14,q13,q12,
q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1,p8,p6,p5,p4,p3
New ordering: q27,q26,q25,q24,q23,q22,q21,q20,q19,q18,q17,q16,q15,q14,q13,q12,
q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1,p8,p6,p5,p3,p4

New level : 1.1.1.2.
CRACK is now called with the new equation e_339 : 
0=q2

e_271,e_234,e_169,e_27,e_221 are consequences of e_339

Step 624: 
Hot list of urgent steps : 
*** Garbage collection starting 
*** GC 325  3-Oct-2003 05:28:35, 20 ms (0%), 1048872 occupied, 23951080 free

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 22 terms

e_263 is a consequence of e_258.
e_250 is a consequence of e_252.
Substitution of q2 found in e_339 : 
q2=0


Step 625: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 21 terms

e_353 is a consequence of e_193.
e_354 is a consequence of e_107.e_163,e_162,e_191,e_291 are consequences of 
e_355

e_356 is a consequence of e_355.
Substitution of q6 found in e_62 : 
q6=0


Step 626: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 20 terms
e_159,e_32,e_205,e_243 are consequences of e_171

e_154 is a consequence of e_171.
Substitution of q4 found in e_7 : 
q4=0


Step 627: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 23 terms
e_132 is a consequence of e_11

Substitution of q1 found in e_193 : 
q1=0


Step 628: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 22 terms

Substitution of q5 found in e_355 : 
q5=0


Step 629: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 21 terms
e_357,e_351,e_254 are consequences of e_107

e_276 is a consequence of e_107.
Substitution of q3 found in e_171 : 
q3=0


Step 630: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 20 terms

Substitution of q25 found in e_107 : 
q25=0


Step 631: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 22 terms

e_57 is a consequence of e_28.
e_293 is a consequence of e_95.
e_65 is a consequence of e_95.
Substitution of q24 by an expression in 
q21, q16, q10 found in e_252 : 
q24=q10 + q16 - q21


Step 632: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 26 terms

e_204 is a consequence of e_235.
e_280 is a consequence of e_228.
Substitution of q21 by an expression in 
q20, q17, q16, q10 found in e_95 : 13 factors in 5 terms

Step 633: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 29 terms

e_301 is a consequence of e_11.
Substitution of q23 by an expression in 
q19, q18, q15, q11 found in e_258 : 13 factors in 5 terms

Step 634: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 32 terms

e_64 is a consequence of e_117.
e_138 is a consequence of e_216.
Substitution of q22 by an expression in 
q19, q18, q15, q11 found in e_11 : 13 factors in 5 terms

Step 635: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 33 terms

Substitution of q26 by an expression in 
q27, q15, p8, p6, p4 found in e_340 : 8 factors in 3 terms

Step 636: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 34 terms

Substitution of q13 by an expression in 
q9, p5, p4 found in e_342 : 
     p4*q9 + p5*q9
q13=---------------
          p4


Step 637: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 36 terms

Substitution of q14 by an expression in 
q9, q8, p6, p3, p4 found in e_157 : 14 factors in 4 terms

Step 638: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 38 terms

Substitution of q20 by an expression in 
q19, q18, q17, p3, p4 found in e_228 : 8 factors in 4 terms

Step 639: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 45 terms

Substitution of q19 by an expression in 
q18, q17, q9, p8, p6, p4 found in e_345 : 13 factors in 4 terms

Step 640: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

e_193 is a consequence of e_169.
Step 641: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_169 and e_27. e_27: 
(#) 5 terms, 16 factors, with derivatives of functions of all variables: 

                       2            2
 (q18,q17,q16,q10,q9,p8 ,p8,p6,p3,p4 ,p4)

is replaced by e_355: 

0=(q10 - q17)*p8


e_355 is a consequence of e_323.
Step 642: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 326  3-Oct-2003 05:28:38, 40 ms (0%), 1076812 occupied, 23923140 free
Eliminate 
q18

from e_306 and e_358. e_358: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                                  2      2      3   2
 (q18,q17,q16,q15,q11,q10,q9,p8,p6 ,p6,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_254: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                       2      2
 (q16,q15,q11,q10,p6,p3 ,p3,p4 ,p4)


Step 643: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_227 and e_353. e_353: 
 12 terms, 36 factors, with derivatives of functions of all variables: 

                                           2
 (q18,q17,q16,q15,q11,q10,q9,p8,p6,p5,p3,p4 ,p4)

is replaced by e_351: 
 12 terms, 36 factors, with derivatives of functions of all variables: 

                                       2
 (q17,q16,q15,q11,q10,q9,p8,p6,p5,p3,p4 ,p4)


Step 644: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 327  3-Oct-2003 05:28:40, 40 ms (0%), 1072057 occupied, 23927895 free
Eliminate 
q18

from e_291 and e_62. e_62: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                                           3   2
 (q18,q17,q16,q15,q11,q10,q9,p8,p6,p5,p3,p4 ,p4 ,p4)

is replaced by e_357: 
 4 terms, 8 factors, with derivatives of functions of all variables: 

 (q16,q15,q11,q10,p3,p4)


Step 645: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 50 terms

The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 49 terms

Substitution of q16 by an expression in 
q15, q11, q10, p3, p4 found in e_357 : 8 factors in 4 terms

Step 646: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_323 and e_107. e_107: 
(#) 7 terms, 22 factors, with derivatives of functions of all variables: 

                           2            2
 (q18,q17,q15,q11,q10,q9,p8 ,p8,p6,p3,p4 ,p4)

is replaced by e_290: 
(#) 5 terms, 12 factors, with derivatives of functions of all variables: 

                       2
 (q18,q15,q11,q10,q9,p8 ,p8,p6,p3,p4)


Step 647: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_195 and e_252. e_252: 
 14 terms, 42 factors, with derivatives of functions of all variables: 

                                2      2
 (q17,q15,q11,q10,q9,p8,p6,p5,p3 ,p3,p4 ,p4)

is replaced by e_50: 
 11 terms, 33 factors, with derivatives of functions of all variables: 

                            2      2
 (q15,q11,q10,q9,p8,p6,p5,p3 ,p3,p4 ,p4)


Step 648: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 328  3-Oct-2003 05:28:43, 40 ms (0%), 1073215 occupied, 23926736 free
Eliminate 
q18

from e_293 and e_280. e_280: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                                          2
 (q18,q17,q15,q11,q10,q9,q8,p8,p6,p5,p3,p4 ,p4)

is replaced by e_328: 
 7 terms, 21 factors, with derivatives of functions of all variables: 

                            2
 (q15,q11,q10,q8,p8,p5,p3,p4 ,p4)


Step 649: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_195 and e_306. e_306: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                          2
 (q18,q17,q15,q11,q9,p8,p6 ,p6,p3,p4)

is replaced by e_326: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                          2
 (q18,q15,q11,q10,q9,p8,p6 ,p6,p3,p4)


Step 650: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q12

from e_229 and e_352. e_352: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                               2
 (q18,q17,q12,q9,p8,p6,p5,p3,p4 ,p4)

is replaced by e_284: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                              2
 (q18,q17,q9,q8,p8,p6,p5,p3,p4 ,p4)


Step 651: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q15

from e_57 and e_133. e_133: 
 12 terms, 36 factors, with derivatives of functions of all variables: 

                              2         2
 (q18,q17,q15,q11,q10,q9,p8,p6 ,p6,p3,p4 ,p4)

is replaced by e_301: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                     2         2
 (q18,q17,q9,q8,p8,p6 ,p6,p3,p4 ,p4)


Step 652: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q9

from e_237 and e_255. e_255: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                                       2
 (q18,q17,q15,q11,q10,q9,p8,p6,p5,p3,p4 ,p4)

is replaced by e_258: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                                       2
 (q18,q17,q15,q11,q10,q7,p8,p6,p5,p3,p4 ,p4)


Step 653: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_346 and e_282. e_282: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                                       3   2
 (q18,q17,q15,q11,q10,q9,p8,p6,p5,p3,p4 ,p4 ,p4)

is replaced by e_303: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                                   2      3   2
 (q17,q15,q11,q10,q9,q7,p8,p6,p5,p3 ,p3,p4 ,p4 ,p4)


Step 654: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 329  3-Oct-2003 05:28:46, 40 ms (0%), 1075383 occupied, 23924566 free
Eliminate 
q18

from e_284 and e_258. e_258: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                                       2
 (q18,q17,q15,q11,q10,q7,p8,p6,p5,p3,p4 ,p4)

is replaced by e_304: 
 11 terms, 44 factors, with derivatives of functions of all variables: 

                                         2
 (q17,q15,q11,q10,q9,q8,q7,p8,p6,p5,p3,p4 ,p4)


Step 655: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 330  3-Oct-2003 05:28:50, 40 ms (0%), 1075938 occupied, 23924012 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_323 we get the alternative equations : 
0=p8


0=q10 - q17


New level : 1.1.1.2.1.
CRACK is now called with the new equation e_312 : 
0=p8

e_290,e_226,e_221,e_215 are consequences of e_312

Step 656: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 42 terms

Substitution of p8 found in e_312 : 
p8=0


Step 657: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 58 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 56 terms

Substitution of q11 by an expression in 
q17, q10, p6, p3, p4 found in e_364 : 18 factors in 5 terms

Step 658: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 659: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 660: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 661: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_376 and e_373. e_376: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                    2      2
 (q18,q17,q15,q10,p6 ,p6,p3 ,p3,p4)

is replaced by e_7: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                2      2      2
 (q17,q15,q10,p6 ,p6,p3 ,p3,p4 ,p4)


Step 662: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_373 and e_374. e_374: 
 15 terms, 60 factors, with derivatives of functions of all variables: 

                    2         2      2
 (q18,q17,q15,q10,p6 ,p6,p5,p3 ,p3,p4 ,p4)

is replaced by e_278: 
 15 terms, 60 factors, with derivatives of functions of all variables: 

                2         2      3   2
 (q17,q15,q10,p6 ,p6,p5,p3 ,p3,p4 ,p4 ,p4)


Step 663: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 331  3-Oct-2003 05:28:53, 40 ms (0%), 1091879 occupied, 23908071 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_342 we get the alternative equations : 
0=q27


0=p3*p6 - p4*p5


New level : 1.1.1.2.1.1.
CRACK is now called with the new equation e_252 : 
0=q27

e_157,e_228,e_313,e_20 are consequences of e_252

Step 664: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 45 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 54 terms

Substitution of q27 found in e_252 : 
q27=0


Step 665: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_205 we get the alternative equations : 
0=p3 + 3*p6


0=p4*q18 - p6*q17


New level : 1.1.1.2.1.1.1.
CRACK is now called with the new equation e_280 : 
0=p3 + 3*p6


Step 666: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 45 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 41 terms

Substitution of p6 by an expression in 
p3 found in e_280 : 
       1
p6= - ---*p3
       3


Step 667: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 668: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 669: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_306 and e_397. e_397: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                2      2
 (q18,q17,q10,p3 ,p3,p4 ,p4)

is replaced by e_400: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

            2   2
 (q17,q10,p3 ,p4 )


Step 670: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_306 and e_255. e_255: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

               2      2
 (q18,q17,p5,p3 ,p3,p4 ,p4)

is replaced by e_401: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

           2   3   2
 (q17,p5,p3 ,p4 ,p4 ,p4)


Step 671: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 672: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_306 and e_282. e_282: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

                    2      2
 (q18,q17,q15,q10,p3 ,p3,p4 ,p4)

is replaced by e_403: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

                2      2
 (q17,q15,q10,p3 ,p3,p4 ,p4)


Step 673: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_400 and e_403. e_403: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

                2      2
 (q17,q15,q10,p3 ,p3,p4 ,p4)

is replaced by e_404: 
 3 terms, 9 factors, with derivatives of functions of all variables: 

            2      2
 (q15,q10,p3 ,p3,p4 ,p4)


Step 674: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q15

from e_404 and e_307. e_307: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                2      2
 (q17,q15,q10,p3 ,p3,p4 ,p4)

is replaced by e_407: 
 3 terms, 9 factors, with derivatives of functions of all variables: 

            2   2
 (q17,q10,p3 ,p4 )


Step 675: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q15

from e_404 and e_309. e_309: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

                2      2
 (q17,q15,q10,p3 ,p3,p4 ,p4)

is replaced by e_410: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

            2   2
 (q17,q10,p3 ,p4 )


Step 676: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_407 and e_138. e_138: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                   2      3   2
 (q17,q15,q10,p5,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_411: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

               2      3   2
 (q15,q10,p5,p3 ,p3,p4 ,p4 ,p4)


Step 677: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q15

from e_404 and e_411. e_411: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

               2      3   2
 (q15,q10,p5,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_412: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

           2   3   2
 (q10,p5,p3 ,p4 ,p4 ,p4)


Step 678: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_407 and e_311. e_311: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                   2      3   2
 (q17,q15,q10,p5,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_369: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

               2      3   2
 (q15,q10,p5,p3 ,p3,p4 ,p4 ,p4)


Step 679: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q15

from e_404 and e_369. e_369: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

               2      3   2
 (q15,q10,p5,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_310: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

           2   3   2
 (q10,p5,p3 ,p4 ,p4 ,p4)

*** Garbage collection starting 
*** GC 332  3-Oct-2003 05:28:57, 40 ms (0%), 1093271 occupied, 23906678 free

Step 680: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q15

from e_404 and e_323. e_323: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                   2      2
 (q17,q15,q10,p5,p3 ,p3,p4 ,p4)

is replaced by e_243: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

               2   3   2
 (q17,q10,p5,p3 ,p4 ,p4 ,p4)


Step 681: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q15

from e_404 and e_290. e_290: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

                   2      3   2
 (q17,q15,q10,p5,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_371: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

               2   3   2
 (q17,q10,p5,p3 ,p4 ,p4 ,p4)


Step 682: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_215 and e_340. e_215: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                    3   2      3   2
 (q18,q17,q15,q10,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_32: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                3   2      3   2
 (q17,q15,q10,p3 ,p3 ,p3,p4 ,p4 ,p4)


Step 683: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_32 and e_11. e_32: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                3   2      3   2
 (q17,q15,q10,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_159: 
 3 terms, 9 factors, with derivatives of functions of all variables: 

            2      2
 (q15,q10,p3 ,p3,p4 ,p4)


Step 684: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_407 and e_221. e_221: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                       3   2      3   2
 (q18,q17,q15,q10,p5,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_374: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                   3   2      3   2
 (q18,q15,q10,p5,p3 ,p3 ,p3,p4 ,p4 ,p4)


Step 685: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_340 and e_392. e_392: 
 11 terms, 44 factors, with derivatives of functions of all variables: 

                       3   2      3   2
 (q18,q17,q15,q10,p5,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_185: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

                   3   2      3   2
 (q17,q15,q10,p5,p3 ,p3 ,p3,p4 ,p4 ,p4)


Step 686: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_398 we get the alternative equations : 
0=q18


    2
0=p3  + 3*p4*p5


New level : 1.1.1.2.1.1.1.1.
CRACK is now called with the new equation e_62 : 
0=q18


Step 687: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 34 terms

Substitution of q18 found in e_62 : 
q18=0


Step 688: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 689: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_357 and e_11. e_11: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                3   2      3   2
 (q17,q15,q10,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_18: 
 4 terms, 16 factors, with derivatives of functions of all variables: 

            3   2      3   2
 (q15,q10,p3 ,p3 ,p3,p4 ,p4 ,p4)


Step 690: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_395 we get the alternative equations : 
0=p3


0=q17


0=p4 - 3*p5


New level : 1.1.1.2.1.1.1.1.1.
CRACK is now called with the new equation e_403 : 
0=p3

e_107,e_352 are consequences of e_403

Step 691: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

g0114*p5 + g0115*p4


The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 16 terms
e_401 is a consequence of e_405
e_412,e_310 are consequences of e_408

e_409 is a consequence of e_408.
e_414 is a consequence of e_307.
*** Garbage collection starting 
*** GC 333  3-Oct-2003 05:29:00, 30 ms (0%), 1095975 occupied, 23903974 free

e_417 is a consequence of e_307.
e_418 is a consequence of e_307.
e_419 is a consequence of e_307.
e_422 is a consequence of e_307.
e_423 is a consequence of e_307.
e_424 is a consequence of e_307.
e_425 is a consequence of e_307.
e_426 is a consequence of e_307.
Substitution of p3 found in e_403 : 
p3=0


Step 692: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 14 terms

e_138 is a consequence of e_408.
e_309 is a consequence of e_408.
e_421 is a consequence of e_408.
e_420 is a consequence of e_408.
e_416 is a consequence of e_408.
e_415 is a consequence of e_408.
Substitution of q17 found in e_405 : 
q17=0


Step 693: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 11 terms

Substitution of q15 found in e_307 : 
q15=0


Step 694: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 7 terms

Substitution of q10 found in e_408 : 
q10=0


Step 695: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 7 terms

Substitution of q12 by an expression in 
q8, p5, p4 found in e_411 : 
      1
     ---*p5*q8
      2
q12=-----------
        p4


Step 696: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 8 terms

Substitution of q7 by an expression in 
q9, p5, p4 found in e_413 : 10 factors in 3 terms

Step 697: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_406 we get the alternative equations : 
0=q9


0=p4 + p5


0=p4 - p5


New level : 1.1.1.2.1.1.1.1.1.1.
CRACK is now called with the new equation e_32 : 
0=q9


Step 698: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 3 terms

The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 3 terms

q8


Substitution of q9 found in e_32 : 
q9=0



>>>>>>>>> Solution of level 1.1.1.2.1.1.1.1.1.1. : 
no equations


Non-vanishing expressions: q8,p4

g0097*p4 - g0099*p5 - 2*g0103*p4


                                                        2
g0013*p5*q8 + 2*g0017*p4*q8 + 2*g0024*p4*p5 + 2*g0025*p4


                                                                      2
g0064*p4*q8 - g0066*p5*q8 - 2*g0070*p4*q8 - 2*g0079*p4*p5 - 2*g0080*p4


g0037*q8 - 2*g0042*q8 - 2*g0050*p4


g0114*p5 + g0115*p4


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


        1
q14= - ---*q8
        2


q13=0


      1
     ---*p5*q8
      2
q12=-----------
        p4


q11=0


q10=0


q9=0

q8, 
q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


p6=0

p5, p4, 
p3=0


p2=0


p1=0


with 37 terms
no equations
3 constants : p4,p5,q8
The equation: 

f =D f*f *p5 + D D f*D f*p4
 t  2   x       1 2   1
The symmetry: 
     1       2                                   1       2
    ---*(D f) *f *p5*q8 + D f*D D f*D f*p4*q8 - ---*(D f) *f *p4*q8
     2    2     x          2   1 2   1           2    1     x
f =-----------------------------------------------------------------
 s                                p4
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,f(1)))*d(1,f(1))*p4$
The symmetry: 
df(f(1),s)=(1/2*d(2,f(1))**2*df(f(1),x)*p5*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1
))*p4*q8 - 1/2*d(1,f(1))**2*df(f(1),x)*p4*q8)/p4$

Time: 0 ms

Time: 0 ms

Time: 0 ms

The list of inequalities got extended by: 

q9

The lexicographical ordering of unknowns is changed
because q9 has to be non-zero, giving q9 a low priority.
Old ordering: q9,q8,p5,p4
New ordering: q8,q9,p5,p4

The list of inequalities got extended by: 

p5


New level : 1.1.1.2.1.1.1.1.1.2.
CRACK is now called with the new equation e_32 : 
0=p4 + p5


Step 699: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 4 terms

Substitution of p5 by an expression in 
p4 found in e_32 : 
p5= - p4



>>>>>>>>> Solution of level 1.1.1.2.1.1.1.1.1.2. : 
no equations


Non-vanishing expressions: p5,p4,q9

g0097*q8 + g0099*q8 - 2*g0102*q9 - 2*g0103*q8


g0013*q8 - 2*g0016*q9 - 2*g0017*q8 + 2*g0024*p4 - 2*g0025*p4


g0064*q8 + g0066*q8 - 2*g0069*q9 - 2*g0070*q8 + 2*g0079*p4 - 2*g0080*p4


g0037*q8 - 2*g0041*q9 - 2*g0042*q8 - 2*g0050*p4


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


        1
q14= - ---*q8
        2


q13=0


        1
q12= - ---*q8
        2


q11=0


q10=0

q9, q8, 
q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


p6=0


p5= - p4

p4, 
p3=0


p2=0


p1=0


with 38 terms
no equations
3 constants : p4,q8,q9
The equation: 

f = - D f*f *p4 + D D f*D f*p4
 t     2   x       1 2   1
The symmetry: 
       1       2                                       2       1       2
f = - ---*(D f) *f *q8 + D f*D D f*D f*q8 + D D f*(D f) *q9 - ---*(D f) *f *q8
 s     2    2     x       2   1 2   1        1 2    1          2    1     x
And now in machine readable form:

The system: 

df(f(1),t)= - d(2,f(1))*df(f(1),x)*p4 + d(1,d(2,f(1)))*d(1,f(1))*p4$
The symmetry: 
df(f(1),s)= - 1/2*d(2,f(1))**2*df(f(1),x)*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1)
)*q8 + d(1,d(2,f(1)))*d(1,f(1))**2*q9 - 1/2*d(1,f(1))**2*df(f(1),x)*q8$

Time: 0 ms

Time: 0 ms

Time: 0 ms

The list of inequalities got extended by: 

q9

The lexicographical ordering of unknowns is changed
because q9 has to be non-zero, giving q9 a low priority.
Old ordering: q9,q8,p5,p4
New ordering: q8,q9,p5,p4

The list of inequalities got extended by: 

p4 + p5


The list of inequalities got extended by: 

p5


New level : 1.1.1.2.1.1.1.1.1.3.
CRACK is now called with the new equation e_32 : 
0=p4 - p5


Step 700: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 6 terms

Substitution of p5 by an expression in 
p4 found in e_32 : 
p5=p4



>>>>>>>>> Solution of level 1.1.1.2.1.1.1.1.1.3. : 
no equations


Non-vanishing expressions: p5,p4,q9

g0097*q8 - 4*g0098*q9 - g0099*q8 - 2*g0102*q9 - 2*g0103*q8 + 2*g0104*q9


4*g0012*q9 + g0013*q8 + 2*g0016*q9 + 2*g0017*q8 - 2*g0018*q9 + 2*g0024*p4

 + 2*g0025*p4


g0064*q8 - 4*g0065*q9 - g0066*q8 - 2*g0069*q9 - 2*g0070*q8 + 2*g0071*q9

 - 2*g0079*p4 - 2*g0080*p4


g0037*q8 - 4*g0038*q9 - 2*g0041*q9 - 2*g0042*q8 + 2*g0043*q9 - 2*g0050*p4


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


        1
q14= - ---*q8
        2


q13=2*q9


     1
q12=---*q8
     2


q11=0


q10=0

q9, q8, 
q7= - q9


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


p6=0


p5=p4

p4, 
p3=0


p2=0


p1=0


with 40 terms
no equations
3 constants : p4,q8,q9
The equation: 

f =D f*f *p4 + D D f*D f*p4
 t  2   x       1 2   1
The symmetry: 
           2             1       2
f = - (D f) *D D f*q9 + ---*(D f) *f *q8 + D f*D D f*D f*q8 + 2*D f*D f*f *q9
 s      2     1 2        2    2     x       2   1 2   1          2   1   x

              2       1       2
 + D D f*(D f) *q9 - ---*(D f) *f *q8
    1 2    1          2    1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*df(f(1),x)*p4 + d(1,d(2,f(1)))*d(1,f(1))*p4$
The symmetry: 
df(f(1),s)= - d(2,f(1))**2*d(1,d(2,f(1)))*q9 + 1/2*d(2,f(1))**2*df(f(1),x)*q8 + 
d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*q8 + 2*d(2,f(1))*d(1,f(1))*df(f(1),x)*q9 + d(
1,d(2,f(1)))*d(1,f(1))**2*q9 - 1/2*d(1,f(1))**2*df(f(1),x)*q8$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p3


New level : 1.1.1.2.1.1.1.1.2.
CRACK is now called with the new equation e_403 : 
0=q17

e_401,e_357 are consequences of e_403

Step 701: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 24 terms

e_416 is a consequence of e_415.
Substitution of q17 found in e_403 : 
q17=0


Step 702: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 22 terms

e_424 is a consequence of e_406.
Substitution of q15 by an expression in 
q10, p3, p4 found in e_404 : 11 factors in 3 terms

Step 703: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 23 terms

Substitution of q7 by an expression in 
q9, p5, p4 found in e_352 : 10 factors in 3 terms

Step 704: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_405 we get the alternative equations : 
0=q10


0=7*p4 - p5


New level : 1.1.1.2.1.1.1.1.2.1.
CRACK is now called with the new equation e_468 : 
0=q10

e_427,e_428,e_429,e_430,e_431,e_426,e_412,e_310,e_413,e_414,e_159,e_425,e_409,
e_309,e_406,e_307,e_408 are consequences of e_468

Step 705: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 9 terms

Substitution of q10 found in e_468 : 
q10=0


Step 706: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 11 terms

e_311 is a consequence of e_433.
Substitution of q12 by an expression in 
q9, q8, p5, p3, p4 found in e_229 : 17 factors in 4 terms

Step 707: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 14 terms

q9

The lexicographical ordering of unknowns is changed
because q9 has to be non-zero, giving q9 a low priority.
Old ordering: q9,q8,p5,p3,p4
New ordering: q8,q9,p5,p3,p4

Substitution of q8 by an expression in 
q9, p5, p3, p4 found in e_433 : 14 factors in 4 terms


>>>>>>>>> Solution of level 1.1.1.2.1.1.1.1.2.1. : 
no equations


Non-vanishing expressions: q9,p3,p4

          2             2
4*g0097*p3  - 9*g0097*p4  - 9*g0097*p4*p5 - 24*g0098*p3*p4 - 24*g0098*p3*p5

              2                             2                               2
 - 12*g0099*p3  + 9*g0099*p4*p5 + 9*g0099*p5  - 24*g0102*p3*p4 - 24*g0103*p3

              2
 + 18*g0103*p4  + 18*g0103*p4*p5 + 18*g0104*p3*p4 + 18*g0104*p3*p5


                                                2
8*g0012*p3*p4*q9 + 8*g0012*p3*p5*q9 + 4*g0013*p3 *q9 - 3*g0013*p4*p5*q9

             2                                   2                2
 - 3*g0013*p5 *q9 + 8*g0016*p3*p4*q9 + 8*g0017*p3 *q9 - 6*g0017*p4 *q9

 - 6*g0017*p4*p5*q9 - 6*g0018*p3*p4*q9 - 6*g0018*p3*p5*q9 + 8*g0024*p3*p4*p5

                2             2
 + 8*g0025*p3*p4  + 8*g0026*p3 *p4


          2                2
4*g0064*p3 *q9 - 9*g0064*p4 *q9 - 9*g0064*p4*p5*q9 - 24*g0065*p3*p4*q9

                                  2                                   2
 - 24*g0065*p3*p5*q9 - 12*g0066*p3 *q9 + 9*g0066*p4*p5*q9 + 9*g0066*p5 *q9

                                  2                 2
 - 24*g0069*p3*p4*q9 - 24*g0070*p3 *q9 + 18*g0070*p4 *q9 + 18*g0070*p4*p5*q9

                                                     2
 + 18*g0071*p3*p4*q9 + 18*g0071*p3*p5*q9 + 8*g0078*p3 *p4 - 24*g0079*p3*p4*p5

                 2              2
 - 24*g0080*p3*p4  - 24*g0081*p3 *p4


          2                2
4*g0037*p3 *q9 - 9*g0037*p4 *q9 - 9*g0037*p4*p5*q9 - 24*g0038*p3*p4*q9

                                                      2                 2
 - 24*g0038*p3*p5*q9 - 24*g0041*p3*p4*q9 - 24*g0042*p3 *q9 + 18*g0042*p4 *q9

                                                                         2
 + 18*g0042*p4*p5*q9 + 18*g0043*p3*p4*q9 + 18*g0043*p3*p5*q9 + 8*g0049*p3 *p4

                 2              2
 - 24*g0050*p3*p4  - 24*g0051*p3 *p4


g0113*p3 - 3*g0114*p5 - 3*g0115*p4 - 3*g0116*p3


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


         1    2       3    2       3
      - ---*p3 *q9 + ---*p4 *q9 + ---*p4*p5*q9
         6            8            8
q14=-------------------------------------------
                       p3*p4


     p4*q9 + p5*q9
q13=---------------
          p4


      1    2       3              3    2
     ---*p3 *q9 - ---*p4*p5*q9 - ---*p5 *q9
      2            8              8
q12=----------------------------------------
                     p3*p4


q11=0


q10=0

q9, 
      2       3    2       3
    p3 *q9 - ---*p4 *q9 - ---*p4*p5*q9
              4            4
q8=------------------------------------
                  p3*p4


        3           3
     - ---*p4*q9 - ---*p5*q9
        4           4
q7=--------------------------
               p4


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


       1
p6= - ---*p3
       3

p5, p4, p3, 
p2=0


p1=0


with 49 terms
no equations
4 constants : p3,p4,p5,q9
The equation: 

                                              1
f =D f*D D f*p3 + D f*f *p5 + D D f*D f*p4 - ---*D f*f *p3
 t  2   1 2        2   x       1 2   1        3   1   x
The symmetry: 
        3       2                   3       2
f =( - ---*(D f) *D D f*p3*p4*q9 - ---*(D f) *D D f*p3*p5*q9
 s      4    2     1 2              4    2     1 2

        1       2      2       3       2                3       2      2
     + ---*(D f) *f *p3 *q9 - ---*(D f) *f *p4*p5*q9 - ---*(D f) *f *p5 *q9
        2    2     x           8    2     x             8    2     x

                       2       3                  2
     + D f*D D f*D f*p3 *q9 - ---*D f*D D f*D f*p4 *q9
        2   1 2   1            4   2   1 2   1

        3
     - ---*D f*D D f*D f*p4*p5*q9 + D f*D f*f *p3*p4*q9 + D f*D f*f *p3*p5*q9
        4   2   1 2   1              2   1   x             2   1   x

                  2             1       2      2       3       2      2
     + D D f*(D f) *p3*p4*q9 - ---*(D f) *f *p3 *q9 + ---*(D f) *f *p4 *q9
        1 2    1                6    1     x           8    1     x

        3       2
     + ---*(D f) *f *p4*p5*q9)/(p3*p4)
        8    1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,f(1))
)*d(1,f(1))*p4 - 1/3*d(1,f(1))*df(f(1),x)*p3$
The symmetry: 
df(f(1),s)=( - 3/4*d(2,f(1))**2*d(1,d(2,f(1)))*p3*p4*q9 - 3/4*d(2,f(1))**2*d(1,d
(2,f(1)))*p3*p5*q9 + 1/2*d(2,f(1))**2*df(f(1),x)*p3**2*q9 - 3/8*d(2,f(1))**2*df(
f(1),x)*p4*p5*q9 - 3/8*d(2,f(1))**2*df(f(1),x)*p5**2*q9 + d(2,f(1))*d(1,d(2,f(1)
))*d(1,f(1))*p3**2*q9 - 3/4*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p4**2*q9 - 3/4*d(
2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p4*p5*q9 + d(2,f(1))*d(1,f(1))*df(f(1),x)*p3*p4
*q9 + d(2,f(1))*d(1,f(1))*df(f(1),x)*p3*p5*q9 + d(1,d(2,f(1)))*d(1,f(1))**2*p3*
p4*q9 - 1/6*d(1,f(1))**2*df(f(1),x)*p3**2*q9 + 3/8*d(1,f(1))**2*df(f(1),x)*p4**2
*q9 + 3/8*d(1,f(1))**2*df(f(1),x)*p4*p5*q9)/(p3*p4)$

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 

q10

The lexicographical ordering of unknowns is changed
because q10 has to be non-zero, giving q10 a low priority.
Old ordering: q12,q10,q9,q8,p5,p3,p4
New ordering: q12,q9,q8,q10,p5,p3,p4

New level : 1.1.1.2.1.1.1.1.2.2.
CRACK is now called with the new equation e_468 : 
0=7*p4 - p5


Step 708: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 21 terms

e_290 is a consequence of e_311.
e_215 is a consequence of e_311.
Substitution of p4 by an expression in 
p5 found in e_468 : 
    1
p4=---*p5
    7


Step 709: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 22 terms

e_385 is a consequence of e_376.
Substitution of q8 by an expression in 
q9, p5, p3 found in e_32 : 10 factors in 3 terms

Step 710: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 23 terms

Substitution of q12 by an expression in 
q9, p5, p3 found in e_376 : 10 factors in 3 terms

Step 711: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 712: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 713: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 714: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 715: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 716: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 717: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
contradiction : 
          2
0=33614*p3

Eliminate 
p5

from e_364 and e_393. e_364: 

          2         2
0=29645*p3  + 117*p5

is replaced by e_342: 

0=1


This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p3


The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 

q17

The lexicographical ordering of unknowns is changed
because q17 has to be non-zero, giving q17 a low priority.
Old ordering: q17,q15,q12,q10,q9,q8,q7,p5,p3,p4
New ordering: q15,q12,q10,q9,q8,q7,q17,p5,p3,p4

New level : 1.1.1.2.1.1.1.1.3.
CRACK is now called with the new equation e_403 : 
0=p4 - 3*p5


Step 718: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 

q10

The lexicographical ordering of unknowns is changed
because q10 has to be non-zero, giving q10 a low priority.
Old ordering: q15,q12,q10,q9,q8,q7,q17,p5,p3,p4
New ordering: q15,q12,q9,q8,q7,q10,q17,p5,p3,p4

e_419 is a consequence of e_415.
Substitution of p4 by an expression in 
p5 found in e_403 : 
p4=3*p5


Step 719: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 33 terms

Substitution of q9 by an expression in 
q7 found in e_406 : 
q9= - q7


Step 720: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 

q17


The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 27 terms

Substitution of q17 by an expression in 
q10 found in e_408 : 
q17= - 40*q10


Step 721: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 25 terms

Substitution of q15 by an expression in 
q10, p5, p3 found in e_138 : 11 factors in 3 terms

Step 722: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 26 terms

e_307 is a consequence of e_414.
Substitution of q8 by an expression in 
q7, p5, p3 found in e_416 : 10 factors in 3 terms

Step 723: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 27 terms

Substitution of q12 by an expression in 
q7, p5, p3 found in e_414 : 11 factors in 3 terms

Step 724: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 725: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 726: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 727: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 728: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 729: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 730: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 731: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 732: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 733: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
contradiction : 
   2880    2
0=------*p3
   199

Eliminate 
p5

from e_369 and e_311. e_369: 

       2         2
0=71*p3  + 351*p5

is replaced by e_323: 

0=1


This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

q18

The lexicographical ordering of unknowns is changed
because q18 has to be non-zero, giving q18 a low priority.
Old ordering: q18,q17,q15,q12,q10,q9,q8,q7,p5,p3,p4
New ordering: q17,q15,q12,q10,q9,q8,q7,q18,p5,p3,p4

New level : 1.1.1.2.1.1.1.2.
CRACK is now called with the new equation e_62 : 
    2
0=p3  + 3*p4*p5


Step 734: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 45 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 41 terms
*** Garbage collection starting 
*** GC 334  3-Oct-2003 05:29:03, 40 ms (0%), 1003697 occupied, 23996254 free

Substitution of p5 by an expression in 
p3, p4 found in e_62 : 
        1    2
     - ---*p3
        3
p5=------------
        p4


Step 735: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 37 terms

e_133 is a consequence of e_280.
Substitution of q15 by an expression in 
q17, q10, p3, p4 found in e_18 : 10 factors in 3 terms

Step 736: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 737: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 738: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_403 and e_407. e_403: 
 3 terms, 9 factors, with derivatives of functions of all variables: 

            2   2
 (q17,q10,p3 ,p4 )

is replaced by e_421: 

           2        2
0=q10*(5*p3  + 21*p4 )


Step 739: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_205 and e_405. e_405: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

            3      2
 (q17,q10,p3 ,p3,p4 )

is replaced by e_423: 

            2     2
0=q10*p3*(p3  + p4 )


Step 740: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 741: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 742: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 743: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 744: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 745: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 746: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 747: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 748: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 749: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 750: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 751: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 752: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_432 and e_221. e_221: 
 3 terms, 15 factors, with derivatives of functions of all variables: 

            4   2   4   2
 (q17,q10,p3 ,p3 ,p4 ,p4 )

is replaced by e_392: 

0=q10

e_421,e_290,e_32,e_425 are consequences of e_392

Step 753: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 26 terms
e_228 is a consequence of e_280
e_430,e_432 are consequences of e_5

Substitution of q10 found in e_392 : 
q10=0


Step 754: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : 
The list of inequalities got extended by: 

p3

shortening by 2 terms
e_280 is a consequence of e_358

Step 755: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 15 terms

Substitution of q17 found in e_5 : 
q17=0


leads to a contradiction in : 10 factors in 3 terms

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p3 + 3*p6


New level : 1.1.1.2.1.1.2.
CRACK is now called with the new equation e_280 : 
0=p4*q18 - p6*q17


Step 756: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 51 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 47 terms

e_282 is a consequence of e_352.
e_307 is a consequence of e_53.
Substitution of q18 by an expression in 
q17, p6, p4 found in e_280 : 
     p6*q17
q18=--------
       p4


Step 757: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_53 and e_394. e_53: 
 10 terms, 40 factors, with derivatives of functions of all variables: 

                2      2      3   2
 (q17,q15,q10,p6 ,p6,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_323: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

               2      2
 (q15,q10,p6,p3 ,p3,p4 ,p4)


Step 758: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_255 and e_366. e_366: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                      2      3   2
 (q17,q15,q10,p6,p5,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_215: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                  2
 (q15,q10,p5,p3,p4 ,p4)


Step 759: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q15

from e_215 and e_382. e_382: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                      2      3   2
 (q17,q15,q10,p6,p5,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_221: 
 10 terms, 40 factors, with derivatives of functions of all variables: 

                  2      3   2
 (q17,q10,p6,p5,p3 ,p3,p4 ,p4 ,p4)


Step 760: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 335  3-Oct-2003 05:29:06, 40 ms (0%), 1008879 occupied, 23991073 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_352 we get the alternative equations : 
0=q17


0=p3*p4 + p5*p6


New level : 1.1.1.2.1.1.2.1.
CRACK is now called with the new equation e_364 : 
0=q17

e_306,e_133 are consequences of e_364

Step 761: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 31 terms

e_406 is a consequence of e_405.
Substitution of q17 found in e_364 : 
q17=0


Step 762: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q15

from e_396 and e_407. e_407: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                  2      2
 (q15,q10,p6,p5,p3 ,p3,p4 ,p4)

is replaced by e_32: 
(#) 6 terms, 19 factors, with derivatives of functions of all variables: 

              2      3   2
 (q10,p6,p5,p3 ,p3,p4 ,p4 ,p4)


Step 763: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q15

from e_396 and e_410. e_410: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

            2         2      3   2
 (q15,q10,p6 ,p6,p5,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_159: 
(#) 7 terms, 22 factors, with derivatives of functions of all variables: 

        2         2      3   2
 (q10,p6 ,p6,p5,p3 ,p3,p4 ,p4 ,p4)


Step 764: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_399 we get the alternative equations : 
0=q10

9 factors in 4 terms

New level : 1.1.1.2.1.1.2.1.1.
CRACK is now called with the new equation e_107 : 
0=q10

e_159,e_403,e_32,e_397,e_398,e_400 are consequences of e_107

Step 765: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 15 terms

e_20 is a consequence of e_342.
e_280 is a consequence of e_313.
Substitution of q10 found in e_107 : 
q10=0


Step 766: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms
e_313,e_307,e_11,e_340,e_205,e_282,e_157,e_252,e_342 are consequences of e_392

Step 767: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 9 terms

Substitution of q15 found in e_392 : 
q15=0


Step 768: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

Substitution of q12 by an expression in 
q9, q8, p5, p3, p4 found in e_229 : 17 factors in 4 terms

Step 769: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_393 we get the alternative equations : 
0=p4 - p5

8 factors in 3 terms

The list of inequalities got extended by: 

p5

The lexicographical ordering of unknowns is changed
because p5 has to be non-zero, giving p5 a low priority.
Old ordering: q9,q8,q7,p6,p5,p3,p4
New ordering: q9,q8,q7,p6,p3,p5,p4

New level : 1.1.1.2.1.1.2.1.1.1.
CRACK is now called with the new equation e_413 : 
0=p4 - p5


Step 770: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

1


The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 8 terms

Substitution of p4 by an expression in 
p5 found in e_413 : 
p4=p5


Step 771: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 12 terms

Substitution of q7 by an expression in 
q9, q8, p6, p3, p5 found in e_310 : 23 factors in 6 terms

Step 772: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization : 
factorizing e_369 we get the alternative equations : 
0=p3 + p6

15 factors in 5 terms

New level : 1.1.1.2.1.1.2.1.1.1.1.
CRACK is now called with the new equation e_374 : 
0=p3 + p6


Step 773: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p3


The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 6 terms

Substitution of p6 by an expression in 
p3 found in e_374 : 
p6= - p3



>>>>>>>>> Solution of level 1.1.1.2.1.1.2.1.1.1.1. : 
no equations


Non-vanishing expressions: p6,p3,p4,p5

g0097*q8 - 4*g0098*q9 - g0099*q8 - 2*g0102*q9 - 2*g0103*q8 + 2*g0104*q9


4*g0012*q9 + g0013*q8 + 2*g0016*q9 + 2*g0017*q8 - 2*g0018*q9 + 2*g0024*p5

 + 2*g0025*p5 + 2*g0026*p3


g0064*q8 - 4*g0065*q9 - g0066*q8 - 2*g0069*q9 - 2*g0070*q8 + 2*g0071*q9

 + 2*g0078*p3 - 2*g0079*p5 - 2*g0080*p5 - 2*g0081*p3


g0037*q8 - 4*g0038*q9 - 2*g0041*q9 - 2*g0042*q8 + 2*g0043*q9 + 2*g0049*p3

 - 2*g0050*p5 - 2*g0051*p3


g0113*p3 - g0114*p5 - g0115*p5 - g0116*p3


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


        1
q14= - ---*q8
        2


q13=2*q9


     1
q12=---*q8
     2


q11=0


q10=0

q9, q8, 
q7= - q9


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


p6= - p3

p5, 
p4=p5

p3, 
p2=0


p1=0


with 41 terms
no equations
4 constants : p3,p5,q8,q9
The equation: 

f =D f*D D f*p3 + D f*f *p5 + D D f*D f*p5 - D f*f *p3
 t  2   1 2        2   x       1 2   1        1   x
The symmetry: 
           2             1       2
f = - (D f) *D D f*q9 + ---*(D f) *f *q8 + D f*D D f*D f*q8 + 2*D f*D f*f *q9
 s      2     1 2        2    2     x       2   1 2   1          2   1   x

              2       1       2
 + D D f*(D f) *q9 - ---*(D f) *f *q8
    1 2    1          2    1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,f(1))
)*d(1,f(1))*p5 - d(1,f(1))*df(f(1),x)*p3$
The symmetry: 
df(f(1),s)= - d(2,f(1))**2*d(1,d(2,f(1)))*q9 + 1/2*d(2,f(1))**2*df(f(1),x)*q8 + 
d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*q8 + 2*d(2,f(1))*d(1,f(1))*df(f(1),x)*q9 + d(
1,d(2,f(1)))*d(1,f(1))**2*q9 - 1/2*d(1,f(1))**2*df(f(1),x)*q8$

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p3 + p6


New level : 1.1.1.2.1.1.2.1.1.1.2.
CRACK is now called with the new equation e_374 : 15 factors in 5 terms

Step 774: 
Hot list of urgent steps : 
Step 775: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms : 
for the substitution of q9 by e_374 we have to consider the case 0=e_172: 
    2               2
0=p3  - p3*p6 - 2*p5

The coefficient to be set = 0 in the first subcase is:

e_172 : 
    2               2
0=p3  - p3*p6 - 2*p5


New level : 1.1.1.2.1.1.2.1.1.1.2.1.
Step 776: 
Hot list of urgent steps : 
Step 777: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_34 we get the alternative equations : 
0=q8


0=p3 - p6


New level : 1.1.1.2.1.1.2.1.1.1.2.1.1.
CRACK is now called with the new equation e_355 : 
0=q8


Step 778: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 7 terms

q9

The lexicographical ordering of unknowns is changed
because q9 has to be non-zero, giving q9 a low priority.
Old ordering: q9,q8,p6,p3,p5
New ordering: q8,q9,p6,p3,p5

Substitution of q8 found in e_355 : 
q8=0


Step 779: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms : 
The list of inequalities got extended by: 

p3


for the substitution of p6 by e_172 we have to consider the case 0=e_358: 
0= - p3

The coefficient to be set = 0 in the first subcase is:

e_358 : 
0=p3


New level : 1.1.1.2.1.1.2.1.1.1.2.1.1.1.
Step 780: 
Hot list of urgent steps : 
contradiction from the substitution:
p3=0

because of the non-vanishing expression:
p3


Time: 0 ms

Time: 0 ms

Time: 0 ms

New level : 1.1.1.2.1.1.2.1.1.1.2.1.1.2.
now back to the substitution of p6 by e_172
The list of inequalities got extended by: 

p3 + p5


p3 - p5


The list of inequalities got extended by: 

    2       2
2*p3  - 3*p5


The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 5 terms

Substitution of p6 by an expression in 
p3, p5 found in e_172 : 
      2       2
    p3  - 2*p5
p6=-------------
        p3



>>>>>>>>> Solution of level 1.1.1.2.1.1.2.1.1.1.2.1.1.2. : 
no equations


Non-vanishing expressions: p5,p4,q9,p3

        2              3                2              2           3
g0097*p3 *p5 - g0097*p5  + 2*g0098*p3*p5  + g0102*p3*p5  - g0104*p3


          2              2              2              3           3
2*g0012*p5 *q9 + g0016*p5 *q9 - g0018*p3 *q9 + g0024*p5  + g0025*p5

              2
 + g0026*p3*p5


        2                 3                   2                 2
g0064*p3 *p5*q9 - g0064*p5 *q9 + 2*g0065*p3*p5 *q9 + g0069*p3*p5 *q9

           3              2   2             4              3              3
 - g0071*p3 *q9 + g0078*p3 *p5  - 2*g0078*p5  + g0079*p3*p5  + g0080*p3*p5

           2   2
 + g0081*p3 *p5


        2                 3                   2                 2
g0037*p3 *p5*q9 - g0037*p5 *q9 + 2*g0038*p3*p5 *q9 + g0041*p3*p5 *q9

           3              2   2             4              3           2   2
 - g0043*p3 *q9 + g0049*p3 *p5  - 2*g0049*p5  + g0050*p3*p5  + g0051*p3 *p5


        2             2                                       2
g0113*p3  - 2*g0113*p5  + g0114*p3*p5 + g0115*p3*p5 + g0116*p3


    2       2
2*p3  - 3*p5


p3 + p5


p3 - p5


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


       2        2
     p3 *q9 - p5 *q9
q14=-----------------
          p3*p5


q13=2*q9


q12=0


q11=0


q10=0

q9, 
q8=0


         2
     - p3 *q9
q7=-----------
         2
       p5


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


      2       2
    p3  - 2*p5
p6=-------------
        p3

p5, 
p4=p5

p3, 
p2=0


p1=0


with 42 terms
no equations
3 constants : p3,p5,q9
The equation: 

                2                                             2              2
    D f*D D f*p3  + D f*f *p3*p5 + D D f*D f*p3*p5 + D f*f *p3  - 2*D f*f *p5
     2   1 2         2   x          1 2   1           1   x          1   x
f =----------------------------------------------------------------------------
 t                                      p3
The symmetry: 
            2         3                        2                 2      2
f =( - (D f) *D D f*p3 *q9 + 2*D f*D f*f *p3*p5 *q9 + D D f*(D f) *p3*p5 *q9
 s       2     1 2              2   1   x              1 2    1

            2      2              2      3           2
     + (D f) *f *p3 *p5*q9 - (D f) *f *p5 *q9)/(p3*p5 )
         1     x               1     x
And now in machine readable form:

The system: 

df(f(1),t)=(d(2,f(1))*d(1,d(2,f(1)))*p3**2 + d(2,f(1))*df(f(1),x)*p3*p5 + d(1,d(
2,f(1)))*d(1,f(1))*p3*p5 + d(1,f(1))*df(f(1),x)*p3**2 - 2*d(1,f(1))*df(f(1),x)*
p5**2)/p3$
The symmetry: 
df(f(1),s)=( - d(2,f(1))**2*d(1,d(2,f(1)))*p3**3*q9 + 2*d(2,f(1))*d(1,f(1))*df(f
(1),x)*p3*p5**2*q9 + d(1,d(2,f(1)))*d(1,f(1))**2*p3*p5**2*q9 + d(1,f(1))**2*df(f
(1),x)*p3**2*p5*q9 - d(1,f(1))**2*df(f(1),x)*p5**3*q9)/(p3*p5**2)$

Time: 0 ms

Time: 0 ms

Time: 0 ms

The list of inequalities got extended by: 

q8


New level : 1.1.1.2.1.1.2.1.1.1.2.1.2.
CRACK is now called with the new equation e_355 : 
0=p3 - p6


Step 781: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p3


The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 9 terms

Substitution of p6 by an expression in 
p3 found in e_355 : 
p6=p3


leads to a contradiction in : 
    2               2
0=p3  - p3*p6 - 2*p5


This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 0 ms

New level : 1.1.1.2.1.1.2.1.1.1.2.2.
now back to the substitution of q9 by e_374
The list of inequalities got extended by: 

  2               2
p3  - p3*p6 - 2*p5


Step 782: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 14 terms

q8


Substitution of q9 by an expression in 
q8, p6, p3, p5 found in e_374 : 12 factors in 3 terms


>>>>>>>>> Solution of level 1.1.1.2.1.1.2.1.1.1.2.2. : 
no equations


Non-vanishing expressions: q8,p4,p5

                        2           2
g0097*p3*p6 + 2*g0097*p5  - g0097*p6  + 4*g0098*p3*p5 - 4*g0098*p5*p6

           2                           2
 + g0099*p3  - g0099*p3*p6 - 2*g0099*p5  + 2*g0102*p3*p5 - 2*g0102*p5*p6

             2                             2
 + 2*g0103*p3  - 2*g0103*p3*p6 - 4*g0103*p5  - 4*g0104*p3*p5


                                              2
4*g0012*p3*p5*q8 - 4*g0012*p5*p6*q8 + g0013*p3 *q8 - g0013*p3*p6*q8

             2                                                      2
 - 2*g0013*p5 *q8 + 2*g0016*p3*p5*q8 - 2*g0016*p5*p6*q8 + 2*g0017*p3 *q8

                                2                                   2
 - 2*g0017*p3*p6*q8 - 4*g0017*p5 *q8 - 4*g0018*p3*p5*q8 + 2*g0024*p3 *p5

                                3             2
 - 2*g0024*p3*p5*p6 - 4*g0024*p5  + 2*g0025*p3 *p5 - 2*g0025*p3*p5*p6

             3             3             2                   2
 - 4*g0025*p5  + 2*g0026*p3  - 2*g0026*p3 *p6 - 4*g0026*p3*p5

107 factors in 26 terms

                           2              2
g0037*p3*p6*q8 + 2*g0037*p5 *q8 - g0037*p6 *q8 + 4*g0038*p3*p5*q8

                                                                      2
 - 4*g0038*p5*p6*q8 + 2*g0041*p3*p5*q8 - 2*g0041*p5*p6*q8 + 2*g0042*p3 *q8

                                2                                   2
 - 2*g0042*p3*p6*q8 - 4*g0042*p5 *q8 - 4*g0043*p3*p5*q8 + 2*g0049*p3 *p6

                2             2                2
 - 2*g0049*p3*p6  - 4*g0049*p5 *p6 + 2*g0050*p3 *p5 - 2*g0050*p3*p5*p6

             3             3             2                   2
 - 4*g0050*p5  + 2*g0051*p3  - 2*g0051*p3 *p6 - 4*g0051*p3*p5


g0113*p6 + g0114*p5 + g0115*p5 + g0116*p3


p3 + 3*p6


p3 + p6


  2               2
p3  - p3*p6 - 2*p5


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


      1               2       1    2
     ---*p3*p6*q8 + p5 *q8 - ---*p6 *q8
      2                       2
q14=------------------------------------
              2               2
            p3  - p3*p6 - 2*p5


     2*p3*p5*q8 - 2*p5*p6*q8
q13=-------------------------
         2               2
       p3  - p3*p6 - 2*p5


     1
q12=---*q8
     2


q11=0


q10=0


    p3*p5*q8 - p5*p6*q8
q9=---------------------
      2               2
    p3  - p3*p6 - 2*p5

q8, 
        - 2*p3*p5*q8
q7=---------------------
      2               2
    p3  - p3*p6 - 2*p5


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0

p6, p5, 
p4=p5

p3, 
p2=0


p1=0


with 45 terms
no equations
4 constants : p3,p5,p6,q8
The equation: 

f =D f*D D f*p3 + D f*f *p5 + D D f*D f*p5 + D f*f *p6
 t  2   1 2        2   x       1 2   1        1   x
The symmetry: 
              2                   1       2      2       1       2
f =( - 2*(D f) *D D f*p3*p5*q8 + ---*(D f) *f *p3 *q8 - ---*(D f) *f *p3*p6*q8
 s         2     1 2              2    2     x           2    2     x

            2      2                      2
     - (D f) *f *p5 *q8 + D f*D D f*D f*p3 *q8 - D f*D D f*D f*p3*p6*q8
         2     x           2   1 2   1            2   1 2   1

                         2
     - 2*D f*D D f*D f*p5 *q8 + 2*D f*D f*f *p3*p5*q8 - 2*D f*D f*f *p5*p6*q8
          2   1 2   1              2   1   x               2   1   x

                  2                       2             1       2
     + D D f*(D f) *p3*p5*q8 - D D f*(D f) *p5*p6*q8 + ---*(D f) *f *p3*p6*q8
        1 2    1                1 2    1                2    1     x

            2      2       1       2      2        2               2
     + (D f) *f *p5 *q8 - ---*(D f) *f *p6 *q8)/(p3  - p3*p6 - 2*p5 )
         1     x           2    1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,f(1))
)*d(1,f(1))*p5 + d(1,f(1))*df(f(1),x)*p6$
The symmetry: 
df(f(1),s)=( - 2*d(2,f(1))**2*d(1,d(2,f(1)))*p3*p5*q8 + 1/2*d(2,f(1))**2*df(f(1)
,x)*p3**2*q8 - 1/2*d(2,f(1))**2*df(f(1),x)*p3*p6*q8 - d(2,f(1))**2*df(f(1),x)*p5
**2*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3**2*q8 - d(2,f(1))*d(1,d(2,f(1)))*
d(1,f(1))*p3*p6*q8 - 2*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p5**2*q8 + 2*d(2,f(1))
*d(1,f(1))*df(f(1),x)*p3*p5*q8 - 2*d(2,f(1))*d(1,f(1))*df(f(1),x)*p5*p6*q8 + d(1
,d(2,f(1)))*d(1,f(1))**2*p3*p5*q8 - d(1,d(2,f(1)))*d(1,f(1))**2*p5*p6*q8 + 1/2*d
(1,f(1))**2*df(f(1),x)*p3*p6*q8 + d(1,f(1))**2*df(f(1),x)*p5**2*q8 - 1/2*d(1,f(1
))**2*df(f(1),x)*p6**2*q8)/(p3**2 - p3*p6 - 2*p5**2)$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p4 - p5


New level : 1.1.1.2.1.1.2.1.1.2.
CRACK is now called with the new equation e_413 : 8 factors in 3 terms

Step 783: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 12 terms
e_369 is a consequence of e_310

Substitution of q7 by an expression in 
q9, q8, p3, p4 found in e_413 : 7 factors in 3 terms

Step 784: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms : 
for the substitution of q8 by e_310 we have to consider the case 0=e_407: 
0=( - p4)*(p3 - p6)

The coefficient to be set = 0 in the first subcase is:

e_407 : 
0=p3 - p6


New level : 1.1.1.2.1.1.2.1.1.2.1.
Step 785: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p3


The list of inequalities got extended by: 

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q9,q8,p6,p5,p3,p4
New ordering: q9,q8,p5,p6,p3,p4

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 11 terms

Substitution of p6 by an expression in 
p3 found in e_407 : 
p6=p3


Step 786: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_410 we get the alternative equations : 
0=q9


0=p4 + p5


New level : 1.1.1.2.1.1.2.1.1.2.1.1.
CRACK is now called with the new equation e_185 : 
0=q9


Step 787: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 4 terms

q8


Substitution of q9 found in e_185 : 
q9=0



>>>>>>>>> Solution of level 1.1.1.2.1.1.2.1.1.2.1.1. : 
no equations


Non-vanishing expressions: q8,p4,p3,p6

g0097*p4 - g0099*p5 - 2*g0103*p4 - 2*g0104*p3


g0064*p4*q8 - g0066*p5*q8 - 2*g0070*p4*q8 - 2*g0071*p3*q8 - 2*g0078*p3*p4

                             2
 - 2*g0079*p4*p5 - 2*g0080*p4  - 2*g0081*p3*p4


                                                                        2
g0037*p4*q8 - 2*g0042*p4*q8 - 2*g0043*p3*q8 - 2*g0049*p3*p4 - 2*g0050*p4

 - 2*g0051*p3*p4


                                                                        2
g0013*p5*q8 + 2*g0017*p4*q8 + 2*g0018*p3*q8 + 2*g0024*p4*p5 + 2*g0025*p4

 + 2*g0026*p3*p4


p4 - p5


g0113*p3 + g0114*p5 + g0115*p4 + g0116*p3


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


        1
q14= - ---*q8
        2


q13=0


      1
     ---*p5*q8
      2
q12=-----------
        p4


q11=0


q10=0


q9=0

q8, 
    p3*q8
q7=-------
     p4


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


p6=p3

p5, p4, p3, 
p2=0


p1=0


with 39 terms
no equations
4 constants : p3,p4,p5,q8
The equation: 

f =D f*D D f*p3 + D f*f *p5 + D D f*D f*p4 + D f*f *p3
 t  2   1 2        2   x       1 2   1        1   x
The symmetry: 
         2                1       2
f =((D f) *D D f*p3*q8 + ---*(D f) *f *p5*q8 + D f*D D f*D f*p4*q8
 s    2     1 2           2    2     x          2   1 2   1

        1       2
     - ---*(D f) *f *p4*q8)/p4
        2    1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,f(1))
)*d(1,f(1))*p4 + d(1,f(1))*df(f(1),x)*p3$
The symmetry: 
df(f(1),s)=(d(2,f(1))**2*d(1,d(2,f(1)))*p3*q8 + 1/2*d(2,f(1))**2*df(f(1),x)*p5*
q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p4*q8 - 1/2*d(1,f(1))**2*df(f(1),x)*p4*
q8)/p4$

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

q9

The lexicographical ordering of unknowns is changed
because q9 has to be non-zero, giving q9 a low priority.
Old ordering: q9,q8,p5,p3,p4
New ordering: q8,q9,p5,p3,p4

The list of inequalities got extended by: 

p5


New level : 1.1.1.2.1.1.2.1.1.2.1.2.
CRACK is now called with the new equation e_185 : 
0=p4 + p5


Step 788: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 8 terms

Substitution of p5 by an expression in 
p4 found in e_185 : 
p5= - p4



>>>>>>>>> Solution of level 1.1.1.2.1.1.2.1.1.2.1.2. : 
no equations


Non-vanishing expressions: p5,p4,p3,p6,q9

                           2                                 2
2*g0097*p3*p4*q9 - g0097*p4 *q8 + 2*g0099*p3*p4*q9 - g0099*p4 *q8

             2                2                2
 + 2*g0102*p4 *q9 + 2*g0103*p4 *q8 - 2*g0104*p3 *q9 + 2*g0104*p3*p4*q8


                           2                                 2
2*g0064*p3*p4*q9 - g0064*p4 *q8 + 2*g0066*p3*p4*q9 - g0066*p4 *q8

             2                2                2
 + 2*g0069*p4 *q9 + 2*g0070*p4 *q8 - 2*g0071*p3 *q9 + 2*g0071*p3*p4*q8

                2             3             3                2
 + 2*g0078*p3*p4  - 2*g0079*p4  + 2*g0080*p4  + 2*g0081*p3*p4


                           2                2                2
2*g0037*p3*p4*q9 - g0037*p4 *q8 + 2*g0041*p4 *q9 + 2*g0042*p4 *q8

             2                                      2             3
 - 2*g0043*p3 *q9 + 2*g0043*p3*p4*q8 + 2*g0049*p3*p4  + 2*g0050*p4

                2
 + 2*g0051*p3*p4


g0113*p3 - g0114*p4 + g0115*p4 + g0116*p3


                           2                2                2
2*g0013*p3*p4*q9 - g0013*p4 *q8 + 2*g0016*p4 *q9 + 2*g0017*p4 *q8

             2                                   3             3
 - 2*g0018*p3 *q9 + 2*g0018*p3*p4*q8 - 2*g0024*p4  + 2*g0025*p4

                2
 + 2*g0026*p3*p4


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


              1
     p3*q9 - ---*p4*q8
              2
q14=-------------------
            p4


q13=0


              1
     p3*q9 - ---*p4*q8
              2
q12=-------------------
            p4


q11=0


q10=0

q9, q8, 
         2
     - p3 *q9 + p3*p4*q8
q7=----------------------
              2
            p4


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


p6=p3


p5= - p4

p4, p3, 
p2=0


p1=0


with 43 terms
no equations
4 constants : p3,p4,q8,q9
The equation: 

f =D f*D D f*p3 - D f*f *p4 + D D f*D f*p4 + D f*f *p3
 t  2   1 2        2   x       1 2   1        1   x
The symmetry: 
            2         2           2                       2
f =( - (D f) *D D f*p3 *q9 + (D f) *D D f*p3*p4*q8 + (D f) *f *p3*p4*q9
 s       2     1 2             2     1 2               2     x

        1       2      2                      2                 2   2
     - ---*(D f) *f *p4 *q8 + D f*D D f*D f*p4 *q8 + D D f*(D f) *p4 *q9
        2    2     x           2   1 2   1            1 2    1

            2                1       2      2       2
     + (D f) *f *p3*p4*q9 - ---*(D f) *f *p4 *q8)/p4
         1     x             2    1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 - d(2,f(1))*df(f(1),x)*p4 + d(1,d(2,f(1))
)*d(1,f(1))*p4 + d(1,f(1))*df(f(1),x)*p3$
The symmetry: 
df(f(1),s)=( - d(2,f(1))**2*d(1,d(2,f(1)))*p3**2*q9 + d(2,f(1))**2*d(1,d(2,f(1))
)*p3*p4*q8 + d(2,f(1))**2*df(f(1),x)*p3*p4*q9 - 1/2*d(2,f(1))**2*df(f(1),x)*p4**
2*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p4**2*q8 + d(1,d(2,f(1)))*d(1,f(1))**2
*p4**2*q9 + d(1,f(1))**2*df(f(1),x)*p3*p4*q9 - 1/2*d(1,f(1))**2*df(f(1),x)*p4**2
*q8)/p4**2$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 10 ms

New level : 1.1.1.2.1.1.2.1.1.2.2.
now back to the substitution of q8 by e_310
The list of inequalities got extended by: 

p3 - p6


Step 789: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 20 terms

q9

The lexicographical ordering of unknowns is changed
because q9 has to be non-zero, giving q9 a low priority.
Old ordering: q9,q8,p6,p5,p3,p4
New ordering: q8,q9,p6,p5,p3,p4

Substitution of q8 by an expression in 
q9, p6, p5, p3, p4 found in e_310 : 15 factors in 5 terms


>>>>>>>>> Solution of level 1.1.1.2.1.1.2.1.1.2.2. : 
no equations


Non-vanishing expressions: q9,p4

                      2                         2
g0097*p3*p6 + g0097*p4  + g0097*p4*p5 - g0097*p6  + 2*g0098*p3*p4

                                                           2
 + 2*g0098*p3*p5 - 2*g0098*p4*p6 - 2*g0098*p5*p6 + g0099*p3  - g0099*p3*p6

                         2                                             2
 - g0099*p4*p5 - g0099*p5  + 2*g0102*p3*p4 - 2*g0102*p4*p6 + 2*g0103*p3

                             2
 - 2*g0103*p3*p6 - 2*g0103*p4  - 2*g0103*p4*p5 - 2*g0104*p3*p4 - 2*g0104*p3*p5


2*g0012*p3*p4*q9 + 2*g0012*p3*p5*q9 - 2*g0012*p4*p6*q9 - 2*g0012*p5*p6*q9

           2                                                2
 + g0013*p3 *q9 - g0013*p3*p6*q9 - g0013*p4*p5*q9 - g0013*p5 *q9

                                                   2
 + 2*g0016*p3*p4*q9 - 2*g0016*p4*p6*q9 + 2*g0017*p3 *q9 - 2*g0017*p3*p6*q9

             2
 - 2*g0017*p4 *q9 - 2*g0017*p4*p5*q9 - 2*g0018*p3*p4*q9 - 2*g0018*p3*p5*q9

                                                      2             2
 + 2*g0024*p3*p4*p5 - 2*g0024*p4*p5*p6 + 2*g0025*p3*p4  - 2*g0025*p4 *p6

             2
 + 2*g0026*p3 *p4 - 2*g0026*p3*p4*p6

122 factors in 28 terms

                         2                               2
g0037*p3*p6*q9 + g0037*p4 *q9 + g0037*p4*p5*q9 - g0037*p6 *q9 + 2*g0038*p3*p4*q9

 + 2*g0038*p3*p5*q9 - 2*g0038*p4*p6*q9 - 2*g0038*p5*p6*q9 + 2*g0041*p3*p4*q9

                                2                                   2
 - 2*g0041*p4*p6*q9 + 2*g0042*p3 *q9 - 2*g0042*p3*p6*q9 - 2*g0042*p4 *q9

 - 2*g0042*p4*p5*q9 - 2*g0043*p3*p4*q9 - 2*g0043*p3*p5*q9 + 2*g0049*p3*p4*p6

                2                2             2                2
 - 2*g0049*p4*p6  + 2*g0050*p3*p4  - 2*g0050*p4 *p6 + 2*g0051*p3 *p4

 - 2*g0051*p3*p4*p6


p4 - p5


g0113*p6 + g0114*p5 + g0115*p4 + g0116*p3


p3 + 3*p6


p3 - p6


functions : 
q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


      1              1    2       1              1    2
     ---*p3*p6*q9 + ---*p4 *q9 + ---*p4*p5*q9 - ---*p6 *q9
      2              2            2              2
q14=-------------------------------------------------------
                         p3*p4 - p4*p6


     p4*q9 + p5*q9
q13=---------------
          p4


      1    2       1              1              1    2
     ---*p3 *q9 - ---*p3*p6*q9 - ---*p4*p5*q9 - ---*p5 *q9
      2            2              2              2
q12=-------------------------------------------------------
                         p3*p4 - p4*p6


q11=0


q10=0

q9, 
      2                   2
    p3 *q9 - p3*p6*q9 - p4 *q9 - p4*p5*q9
q8=---------------------------------------
                p3*p4 - p4*p6


     - p3*p4*q9 - p3*p5*q9
q7=------------------------
        p3*p4 - p4*p6


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0

p6, p5, p4, p3, 
p2=0


p1=0


with 51 terms
no equations
5 constants : p3,p4,p5,p6,q9
The equation: 

f =D f*D D f*p3 + D f*f *p5 + D D f*D f*p4 + D f*f *p6
 t  2   1 2        2   x       1 2   1        1   x
The symmetry: 
*** Garbage collection starting 
*** GC 336  3-Oct-2003 05:29:09, 30 ms (0%), 989700 occupied, 24010251 free
            2                       2                   1       2      2
f =( - (D f) *D D f*p3*p4*q9 - (D f) *D D f*p3*p5*q9 + ---*(D f) *f *p3 *q9
 s       2     1 2               2     1 2              2    2     x

        1       2                1       2                1       2      2
     - ---*(D f) *f *p3*p6*q9 - ---*(D f) *f *p4*p5*q9 - ---*(D f) *f *p5 *q9
        2    2     x             2    2     x             2    2     x

                       2                                               2
     + D f*D D f*D f*p3 *q9 - D f*D D f*D f*p3*p6*q9 - D f*D D f*D f*p4 *q9
        2   1 2   1            2   1 2   1              2   1 2   1

     - D f*D D f*D f*p4*p5*q9 + D f*D f*f *p3*p4*q9 + D f*D f*f *p3*p5*q9
        2   1 2   1              2   1   x             2   1   x

                                                              2
     - D f*D f*f *p4*p6*q9 - D f*D f*f *p5*p6*q9 + D D f*(D f) *p3*p4*q9
        2   1   x             2   1   x             1 2    1

                  2             1       2                1       2      2
     - D D f*(D f) *p4*p6*q9 + ---*(D f) *f *p3*p6*q9 + ---*(D f) *f *p4 *q9
        1 2    1                2    1     x             2    1     x

        1       2                1       2      2
     + ---*(D f) *f *p4*p5*q9 - ---*(D f) *f *p6 *q9)/(p3*p4 - p4*p6)
        2    1     x             2    1     x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,f(1))
)*d(1,f(1))*p4 + d(1,f(1))*df(f(1),x)*p6$
The symmetry: 
df(f(1),s)=( - d(2,f(1))**2*d(1,d(2,f(1)))*p3*p4*q9 - d(2,f(1))**2*d(1,d(2,f(1))
)*p3*p5*q9 + 1/2*d(2,f(1))**2*df(f(1),x)*p3**2*q9 - 1/2*d(2,f(1))**2*df(f(1),x)*
p3*p6*q9 - 1/2*d(2,f(1))**2*df(f(1),x)*p4*p5*q9 - 1/2*d(2,f(1))**2*df(f(1),x)*p5
**2*q9 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3**2*q9 - d(2,f(1))*d(1,d(2,f(1)))*
d(1,f(1))*p3*p6*q9 - d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p4**2*q9 - d(2,f(1))*d(1
,d(2,f(1)))*d(1,f(1))*p4*p5*q9 + d(2,f(1))*d(1,f(1))*df(f(1),x)*p3*p4*q9 + d(2,f
(1))*d(1,f(1))*df(f(1),x)*p3*p5*q9 - d(2,f(1))*d(1,f(1))*df(f(1),x)*p4*p6*q9 - d
(2,f(1))*d(1,f(1))*df(f(1),x)*p5*p6*q9 + d(1,d(2,f(1)))*d(1,f(1))**2*p3*p4*q9 - 
d(1,d(2,f(1)))*d(1,f(1))**2*p4*p6*q9 + 1/2*d(1,f(1))**2*df(f(1),x)*p3*p6*q9 + 1/
2*d(1,f(1))**2*df(f(1),x)*p4**2*q9 + 1/2*d(1,f(1))**2*df(f(1),x)*p4*p5*q9 - 1/2*
d(1,f(1))**2*df(f(1),x)*p6**2*q9)/(p3*p4 - p4*p6)$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

q10

The lexicographical ordering of unknowns is changed
because q10 has to be non-zero, giving q10 a low priority.
Old ordering: q15,q12,q10,q9,q8,q7,p6,p5,p3,p4
New ordering: q15,q12,q9,q8,q7,q10,p6,p5,p3,p4

New level : 1.1.1.2.1.1.2.1.2.
CRACK is now called with the new equation e_107 : 9 factors in 4 terms

Step 790: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 32 terms

e_20 is a consequence of e_398.
e_313 is a consequence of e_398.
Substitution of p5 by an expression in 
p6, p3, p4 found in e_107 : 10 factors in 4 terms

Step 791: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 792: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 793: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_398 and e_389. e_389: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

            2         2
 (q15,q10,p6 ,p6,p3,p4 ,p4)

is replaced by e_390: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

               2      2
 (q15,q10,p6,p3 ,p3,p4 ,p4)


Step 794: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 795: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_398 and e_312. e_312: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

            2         2
 (q15,q10,p6 ,p6,p3,p4 ,p4)

is replaced by e_392: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

               2      2
 (q15,q10,p6,p3 ,p3,p4 ,p4)


Step 796: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_398 and e_404. e_404: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

            2      2      3   2
 (q15,q10,p6 ,p6,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_393: 
(#) 6 terms, 10 factors, with derivatives of functions of all variables: 

               3   2      3   2
 (q15,q10,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)


Step 797: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_398 and e_382. e_382: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

            2      3   2      3   2
 (q15,q10,p6 ,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_306: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

               3   2      3   2
 (q15,q10,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)


Step 798: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_398 and e_366. e_366: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

            2      3   2      3   2
 (q15,q10,p6 ,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_406: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

               3   2      3   2
 (q15,q10,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)


Step 799: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_398 and e_53. e_53: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

            2      3   2      3   2
 (q15,q10,p6 ,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_364: 
(#) 6 terms, 10 factors, with derivatives of functions of all variables: 

               3   2      3   2
 (q15,q10,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)


e_364 is a consequence of e_205.
Step 800: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_398 and e_311. e_311: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

            2      3   2      3   2
 (q15,q10,p6 ,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_413: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

               3   2      3   2
 (q15,q10,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)


Step 801: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_398 and e_340. e_340: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

            2      3   2      3   2
 (q15,q10,p6 ,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_414: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

               3   2      3   2
 (q15,q10,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)


Step 802: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 42 terms

The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 36 terms

Substitution of q7 by an expression in 
q9, q8, p6, p3, p4 found in e_280 : 23 factors in 6 terms

Step 803: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_398 and e_342. e_342: 
 12 terms, 60 factors, with derivatives of functions of all variables: 

              2      4   3   2      4   3   2
 (q12,q9,q8,p6 ,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4)

is replaced by e_369: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

                 4   3   2      4   3   2
 (q12,q9,q8,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4)


Step 804: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q12

from e_157 and e_369. e_369: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

                 4   3   2      4   3   2
 (q12,q9,q8,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4)

is replaced by e_310: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

             4   3   2      4   3   2
 (q9,q8,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4)


Step 805: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 47 terms

The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 41 terms

Substitution of q12 by an expression in 
q9, q8, p6, p3, p4 found in e_157 : 31 factors in 7 terms

Step 806: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_398 and e_282. e_358 is added: 

     2     2       2     2
0=(p3  + p4 )*(9*p3  + p4 )


Step 807: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_358 and e_307. e_307: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

    2      4   3   2      4   2
 (p6 ,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 )

is replaced by e_353: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

    2      3   2      4   2
 (p6 ,p6,p3 ,p3 ,p3,p4 ,p4 )


Step 808: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_358 and e_11. e_11: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

    2      4   3   2      4   2
 (p6 ,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 )

is replaced by e_62: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

    2      3   2      4   2
 (p6 ,p6,p3 ,p3 ,p3,p4 ,p4 )


Step 809: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_358 and e_310. e_310: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

             4   3   2      4   3   2
 (q9,q8,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4)

is replaced by e_357: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

             3   2      4   3   2
 (q9,q8,p6,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4)


Step 810: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p3

from e_358 and e_282. e_282: 
(#) 9 terms, 12 factors, with derivatives of functions of all variables: 

    2      4   3   2      4   2
 (p6 ,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 )

is replaced by e_107: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

    2      3   2      4   2
 (p6 ,p6,p3 ,p3 ,p3,p4 ,p4 )


Step 811: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_398 and e_107. e_226 is added: 
(#) 12 terms, 20 factors, with derivatives of functions of all variables: 

    8   6   4   2   8   6   4   2
 (p3 ,p3 ,p3 ,p3 ,p4 ,p4 ,p4 ,p4 )


e_226 is a consequence of e_358.
Step 812: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_398 and e_353. e_290 is added: 
(#) 12 terms, 20 factors, with derivatives of functions of all variables: 

    8   6   4   2   8   6   4   2
 (p3 ,p3 ,p3 ,p3 ,p4 ,p4 ,p4 ,p4 )


e_290 is a consequence of e_358.
Step 813: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_398 and e_62. e_402 is added: 
(#) 12 terms, 20 factors, with derivatives of functions of all variables: 

    8   6   4   2   8   6   4   2
 (p3 ,p3 ,p3 ,p3 ,p4 ,p4 ,p4 ,p4 )


e_402 is a consequence of e_358.
Step 814: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_107 and e_353. e_401 is added: 

     2     2       2     2
0=(p3  + p4 )*(9*p3  + p4 )


e_401 is a consequence of e_358.
Step 815: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_107 and e_62. e_389 is added: 
(#) 12 terms, 20 factors, with derivatives of functions of all variables: 

    8   6   4   2   8   6   4   2
 (p3 ,p3 ,p3 ,p3 ,p4 ,p4 ,p4 ,p4 )


e_389 is a consequence of e_358.
Step 816: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_353 and e_62. e_390 is added: 
(#) 12 terms, 20 factors, with derivatives of functions of all variables: 

    8   6   4   2   8   6   4   2
 (p3 ,p3 ,p3 ,p3 ,p4 ,p4 ,p4 ,p4 )


e_390 is a consequence of e_358.
Step 817: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q15

from e_391 and e_393. e_312 is added: 
(#) 8 terms, 12 factors, with derivatives of functions of all variables: 

    2      4   3   2      4   2
 (p6 ,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 )


Step 818: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p3

from e_358 and e_312. e_312: 
(#) 8 terms, 12 factors, with derivatives of functions of all variables: 

    2      4   3   2      4   2
 (p6 ,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 )

is replaced by e_352: 
(#) 6 terms, 10 factors, with derivatives of functions of all variables: 

    2      3   2      4   2
 (p6 ,p6,p3 ,p3 ,p3,p4 ,p4 )


Step 819: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_398 and e_352. e_382 is added: 
(#) 6 terms, 16 factors, with derivatives of functions of all variables: 

    6   4   2   6   4   2
 (p3 ,p3 ,p3 ,p4 ,p4 ,p4 )


Step 820: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_358 and e_382. 
Step 821: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_352 and e_107. e_53 is added: 
(#) 8 terms, 28 factors, with derivatives of functions of all variables: 

    8   6   4   2   8   6   4   2
 (p3 ,p3 ,p3 ,p3 ,p4 ,p4 ,p4 ,p4 )


Step 822: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_358 and e_53. 
Step 823: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_382 and e_53. 
Step 824: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_352 and e_353. e_311 is added: 
(#) 8 terms, 28 factors, with derivatives of functions of all variables: 

    8   6   4   2   8   6   4   2
 (p3 ,p3 ,p3 ,p3 ,p4 ,p4 ,p4 ,p4 )


Step 825: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_358 and e_311. 
Step 826: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_382 and e_311. 
Step 827: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_311 and e_53. 
Step 828: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_352 and e_62. e_415 is added: 
(#) 8 terms, 28 factors, with derivatives of functions of all variables: 

    8   6   4   2   8   6   4   2
 (p3 ,p3 ,p3 ,p3 ,p4 ,p4 ,p4 ,p4 )


Step 829: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_358 and e_415. 
Step 830: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_382 and e_415. 
Step 831: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_415 and e_311. 
Step 832: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_415 and e_53. 
Step 833: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q15

from e_391 and e_205. e_417 is added: 
(#) 8 terms, 12 factors, with derivatives of functions of all variables: 

    2      4   3   2      4   2
 (p6 ,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 )


Step 834: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_352 and e_417. e_417: 
(#) 8 terms, 12 factors, with derivatives of functions of all variables: 

    2      4   3   2      4   2
 (p6 ,p6,p3 ,p3 ,p3 ,p3,p4 ,p4 )

is replaced by e_418: 

     2     2       2        2
0=(p3  + p4 )*(9*p3  - 80*p4 )


Step 835: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_418 and e_358. 
Step 836: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_418 and e_382. 
Step 837: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_418 and e_415. 
Step 838: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_418 and e_311. 
Step 839: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_418 and e_53. 
Step 840: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q15

from e_391 and e_396. e_420 is added: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

    2      3   2      2
 (p6 ,p6,p3 ,p3 ,p3,p4 )

*** Garbage collection starting 
*** GC 337  3-Oct-2003 05:29:13, 40 ms (0%), 1007693 occupied, 23992257 free

Step 841: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_398 and e_420. e_421 is added: 

     2     2     2       2
0=(p3  + p4 )*(p3  + 9*p4 )


Step 842: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_421 and e_418. 
Step 843: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_421 and e_358. 
Step 844: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_421 and e_382. 
Step 845: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_421 and e_415. 
Step 846: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_421 and e_311. 
Step 847: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_421 and e_53. 
Step 848: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_420 and e_107. e_423 is added: 
(#) 6 terms, 16 factors, with derivatives of functions of all variables: 

    6   4   2   6   4   2
 (p3 ,p3 ,p3 ,p4 ,p4 ,p4 )


Step 849: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_421 and e_423. 
Step 850: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_418 and e_423. 
Step 851: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_358 and e_423. 
Step 852: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_423 and e_382. 
Step 853: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_423 and e_415. 
Step 854: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_423 and e_311. 
Step 855: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_423 and e_53. 
Step 856: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_420 and e_353. e_425 is added: 
(#) 6 terms, 16 factors, with derivatives of functions of all variables: 

    6   4   2   6   4   2
 (p3 ,p3 ,p3 ,p4 ,p4 ,p4 )


Step 857: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_421 and e_425. 
Step 858: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_418 and e_425. 
Step 859: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_358 and e_425. 
Step 860: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_425 and e_423. 
Step 861: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_425 and e_382. 
Step 862: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_425 and e_415. 
Step 863: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_425 and e_311. 
Step 864: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_425 and e_53. 
Step 865: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_352 and e_420. e_427 is added: 
(#) 8 terms, 28 factors, with derivatives of functions of all variables: 

    8   6   4   2   8   6   4   2
 (p3 ,p3 ,p3 ,p3 ,p4 ,p4 ,p4 ,p4 )


Step 866: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_421 and e_427. 
Step 867: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_418 and e_427. 
Step 868: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_358 and e_427. 
Step 869: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_425 and e_427. 
Step 870: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_423 and e_427. 
Step 871: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_382 and e_427. 
Step 872: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_427 and e_415. 
Step 873: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_427 and e_311. 
Step 874: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_427 and e_53. 
Step 875: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
p6

from e_420 and e_62. e_280 is added: 
(#) 8 terms, 29 factors, with derivatives of functions of all variables: 

    9   7   6   5   4   3   2      8   6   4   2
 (p3 ,p3 ,p3 ,p3 ,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4 )


Step 876: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_421 and e_280. 
Step 877: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_418 and e_280. 
Step 878: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_358 and e_280. 
Step 879: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_425 and e_280. 
Step 880: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_423 and e_280. 
Step 881: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_382 and e_280. 
Step 882: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_427 and e_280. 
Step 883: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_415 and e_280. 
Step 884: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_311 and e_280. 
Step 885: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
*** Garbage collection starting 
*** GC 338  3-Oct-2003 05:29:16, 30 ms (0%), 1013062 occupied, 23986886 free
 --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
p3

from e_53 and e_280. 
Step 886: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q15

from e_393 and e_205. e_393: 
(#) 6 terms, 10 factors, with derivatives of functions of all variables: 

               3   2      3   2
 (q15,q10,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_431: 

                 2     2
0=(p3 + 4*p6)*(p3  + p4 )


Step 887: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_431 and e_205. e_205: 
(#) 6 terms, 10 factors, with derivatives of functions of all variables: 

               3   2      3   2
 (q15,q10,p6,p3 ,p3 ,p3,p4 ,p4 ,p4)

is replaced by e_433: 

         2     2
0=q15*(p3  + p4 )


Step 888: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 889: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
The list of inequalities got extended by: 

p3

Eliminate 
p6

from e_431 and e_398. e_385 is added: 

    2     2
0=p3  + p4

e_280,e_53,e_311,e_415,e_427,e_382,e_423,e_425,e_352,e_358,e_418,e_421,e_431,
e_433 are consequences of e_385

Step 890: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 

p3 + 2*p6


q15

The lexicographical ordering of unknowns is changed
because q15 has to be non-zero, giving q15 a low priority.
Old ordering: q15,q9,q8,q10,p6,p3,p4
New ordering: q9,q8,q10,q15,p6,p3,p4

The list of inequalities got extended by: 
An expression with 54 terms

The list of inequalities got extended by: 
An expression with 45 terms

The list of inequalities got extended by: 
An expression with 48 terms

e_376 is a consequence of e_420.
e_392 is a consequence of e_420.
The list of inequalities got extended by: 

p6


Substitution of q10 by an expression in 
q15, p6, p3, p4 found in e_391 : 7 factors in 3 terms

Step 891: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 4 terms

Step 892: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 4 terms

Step 893: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 4 terms

Step 894: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_374 and e_172. e_172: 

      2     2       2
0=7*p3  + p4  - 6*p6

is replaced by e_34: 

    2     2
0=p3  + p4


e_34 is a consequence of e_385.
Step 895: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_374 and e_5. e_5: 

      2        2       2
0=5*p3  + 13*p4  + 8*p6

is replaced by e_132: 

    2     2
0=p3  + p4


e_132 is a consequence of e_385.
Step 896: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_374 and e_185. e_185: 

      2     2       2
0=7*p3  - p4  - 8*p6

is replaced by e_234: 

    2     2
0=p3  + p4


e_234 is a consequence of e_385.
Step 897: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_385 and e_398. e_398: 
 4 terms, 8 factors, with derivatives of functions of all variables: 

    2      2      2
 (p6 ,p6,p3 ,p3,p4 )

is replaced by e_193: 

            2       2
0=p3*p6 + p4  + 2*p6


Step 898: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 

  2       2
p4  + 2*p6


The list of inequalities got extended by: 

p3


The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 

p4 + p6


p4 - p6


The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 37 terms

e_385 is a consequence of e_374.
e_228 is a consequence of e_374.
e_420 is a consequence of e_374.
e_252 is a consequence of e_374.
e_107 is a consequence of e_374.
e_353 is a consequence of e_374.
e_435 is a consequence of e_374.
e_62 is a consequence of e_374.
e_357 is a consequence of e_374.
Substitution of p3 by an expression in 
p6, p4 found in e_193 : 
         2       2
     - p4  - 2*p6
p3=----------------
          p6


Step 899: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.1.2.1.1.2.1.2. : 
equations : 

e_374 : 
    2     2
0=p4  + p6



Non-vanishing expressions: p3,p4,q15,p6
180 factors in 37 terms
174 factors in 37 terms
208 factors in 44 terms
133 factors in 28 terms

p4 + p6


p4 - p6


             3           4           2   2             4             2   2
4*g0113*p4*p6  + g0114*p4  + g0114*p4 *p6  - 4*g0114*p6  + 4*g0115*p4 *p6

             3                   3
 - 4*g0116*p4 *p6 - 8*g0116*p4*p6


  2       2
p4  + 2*p6


functions : 
q27=0


q26=0


q25=0


         1    4        3    2   2        1    4
      - ---*p4 *q15 - ---*p4 *p6 *q15 - ---*p6 *q15
         6             2                 3
q24=------------------------------------------------
                              3
                         p4*p6


      1    2        5    2
     ---*p4 *q15 - ---*p6 *q15
      6             6
q23=---------------------------
                  2
                p6


         1    2        5    2
      - ---*p4 *q15 + ---*p6 *q15
         6             6
q22=------------------------------
                   2
                 p6


         1    4        3    2   2        1    4
      - ---*p4 *q15 - ---*p4 *p6 *q15 - ---*p6 *q15
         6             2                 3
q21=------------------------------------------------
                              3
                         p4*p6


q20=0


q19=0


q18=0


q17=0


         1    4           2   2        2    4
      - ---*p4 *q15 - 2*p4 *p6 *q15 - ---*p6 *q15
         3                             3
q16=----------------------------------------------
                             3
                        p4*p6

q15, 
         1    2       1              1    2
      - ---*p4 *q9 - ---*p4*p6*q8 - ---*p6 *q9
         2            2              2
q14=-------------------------------------------
                       p4*p6


      1    4       5    2   2        4
     ---*p4 *q9 + ---*p4 *p6 *q9 - p6 *q9
      4            4
q13=--------------------------------------
                     2   2
                   p4 *p6


      1    6       1    5          1    4   2       1    3   3
q12=(---*p4 *q9 + ---*p4 *p6*q8 - ---*p4 *p6 *q9 + ---*p4 *p6 *q8
      8            8               8                8

         5    2   4       1       5        6        3   3
      - ---*p4 *p6 *q9 - ---*p4*p6 *q8 - p6 *q9)/(p4 *p6 )
         4                2


      1    2        2    2
     ---*p4 *q15 - ---*p6 *q15
      3             3
q11=---------------------------
                  2
                p6


      - p4*q15
q10=-----------
        p6

q9, q8, 
q7

      5    4       1    3          17    2   2       1       3       1    4
   - ---*p4 *q9 - ---*p4 *p6*q8 - ----*p4 *p6 *q9 - ---*p4*p6 *q8 - ---*p6 *q9
      8            2               8                 2               2
=------------------------------------------------------------------------------
                                      2   2
                                    p4 *p6


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0

p6, 
     1    4    1    2   2     4
    ---*p4  + ---*p4 *p6  - p6
     4         4
p5=-----------------------------
                   2
              p4*p6

p4, 
         2       2
     - p4  - 2*p6
p3=----------------
          p6


p2=0


p1=0


with 74 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_374(2a)
5 constants : p4,p6,q8,q9,q15
The equation: 

                   3                       3    1           4
f =( - D f*D D f*p4 *p6 - 2*D f*D D f*p4*p6  + ---*D f*f *p4
 t      2   1 2              2   1 2            4   2   x

        1           2   2            4               2   2               3
     + ---*D f*f *p4 *p6  - D f*f *p6  + D D f*D f*p4 *p6  + D f*f *p4*p6 )/(p4
        4   2   x            2   x        1 2   1             1   x

      2
   *p6 )
The symmetry: 
     1                5           2                3   3
f =(---*D f  *D D f*p4 *p6*q15 - ---*D f  *D D f*p4 *p6 *q15
 s   3   2 2x  1 2                3   2 2x  1 2

        1             6                    4   2        2             2   4
     - ---*D f  *f *p4 *q15 - 2*D f  *f *p4 *p6 *q15 - ---*D f  *f *p4 *p6 *q15
        3   2 2x  x              2 2x  x                3   2 2x  x

        5       2         5          1       2         4   2
     - ---*(D f) *D D f*p4 *p6*q9 - ---*(D f) *D D f*p4 *p6 *q8
        8    2     1 2               2    2     1 2

        17       2         3   3       1       2         2   4
     - ----*(D f) *D D f*p4 *p6 *q9 - ---*(D f) *D D f*p4 *p6 *q8
        8     2     1 2                2    2     1 2

        1       2            5       1       2      6
     - ---*(D f) *D D f*p4*p6 *q9 + ---*(D f) *f *p4 *q9
        2    2     1 2               8    2     x

        1       2      5          1       2      4   2
     + ---*(D f) *f *p4 *p6*q8 - ---*(D f) *f *p4 *p6 *q9
        8    2     x              8    2     x

        1       2      3   3       5       2      2   4
     + ---*(D f) *f *p4 *p6 *q8 - ---*(D f) *f *p4 *p6 *q9
        8    2     x               4    2     x

        1       2         5           2      6       1                5
     - ---*(D f) *f *p4*p6 *q8 - (D f) *f *p6 *q9 + ---*D f*D D f  *p4 *p6*q15
        2    2     x               2     x           6   2   1 2 2x

        5                3   3                       3   3
     - ---*D f*D D f  *p4 *p6 *q15 + D f*D D f*D f*p4 *p6 *q8
        6   2   1 2 2x                2   1 2   1

        1               5          5               3   3
     + ---*D f*D f*f *p4 *p6*q9 + ---*D f*D f*f *p4 *p6 *q9
        4   2   1   x              4   2   1   x

                       5       1            6        3            4   2
     - D f*D f*f *p4*p6 *q9 - ---*D f*f  *p4 *q15 - ---*D f*f  *p4 *p6 *q15
        2   1   x              6   2   3x            2   2   3x

        1            2   4        1                6
     - ---*D f*f  *p4 *p6 *q15 - ---*D D f  *D f*p4 *q15
        3   2   3x                6   1 2 2x  1

        3                4   2        1                2   4
     - ---*D D f  *D f*p4 *p6 *q15 - ---*D D f  *D f*p4 *p6 *q15
        2   1 2 2x  1                 3   1 2 2x  1

                     4   2                  2   3   3                 3   3
     - D D f*D f  *p4 *p6 *q15 + D D f*(D f) *p4 *p6 *q9 + D f  *f *p4 *p6 *q15
        1 2   1 2x                1 2    1                  1 2x  x

        1       2      4   2       1       2      3   3
     - ---*(D f) *f *p4 *p6 *q9 - ---*(D f) *f *p4 *p6 *q8
        2    1     x               2    1     x

        1       2      2   4       1            5
     - ---*(D f) *f *p4 *p6 *q9 - ---*D f*f  *p4 *p6*q15
        2    1     x               6   1   3x

        5            3   3         3   3
     + ---*D f*f  *p4 *p6 *q15)/(p4 *p6 )
        6   1   3x
And now in machine readable form:

The system: 

df(f(1),t)=( - d(2,f(1))*d(1,d(2,f(1)))*p4**3*p6 - 2*d(2,f(1))*d(1,d(2,f(1)))*p4
*p6**3 + 1/4*d(2,f(1))*df(f(1),x)*p4**4 + 1/4*d(2,f(1))*df(f(1),x)*p4**2*p6**2 -
 d(2,f(1))*df(f(1),x)*p6**4 + d(1,d(2,f(1)))*d(1,f(1))*p4**2*p6**2 + d(1,f(1))*
df(f(1),x)*p4*p6**3)/(p4*p6**2)$
The symmetry: 
df(f(1),s)=(1/3*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p4**5*p6*q15 - 2/3*d(2,df(f(1),
x,2))*d(1,d(2,f(1)))*p4**3*p6**3*q15 - 1/3*d(2,df(f(1),x,2))*df(f(1),x)*p4**6*
q15 - 2*d(2,df(f(1),x,2))*df(f(1),x)*p4**4*p6**2*q15 - 2/3*d(2,df(f(1),x,2))*df(
f(1),x)*p4**2*p6**4*q15 - 5/8*d(2,f(1))**2*d(1,d(2,f(1)))*p4**5*p6*q9 - 1/2*d(2,
f(1))**2*d(1,d(2,f(1)))*p4**4*p6**2*q8 - 17/8*d(2,f(1))**2*d(1,d(2,f(1)))*p4**3*
p6**3*q9 - 1/2*d(2,f(1))**2*d(1,d(2,f(1)))*p4**2*p6**4*q8 - 1/2*d(2,f(1))**2*d(1
,d(2,f(1)))*p4*p6**5*q9 + 1/8*d(2,f(1))**2*df(f(1),x)*p4**6*q9 + 1/8*d(2,f(1))**
2*df(f(1),x)*p4**5*p6*q8 - 1/8*d(2,f(1))**2*df(f(1),x)*p4**4*p6**2*q9 + 1/8*d(2,
f(1))**2*df(f(1),x)*p4**3*p6**3*q8 - 5/4*d(2,f(1))**2*df(f(1),x)*p4**2*p6**4*q9 
- 1/2*d(2,f(1))**2*df(f(1),x)*p4*p6**5*q8 - d(2,f(1))**2*df(f(1),x)*p6**6*q9 + 1
/6*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p4**5*p6*q15 - 5/6*d(2,f(1))*d(1,d(2,df(f(1)
,x,2)))*p4**3*p6**3*q15 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p4**3*p6**3*q8 + 1/
4*d(2,f(1))*d(1,f(1))*df(f(1),x)*p4**5*p6*q9 + 5/4*d(2,f(1))*d(1,f(1))*df(f(1),x
)*p4**3*p6**3*q9 - d(2,f(1))*d(1,f(1))*df(f(1),x)*p4*p6**5*q9 - 1/6*d(2,f(1))*df
(f(1),x,3)*p4**6*q15 - 3/2*d(2,f(1))*df(f(1),x,3)*p4**4*p6**2*q15 - 1/3*d(2,f(1)
)*df(f(1),x,3)*p4**2*p6**4*q15 - 1/6*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p4**6*q15 
- 3/2*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p4**4*p6**2*q15 - 1/3*d(1,d(2,df(f(1),x,2
)))*d(1,f(1))*p4**2*p6**4*q15 - d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p4**4*p6**2*q15
 + d(1,d(2,f(1)))*d(1,f(1))**2*p4**3*p6**3*q9 + d(1,df(f(1),x,2))*df(f(1),x)*p4
**3*p6**3*q15 - 1/2*d(1,f(1))**2*df(f(1),x)*p4**4*p6**2*q9 - 1/2*d(1,f(1))**2*df
(f(1),x)*p4**3*p6**3*q8 - 1/2*d(1,f(1))**2*df(f(1),x)*p4**2*p6**4*q9 - 1/6*d(1,f
(1))*df(f(1),x,3)*p4**5*p6*q15 + 5/6*d(1,f(1))*df(f(1),x,3)*p4**3*p6**3*q15)/(p4
**3*p6**3)$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q17,q15,q12,q10,q9,q8,q7,p6,p5,p3,p4
New ordering: q17,q15,q12,q10,q9,q8,q7,p5,p3,p6,p4

The list of inequalities got extended by: 

q17

The lexicographical ordering of unknowns is changed
because q17 has to be non-zero, giving q17 a low priority.
Old ordering: q17,q15,q12,q10,q9,q8,q7,p5,p3,p6,p4
New ordering: q15,q12,q10,q9,q8,q7,q17,p5,p3,p6,p4

New level : 1.1.1.2.1.1.2.2.
CRACK is now called with the new equation e_364 : 
0=p3*p4 + p5*p6


Step 900: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 51 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 47 terms

e_395 is a consequence of e_306.
e_407 is a consequence of e_406.
Substitution of p5 by an expression in 
p3, p6, p4 found in e_364 : 
     - p3*p4
p5=----------
       p6


Step 901: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 4 terms

Step 902: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 3 terms

Step 903: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 904: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_185 is a consequence of e_306.
Step 905: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 906: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 907: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 4 terms

Step 908: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 909: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 910: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 911: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_306 and e_172. e_172: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

               2      2
 (q15,q10,p3,p6 ,p6,p4 ,p4)

is replaced by e_358: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                  2
 (q15,q10,p3,p6,p4 ,p4)


Step 912: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_306 and e_405. e_405: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

            3   2      2      2
 (q10,q17,p3 ,p3 ,p3,p6 ,p6,p4 )

is replaced by e_353: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

            3   2         2
 (q10,q17,p3 ,p3 ,p3,p6,p4 )


Step 913: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_306 and e_404. e_404: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

               3   2      2
 (q10,q17,p3,p6 ,p6 ,p6,p4 )

is replaced by e_62: 
(#) 6 terms, 11 factors, with derivatives of functions of all variables: 

               2      2
 (q10,q17,p3,p6 ,p6,p4 )


Step 914: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 915: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_306 and e_403. e_403: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

            2      2      2
 (q10,q17,p3 ,p3,p6 ,p6,p4 )

is replaced by e_228: 

                 2     2
0=(q10 + q17)*(p3  + p4 )


Step 916: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_306 and e_355. e_355: 
 7 terms, 21 factors, with derivatives of functions of all variables: 

                   2      2
 (q15,q10,q17,p3,p6 ,p6,p4 ,p4)

is replaced by e_205: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                  2
 (q15,q10,p3,p6,p4 ,p4)


Step 917: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 918: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 919: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 920: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 921: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 4 terms

Step 922: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 923: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_382 is a consequence of e_132.
Step 924: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 3 terms

Step 925: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 3 terms

Step 926: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 3 terms

Step 927: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 3 terms

Step 928: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 929: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 930: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 931: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 932: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 933: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 934: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 935: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 936: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 937: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 938: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 939: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 940: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 941: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 942: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
The list of inequalities got extended by: 

p3

Eliminate 
q10

from e_307 and e_228. e_307: 

                     2     2
0=(4*q10 + 3*q17)*(p3  + p4 )

is replaced by e_185: 

    2     2
0=p3  + p4

e_228 is a consequence of e_185

Step 943: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 49 terms

The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 45 terms

e_243 is a consequence of e_389.
e_407 is a consequence of e_389.
e_132 is a consequence of e_389.
e_358 is a consequence of e_205.
Substitution of q15 by an expression in 
q10, p3, p6, p4 found in e_159 : 12 factors in 3 terms

Step 944: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_397. e_397: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

        2      2      2
 (q10,p3 ,p3,p6 ,p6,p4 )

is replaced by e_27: 

         2     2
0=q10*(p4  + p6 )


e_27 is a consequence of e_306.
Step 945: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_290. e_290: 
(#) 5 terms, 21 factors, with derivatives of functions of all variables: 

        3   2      2      4   2
 (q10,p3 ,p3 ,p3,p6 ,p6,p4 ,p4 )

is replaced by e_172: 
(#) 3 terms, 13 factors, with derivatives of functions of all variables: 

        2   2   4   2
 (q10,p3 ,p6 ,p4 ,p4 )


Step 946: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_172. e_172: 
(#) 3 terms, 13 factors, with derivatives of functions of all variables: 

        2   2   4   2
 (q10,p3 ,p6 ,p4 ,p4 )

is replaced by e_405: 

         2     2
0=q10*(p4  + p6 )


e_405 is a consequence of e_306.
Step 947: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_234. e_234: 
(#) 5 terms, 21 factors, with derivatives of functions of all variables: 

        3   2      2      4   2
 (q10,p3 ,p3 ,p3,p6 ,p6,p4 ,p4 )

is replaced by e_404: 
(#) 3 terms, 13 factors, with derivatives of functions of all variables: 

        2   2   4   2
 (q10,p3 ,p6 ,p4 ,p4 )


Step 948: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_404. e_404: 
(#) 3 terms, 13 factors, with derivatives of functions of all variables: 

        2   2   4   2
 (q10,p3 ,p6 ,p4 ,p4 )

is replaced by e_357: 

         2     2
0=q10*(p4  + p6 )


e_357 is a consequence of e_306.
Step 949: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_258. e_258: 
(#) 6 terms, 31 factors, with derivatives of functions of all variables: 

        3   2      3   2      4   2
 (q10,p3 ,p3 ,p3,p6 ,p6 ,p6,p4 ,p4 )

is replaced by e_107: 
(#) 5 terms, 26 factors, with derivatives of functions of all variables: 

        2      3   2      4   2
 (q10,p3 ,p3,p6 ,p6 ,p6,p4 ,p4 )


Step 950: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_107. e_107: 
(#) 5 terms, 26 factors, with derivatives of functions of all variables: 

        2      3   2      4   2
 (q10,p3 ,p3,p6 ,p6 ,p6,p4 ,p4 )

is replaced by e_62: 
(#) 4 terms, 7 factors, with derivatives of functions of all variables: 

           3   2      2
 (q10,p3,p6 ,p6 ,p6,p4 )


e_62 is a consequence of e_306.
Step 951: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_374. e_374: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

            2      3   2      2
 (q10,q17,p3 ,p3,p6 ,p6 ,p6,p4 )

is replaced by e_20: 
(#) 6 terms, 10 factors, with derivatives of functions of all variables: 

               3   2      2
 (q10,q17,p3,p6 ,p6 ,p6,p4 )


e_20 is a consequence of e_306.
Step 952: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 953: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_313. e_313: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

            2      2      2
 (q10,q17,p3 ,p3,p6 ,p6,p4 )

is replaced by e_403: 

                     2     2
0=(3*q10 - 2*q17)*(p4  + p6 )


e_403 is a consequence of e_306.
Step 954: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_398. e_398: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

              2
 (q12,q9,q8,p3 ,p3,p6,p4)

is replaced by e_157: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                    2
 (q12,q9,q8,p3,p6,p4 ,p4)


Step 955: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_401. e_401: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

             2      2      2
 (q9,q8,q7,p3 ,p3,p6 ,p6,p4 ,p4)

is replaced by e_252: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

                2      2
 (q9,q8,q7,p3,p6 ,p6,p4 ,p4)


Step 956: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_306 and e_252. e_252: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

                2      2
 (q9,q8,q7,p3,p6 ,p6,p4 ,p4)

is replaced by e_355: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                   2
 (q9,q8,q7,p3,p6,p4 ,p4)


Step 957: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_402 we get the alternative equations : 
0=p3 + p6


0=q10 + q17


New level : 1.1.1.2.1.1.2.2.1.
CRACK is now called with the new equation e_406 : 
0=p3 + p6

e_205 is a consequence of e_406

Step 958: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 24 terms

e_312 is a consequence of e_185.
e_390 is a consequence of e_185.
e_411 is a consequence of e_185.
Substitution of p6 by an expression in 
p3 found in e_406 : 
p6= - p3


Step 959: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 24 terms

e_392 is a consequence of e_185.
Substitution of q9 by an expression in 
q7 found in e_391 : 
q9= - q7


Step 960: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 24 terms

e_409 is a consequence of e_185.
Substitution of q12 by an expression in 
q8 found in e_352 : 
     1
q12=---*q8
     2


Step 961: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.1.2.1.1.2.2.1. : 
equations : 

e_185 : 
    2     2
0=p3  + p4



Non-vanishing expressions: p6,p3,p4,q17
110 factors in 24 terms

        3                    2                 2                  3
g0005*p3 *q10 - 3*g0005*p3*p4 *q10 + 3*g0006*p3 *p4*q10 - g0006*p4 *q10

           3                    2                    2                 2
 + g0007*p3 *q10 - 3*g0007*p3*p4 *q10 - 4*g0008*p3*p4 *q17 + 4*g0009*p3 *p4*q17

                2                 3                    2                    2
 - 4*g0010*p3*p4 *q17 + 2*g0011*p3 *q10 - 2*g0011*p3*p4 *q10 + 8*g0012*p3*p4 *q7

                2                2                       2
 - 2*g0013*p3*p4 *q8 + 4*g0014*p3 *p4*q10 - 4*g0015*p3*p4 *q10

                2                   2                   2                   3
 + 4*g0016*p3*p4 *q7 - 4*g0017*p3*p4 *q8 - 4*g0018*p3*p4 *q7 - 4*g0024*p3*p4

                3             2   2
 - 4*g0025*p3*p4  - 4*g0026*p3 *p4

126 factors in 28 terms

g0113*p3 - g0114*p4 - g0115*p4 - g0116*p3


        3                    2                 2                  3
g0030*p3 *q10 - 3*g0030*p3*p4 *q10 + 3*g0031*p3 *p4*q10 - g0031*p4 *q10

             2                  3                 2                    2
 - 3*g0032*p3 *p4*q10 + g0032*p4 *q10 - 4*g0033*p3 *p4*q17 + 4*g0034*p3 *p4*q17

                2                 2                    3                    2
 - 4*g0035*p3*p4 *q17 - 2*g0036*p3 *p4*q10 + 2*g0036*p4 *q10 + 2*g0037*p3*p4 *q8

                2                2                       2
 + 8*g0038*p3*p4 *q7 + 4*g0039*p3 *p4*q10 - 4*g0040*p3*p4 *q10

                2                   2                   2                2   2
 + 4*g0041*p3*p4 *q7 - 4*g0042*p3*p4 *q8 - 4*g0043*p3*p4 *q7 + 4*g0049*p3 *p4

                3             2   2
 - 4*g0050*p3*p4  - 4*g0051*p3 *p4


functions : 
q27=0


q26=0


q25=0


         1    2        3    2
      - ---*p3 *q10 + ---*p4 *q10
         4             4
q24=------------------------------
                   2
                 p4


         3    2        1    2
      - ---*p3 *q10 + ---*p4 *q10
         4             4
q23=------------------------------
                p3*p4


      3    2        1    2
     ---*p3 *q10 - ---*p4 *q10
      4             4
q22=---------------------------
               p3*p4


         1    2        3    2
      - ---*p3 *q10 + ---*p4 *q10
         4             4
q21=------------------------------
                   2
                 p4


q20=q17


     p3*q17
q19=--------
       p4


      - p3*q17
q18=-----------
        p4

q17, 
         1    2        1    2
      - ---*p3 *q10 + ---*p4 *q10
         2             2
q16=------------------------------
                   2
                 p4


      1    2        1    2
     ---*p3 *q10 - ---*p4 *q10
      2             2
q15=---------------------------
               p3*p4


        1
q14= - ---*q8
        2


q13= - 2*q7


     1
q12=---*q8
     2


      - p3*q10
q11=-----------
        p4

q10, 
q9= - q7

q8, q7, 
q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


p6= - p3


p5=p4

p4, p3, 
p2=0


p1=0


with 57 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_185(2a)
6 constants : p3,p4,q7,q8,q10,q17
The equation: 

f =D f*D D f*p3 + D f*f *p4 + D D f*D f*p4 - D f*f *p3
 t  2   1 2        2   x       1 2   1        1   x
The symmetry: 
                     2           1             3        1                2
f =( - D f  *D D f*p3 *p4*q10 - ---*D f  *f *p3 *q10 + ---*D f  *f *p3*p4 *q10
 s      2 2x  1 2                2   2 2x  x            2   2 2x  x

                     2                        2            2            2
     - D f *D D f *p3 *p4*q17 + D f *f  *p3*p4 *q17 + (D f) *D D f*p3*p4 *q7
        2 x  1 2 x               2 x  2x                2     1 2

        1       2         2       3                2
     + ---*(D f) *f *p3*p4 *q8 - ---*D f*D D f  *p3 *p4*q10
        2    2     x              4   2   1 2 2x

        1                3                          2
     + ---*D f*D D f  *p4 *q10 + D f*D D f*D f*p3*p4 *q8
        4   2   1 2 2x            2   1 2   1

                         2       1            3        3               2
     - 2*D f*D f*f *p3*p4 *q7 - ---*D f*f  *p3 *q10 + ---*D f*f  *p3*p4 *q10
          2   1   x              4   2   3x            4   2   3x

        1                3        3                   2
     - ---*D D f  *D f*p3 *q10 + ---*D D f  *D f*p3*p4 *q10
        4   1 2 2x  1             4   1 2 2x  1

                        2                        2                  2      2
     + D D f *D f *p3*p4 *q17 + D D f*D f  *p3*p4 *q10 - D D f*(D f) *p3*p4 *q7
        1 2 x  1 x               1 2   1 2x               1 2    1

        1             2           1             3                  2
     + ---*D f  *f *p3 *p4*q10 - ---*D f  *f *p4 *q10 + D f *f  *p3 *p4*q17
        2   1 2x  x               2   1 2x  x            1 x  2x

        1       2         2       3            2           1            3
     - ---*(D f) *f *p3*p4 *q8 + ---*D f*f  *p3 *p4*q10 - ---*D f*f  *p4 *q10)/(
        2    1     x              4   1   3x               4   1   3x

        2
   p3*p4 )
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(2,f(1))*df(f(1),x)*p4 + d(1,d(2,f(1))
)*d(1,f(1))*p4 - d(1,f(1))*df(f(1),x)*p3$
The symmetry: 
df(f(1),s)=( - d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p3**2*p4*q10 - 1/2*d(2,df(f(1),x
,2))*df(f(1),x)*p3**3*q10 + 1/2*d(2,df(f(1),x,2))*df(f(1),x)*p3*p4**2*q10 - d(2,
df(f(1),x))*d(1,d(2,df(f(1),x)))*p3**2*p4*q17 + d(2,df(f(1),x))*df(f(1),x,2)*p3*
p4**2*q17 + d(2,f(1))**2*d(1,d(2,f(1)))*p3*p4**2*q7 + 1/2*d(2,f(1))**2*df(f(1),x
)*p3*p4**2*q8 - 3/4*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p3**2*p4*q10 + 1/4*d(2,f(1)
)*d(1,d(2,df(f(1),x,2)))*p4**3*q10 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3*p4**2
*q8 - 2*d(2,f(1))*d(1,f(1))*df(f(1),x)*p3*p4**2*q7 - 1/4*d(2,f(1))*df(f(1),x,3)*
p3**3*q10 + 3/4*d(2,f(1))*df(f(1),x,3)*p3*p4**2*q10 - 1/4*d(1,d(2,df(f(1),x,2)))
*d(1,f(1))*p3**3*q10 + 3/4*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p3*p4**2*q10 + d(1,d
(2,df(f(1),x)))*d(1,df(f(1),x))*p3*p4**2*q17 + d(1,d(2,f(1)))*d(1,df(f(1),x,2))*
p3*p4**2*q10 - d(1,d(2,f(1)))*d(1,f(1))**2*p3*p4**2*q7 + 1/2*d(1,df(f(1),x,2))*
df(f(1),x)*p3**2*p4*q10 - 1/2*d(1,df(f(1),x,2))*df(f(1),x)*p4**3*q10 + d(1,df(f(
1),x))*df(f(1),x,2)*p3**2*p4*q17 - 1/2*d(1,f(1))**2*df(f(1),x)*p3*p4**2*q8 + 3/4
*d(1,f(1))*df(f(1),x,3)*p3**2*p4*q10 - 1/4*d(1,f(1))*df(f(1),x,3)*p4**3*q10)/(p3
*p4**2)$

Time: 0 ms

Time: 10 ms

Time: 10 ms
*** Garbage collection starting 
*** GC 339  3-Oct-2003 05:29:19, 30 ms (0%), 992333 occupied, 24007619 free

The list of inequalities got extended by: 

q10

The lexicographical ordering of unknowns is changed
because q10 has to be non-zero, giving q10 a low priority.
Old ordering: q12,q10,q9,q8,q7,q17,p3,p6,p4
New ordering: q12,q9,q8,q7,q10,q17,p3,p6,p4

The list of inequalities got extended by: 

p3 + p6


New level : 1.1.1.2.1.1.2.2.2.
CRACK is now called with the new equation e_406 : 
0=q10 + q17

e_342 is a consequence of e_406

Step 962: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

1


The list of inequalities got extended by: 

q17


The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 27 terms

Substitution of q17 by an expression in 
q10 found in e_406 : 
q17= - q10


Step 963: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 

p3 + p4


p3 - p4


The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 

  2       2
p3  - 3*p4


The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 19 terms

e_312 is a consequence of e_185.
e_399 is a consequence of e_185.
Substitution of p6 by an expression in 
p3, p4 found in e_205 : 
         2
     - p4
p6=--------
      p3


Step 964: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 22 terms

Substitution of q9 by an expression in 
q8, q7, p3, p4 found in e_355 : 7 factors in 3 terms

Step 965: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p3

from e_185 and e_396. e_396: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

              2      2
 (q12,q8,q7,p3 ,p3,p4 ,p4)

is replaced by e_390: 
 3 terms, 6 factors, with derivatives of functions of all variables: 

 (q12,q8,q7,p3,p4)


Step 966: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 23 terms

e_391 is a consequence of e_185.
Substitution of q12 by an expression in 
q8, q7, p3, p4 found in e_390 : 8 factors in 3 terms

Step 967: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.1.2.1.1.2.2.2. : 
equations : 

e_185 : 
    2     2
0=p3  + p4



Non-vanishing expressions: p6,q10,p4,p3,q17
105 factors in 23 terms

        2                     2               2                    2
g0005*p3 *p4*q10 - g0006*p3*p4 *q10 + g0007*p3 *p4*q10 - 2*g0008*p3 *p4*q10

                2                 2                    3                2
 + 2*g0009*p3*p4 *q10 - 2*g0010*p3 *p4*q10 + 2*g0012*p3 *q8 - 2*g0012*p3 *p4*q7

                2                3              2                      2
 + 2*g0012*p3*p4 *q8 - 2*g0012*p4 *q7 + g0013*p3 *p4*q8 - 2*g0013*p3*p4 *q7

                2                 2                       2                3
 - 2*g0014*p3*p4 *q10 + 2*g0015*p3 *p4*q10 + 2*g0016*p3*p4 *q8 - 2*g0016*p4 *q7

             2                   2                   4             2   2
 + 2*g0017*p3 *p4*q8 + 2*g0018*p3 *p4*q7 + 2*g0024*p3  + 2*g0025*p3 *p4

             3
 + 2*g0026*p3 *p4

120 factors in 27 terms

        3           3              2           2
g0113*p4  - g0114*p3  - g0115*p3*p4  - g0116*p3 *p4


  2       2
p3  - 3*p4


p3 + p4


p3 - p4


        3                  2   2               2   2                 2   2
g0030*p3 *p4*q10 - g0031*p3 *p4 *q10 + g0032*p3 *p4 *q10 - 2*g0033*p3 *p4 *q10

             2   2                 3                  2   2                 3
 + 2*g0034*p3 *p4 *q10 - 2*g0035*p3 *p4*q10 - g0037*p3 *p4 *q7 - g0037*p3*p4 *q8

           4                4                3                   2   2
 + g0037*p4 *q7 + 2*g0038*p3 *q8 - 2*g0038*p3 *p4*q7 + 2*g0038*p3 *p4 *q8

                3                2   2                 3
 - 2*g0038*p3*p4 *q7 - 2*g0039*p3 *p4 *q10 + 2*g0040*p3 *p4*q10

             2   2                   3                3
 + 2*g0041*p3 *p4 *q8 - 2*g0041*p3*p4 *q7 + 2*g0042*p3 *p4*q8

             3                   2   3             3   2             4
 + 2*g0043*p3 *p4*q7 - 2*g0049*p3 *p4  + 2*g0050*p3 *p4  + 2*g0051*p3 *p4


functions : 
q27=0


q26=0


q25=0


     1
q24=---*q10
     2


         1
      - ---*p4*q10
         2
q23=---------------
          p3


      1
     ---*p4*q10
      2
q22=------------
         p3


     1
q21=---*q10
     2


q20= - q10


      - p4*q10
q19=-----------
        p3


     p4*q10
q18=--------
       p3


q17= - q10


q16=0


q15=0


         1    2          1       2       1    3
      - ---*p3 *p4*q7 - ---*p3*p4 *q8 + ---*p4 *q7
         2               2               2
q14=-----------------------------------------------
                            3
                          p3


       3        2              2        3
     p3 *q8 - p3 *p4*q7 + p3*p4 *q8 - p4 *q7
q13=-----------------------------------------
                       2
                     p3 *p4


      1
     ---*p3*q8 - p4*q7
      2
q12=-------------------
            p3


      - p4*q10
q11=-----------
        p3

q10, 
                 2
    p3*p4*q8 - p4 *q7
q9=-------------------
             2
           p3

q8, q7, 
q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


         2
     - p4
p6=--------
      p3


      2
    p3
p5=-----
    p4

p4, p3, 
p2=0


p1=0


with 57 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_185(2a)
5 constants : p3,p4,q7,q8,q10
The equation: 

                2               3                  2            3
    D f*D D f*p3 *p4 + D f*f *p3  + D D f*D f*p3*p4  - D f*f *p4
     2   1 2            2   x        1 2   1            1   x
f =---------------------------------------------------------------
 t                              p3*p4
The symmetry: 
                     2   2                     2   2                  3
f =( - D f  *D D f*p3 *p4 *q10 + D f *D D f *p3 *p4 *q10 - D f *f  *p3 *p4*q10
 s      2 2x  1 2                 2 x  1 2 x                2 x  2x

            2         3          1       2      3              2      2   2
     + (D f) *D D f*p3 *p4*q7 + ---*(D f) *f *p3 *p4*q8 - (D f) *f *p3 *p4 *q7
         2     1 2               2    2     x               2     x

        1                2   2                       3                      4
     - ---*D f*D D f  *p3 *p4 *q10 + D f*D D f*D f*p3 *p4*q8 + D f*D f*f *p3 *q8
        2   2   1 2 2x                2   1 2   1               2   1   x

                    3                      2   2                      3
     - D f*D f*f *p3 *p4*q7 + D f*D f*f *p3 *p4 *q8 - D f*D f*f *p3*p4 *q7
        2   1   x              2   1   x               2   1   x

        1            3           1                3
     + ---*D f*f  *p3 *p4*q10 + ---*D D f  *D f*p3 *p4*q10
        2   2   3x               2   1 2 2x  1

                     3                        3                     2   2   2
     - D D f *D f *p3 *p4*q10 + D D f*D f  *p3 *p4*q10 + D D f*(D f) *p3 *p4 *q8
        1 2 x  1 x               1 2   1 2x               1 2    1

                  2      3                 2   2        1       2      2   2
     - D D f*(D f) *p3*p4 *q7 - D f *f  *p3 *p4 *q10 - ---*(D f) *f *p3 *p4 *q7
        1 2    1                 1 x  2x                2    1     x

        1       2         3       1       2      4       1            2   2
     - ---*(D f) *f *p3*p4 *q8 + ---*(D f) *f *p4 *q7 + ---*D f*f  *p3 *p4 *q10)
        2    1     x              2    1     x           2   1   3x

    3
/(p3 *p4)
And now in machine readable form:

The system: 

df(f(1),t)=(d(2,f(1))*d(1,d(2,f(1)))*p3**2*p4 + d(2,f(1))*df(f(1),x)*p3**3 + d(1
,d(2,f(1)))*d(1,f(1))*p3*p4**2 - d(1,f(1))*df(f(1),x)*p4**3)/(p3*p4)$
The symmetry: 
df(f(1),s)=( - d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p3**2*p4**2*q10 + d(2,df(f(1),x)
)*d(1,d(2,df(f(1),x)))*p3**2*p4**2*q10 - d(2,df(f(1),x))*df(f(1),x,2)*p3**3*p4*
q10 + d(2,f(1))**2*d(1,d(2,f(1)))*p3**3*p4*q7 + 1/2*d(2,f(1))**2*df(f(1),x)*p3**
3*p4*q8 - d(2,f(1))**2*df(f(1),x)*p3**2*p4**2*q7 - 1/2*d(2,f(1))*d(1,d(2,df(f(1)
,x,2)))*p3**2*p4**2*q10 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3**3*p4*q8 + d(2,f
(1))*d(1,f(1))*df(f(1),x)*p3**4*q8 - d(2,f(1))*d(1,f(1))*df(f(1),x)*p3**3*p4*q7 
+ d(2,f(1))*d(1,f(1))*df(f(1),x)*p3**2*p4**2*q8 - d(2,f(1))*d(1,f(1))*df(f(1),x)
*p3*p4**3*q7 + 1/2*d(2,f(1))*df(f(1),x,3)*p3**3*p4*q10 + 1/2*d(1,d(2,df(f(1),x,2
)))*d(1,f(1))*p3**3*p4*q10 - d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p3**3*p4*q10 +
 d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p3**3*p4*q10 + d(1,d(2,f(1)))*d(1,f(1))**2*p3
**2*p4**2*q8 - d(1,d(2,f(1)))*d(1,f(1))**2*p3*p4**3*q7 - d(1,df(f(1),x))*df(f(1)
,x,2)*p3**2*p4**2*q10 - 1/2*d(1,f(1))**2*df(f(1),x)*p3**2*p4**2*q7 - 1/2*d(1,f(1
))**2*df(f(1),x)*p3*p4**3*q8 + 1/2*d(1,f(1))**2*df(f(1),x)*p4**4*q7 + 1/2*d(1,f(
1))*df(f(1),x,3)*p3**2*p4**2*q10)/(p3**3*p4)$

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q27,q18,q17,q15,q12,q10,q9,q8,q7,p6,p5,p3,p4
New ordering: q27,q18,q17,q15,q12,q10,q9,q8,q7,p5,p3,p6,p4

The list of inequalities got extended by: 

q27

The lexicographical ordering of unknowns is changed
because q27 has to be non-zero, giving q27 a low priority.
Old ordering: q27,q18,q17,q15,q12,q10,q9,q8,q7,p5,p3,p6,p4
New ordering: q18,q17,q15,q12,q10,q9,q8,q7,q27,p5,p3,p6,p4

The list of inequalities got extended by: 

p5

The lexicographical ordering of unknowns is changed
because p5 has to be non-zero, giving p5 a low priority.
Old ordering: q18,q17,q15,q12,q10,q9,q8,q7,q27,p5,p3,p6,p4
New ordering: q18,q17,q15,q12,q10,q9,q8,q7,q27,p3,p5,p6,p4

The list of inequalities got extended by: 

p3


New level : 1.1.1.2.1.2.
CRACK is now called with the new equation e_252 : 
0=p3*p6 - p4*p5


Step 968: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 58 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 56 terms

e_306 is a consequence of e_228.
Substitution of p5 by an expression in 
p3, p6, p4 found in e_252 : 
    p3*p6
p5=-------
     p4


Step 969: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 

1


The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 53 terms

The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 51 terms
e_290,e_53 are consequences of e_313

e_312 is a consequence of e_313.e_389 is a consequence of e_258

e_282 is a consequence of e_313.
e_133 is a consequence of e_352.
e_307 is a consequence of e_313.
e_364 is a consequence of e_313.
e_309 is a consequence of e_313.
e_395 is a consequence of e_313.
e_215 is a consequence of e_313.
Substitution of p6 by an expression in 
p3, p4 found in e_280 : 
      2
    p4
p6=-----
    p3


Step 970: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 53 terms

The list of inequalities got extended by: 
An expression with 51 terms

Substitution of q12 by an expression in 
q8 found in e_352 : 
     1
q12=---*q8
     2


Step 971: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 47 terms

The list of inequalities got extended by: 
An expression with 45 terms

e_396 is a consequence of e_138.
e_308 is a consequence of e_313.
e_390 is a consequence of e_313.
e_397 is a consequence of e_138.
e_323 is a consequence of e_392.
Substitution of q18 by an expression in 
q17, p3, p4 found in e_258 : 
     p4*q17
q18=--------
       p3


Step 972: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 42 terms

The list of inequalities got extended by: 
An expression with 40 terms

e_391 is a consequence of e_313.
e_64 is a consequence of e_313.
e_18 is a consequence of e_313.
e_311 is a consequence of e_313.
e_340 is a consequence of e_313.
e_221 is a consequence of e_313.
e_226 is a consequence of e_313.
e_11 is a consequence of e_313.
e_393 is a consequence of e_313.
e_392 is a consequence of e_313.
Substitution of q15 by an expression in 
q10, p3, p4 found in e_138 : 
      - p4*q10
q15=-----------
        p3


Step 973: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 42 terms

e_305 is a consequence of e_313.
Substitution of q9 by an expression in 
q7, p3, p4 found in e_255 : 10 factors in 3 terms

Step 974: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.1.2.1.2. : 
equations : 

e_313 : 
    2     2
0=p3  + p4



Non-vanishing expressions: p6,p3,q27,p4,p5
203 factors in 42 terms
209 factors in 44 terms
155 factors in 35 terms
164 factors in 34 terms

        2                                       2
g0113*p4  + g0114*p3*p4 + g0115*p3*p4 + g0116*p3


functions : q27, 
     p4*q27
q26=--------
       p3


q25=0


      1    2        1    2        7    2        1    2
     ---*p3 *q10 + ---*p3 *q17 + ---*p4 *q10 + ---*p4 *q17
      6             6             6             6
q24=-------------------------------------------------------
                                2
                              p4


      1    2        1    2        7    2        1    2
     ---*p3 *q10 + ---*p3 *q17 + ---*p4 *q10 + ---*p4 *q17
      6             6             6             6
q23=-------------------------------------------------------
                             p3*p4


         1    2        1    2        7    2        1    2
      - ---*p3 *q10 - ---*p3 *q17 - ---*p4 *q10 - ---*p4 *q17
         6             6             6             6
q22=----------------------------------------------------------
                              p3*p4


      1    2        1    2        7    2        1    2
     ---*p3 *q10 + ---*p3 *q17 + ---*p4 *q10 + ---*p4 *q17
      6             6             6             6
q21=-------------------------------------------------------
                                2
                              p4


q20=q17


      - p4*q17
q19=-----------
        p3


     p4*q17
q18=--------
       p3

q17, 
      1    2        1    2        4    2        1    2
     ---*p3 *q10 + ---*p3 *q17 + ---*p4 *q10 + ---*p4 *q17
      3             3             3             3
q16=-------------------------------------------------------
                                2
                              p4


      - p4*q10
q15=-----------
        p3


         1    4       1    3          1    4
      - ---*p3 *q7 - ---*p3 *p4*q8 + ---*p4 *q7
         4            2               4
q14=--------------------------------------------
                         3
                       p3 *p4


          2        2
      - p3 *q7 + p4 *q7
q13=--------------------
              2
            p3


     1
q12=---*q8
     2


      1    2        1    2        4    2        1    2
     ---*p3 *q10 + ---*p3 *q17 + ---*p4 *q10 + ---*p4 *q17
      3             3             3             3
q11=-------------------------------------------------------
                             p3*p4

q10, 
        1    2       1    2
     - ---*p3 *q7 + ---*p4 *q7
        2            2
q9=----------------------------
                 2
               p3

q8, q7, 
q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p8=0


p7=0


      2
    p4
p6=-----
    p3


p5=p4

p4, p3, 
p2=0


p1=0


with 74 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_313(2a)
7 constants : p3,p4,q7,q8,q10,q17,q27
The equation: 

                2                                             2
    D f*D D f*p3  + D f*f *p3*p4 + D D f*D f*p3*p4 + D f*f *p4
     2   1 2         2   x          1 2   1           1   x
f =-------------------------------------------------------------
 t                              p3
The symmetry: 
     1                4           1                4
f =(---*D f  *D D f*p3 *p4*q10 + ---*D f  *D D f*p3 *p4*q17
 s   3   2 2x  1 2                3   2 2x  1 2

        4                2   3        1                2   3
     + ---*D f  *D D f*p3 *p4 *q10 + ---*D f  *D D f*p3 *p4 *q17
        3   2 2x  1 2                 3   2 2x  1 2

        1             5        1             5        4             3   2
     + ---*D f  *f *p3 *q10 + ---*D f  *f *p3 *q17 + ---*D f  *f *p3 *p4 *q10
        3   2 2x  x            3   2 2x  x            3   2 2x  x

        1             3   2                     2   3                  3   2
     + ---*D f  *f *p3 *p4 *q17 + D f *D D f *p3 *p4 *q17 + D f *f  *p3 *p4 *q17
        3   2 2x  x                2 x  1 2 x                2 x  2x

            2         3   2       1       2      3   2
     + (D f) *D D f*p3 *p4 *q7 + ---*(D f) *f *p3 *p4 *q8
         2     1 2                2    2     x

        1                4           1                4
     + ---*D f*D D f  *p3 *p4*q10 + ---*D f*D D f  *p3 *p4*q17
        6   2   1 2 2x               6   2   1 2 2x

        7                2   3        1                2   3
     + ---*D f*D D f  *p3 *p4 *q10 + ---*D f*D D f  *p3 *p4 *q17
        6   2   1 2 2x                6   2   1 2 2x

                       3   2                   3   2                      4
     + D f*D D f*D f*p3 *p4 *q8 - D f*D f*f *p3 *p4 *q7 + D f*D f*f *p3*p4 *q7
        2   1 2   1                2   1   x               2   1   x

        1            5        1            5        7            3   2
     + ---*D f*f  *p3 *q10 + ---*D f*f  *p3 *q17 + ---*D f*f  *p3 *p4 *q10
        6   2   3x            6   2   3x            6   2   3x

        1            3   2                 2   3        1                5
     + ---*D f*f  *p3 *p4 *q17 + D D f  *p3 *p4 *q27 + ---*D D f  *D f*p3 *q10
        6   2   3x                1 2 4x                6   1 2 2x  1

        1                5        7                3   2
     + ---*D D f  *D f*p3 *q17 + ---*D D f  *D f*p3 *p4 *q10
        6   1 2 2x  1             6   1 2 2x  1

        1                3   2                     3   2
     + ---*D D f  *D f*p3 *p4 *q17 + D D f *D f *p3 *p4 *q17
        6   1 2 2x  1                 1 2 x  1 x

                     3   2        1             2   3   2
     + D D f*D f  *p3 *p4 *q10 - ---*D D f*(D f) *p3 *p4 *q7
        1 2   1 2x                2   1 2    1

        1             2      4                 2   3                  2   3
     + ---*D D f*(D f) *p3*p4 *q7 - D f  *f *p3 *p4 *q10 - D f *f  *p3 *p4 *q17
        2   1 2    1                 1 2x  x                1 x  2x

        1       2      4          1       2      3   2       1       2      5
     - ---*(D f) *f *p3 *p4*q7 - ---*(D f) *f *p3 *p4 *q8 + ---*(D f) *f *p4 *q7
        4    1     x              2    1     x               4    1     x

        1            4           1            4           7            2   3
     - ---*D f*f  *p3 *p4*q10 - ---*D f*f  *p3 *p4*q17 - ---*D f*f  *p3 *p4 *q10
        6   1   3x               6   1   3x               6   1   3x

        1            2   3             3   2         3   2
     - ---*D f*f  *p3 *p4 *q17 + f  *p3 *p4 *q27)/(p3 *p4 )
        6   1   3x                5x
And now in machine readable form:

The system: 

df(f(1),t)=(d(2,f(1))*d(1,d(2,f(1)))*p3**2 + d(2,f(1))*df(f(1),x)*p3*p4 + d(1,d(
2,f(1)))*d(1,f(1))*p3*p4 + d(1,f(1))*df(f(1),x)*p4**2)/p3$
The symmetry: 
df(f(1),s)=(1/3*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p3**4*p4*q10 + 1/3*d(2,df(f(1),
x,2))*d(1,d(2,f(1)))*p3**4*p4*q17 + 4/3*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p3**2*
p4**3*q10 + 1/3*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p3**2*p4**3*q17 + 1/3*d(2,df(f(
1),x,2))*df(f(1),x)*p3**5*q10 + 1/3*d(2,df(f(1),x,2))*df(f(1),x)*p3**5*q17 + 4/3
*d(2,df(f(1),x,2))*df(f(1),x)*p3**3*p4**2*q10 + 1/3*d(2,df(f(1),x,2))*df(f(1),x)
*p3**3*p4**2*q17 + d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p3**2*p4**3*q17 + d(2,df
(f(1),x))*df(f(1),x,2)*p3**3*p4**2*q17 + d(2,f(1))**2*d(1,d(2,f(1)))*p3**3*p4**2
*q7 + 1/2*d(2,f(1))**2*df(f(1),x)*p3**3*p4**2*q8 + 1/6*d(2,f(1))*d(1,d(2,df(f(1)
,x,2)))*p3**4*p4*q10 + 1/6*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p3**4*p4*q17 + 7/6*d
(2,f(1))*d(1,d(2,df(f(1),x,2)))*p3**2*p4**3*q10 + 1/6*d(2,f(1))*d(1,d(2,df(f(1),
x,2)))*p3**2*p4**3*q17 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3**3*p4**2*q8 - d(2
,f(1))*d(1,f(1))*df(f(1),x)*p3**3*p4**2*q7 + d(2,f(1))*d(1,f(1))*df(f(1),x)*p3*
p4**4*q7 + 1/6*d(2,f(1))*df(f(1),x,3)*p3**5*q10 + 1/6*d(2,f(1))*df(f(1),x,3)*p3
**5*q17 + 7/6*d(2,f(1))*df(f(1),x,3)*p3**3*p4**2*q10 + 1/6*d(2,f(1))*df(f(1),x,3
)*p3**3*p4**2*q17 + d(1,d(2,df(f(1),x,4)))*p3**2*p4**3*q27 + 1/6*d(1,d(2,df(f(1)
,x,2)))*d(1,f(1))*p3**5*q10 + 1/6*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p3**5*q17 + 7
/6*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p3**3*p4**2*q10 + 1/6*d(1,d(2,df(f(1),x,2)))
*d(1,f(1))*p3**3*p4**2*q17 + d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p3**3*p4**2*
q17 + d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p3**3*p4**2*q10 - 1/2*d(1,d(2,f(1)))*d(1,
f(1))**2*p3**3*p4**2*q7 + 1/2*d(1,d(2,f(1)))*d(1,f(1))**2*p3*p4**4*q7 - d(1,df(f
(1),x,2))*df(f(1),x)*p3**2*p4**3*q10 - d(1,df(f(1),x))*df(f(1),x,2)*p3**2*p4**3*
q17 - 1/4*d(1,f(1))**2*df(f(1),x)*p3**4*p4*q7 - 1/2*d(1,f(1))**2*df(f(1),x)*p3**
3*p4**2*q8 + 1/4*d(1,f(1))**2*df(f(1),x)*p4**5*q7 - 1/6*d(1,f(1))*df(f(1),x,3)*
p3**4*p4*q10 - 1/6*d(1,f(1))*df(f(1),x,3)*p3**4*p4*q17 - 7/6*d(1,f(1))*df(f(1),x
,3)*p3**2*p4**3*q10 - 1/6*d(1,f(1))*df(f(1),x,3)*p3**2*p4**3*q17 + df(f(1),x,5)*
p3**3*p4**2*q27)/(p3**3*p4**2)$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p8

The lexicographical ordering of unknowns is changed
because p8 has to be non-zero, giving p8 a low priority.
Old ordering: q27,q18,q17,q15,q12,q11,q10,q9,q8,q7,p8,p6,p5,p3,p4
New ordering: q27,q18,q17,q15,q12,q11,q10,q9,q8,q7,p6,p5,p3,p8,p4

New level : 1.1.1.2.2.
CRACK is now called with the new equation e_312 : 
0=q10 - q17


Step 975: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 50 terms

The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 49 terms
e_290 is a consequence of e_20

Substitution of q17 by an expression in 
q10 found in e_312 : 
q17=q10


Step 976: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 45 terms

e_20 is a consequence of e_342.
e_374 is a consequence of e_342.
e_372 is a consequence of e_342.
Substitution of q18 by an expression in 
q15, q10, q9, p6, p8, p4 found in e_313 : 11 factors in 4 terms

Step 977: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 42 terms

The list of inequalities got extended by: 
An expression with 50 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 49 terms

Substitution of q11 by an expression in 
q10, q9, p6, p3, p8, p4 found in e_157 : 13 factors in 4 terms

Step 978: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 43 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 44 terms

e_382 is a consequence of e_368.
e_388 is a consequence of e_365.
e_386 is a consequence of e_368.
Substitution of q15 by an expression in 
q10, q9, p6, p3, p8, p4 found in e_342 : 13 factors in 4 terms

Step 979: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 4 terms

Step 980: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 340  3-Oct-2003 05:29:22, 30 ms (0%), 1017355 occupied, 23982596 free
Eliminate 
q9

from e_237 and e_371. e_371: 
 10 terms, 40 factors, with derivatives of functions of all variables: 

                       2         2
 (q10,q9,q8,q7,p6,p5,p3 ,p3,p8,p4 ,p4)

is replaced by e_7: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                    2         2
 (q10,q8,q7,p6,p5,p3 ,p3,p8,p4 ,p4)


Step 981: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q9

from e_237 and e_369. e_369: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                    2         2
 (q10,q9,q8,p6,p5,p3 ,p3,p8,p4 ,p4)

is replaced by e_278: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                    2         2
 (q10,q8,q7,p6,p5,p3 ,p3,p8,p4 ,p4)


e_278 is a consequence of e_7.
Step 982: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 341  3-Oct-2003 05:29:25, 30 ms (0%), 1022211 occupied, 23977741 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_368 we get the alternative equations : 
0=p3 + p6

9 factors in 3 terms

New level : 1.1.1.2.2.1.
CRACK is now called with the new equation e_252 : 
0=p3 + p6

e_377,e_32 are consequences of e_252

Step 983: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 29 terms

e_255 is a consequence of e_345.
e_305 is a consequence of e_345.e_306 is a consequence of e_53

e_307 is a consequence of e_280.
e_11 is a consequence of e_352.
e_340 is a consequence of e_18.
Substitution of p6 by an expression in 
p3 found in e_252 : 
p6= - p3


Step 984: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 30 terms

e_64 is a consequence of e_133.
Substitution of q7 by an expression in 
q9, p5, p4 found in e_53 : 10 factors in 3 terms

Step 985: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_404 is a consequence of e_280.
Step 986: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_295 is a consequence of e_280.
Step 987: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_310 is a consequence of e_280.
Step 988: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_243 is a consequence of e_280.
Step 989: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_205 is a consequence of e_280.
Step 990: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_390 is a consequence of e_280.
Step 991: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 992: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q9

from e_18 and e_394. e_394: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

              2      2
 (q12,q9,q8,p5 ,p3,p4 ,p4)

is replaced by e_369: 

0=(2*q12 - q8)*p3


Step 993: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q9

from e_18 and e_229. e_229: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                    2
 (q12,q9,q8,p5,p3,p4 ,p4)

is replaced by e_5: 

0=2*p4*q12 - p5*q8


Step 994: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 30 terms

Substitution of q12 by an expression in 
q8, p5, p4 found in e_5 : 
      1
     ---*p5*q8
      2
q12=-----------
        p4


Step 995: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_290 and e_138. e_138: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

                 2         2
 (q10,q9,q8,p5,p3 ,p3,p8,p4 ,p4)

is replaced by e_34: 

0=q9*(p4 - p5)*p3


e_34 is a consequence of e_18.
Step 996: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_280 we get the alternative equations : 
0=q10


0=p4 - p5


New level : 1.1.1.2.2.1.1.
CRACK is now called with the new equation e_377 : 
0=q10


Step 997: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 17 terms

e_307 is a consequence of e_306.
e_11 is a consequence of e_306.
Substitution of q10 found in e_377 : 
q10=0


Step 998: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 17 terms

e_305 is a consequence of e_18.
e_372 is a consequence of e_18.
Substitution of q8 by an expression in 
q9, p3, p4 found in e_306 : 
    2*p3*q9
q8=---------
      p4


Step 999: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_18 we get the alternative equations : 
0=q9


0=p4 - p5


New level : 1.1.1.2.2.1.1.1.
CRACK is now called with the new equation e_386 : 
0=q9


Step 1000: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

g0084*p4 - g0085*p3


q27

The lexicographical ordering of unknowns is changed
because q27 has to be non-zero, giving q27 a low priority.
Old ordering: q27,q9,p5,p3,p8,p4
New ordering: q9,q27,p5,p3,p8,p4

The list of inequalities got extended by: 

p3


The list of inequalities got extended by: 

p5


Substitution of q9 found in e_386 : 
q9=0


Step 1001: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 4 terms

e_393 is a consequence of e_342.
Substitution of p5 by an expression in 
p4 found in e_255 : 
p5=p4


Step 1002: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.1.2.2.1.1.1. : 
equations : 

e_342 : 
    2     2
0=p3  + p4



Non-vanishing expressions: p5,p4,p8,q27,p3

g0078*p3 - g0079*p4 - g0080*p4 - g0081*p3


                       2           2
g0003*p3*q27 - g0024*p4  - g0025*p4  - g0026*p3*p4


g0111*p8 - g0113*p3 + g0114*p4 + g0115*p4 + g0116*p3


                                     2
g0028*p3*q27 + g0049*p3*p4 - g0050*p4  - g0051*p3*p4


g0084*p4 - g0085*p3


functions : q27, 
      - p3*q27
q26=-----------
        p4


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, 
p7=0


p6= - p3


p5=p4

p4, p3, 
p2=0


p1=0


with 38 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_342(2a)
4 constants : p3,p4,p8,q27
The equation: 

f =D f*D D f*p3 + D f*f *p4 + D D f*D f*p4 - D f*f *p3 + f  *p8
 t  2   1 2        2   x       1 2   1        1   x       3x
The symmetry: 
     - D D f  *p3*q27 + f  *p4*q27
        1 2 4x           5x
f =--------------------------------
 s                p4
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(2,f(1))*df(f(1),x)*p4 + d(1,d(2,f(1))
)*d(1,f(1))*p4 - d(1,f(1))*df(f(1),x)*p3 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=( - d(1,d(2,df(f(1),x,4)))*p3*q27 + df(f(1),x,5)*p4*q27)/p4$

Time: 0 ms

Time: 0 ms

Time: 0 ms

The list of inequalities got extended by: 

p5

The lexicographical ordering of unknowns is changed
because p5 has to be non-zero, giving p5 a low priority.
Old ordering: q27,q9,p5,p3,p8,p4
New ordering: q27,q9,p3,p5,p8,p4

The list of inequalities got extended by: 

q9


New level : 1.1.1.2.2.1.1.2.
CRACK is now called with the new equation e_386 : 
0=p4 - p5

e_255 is a consequence of e_386

Step 1003: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

1


The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 15 terms

e_393 is a consequence of e_342.
Substitution of p4 by an expression in 
p5 found in e_386 : 
p4=p5


Step 1004: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms : 
for the substitution of q9 by e_342 we have to consider the case 0=e_395: 
         2
0=6*p3*p8

The coefficient to be set = 0 in the first subcase is:

e_395 : 
0=p3


New level : 1.1.1.2.2.1.1.2.1.
Step 1005: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

g0111*p8 + g0114*p5 + g0115*p5


The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

Substitution of p3 found in e_395 : 
p3=0


Step 1006: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 10 terms

Substitution of q27 found in e_396 : 
q27=0



>>>>>>>>> Solution of level 1.1.1.2.2.1.1.2.1. : 
no equations


Non-vanishing expressions: p4,p8,p5,q9

          2
6*g0085*p8  + 10*g0088*p5*p8 - 10*g0089*p5*p8 - 10*g0092*p5*p8 + 10*g0093*p5*p8

                               2                              2             2
 - 10*g0096*p5*p8 - 10*g0098*p5  + 10*g0100*p5*p8 - 5*g0102*p5  + 5*g0104*p5


g0111*p8 + g0114*p5 + g0115*p5


          2
6*g0028*p8 *q9 + 10*g0031*p5*p8*q9 - 10*g0032*p5*p8*q9 - 10*g0033*p5*p8*q9

                                                      2
 + 10*g0034*p5*p8*q9 - 10*g0036*p5*p8*q9 - 10*g0038*p5 *q9 + 10*g0039*p5*p8*q9

             2                2                3
 - 5*g0041*p5 *q9 + 5*g0043*p5 *q9 - 5*g0050*p5


          2                                                         2
6*g0003*p8 *q9 + 10*g0006*p5*p8*q9 + 10*g0009*p5*p8*q9 - 10*g0012*p5 *q9

                                 2                2                3
 + 10*g0014*p5*p8*q9 - 5*g0016*p5 *q9 + 5*g0018*p5 *q9 - 5*g0024*p5

             3
 - 5*g0025*p5


2*g0055*p8*q9 - 2*g0056*p8*q9 - 2*g0059*p8*q9 + 2*g0060*p8*q9 - 2*g0063*p8*q9

                                                                       2
 - 2*g0065*p5*q9 + 2*g0067*p8*q9 - g0069*p5*q9 + g0071*p5*q9 - g0079*p5

           2
 - g0080*p5


functions : 
q27=0


         6    2
      - ---*p8 *q9
         5
q26=---------------
            2
          p5


q25=0


q24=0


      - 2*p8*q9
q23=------------
         p5


     2*p8*q9
q22=---------
       p5


q21=0


q20=0


     2*p8*q9
q19=---------
       p5


      - 2*p8*q9
q18=------------
         p5


q17=0


q16=0


     2*p8*q9
q15=---------
       p5


q14=0


q13=2*q9


q12=0


      - 2*p8*q9
q11=------------
         p5


q10=0

q9, 
q8=0


q7= - q9


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, 
p7=0


p6=0

p5, 
p4=p5


p3=0


p2=0


p1=0


with 45 terms
no equations
3 constants : p5,p8,q9
The equation: 

f =D f*f *p5 + D D f*D f*p5 + f  *p8
 t  2   x       1 2   1        3x
The symmetry: 
                                                              2         2
f =( - 2*D f  *D D f*p5*p8*q9 - 2*D f *D D f *p5*p8*q9 - (D f) *D D f*p5 *q9
 s        2 2x  1 2                2 x  1 2 x              2     1 2

                                               2       6            2
     - 2*D f*D D f  *p5*p8*q9 + 2*D f*D f*f *p5 *q9 - ---*D D f  *p8 *q9
          2   1 2 2x               2   1   x           5   1 2 4x

                  2   2
     + D D f*(D f) *p5 *q9 + 2*D f  *f *p5*p8*q9 + 2*D f *f  *p5*p8*q9
        1 2    1                1 2x  x               1 x  2x

                             2
     + 2*D f*f  *p5*p8*q9)/p5
          1   3x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,f(1)))*d(1,f(1))*p5 + df(f(1),x,3)*
p8$
The symmetry: 
df(f(1),s)=( - 2*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5*p8*q9 - 2*d(2,df(f(1),x))*d
(1,d(2,df(f(1),x)))*p5*p8*q9 - d(2,f(1))**2*d(1,d(2,f(1)))*p5**2*q9 - 2*d(2,f(1)
)*d(1,d(2,df(f(1),x,2)))*p5*p8*q9 + 2*d(2,f(1))*d(1,f(1))*df(f(1),x)*p5**2*q9 - 
6/5*d(1,d(2,df(f(1),x,4)))*p8**2*q9 + d(1,d(2,f(1)))*d(1,f(1))**2*p5**2*q9 + 2*d
(1,df(f(1),x,2))*df(f(1),x)*p5*p8*q9 + 2*d(1,df(f(1),x))*df(f(1),x,2)*p5*p8*q9 +
 2*d(1,f(1))*df(f(1),x,3)*p5*p8*q9)/p5**2$

Time: 0 ms

Time: 0 ms

Time: 0 ms

New level : 1.1.1.2.2.1.1.2.2.
now back to the substitution of q9 by e_342
The list of inequalities got extended by: 

p3


Step 1007: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 

  2     2
p3  + p5


q27

The lexicographical ordering of unknowns is changed
because q27 has to be non-zero, giving q27 a low priority.
Old ordering: q27,q9,p3,p5,p8
New ordering: q9,q27,p3,p5,p8

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 26 terms

Substitution of q9 by an expression in 
q27, p3, p5, p8 found in e_342 : 12 factors in 3 terms


>>>>>>>>> Solution of level 1.1.1.2.2.1.1.2.2. : 
no equations


Non-vanishing expressions: q27,p5,p8,p4,p3

             2                2              2                 2
6*g0084*p3*p8  + 6*g0085*p5*p8  + 10*g0088*p3 *p8 + 10*g0088*p5 *p8

              2                 2                 2                 2
 - 10*g0089*p3 *p8 - 10*g0089*p5 *p8 - 10*g0092*p3 *p8 - 10*g0092*p5 *p8

              2                 2                 2                 2
 + 10*g0093*p3 *p8 + 10*g0093*p5 *p8 - 10*g0096*p3 *p8 - 10*g0096*p5 *p8

             3                2              2                 3             3
 + 5*g0097*p3  + 5*g0097*p3*p5  - 10*g0098*p3 *p5 - 10*g0098*p5  - 5*g0099*p3

                2              2                 2                2
 - 5*g0099*p3*p5  + 10*g0100*p3 *p8 + 10*g0100*p5 *p8 - 5*g0102*p3 *p5

             3              3                 2             2                3
 - 5*g0102*p5  - 10*g0103*p3  - 10*g0103*p3*p5  + 5*g0104*p3 *p5 + 5*g0104*p5

132 factors in 28 terms

             2                  2                     2
6*g0003*p5*p8 *q27 + 10*g0006*p3 *p8*q27 + 10*g0006*p5 *p8*q27

              2                     2                     2
 + 10*g0009*p3 *p8*q27 + 10*g0009*p5 *p8*q27 - 10*g0012*p3 *p5*q27

              3                 3                    2                  2
 - 10*g0012*p5 *q27 - 5*g0013*p3 *q27 - 5*g0013*p3*p5 *q27 + 10*g0014*p3 *p8*q27

              2                    2                    3                  3
 + 10*g0014*p5 *p8*q27 - 5*g0016*p3 *p5*q27 - 5*g0016*p5 *q27 - 10*g0017*p3 *q27

                 2                 2                    3
 - 10*g0017*p3*p5 *q27 + 5*g0018*p3 *p5*q27 + 5*g0018*p5 *q27

                   2                   2             2   2
 + 6*g0024*p3*p5*p8  + 6*g0025*p3*p5*p8  + 6*g0026*p3 *p8

123 factors in 26 terms

  2     2
p3  + p5


g0111*p8 - g0113*p3 + g0114*p5 + g0115*p5 + g0116*p3


functions : q27, 
     p5*q27
q26=--------
       p3


q25=0


q24=0


      5    2        5    2
     ---*p3 *q27 + ---*p5 *q27
      3             3
q23=---------------------------
               p3*p8


         5    2        5    2
      - ---*p3 *q27 - ---*p5 *q27
         3             3
q22=------------------------------
                p3*p8


q21=0


q20=0


         5    2        5    2
      - ---*p3 *q27 - ---*p5 *q27
         3             3
q19=------------------------------
                p3*p8


      5    2        5    2
     ---*p3 *q27 + ---*p5 *q27
      3             3
q18=---------------------------
               p3*p8


q17=0


q16=0


         5    2        5    2
      - ---*p3 *q27 - ---*p5 *q27
         3             3
q15=------------------------------
                p3*p8


      5    2        5    2
     ---*p3 *q27 + ---*p5 *q27
      6             6
q14=---------------------------
                  2
                p8


         5    2           5    3
      - ---*p3 *p5*q27 - ---*p5 *q27
         3                3
q13=---------------------------------
                      2
                 p3*p8


         5    2        5    2
      - ---*p3 *q27 - ---*p5 *q27
         6             6
q12=------------------------------
                   2
                 p8


      5    2        5    2
     ---*p3 *q27 + ---*p5 *q27
      3             3
q11=---------------------------
               p3*p8


q10=0


        5    2           5    3
     - ---*p3 *p5*q27 - ---*p5 *q27
        6                6
q9=---------------------------------
                     2
                p3*p8


        5    2        5    2
     - ---*p3 *q27 - ---*p5 *q27
        3             3
q8=------------------------------
                  2
                p8


     5    2           5    3
    ---*p3 *p5*q27 + ---*p5 *q27
     6                6
q7=------------------------------
                    2
               p3*p8


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, 
p7=0


p6= - p3

p5, 
p4=p5

p3, 
p2=0


p1=0


with 62 terms
no equations
4 constants : p3,p5,p8,q27
The equation: 

f =D f*D D f*p3 + D f*f *p5 + D D f*D f*p5 - D f*f *p3 + f  *p8
 t  2   1 2        2   x       1 2   1        1   x       3x
The symmetry: 
     5                2           5                2
f =(---*D f  *D D f*p3 *p8*q27 + ---*D f  *D D f*p5 *p8*q27
 s   3   2 2x  1 2                3   2 2x  1 2

        5                2           5                2
     + ---*D f *D D f *p3 *p8*q27 + ---*D f *D D f *p5 *p8*q27
        3   2 x  1 2 x               3   2 x  1 2 x

        5       2         2           5       2         3
     + ---*(D f) *D D f*p3 *p5*q27 + ---*(D f) *D D f*p5 *q27
        6    2     1 2                6    2     1 2

        5       2      3        5       2         2
     - ---*(D f) *f *p3 *q27 - ---*(D f) *f *p3*p5 *q27
        6    2     x            6    2     x

        5                2           5                2
     + ---*D f*D D f  *p3 *p8*q27 + ---*D f*D D f  *p5 *p8*q27
        3   2   1 2 2x               3   2   1 2 2x

        5                  3        5                     2
     - ---*D f*D D f*D f*p3 *q27 - ---*D f*D D f*D f*p3*p5 *q27
        3   2   1 2   1             3   2   1 2   1

        5               2           5               3                    2
     - ---*D f*D f*f *p3 *p5*q27 - ---*D f*D f*f *p5 *q27 + D D f  *p5*p8 *q27
        3   2   1   x               3   2   1   x            1 2 4x

        5             2   2           5             2   3
     - ---*D D f*(D f) *p3 *p5*q27 - ---*D D f*(D f) *p5 *q27
        6   1 2    1                  6   1 2    1

        5             2           5             2
     - ---*D f  *f *p3 *p8*q27 - ---*D f  *f *p5 *p8*q27
        3   1 2x  x               3   1 2x  x

        5             2           5             2           5       2      3
     - ---*D f *f  *p3 *p8*q27 - ---*D f *f  *p5 *p8*q27 + ---*(D f) *f *p3 *q27
        3   1 x  2x               3   1 x  2x               6    1     x

        5       2         2        5            2
     + ---*(D f) *f *p3*p5 *q27 - ---*D f*f  *p3 *p8*q27
        6    1     x               3   1   3x

        5            2                   2            2
     - ---*D f*f  *p5 *p8*q27 + f  *p3*p8 *q27)/(p3*p8 )
        3   1   3x               5x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,f(1))
)*d(1,f(1))*p5 - d(1,f(1))*df(f(1),x)*p3 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=(5/3*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p3**2*p8*q27 + 5/3*d(2,df(f(1),
x,2))*d(1,d(2,f(1)))*p5**2*p8*q27 + 5/3*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p3
**2*p8*q27 + 5/3*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**2*p8*q27 + 5/6*d(2,f(1
))**2*d(1,d(2,f(1)))*p3**2*p5*q27 + 5/6*d(2,f(1))**2*d(1,d(2,f(1)))*p5**3*q27 - 
5/6*d(2,f(1))**2*df(f(1),x)*p3**3*q27 - 5/6*d(2,f(1))**2*df(f(1),x)*p3*p5**2*q27
 + 5/3*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p3**2*p8*q27 + 5/3*d(2,f(1))*d(1,d(2,df(
f(1),x,2)))*p5**2*p8*q27 - 5/3*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3**3*q27 - 5/
3*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3*p5**2*q27 - 5/3*d(2,f(1))*d(1,f(1))*df(f
(1),x)*p3**2*p5*q27 - 5/3*d(2,f(1))*d(1,f(1))*df(f(1),x)*p5**3*q27 + d(1,d(2,df(
f(1),x,4)))*p5*p8**2*q27 - 5/6*d(1,d(2,f(1)))*d(1,f(1))**2*p3**2*p5*q27 - 5/6*d(
1,d(2,f(1)))*d(1,f(1))**2*p5**3*q27 - 5/3*d(1,df(f(1),x,2))*df(f(1),x)*p3**2*p8*
q27 - 5/3*d(1,df(f(1),x,2))*df(f(1),x)*p5**2*p8*q27 - 5/3*d(1,df(f(1),x))*df(f(1
),x,2)*p3**2*p8*q27 - 5/3*d(1,df(f(1),x))*df(f(1),x,2)*p5**2*p8*q27 + 5/6*d(1,f(
1))**2*df(f(1),x)*p3**3*q27 + 5/6*d(1,f(1))**2*df(f(1),x)*p3*p5**2*q27 - 5/3*d(1
,f(1))*df(f(1),x,3)*p3**2*p8*q27 - 5/3*d(1,f(1))*df(f(1),x,3)*p5**2*p8*q27 + df(
f(1),x,5)*p3*p8**2*q27)/(p3*p8**2)$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p5

The lexicographical ordering of unknowns is changed
because p5 has to be non-zero, giving p5 a low priority.
Old ordering: q27,q10,q9,q8,p5,p3,p8,p4
New ordering: q27,q10,q9,q8,p3,p5,p8,p4

The list of inequalities got extended by: 

q10

The lexicographical ordering of unknowns is changed
because q10 has to be non-zero, giving q10 a low priority.
Old ordering: q27,q10,q9,q8,p3,p5,p8,p4
New ordering: q27,q9,q8,q10,p3,p5,p8,p4

New level : 1.1.1.2.2.1.2.
CRACK is now called with the new equation e_377 : 
0=p4 - p5

e_374,e_159,e_369,e_18 are consequences of e_377

Step 1008: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 

1


The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 28 terms

e_305 is a consequence of e_255.
e_306 is a consequence of e_255.
e_11 is a consequence of e_307.
Substitution of p4 by an expression in 
p5 found in e_377 : 
p4=p5


Step 1009: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1010: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 34 terms

Substitution of q8 by an expression in 
q9, q10, p3, p5, p8 found in e_255 : 11 factors in 4 terms

Step 1011: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms : 
for the substitution of q9 by e_340 we have to consider the case 0=e_157: 
         2
0=6*p3*p8

The coefficient to be set = 0 in the first subcase is:

e_157 : 
0=p3


New level : 1.1.1.2.2.1.2.1.
Step 1012: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

g0111*p8 + g0114*p5 + g0115*p5


The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 

q27

The lexicographical ordering of unknowns is changed
because q27 has to be non-zero, giving q27 a low priority.
Old ordering: q27,q9,q10,p3,p5,p8
New ordering: q9,q27,q10,p3,p5,p8

Substitution of p3 found in e_157 : 
p3=0


Step 1013: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 

q27


Substitution of q27 by an expression in 
q10, p5, p8 found in e_382 : 
      3
     ---*p8*q10
      5
q27=------------
         p5



>>>>>>>>> Solution of level 1.1.1.2.2.1.2.1. : 
no equations


Non-vanishing expressions: q27,q10,p5,p8,p4

             2                  3                 2                        2
6*g0084*p5*p8 *q10 - 12*g0085*p8 *q9 + 10*g0087*p5 *p8*q10 - 20*g0088*p5*p8 *q9

                 2                 2                     2
 + 20*g0089*p5*p8 *q9 + 10*g0090*p5 *p8*q10 + 10*g0091*p5 *p8*q10

                 2                    2                 2
 + 20*g0092*p5*p8 *q9 - 20*g0093*p5*p8 *q9 + 10*g0094*p5 *p8*q10

              2                        2                3
 + 10*g0095*p5 *p8*q10 + 20*g0096*p5*p8 *q9 - 5*g0097*p5 *q10

              2                   3                     2
 + 20*g0098*p5 *p8*q9 + 5*g0099*p5 *q10 - 20*g0100*p5*p8 *q9

              2                     2                    3
 + 10*g0101*p5 *p8*q10 + 10*g0102*p5 *p8*q9 + 10*g0103*p5 *q10

              2
 - 10*g0104*p5 *p8*q9


g0111*p8 + g0114*p5 + g0115*p5


           3                 2                        2                    2
12*g0028*p8 *q9 - 10*g0030*p5 *p8*q10 + 20*g0031*p5*p8 *q9 - 20*g0032*p5*p8 *q9

                 2                    2                 2
 - 20*g0033*p5*p8 *q9 + 20*g0034*p5*p8 *q9 - 10*g0035*p5 *p8*q10

                 2                3                  2
 - 20*g0036*p5*p8 *q9 + 5*g0037*p5 *q10 - 20*g0038*p5 *p8*q9

                 2                 2                     2
 + 20*g0039*p5*p8 *q9 - 10*g0040*p5 *p8*q10 - 10*g0041*p5 *p8*q9

              3                  2                    3
 - 10*g0042*p5 *q10 + 10*g0043*p5 *p8*q9 - 10*g0050*p5 *p8


           3                 2                        2                 2
12*g0003*p8 *q9 - 10*g0005*p5 *p8*q10 + 20*g0006*p5*p8 *q9 - 10*g0007*p5 *p8*q10

              2                        2                 2
 - 10*g0008*p5 *p8*q10 + 20*g0009*p5*p8 *q9 - 10*g0010*p5 *p8*q10

              2                     2                   3
 - 10*g0011*p5 *p8*q10 - 20*g0012*p5 *p8*q9 - 5*g0013*p5 *q10

                 2                 2                     2
 + 20*g0014*p5*p8 *q9 - 10*g0015*p5 *p8*q10 - 10*g0016*p5 *p8*q9

              3                  2                    3                 3
 - 10*g0017*p5 *q10 + 10*g0018*p5 *p8*q9 - 10*g0024*p5 *p8 - 10*g0025*p5 *p8


                              2                2
2*g0054*p5*p8*q10 - 4*g0055*p8 *q9 + 4*g0056*p8 *q9 + 2*g0057*p5*p8*q10

                                 2                2
 + 2*g0058*p5*p8*q10 + 4*g0059*p8 *q9 - 4*g0060*p8 *q9 + 2*g0061*p5*p8*q10

                                 2              2
 + 2*g0062*p5*p8*q10 + 4*g0063*p8 *q9 - g0064*p5 *q10 + 4*g0065*p5*p8*q9

           2                 2
 + g0066*p5 *q10 - 4*g0067*p8 *q9 + 2*g0068*p5*p8*q10 + 2*g0069*p5*p8*q9

             2                                    2                2
 + 2*g0070*p5 *q10 - 2*g0071*p5*p8*q9 + 2*g0079*p5 *p8 + 2*g0080*p5 *p8


functions : 
      3
     ---*p8*q10
      5
q27=------------
         p5


         6    2
      - ---*p8 *q9
         5
q26=---------------
            2
          p5


q25=0


q24=q10


      - 2*p8*q9
q23=------------
         p5


     2*p8*q9
q22=---------
       p5


q21=q10


q20=q10


     2*p8*q9
q19=---------
       p5


      - 2*p8*q9
q18=------------
         p5


q17=q10


q16=q10


     2*p8*q9
q15=---------
       p5


         1
      - ---*p5*q10
         2
q14=---------------
          p8


q13=2*q9


      1
     ---*p5*q10
      2
q12=------------
         p8


      - 2*p8*q9
q11=------------
         p5

q10, q9, 
    p5*q10
q8=--------
      p8


q7= - q9


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, 
p7=0


p6=0

p5, 
p4=p5


p3=0


p2=0


p1=0


with 54 terms
no equations
4 constants : p5,p8,q9,q10
The equation: 

f =D f*f *p5 + D D f*D f*p5 + f  *p8
 t  2   x       1 2   1        3x
The symmetry: 
                          2                 2                             2
f =( - 2*D f  *D D f*p5*p8 *q9 + D f  *f *p5 *p8*q10 - 2*D f *D D f *p5*p8 *q9
 s        2 2x  1 2               2 2x  x                 2 x  1 2 x

                  2               2         2          1       2      3
     + D f *f  *p5 *p8*q10 - (D f) *D D f*p5 *p8*q9 + ---*(D f) *f *p5 *q10
        2 x  2x                2     1 2               2    2     x

                          2                      3                      2
     - 2*D f*D D f  *p5*p8 *q9 + D f*D D f*D f*p5 *q10 + 2*D f*D f*f *p5 *p8*q9
          2   1 2 2x              2   1 2   1               2   1   x

                 2           6            3                    2
     + D f*f  *p5 *p8*q10 - ---*D D f  *p8 *q9 + D D f  *D f*p5 *p8*q10
        2   3x               5   1 2 4x           1 2 2x  1

                     2                        2                     2   2
     + D D f *D f *p5 *p8*q10 + D D f*D f  *p5 *p8*q10 + D D f*(D f) *p5 *p8*q9
        1 2 x  1 x               1 2   1 2x               1 2    1

                       2                      2       1       2      3
     + 2*D f  *f *p5*p8 *q9 + 2*D f *f  *p5*p8 *q9 - ---*(D f) *f *p5 *q10
          1 2x  x                1 x  2x              2    1     x

                      2       3           2         2
     + 2*D f*f  *p5*p8 *q9 + ---*f  *p5*p8 *q10)/(p5 *p8)
          1   3x              5   5x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,f(1)))*d(1,f(1))*p5 + df(f(1),x,3)*
p8$
The symmetry: 
df(f(1),s)=( - 2*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5*p8**2*q9 + d(2,df(f(1),x,2)
)*df(f(1),x)*p5**2*p8*q10 - 2*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5*p8**2*q9 +
 d(2,df(f(1),x))*df(f(1),x,2)*p5**2*p8*q10 - d(2,f(1))**2*d(1,d(2,f(1)))*p5**2*
p8*q9 + 1/2*d(2,f(1))**2*df(f(1),x)*p5**3*q10 - 2*d(2,f(1))*d(1,d(2,df(f(1),x,2)
))*p5*p8**2*q9 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p5**3*q10 + 2*d(2,f(1))*d(1,
f(1))*df(f(1),x)*p5**2*p8*q9 + d(2,f(1))*df(f(1),x,3)*p5**2*p8*q10 - 6/5*d(1,d(2
,df(f(1),x,4)))*p8**3*q9 + d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p5**2*p8*q10 + d(1,d
(2,df(f(1),x)))*d(1,df(f(1),x))*p5**2*p8*q10 + d(1,d(2,f(1)))*d(1,df(f(1),x,2))*
p5**2*p8*q10 + d(1,d(2,f(1)))*d(1,f(1))**2*p5**2*p8*q9 + 2*d(1,df(f(1),x,2))*df(
f(1),x)*p5*p8**2*q9 + 2*d(1,df(f(1),x))*df(f(1),x,2)*p5*p8**2*q9 - 1/2*d(1,f(1))
**2*df(f(1),x)*p5**3*q10 + 2*d(1,f(1))*df(f(1),x,3)*p5*p8**2*q9 + 3/5*df(f(1),x,
5)*p5*p8**2*q10)/(p5**2*p8)$

Time: 0 ms

Time: 0 ms

Time: 10 ms

New level : 1.1.1.2.2.1.2.2.
now back to the substitution of q9 by e_340
The list of inequalities got extended by: 

p3


Step 1014: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 49 terms

The list of inequalities got extended by: 
An expression with 48 terms

Substitution of q9 by an expression in 
q27, q10, p3, p5, p8 found in e_340 : 22 factors in 5 terms


>>>>>>>>> Solution of level 1.1.1.2.2.1.2.2. : 
no equations


Non-vanishing expressions: p4,p8,p5,q10,p3
236 factors in 48 terms
240 factors in 49 terms
185 factors in 38 terms
214 factors in 44 terms

g0111*p8 - g0113*p3 + g0114*p5 + g0115*p5 + g0116*p3


functions : q27, 
               3
     p5*q27 - ---*p8*q10
               5
q26=---------------------
             p3


q25=0


q24=q10


      5    2        5    2
     ---*p3 *q27 + ---*p5 *q27 - p5*p8*q10
      3             3
q23=---------------------------------------
                     p3*p8


         5    2        5    2
      - ---*p3 *q27 - ---*p5 *q27 + p5*p8*q10
         3             3
q22=------------------------------------------
                      p3*p8


q21=q10


q20=q10


         5    2        5    2
      - ---*p3 *q27 - ---*p5 *q27 + p5*p8*q10
         3             3
q19=------------------------------------------
                      p3*p8


      5    2        5    2
     ---*p3 *q27 + ---*p5 *q27 - p5*p8*q10
      3             3
q18=---------------------------------------
                     p3*p8


q17=q10


q16=q10


         5    2        5    2
      - ---*p3 *q27 - ---*p5 *q27 + p5*p8*q10
         3             3
q15=------------------------------------------
                      p3*p8


      5    2        5    2
     ---*p3 *q27 + ---*p5 *q27 - p5*p8*q10
      6             6
q14=---------------------------------------
                        2
                      p8


         5    2            2           5    3         2
      - ---*p3 *p5*q27 - p3 *p8*q10 - ---*p5 *q27 + p5 *p8*q10
         3                             3
q13=-----------------------------------------------------------
                                   2
                              p3*p8


         5    2        5    2
      - ---*p3 *q27 - ---*p5 *q27 + p5*p8*q10
         6             6
q12=------------------------------------------
                         2
                       p8


      5    2        5    2
     ---*p3 *q27 + ---*p5 *q27 - p5*p8*q10
      3             3
q11=---------------------------------------
                     p3*p8

q10, 
        5    2           1    2           5    3        1    2
     - ---*p3 *p5*q27 - ---*p3 *p8*q10 - ---*p5 *q27 + ---*p5 *p8*q10
        6                2                6             2
q9=-------------------------------------------------------------------
                                      2
                                 p3*p8


        5    2        5    2
     - ---*p3 *q27 - ---*p5 *q27 + 2*p5*p8*q10
        3             3
q8=--------------------------------------------
                         2
                       p8


     5    2           1    2           5    3        1    2
    ---*p3 *p5*q27 + ---*p3 *p8*q10 + ---*p5 *q27 - ---*p5 *p8*q10
     6                2                6             2
q7=----------------------------------------------------------------
                                     2
                                p3*p8


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, 
p7=0


p6= - p3

p5, 
p4=p5

p3, 
p2=0


p1=0


with 83 terms
no equations
5 constants : p3,p5,p8,q10,q27
The equation: 

f =D f*D D f*p3 + D f*f *p5 + D D f*D f*p5 - D f*f *p3 + f  *p8
 t  2   1 2        2   x       1 2   1        1   x       3x
The symmetry: 
     5                2           5                2
f =(---*D f  *D D f*p3 *p8*q27 + ---*D f  *D D f*p5 *p8*q27
 s   3   2 2x  1 2                3   2 2x  1 2

                        2                     2        5                2
     - D f  *D D f*p5*p8 *q10 + D f  *f *p3*p8 *q10 + ---*D f *D D f *p3 *p8*q27
        2 2x  1 2                2 2x  x               3   2 x  1 2 x

        5                2                           2                     2
     + ---*D f *D D f *p5 *p8*q27 - D f *D D f *p5*p8 *q10 + D f *f  *p3*p8 *q10
        3   2 x  1 2 x               2 x  1 2 x               2 x  2x

        5       2         2           1       2         2
     + ---*(D f) *D D f*p3 *p5*q27 + ---*(D f) *D D f*p3 *p8*q10
        6    2     1 2                2    2     1 2

        5       2         3        1       2         2
     + ---*(D f) *D D f*p5 *q27 - ---*(D f) *D D f*p5 *p8*q10
        6    2     1 2             2    2     1 2

        5       2      3        5       2         2            2
     - ---*(D f) *f *p3 *q27 - ---*(D f) *f *p3*p5 *q27 + (D f) *f *p3*p5*p8*q10
        6    2     x            6    2     x                2     x

        5                2           5                2
     + ---*D f*D D f  *p3 *p8*q27 + ---*D f*D D f  *p5 *p8*q27
        3   2   1 2 2x               3   2   1 2 2x

                        2        5                  3
     - D f*D D f  *p5*p8 *q10 - ---*D f*D D f*D f*p3 *q27
        2   1 2 2x               3   2   1 2   1

        5                     2
     - ---*D f*D D f*D f*p3*p5 *q27 + 2*D f*D D f*D f*p3*p5*p8*q10
        3   2   1 2   1                  2   1 2   1

        5               2                       2
     - ---*D f*D f*f *p3 *p5*q27 - D f*D f*f *p3 *p8*q10
        3   2   1   x               2   1   x

        5               3                    2                       2
     - ---*D f*D f*f *p5 *q27 + D f*D f*f *p5 *p8*q10 + D f*f  *p3*p8 *q10
        3   2   1   x            2   1   x               2   3x

                    2        3            3                        2
     + D D f  *p5*p8 *q27 - ---*D D f  *p8 *q10 + D D f  *D f*p3*p8 *q10
        1 2 4x               5   1 2 4x            1 2 2x  1

                        2                        2
     + D D f *D f *p3*p8 *q10 + D D f*D f  *p3*p8 *q10
        1 2 x  1 x               1 2   1 2x

        5             2   2           1             2   2
     - ---*D D f*(D f) *p3 *p5*q27 - ---*D D f*(D f) *p3 *p8*q10
        6   1 2    1                  2   1 2    1

        5             2   3        1             2   2
     - ---*D D f*(D f) *p5 *q27 + ---*D D f*(D f) *p5 *p8*q10
        6   1 2    1               2   1 2    1

        5             2           5             2                        2
     - ---*D f  *f *p3 *p8*q27 - ---*D f  *f *p5 *p8*q27 + D f  *f *p5*p8 *q10
        3   1 2x  x               3   1 2x  x               1 2x  x

        5             2           5             2                        2
     - ---*D f *f  *p3 *p8*q27 - ---*D f *f  *p5 *p8*q27 + D f *f  *p5*p8 *q10
        3   1 x  2x               3   1 x  2x               1 x  2x

        5       2      3        5       2         2            2
     + ---*(D f) *f *p3 *q27 + ---*(D f) *f *p3*p5 *q27 - (D f) *f *p3*p5*p8*q10
        6    1     x            6    1     x                1     x

        5            2           5            2                       2
     - ---*D f*f  *p3 *p8*q27 - ---*D f*f  *p5 *p8*q27 + D f*f  *p5*p8 *q10
        3   1   3x               3   1   3x               1   3x

                2            2
     + f  *p3*p8 *q27)/(p3*p8 )
        5x
*** Garbage collection starting 
*** GC 342  3-Oct-2003 05:29:28, 30 ms (0%), 1001124 occupied, 23998827 free
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,f(1))
)*d(1,f(1))*p5 - d(1,f(1))*df(f(1),x)*p3 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=(5/3*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p3**2*p8*q27 + 5/3*d(2,df(f(1),
x,2))*d(1,d(2,f(1)))*p5**2*p8*q27 - d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5*p8**2*
q10 + d(2,df(f(1),x,2))*df(f(1),x)*p3*p8**2*q10 + 5/3*d(2,df(f(1),x))*d(1,d(2,df
(f(1),x)))*p3**2*p8*q27 + 5/3*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**2*p8*q27 
- d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5*p8**2*q10 + d(2,df(f(1),x))*df(f(1),x,
2)*p3*p8**2*q10 + 5/6*d(2,f(1))**2*d(1,d(2,f(1)))*p3**2*p5*q27 + 1/2*d(2,f(1))**
2*d(1,d(2,f(1)))*p3**2*p8*q10 + 5/6*d(2,f(1))**2*d(1,d(2,f(1)))*p5**3*q27 - 1/2*
d(2,f(1))**2*d(1,d(2,f(1)))*p5**2*p8*q10 - 5/6*d(2,f(1))**2*df(f(1),x)*p3**3*q27
 - 5/6*d(2,f(1))**2*df(f(1),x)*p3*p5**2*q27 + d(2,f(1))**2*df(f(1),x)*p3*p5*p8*
q10 + 5/3*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p3**2*p8*q27 + 5/3*d(2,f(1))*d(1,d(2,
df(f(1),x,2)))*p5**2*p8*q27 - d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p5*p8**2*q10 - 5/
3*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3**3*q27 - 5/3*d(2,f(1))*d(1,d(2,f(1)))*d(
1,f(1))*p3*p5**2*q27 + 2*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3*p5*p8*q10 - 5/3*d
(2,f(1))*d(1,f(1))*df(f(1),x)*p3**2*p5*q27 - d(2,f(1))*d(1,f(1))*df(f(1),x)*p3**
2*p8*q10 - 5/3*d(2,f(1))*d(1,f(1))*df(f(1),x)*p5**3*q27 + d(2,f(1))*d(1,f(1))*df
(f(1),x)*p5**2*p8*q10 + d(2,f(1))*df(f(1),x,3)*p3*p8**2*q10 + d(1,d(2,df(f(1),x,
4)))*p5*p8**2*q27 - 3/5*d(1,d(2,df(f(1),x,4)))*p8**3*q10 + d(1,d(2,df(f(1),x,2))
)*d(1,f(1))*p3*p8**2*q10 + d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p3*p8**2*q10 + d
(1,d(2,f(1)))*d(1,df(f(1),x,2))*p3*p8**2*q10 - 5/6*d(1,d(2,f(1)))*d(1,f(1))**2*
p3**2*p5*q27 - 1/2*d(1,d(2,f(1)))*d(1,f(1))**2*p3**2*p8*q10 - 5/6*d(1,d(2,f(1)))
*d(1,f(1))**2*p5**3*q27 + 1/2*d(1,d(2,f(1)))*d(1,f(1))**2*p5**2*p8*q10 - 5/3*d(1
,df(f(1),x,2))*df(f(1),x)*p3**2*p8*q27 - 5/3*d(1,df(f(1),x,2))*df(f(1),x)*p5**2*
p8*q27 + d(1,df(f(1),x,2))*df(f(1),x)*p5*p8**2*q10 - 5/3*d(1,df(f(1),x))*df(f(1)
,x,2)*p3**2*p8*q27 - 5/3*d(1,df(f(1),x))*df(f(1),x,2)*p5**2*p8*q27 + d(1,df(f(1)
,x))*df(f(1),x,2)*p5*p8**2*q10 + 5/6*d(1,f(1))**2*df(f(1),x)*p3**3*q27 + 5/6*d(1
,f(1))**2*df(f(1),x)*p3*p5**2*q27 - d(1,f(1))**2*df(f(1),x)*p3*p5*p8*q10 - 5/3*d
(1,f(1))*df(f(1),x,3)*p3**2*p8*q27 - 5/3*d(1,f(1))*df(f(1),x,3)*p5**2*p8*q27 + d
(1,f(1))*df(f(1),x,3)*p5*p8**2*q10 + df(f(1),x,5)*p3*p8**2*q27)/(p3*p8**2)$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p3 + p6


New level : 1.1.1.2.2.2.
CRACK is now called with the new equation e_252 : 9 factors in 3 terms

Step 1015: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 34 terms

e_133 is a consequence of e_32.
e_290 is a consequence of e_364.
Substitution of q9 by an expression in 
q10, p6, p3, p8 found in e_252 : 10 factors in 3 terms

Step 1016: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 35 terms

e_64 is a consequence of e_364.
e_312 is a consequence of e_364.
Substitution of q7 by an expression in 
q10, p5, p3, p8, p4 found in e_305 : 13 factors in 3 terms

Step 1017: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q12

from e_323 and e_306. e_306: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                     2         2
 (q12,q10,q8,p6,p5,p3 ,p3,p8,p4 ,p4)

is replaced by e_396: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                 2         2
 (q10,q8,p6,p5,p3 ,p3,p8,p4 ,p4)


Step 1018: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_255 we get the alternative equations : 
0=q10


0=3*p4 - p5


New level : 1.1.1.2.2.2.1.
CRACK is now called with the new equation e_420 : 
0=q10

e_376,e_18,e_11,e_340,e_311,e_364,e_352,e_377 are consequences of e_420

Step 1019: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 5 terms

e_390 is a consequence of e_205.
e_159 is a consequence of e_205.
e_154 is a consequence of e_205.
e_278 is a consequence of e_205.
e_185 is a consequence of e_205.
e_172 is a consequence of e_205.
e_34 is a consequence of e_205.
Substitution of q10 found in e_420 : 
q10=0


Step 1020: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 3 terms

e_371 is a consequence of e_5.
Substitution of q8 found in e_205 : 
q8=0


Step 1021: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

g0084*p4 + g0085*p6


q27

The lexicographical ordering of unknowns is changed
because q27 has to be non-zero, giving q27 a low priority.
Old ordering: q27,q12,p6,p5,p3,p8,p4
New ordering: q12,q27,p6,p5,p3,p8,p4

The list of inequalities got extended by: 

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q12,q27,p6,p5,p3,p8,p4
New ordering: q12,q27,p5,p3,p6,p8,p4

Substitution of q12 found in e_5 : 
q12=0


Step 1022: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
contradiction from the substitution:
p6=0

because of the non-vanishing expression:
p6


Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p5

The lexicographical ordering of unknowns is changed
because p5 has to be non-zero, giving p5 a low priority.
Old ordering: q27,q12,q10,q8,p6,p5,p3,p8,p4
New ordering: q27,q12,q10,q8,p6,p3,p5,p8,p4

The list of inequalities got extended by: 

p3


p6


The list of inequalities got extended by: 

q10

The lexicographical ordering of unknowns is changed
because q10 has to be non-zero, giving q10 a low priority.
Old ordering: q27,q12,q10,q8,p6,p3,p5,p8,p4
New ordering: q27,q12,q8,q10,p6,p3,p5,p8,p4

The list of inequalities got extended by: 

q27

The lexicographical ordering of unknowns is changed
because q27 has to be non-zero, giving q27 a low priority.
Old ordering: q27,q12,q8,q10,p6,p3,p5,p8,p4
New ordering: q12,q8,q27,q10,p6,p3,p5,p8,p4

New level : 1.1.1.2.2.2.2.
CRACK is now called with the new equation e_420 : 
0=3*p4 - p5


Step 1023: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 32 terms

e_205 is a consequence of e_295.
e_390 is a consequence of e_295.
e_132 is a consequence of e_159.
e_193 is a consequence of e_234.
e_27 is a consequence of e_371.
*** Garbage collection starting 
*** GC 343  3-Oct-2003 05:29:31, 30 ms (0%), 1005766 occupied, 23994183 free

Substitution of p4 by an expression in 
p5 found in e_420 : 
    1
p4=---*p5
    3


Step 1024: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 

p3


The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 25 terms

e_159 is a consequence of e_310.
e_371 is a consequence of e_355.
e_234 is a consequence of e_310.
e_34 is a consequence of e_310.
e_172 is a consequence of e_310.
e_278 is a consequence of e_355.
e_369 is a consequence of e_355.
e_5 is a consequence of e_310.
Substitution of p3 by an expression in 
p6 found in e_243 : 
       1
p3= - ---*p6
       3


Step 1025: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 

q10


The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 23 terms

Substitution of q10 by an expression in 
q27, p5, p8 found in e_295 : 
      5
     ---*p5*q27
      9
q10=------------
         p8


Step 1026: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 24 terms

Substitution of q12 by an expression in 
q8, q27, p5, p8 found in e_185 : 10 factors in 3 terms

Step 1027: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 25 terms

e_358 is a consequence of e_310.
e_355 is a consequence of e_310.
e_154 is a consequence of e_310.
e_353 is a consequence of e_310.
Substitution of q8 by an expression in 
q27, p6, p5, p8 found in e_62 : 10 factors in 3 terms

Step 1028: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.1.2.2.2.2. : 
equations : 

e_310 : 
    2     2
0=p5  + p6



Non-vanishing expressions: q10,p4,p8,p5,p6,q27,p3
103 factors in 25 terms
141 factors in 28 terms
109 factors in 22 terms

45*g0030*p5*p8*q27 - 45*g0031*p6*p8*q27 + 135*g0032*p6*p8*q27

 + 135*g0033*p6*p8*q27 - 45*g0034*p6*p8*q27 + 45*g0035*p5*p8*q27

                                    2                  2
 + 135*g0036*p6*p8*q27 - 20*g0037*p5 *q27 + 60*g0037*p6 *q27

 + 160*g0038*p5*p6*q27 - 45*g0039*p6*p8*q27 + 45*g0040*p5*p8*q27

                                   2                  2
 + 40*g0041*p5*p6*q27 + 40*g0042*p5 *q27 - 40*g0042*p6 *q27 - 40*g0043*p5*p6*q27

                 2                 2                 2
 + 81*g0049*p6*p8  + 27*g0050*p5*p8  - 27*g0051*p6*p8


3*g0111*p8 + 3*g0113*p6 + 3*g0114*p5 + g0115*p5 - g0116*p6


functions : q27, 
q26=0


q25=0


      5
     ---*p5*q27
      9
q24=------------
         p8


         5
      - ---*p6*q27
         9
q23=---------------
          p8


      5
     ---*p6*q27
      3
q22=------------
         p8


      5    2        10    2
     ---*p5 *q27 - ----*p6 *q27
      9             9
q21=----------------------------
               p5*p8


      5    2        10    2
     ---*p5 *q27 - ----*p6 *q27
      9             9
q20=----------------------------
               p5*p8


      5
     ---*p6*q27
      3
q19=------------
         p8


         5
      - ---*p6*q27
         9
q18=---------------
          p8


      5
     ---*p5*q27
      9
q17=------------
         p8


      5    2        10    2
     ---*p5 *q27 - ----*p6 *q27
      9             9
q16=----------------------------
               p5*p8


      5
     ---*p6*q27
      3
q15=------------
         p8


         20    2        20    2
      - ----*p5 *q27 + ----*p6 *q27
         81             27
q14=--------------------------------
                    2
                  p8


      160
     -----*p5*p6*q27
      81
q13=-----------------
             2
           p8


      20    2        20    2
     ----*p5 *q27 - ----*p6 *q27
      27             81
q12=-----------------------------
                   2
                 p8


         5
      - ---*p6*q27
         9
q11=---------------
          p8


      5
     ---*p5*q27
      9
q10=------------
         p8


     40
    ----*p5*p6*q27
     81
q9=----------------
           2
         p8


     40    2        40    2
    ----*p5 *q27 - ----*p6 *q27
     81             81
q8=-----------------------------
                  2
                p8


        40
     - ----*p5*p6*q27
        81
q7=-------------------
             2
           p8


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, 
p7=0

p6, p5, 
    1
p4=---*p5
    3


       1
p3= - ---*p6
       3


p2=0


p1=0


with 61 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_310(2a)
4 constants : p5,p6,p8,q27
The equation: 

       1                              1
f = - ---*D f*D D f*p6 + D f*f *p5 + ---*D D f*D f*p5 + D f*f *p6 + f  *p8
 t     3   2   1 2        2   x       3   1 2   1        1   x       3x
The symmetry: 
        5                              5             2
f =( - ---*D f  *D D f*p5*p6*p8*q27 + ---*D f  *f *p5 *p8*q27
 s      9   2 2x  1 2                  9   2 2x  x

        10             2           5
     - ----*D f  *f *p6 *p8*q27 - ---*D f *D D f *p5*p6*p8*q27
        9    2 2x  x               9   2 x  1 2 x

        5             2           10             2
     + ---*D f *f  *p5 *p8*q27 - ----*D f *f  *p6 *p8*q27
        9   2 x  2x               9    2 x  2x

        40       2         2           20       2      3
     - ----*(D f) *D D f*p5 *p6*q27 + ----*(D f) *f *p5 *q27
        81    2     1 2                27    2     x

        20       2         2        5
     - ----*(D f) *f *p5*p6 *q27 - ---*D f*D D f  *p5*p6*p8*q27
        81    2     x               9   2   1 2 2x

        40                  3        40                     2
     + ----*D f*D D f*D f*p5 *q27 - ----*D f*D D f*D f*p5*p6 *q27
        81   2   1 2   1             81   2   1 2   1

        160               2           5            2
     + -----*D f*D f*f *p5 *p6*q27 + ---*D f*f  *p5 *p8*q27
        81    2   1   x               9   2   3x

        10            2           5                2
     - ----*D f*f  *p6 *p8*q27 + ---*D D f  *D f*p5 *p8*q27
        9    2   3x               9   1 2 2x  1

        5                2           5                2
     + ---*D D f *D f *p5 *p8*q27 + ---*D D f*D f  *p5 *p8*q27
        9   1 2 x  1 x               9   1 2   1 2x

        40             2   2           5
     + ----*D D f*(D f) *p5 *p6*q27 + ---*D f  *f *p5*p6*p8*q27
        81   1 2    1                  3   1 2x  x

        5                           20       2      3
     + ---*D f *f  *p5*p6*p8*q27 - ----*(D f) *f *p5 *q27
        3   1 x  2x                 81    1     x

        20       2         2        5                                  2
     + ----*(D f) *f *p5*p6 *q27 + ---*D f*f  *p5*p6*p8*q27 + f  *p5*p8 *q27)/(
        27    1     x               3   1   3x                 5x

        2
   p5*p8 )
And now in machine readable form:

The system: 

df(f(1),t)= - 1/3*d(2,f(1))*d(1,d(2,f(1)))*p6 + d(2,f(1))*df(f(1),x)*p5 + 1/3*d(
1,d(2,f(1)))*d(1,f(1))*p5 + d(1,f(1))*df(f(1),x)*p6 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=( - 5/9*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5*p6*p8*q27 + 5/9*d(2,df(f(
1),x,2))*df(f(1),x)*p5**2*p8*q27 - 10/9*d(2,df(f(1),x,2))*df(f(1),x)*p6**2*p8*
q27 - 5/9*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5*p6*p8*q27 + 5/9*d(2,df(f(1),x)
)*df(f(1),x,2)*p5**2*p8*q27 - 10/9*d(2,df(f(1),x))*df(f(1),x,2)*p6**2*p8*q27 - 
40/81*d(2,f(1))**2*d(1,d(2,f(1)))*p5**2*p6*q27 + 20/27*d(2,f(1))**2*df(f(1),x)*
p5**3*q27 - 20/81*d(2,f(1))**2*df(f(1),x)*p5*p6**2*q27 - 5/9*d(2,f(1))*d(1,d(2,
df(f(1),x,2)))*p5*p6*p8*q27 + 40/81*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p5**3*q27
 - 40/81*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p5*p6**2*q27 + 160/81*d(2,f(1))*d(1,
f(1))*df(f(1),x)*p5**2*p6*q27 + 5/9*d(2,f(1))*df(f(1),x,3)*p5**2*p8*q27 - 10/9*d
(2,f(1))*df(f(1),x,3)*p6**2*p8*q27 + 5/9*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p5**2*
p8*q27 + 5/9*d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p5**2*p8*q27 + 5/9*d(1,d(2,f(1
)))*d(1,df(f(1),x,2))*p5**2*p8*q27 + 40/81*d(1,d(2,f(1)))*d(1,f(1))**2*p5**2*p6*
q27 + 5/3*d(1,df(f(1),x,2))*df(f(1),x)*p5*p6*p8*q27 + 5/3*d(1,df(f(1),x))*df(f(1
),x,2)*p5*p6*p8*q27 - 20/81*d(1,f(1))**2*df(f(1),x)*p5**3*q27 + 20/27*d(1,f(1))
**2*df(f(1),x)*p5*p6**2*q27 + 5/3*d(1,f(1))*df(f(1),x,3)*p5*p6*p8*q27 + df(f(1),
x,5)*p5*p8**2*q27)/(p5*p8**2)$

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 70 ms

The list of inequalities got extended by: 

p7

The lexicographical ordering of unknowns is changed
because p7 has to be non-zero, giving p7 a low priority.
Old ordering: q27,q26,q25,q24,q23,q22,q21,q20,q19,q18,q17,q16,q15,q14,q13,q12,
q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1,p8,p7,p6,p5,p4,p3
New ordering: q27,q26,q25,q24,q23,q22,q21,q20,q19,q18,q17,q16,q15,q14,q13,q12,
q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1,p8,p6,p5,p4,p3,p7

New level : 1.1.2.
CRACK is now called with the new equation e_310 : 
0=q1

e_141,e_3 are consequences of e_310

Step 1029: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 28 terms
e_163,e_162,e_191,e_226 are consequences of e_5
e_161,e_62,e_169 are consequences of e_193

e_204 is a consequence of e_53.
Substitution of q1 found in e_310 : 
q1=0


Step 1030: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 27 terms

e_239 is a consequence of e_12.
e_156 is a consequence of e_12.e_159,e_32,e_205,e_155 are consequences of e_23
e_54,e_7,e_117 are consequences of e_148

e_262 is a consequence of e_235.e_95 is a consequence of e_279

e_154 is a consequence of e_279.
Substitution of q2 found in e_101 : 
q2=0


Step 1031: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 26 terms

e_277 is a consequence of e_193.
e_278 is a consequence of e_193.
Substitution of q5 found in e_5 : 
q5=0


Step 1032: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 25 terms

e_274 is a consequence of e_12.
e_282 is a consequence of e_12.
Substitution of q6 found in e_193 : 
q6=0


Step 1033: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 24 terms

e_255 is a consequence of e_23.
e_216 is a consequence of e_23.
e_286 is a consequence of e_23.
Substitution of q25 found in e_12 : 
q25=0


Step 1034: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 23 terms

e_194 is a consequence of e_148.
e_103 is a consequence of e_148.
Substitution of q3 found in e_23 : 
q3=0


Step 1035: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 22 terms

Substitution of q4 found in e_148 : 
q4=0


Step 1036: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 24 terms

e_289 is a consequence of e_284.
e_290 is a consequence of e_166.
Substitution of q23 by an expression in 
q22, q15, q11 found in e_235 : 
q23=q11 - q15 + q22


Step 1037: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 26 terms
e_227 is a consequence of e_53

e_302 is a consequence of e_183.
Substitution of q24 by an expression in 
q21, q16, q10 found in e_279 : 
q24=q10 + q16 - q21


Step 1038: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 30 terms

e_304 is a consequence of e_228.
e_313 is a consequence of e_263.
Substitution of q21 by an expression in 
q20, q17, q16, q10 found in e_53 : 13 factors in 5 terms

Step 1039: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 33 terms

Substitution of q15 by an expression in 
q26, q11, p6, p3, p7 found in e_143 : 8 factors in 4 terms

Step 1040: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 35 terms

Substitution of q18 by an expression in 
q27, q26, q20, p8, p5, p3, p7 found in e_28 : 12 factors in 4 terms

Step 1041: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 37 terms
*** Garbage collection starting 
*** GC 344  3-Oct-2003 05:29:34, 30 ms (0%), 1094893 occupied, 23905056 free

Substitution of q19 by an expression in 
q27, q26, q17, p8, p6, p4, p7 found in e_237 : 12 factors in 4 terms

Step 1042: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 41 terms

Substitution of q16 by an expression in 
q26, q10, p5, p4, p7 found in e_246 : 8 factors in 4 terms

Step 1043: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_27 and e_161. e_161: 
 11 terms, 33 factors, with derivatives of functions of all variables: 

                                     2
 (q27,q26,q20,q17,q11,q10,p8,p6,p5,p4 ,p4,p3,p7)

is replaced by e_227: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

 (q26,q17,q10,p8,p6,p4,p3,p7)


Step 1044: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 345  3-Oct-2003 05:29:37, 50 ms (0%), 1125350 occupied, 23874594 free
Eliminate 
q27

from e_312 and e_278. e_278: 
 11 terms, 33 factors, with derivatives of functions of all variables: 

                                      2         2
 (q27,q26,q22,q20,q17,q11,q10,p8,p6,p5 ,p5,p4,p3 ,p3,p7)

is replaced by e_302: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                              2         2
 (q26,q22,q20,q17,q11,p8,p6,p5 ,p5,p4,p3 ,p3,p7)


Step 1045: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 346  3-Oct-2003 05:29:39, 40 ms (0%), 1108236 occupied, 23891711 free
*** Garbage collection starting 
*** GC 347  3-Oct-2003 05:29:42, 40 ms (0%), 1106312 occupied, 23893636 free
Eliminate 
q27

from e_226 and e_103. e_103: 
 14 terms, 42 factors, with derivatives of functions of all variables: 

                                         2         2      2
 (q27,q26,q20,q17,q13,q11,q10,q8,p8,p6,p5 ,p5,p4,p3 ,p3,p7 ,p7)

is replaced by e_279: 
 12 terms, 36 factors, with derivatives of functions of all variables: 

                                     2         2      2
 (q26,q20,q17,q13,q11,q10,q8,p8,p6,p5 ,p5,p4,p3 ,p3,p7 ,p7)


Step 1046: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 348  3-Oct-2003 05:29:45, 40 ms (0%), 1122801 occupied, 23877143 free
*** Garbage collection starting 
*** GC 349  3-Oct-2003 05:29:48, 50 ms (0%), 1115553 occupied, 23884391 free
Eliminate 
q27

from e_338 and e_23. e_23: 
 13 terms, 39 factors, with derivatives of functions of all variables: 

                                            2         2
 (q27,q26,q22,q20,q17,q13,q10,q8,p8,p6,p5,p4 ,p4,p3,p7 ,p7)

is replaced by e_304: 
 11 terms, 33 factors, with derivatives of functions of all variables: 

                                                  2
 (q26,q22,q20,q17,q13,q11,q10,q8,p8,p6,p5,p4,p3,p7 ,p7)


Step 1047: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_239 and e_101. e_101: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                               2         2
 (q27,q26,q22,q20,q17,q10,p8,p6 ,p6,p5,p4 ,p4,p7)

is replaced by e_313: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                                        2      2
 (q26,q22,q20,q17,q14,q10,q9,p8,p6,p5,p4 ,p4,p7 ,p7)


Step 1048: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 350  3-Oct-2003 05:29:51, 50 ms (0%), 1110528 occupied, 23889420 free
Eliminate 
q27

from e_339 and e_95. e_95: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                            2               2
 (q27,q26,q22,q20,q17,q10,p8 ,p8,p6,p5,p4,p7 ,p7)

is replaced by e_53: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                                       2
 (q26,q22,q20,q17,q11,p8,p6,p5,p4,p3,p7 ,p7)


e_53 is a consequence of e_277.
Step 1049: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_27 and e_191. e_191: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                                    2         2
 (q27,q26,q20,q17,q14,q9,p8,p6,p5,p4 ,p4,p3,p7 ,p7)

is replaced by e_315: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                                       2
 (q26,q17,q14,q11,q10,q9,p8,p6,p4,p3,p7 ,p7)


Step 1050: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_315 and e_227. e_315: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                                       2
 (q26,q17,q14,q11,q10,q9,p8,p6,p4,p3,p7 ,p7)

is replaced by e_316: 
 7 terms, 14 factors, with derivatives of functions of all variables: 

 (q17,q14,q11,q10,q9,p8,p6,p4,p3,p7)


Step 1051: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_316 and e_255. e_255: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                                          2
 (q26,q17,q13,q11,q10,q8,p8,p6,p5,p4,p3,p7 ,p7)

is replaced by e_317: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                                             2
 (q26,q14,q13,q11,q10,q9,q8,p8,p6,p5,p4,p3,p7 ,p7)


Step 1052: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_313 and e_172. e_313: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                                        2      2
 (q26,q22,q20,q17,q14,q10,q9,p8,p6,p5,p4 ,p4,p7 ,p7)

is replaced by e_318: 
 8 terms, 16 factors, with derivatives of functions of all variables: 

 (q22,q20,q17,q14,q10,q9,q8,p8,p6,p4,p3,p7)


Step 1053: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 351  3-Oct-2003 05:29:54, 40 ms (0%), 1114402 occupied, 23885545 free
Eliminate 
q27

from e_185 and e_274. e_274: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                                      2
 (q27,q26,q22,q20,q17,q11,q10,p8,p6,p5 ,p5,p4,p3,p7)

is replaced by e_319: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                                                  2
 (q26,q22,q20,q17,q12,q11,q10,q7,p8,p6,p5,p4,p3,p7 ,p7)


Step 1054: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 352  3-Oct-2003 05:29:57, 40 ms (0%), 1118309 occupied, 23881637 free
Eliminate 
q17

from e_316 and e_216. e_216: 
 12 terms, 36 factors, with derivatives of functions of all variables: 

                                       2
 (q26,q20,q17,q14,q10,q8,p6,p5,p4,p3,p7 ,p7)

is replaced by e_320: 
 12 terms, 36 factors, with derivatives of functions of all variables: 

                                             2
 (q26,q20,q14,q11,q10,q9,q8,p8,p6,p5,p4,p3,p7 ,p7)


Step 1055: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 353  3-Oct-2003 05:30:01, 50 ms (0%), 1112407 occupied, 23887536 free
Eliminate 
q17

from e_65 and e_238. e_238: 
 11 terms, 33 factors, with derivatives of functions of all variables: 

                           2      2      2
 (q26,q20,q17,q13,q10,q9,p5 ,p5,p4 ,p4,p7 ,p7)

is replaced by e_321: 
 11 terms, 33 factors, with derivatives of functions of all variables: 

                                    2      2      2
 (q26,q20,q13,q11,q10,q9,q8,p8,p6,p5 ,p5,p4 ,p4,p7 ,p7)


Step 1056: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 354  3-Oct-2003 05:30:05, 40 ms (0%), 1115442 occupied, 23884506 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_338 we get the alternative equations : 
0=p4

25 factors in 8 terms

New level : 1.1.2.1.
CRACK is now called with the new equation e_326 : 
0=p4


Step 1057: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 36 terms

Substitution of p4 found in e_326 : 
p4=0


Step 1058: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 37 terms

Substitution of q9 by an expression in 
q22, q8, p8, p3, p7 found in e_366 : 10 factors in 3 terms

Step 1059: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
*** Garbage collection starting 
*** GC 355  3-Oct-2003 05:30:10, 40 ms (0%), 1119439 occupied, 23880511 free

The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 40 terms

Substitution of q13 by an expression in 
q17, q11, q10, q8, p8, p6, p5, p7 found in e_334 : 14 factors in 5 terms

Step 1060: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1061: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1062: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q20

from e_358 and e_371. e_371: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                                  2
 (q27,q26,q20,q17,q11,q10,p8,p5,p3 ,p3,p7)

is replaced by e_101: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                              2
 (q27,q26,q17,q11,q10,p8,p5,p3 ,p3,p7)


Step 1063: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_420 and e_370. e_370: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                                    2      2
 (q27,q26,q20,q17,q12,q7,p8,p6,p5,p3 ,p3,p7 ,p7)

is replaced by e_95: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                                   2
 (q26,q20,q17,q12,q7,p8,p6,p5,p3,p7 ,p7)


Step 1064: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1065: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 356  3-Oct-2003 05:30:13, 40 ms (0%), 1134803 occupied, 23865145 free
Eliminate 
q27

from e_336 and e_376. e_376: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                                        2
 (q27,q26,q20,q17,q11,q10,p8,p6,p5,p3,p7 ,p7)

is replaced by e_191: 
 7 terms, 21 factors, with derivatives of functions of all variables: 

                                    2
 (q26,q20,q17,q11,q10,p8,p6,p5,p3,p7 ,p7)


Step 1066: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_364 and e_388. e_388: 
 11 terms, 33 factors, with derivatives of functions of all variables: 

                           2               2
 (q26,q20,q17,q11,q10,q8,p8 ,p8,p6,p5,p3,p7 ,p7)

is replaced by e_315: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                       2               2
 (q20,q17,q11,q10,q8,p8 ,p8,p6,p5,p3,p7 ,p7)


Step 1067: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_382 and e_387. e_387: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                                  2
 (q27,q26,q20,q17,q11,q10,p8,p6,p5 ,p5,p3,p7)

is replaced by e_255: 
 4 terms, 8 factors, with derivatives of functions of all variables: 

 (q17,q10,p6,p3)


e_255 is a consequence of e_362.
Step 1068: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q20

from e_358 and e_378. e_378: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                               2               2
 (q26,q22,q20,q17,q11,q10,q8,p8 ,p8,p6,p5,p3,p7 ,p7)

is replaced by e_313: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                           2               2
 (q26,q22,q17,q11,q10,q8,p8 ,p8,p6,p5,p3,p7 ,p7)


Step 1069: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_336 and e_381. e_381: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                                            2
 (q27,q26,q22,q20,q17,q11,q10,p8,p6,p5,p3,p7 ,p7)

is replaced by e_274: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                                        2
 (q26,q22,q20,q17,q11,q10,p8,p6,p5,p3,p7 ,p7)


Step 1070: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_336 and e_375. e_375: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                                            2
 (q27,q26,q22,q20,q17,q11,q10,p8,p6,p5,p3,p7 ,p7)

is replaced by e_216: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                                        2
 (q26,q22,q20,q17,q11,q10,p8,p6,p5,p3,p7 ,p7)


Step 1071: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 357  3-Oct-2003 05:30:16, 40 ms (0%), 1137818 occupied, 23862128 free
Eliminate 
q27

from e_336 and e_380. e_380: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                                2               2
 (q27,q26,q22,q20,q17,q11,q10,p8 ,p8,p6,p5,p3,p7 ,p7)

is replaced by e_238: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                            2               2
 (q26,q22,q20,q17,q11,q10,p8 ,p8,p6,p5,p3,p7 ,p7)


Step 1072: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_336 and e_386. e_386: 
 11 terms, 33 factors, with derivatives of functions of all variables: 

                               2         2         2
 (q27,q26,q20,q17,q11,q10,q8,p8 ,p8,p6,p5 ,p5,p3,p7 ,p7)

is replaced by e_322: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                   2               2
 (q26,q11,q10,q8,p8 ,p8,p6,p5,p3,p7 ,p7)


Step 1073: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_420 and e_101. e_101: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                              2
 (q27,q26,q17,q11,q10,p8,p5,p3 ,p3,p7)

is replaced by e_323: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

 (q26,q17,q11,q10,p8,p6,p5,p3,p7)


Step 1074: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q20

from e_358 and e_372. e_372: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                                               2
 (q26,q22,q20,q17,q12,q11,q10,q7,p8,p6,p5,p3,p7 ,p7)

is replaced by e_324: 
 7 terms, 21 factors, with derivatives of functions of all variables: 

                                       2
 (q26,q22,q12,q11,q10,q7,p8,p6,p5,p3,p7 ,p7)


Step 1075: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 358  3-Oct-2003 05:30:18, 40 ms (0%), 1126347 occupied, 23873602 free
Eliminate 
q22

from e_332 and e_384. e_384: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                           2               2
 (q26,q22,q20,q14,q10,q8,p8 ,p8,p6,p5,p3,p7 ,p7)

is replaced by e_325: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                                    2
 (q26,q20,q17,q14,q10,q8,p6,p5,p3,p7 ,p7)


Step 1076: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 359  3-Oct-2003 05:30:21, 50 ms (0%), 1122008 occupied, 23877940 free
Eliminate 
q26

from e_364 and e_361. e_361: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                               2               2
 (q26,q22,q17,q14,q11,q10,q8,p8 ,p8,p6,p5,p3,p7 ,p7)

is replaced by e_338: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                               2               2
 (q22,q20,q17,q14,q11,q10,q8,p8 ,p8,p6,p5,p3,p7 ,p7)


Step 1077: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q22

from e_335 and e_415. e_415: 
 11 terms, 33 factors, with derivatives of functions of all variables: 

                                 2         2      2
 (q26,q22,q17,q11,q10,q8,q7,p8,p6 ,p6,p5,p3 ,p3,p7 ,p7)

is replaced by e_326: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                                 2         2      2
 (q26,q17,q14,q11,q10,q8,q7,p8,p6 ,p6,p5,p3 ,p3,p7 ,p7)


Step 1078: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_414 and e_329. e_329: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

                             2
 (q22,q17,q11,q10,q8,p6,p5,p3 ,p3,p7)

is replaced by e_392: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

                       2
 (q22,q8,q7,p8,p6,p5,p3 ,p3,p7)


Step 1079: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_382 and e_185. e_185: 
 7 terms, 21 factors, with derivatives of functions of all variables: 

                              2         2
 (q27,q26,q20,q17,q12,q7,p8,p5 ,p5,p3,p7 ,p7)

is replaced by e_393: 
 6 terms, 12 factors, with derivatives of functions of all variables: 

 (q20,q17,q12,q11,q10,q7,p8,p5,p3,p7)


Step 1080: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q20

from e_358 and e_393. e_393: 
 6 terms, 12 factors, with derivatives of functions of all variables: 

 (q20,q17,q12,q11,q10,q7,p8,p5,p3,p7)

is replaced by e_394: 
 5 terms, 10 factors, with derivatives of functions of all variables: 

 (q17,q12,q11,q10,q7,p8,p5,p3,p7)


Step 1081: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 42 terms

The list of inequalities got extended by: 
An expression with 43 terms

Substitution of q12 by an expression in 
q17, q11, q10, q7, p8, p5, p3, p7 found in e_394 : 14 factors in 5 terms

Step 1082: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 360  3-Oct-2003 05:30:24, 50 ms (0%), 1130556 occupied, 23869393 free
Eliminate 
q27

from e_336 and e_389. e_389: 
 15 terms, 45 factors, with derivatives of functions of all variables: 

                               2         2      2      2
 (q27,q26,q20,q17,q11,q10,q7,p8 ,p8,p6,p5 ,p5,p3 ,p3,p7 ,p7)

is replaced by e_395: 
 14 terms, 42 factors, with derivatives of functions of all variables: 

                       2      2      2      2      2
 (q26,q17,q11,q10,q7,p8 ,p8,p6 ,p6,p5 ,p5,p3 ,p3,p7 ,p7)


Step 1083: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_362 and e_395. e_395: 
 14 terms, 42 factors, with derivatives of functions of all variables: 

                       2      2      2      2      2
 (q26,q17,q11,q10,q7,p8 ,p8,p6 ,p6,p5 ,p5,p3 ,p3,p7 ,p7)

is replaced by e_396: 
 12 terms, 36 factors, with derivatives of functions of all variables: 

                   2      2      2      2      2
 (q26,q11,q10,q7,p8 ,p8,p6 ,p6,p5 ,p5,p3 ,p3,p7 ,p7)


Step 1084: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 361  3-Oct-2003 05:30:27, 40 ms (0%), 1130357 occupied, 23869592 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_358 we get the alternative equations : 
0=p3


0=q17 - q20


New level : 1.1.2.1.1.
CRACK is now called with the new equation e_406 : 
0=p3

e_246,e_420 are consequences of e_406

Step 1085: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 36 terms

e_409 is a consequence of e_407.
e_435 is a consequence of e_369.
*** Garbage collection starting 
*** GC 362  3-Oct-2003 05:30:32, 40 ms (0%), 1129534 occupied, 23870414 free

Substitution of p3 found in e_406 : 
p3=0


Step 1086: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 40 terms

Substitution of q20 by an expression in 
q26, q17, q11, q10, p8, p5, p7 found in e_412 : 13 factors in 5 terms

Step 1087: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term
e_408 is a consequence of e_370

Step 1088: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_417 and e_440. e_440: 
(#) 4 terms, 9 factors, with derivatives of functions of all variables: 

                       2
 (q26,q17,q11,q10,p8,p5 ,p5,p7)

is replaced by e_376: 
(#) 3 terms, 7 factors, with derivatives of functions of all variables: 

                   2
 (q26,q11,q10,p8,p5 ,p5,p7)


Step 1089: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_411 and e_424. e_424: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                   2      2
 (q17,q14,q10,q8,p8 ,p6,p7 ,p7)

is replaced by e_378: 
 3 terms, 9 factors, with derivatives of functions of all variables: 

               2      2
 (q14,q10,q8,p8 ,p6,p7 ,p7)


Step 1090: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 41 terms

Substitution of q14 by an expression in 
q10, q8, p8, p6, p7 found in e_378 : 9 factors in 3 terms

Step 1091: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_411 and e_418. e_418: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

                   3      2      2
 (q26,q17,q10,q8,p8 ,p8,p6 ,p6,p7 ,p7)

is replaced by e_381: 
 4 terms, 16 factors, with derivatives of functions of all variables: 

               3      2      2
 (q26,q10,q8,p8 ,p8,p6 ,p6,p7 ,p7)


Step 1092: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_411 and e_471. e_471: 
(#) 4 terms, 9 factors, with derivatives of functions of all variables: 

 (q26,q17,q11,q10,p8,p6,p5,p7)

is replaced by e_375: 
(#) 3 terms, 7 factors, with derivatives of functions of all variables: 

 (q26,q11,q10,p8,p6,p5,p7)


Step 1093: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1094: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_334 and e_422. e_422: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                           2
 (q26,q22,q8,q7,p8,p6,p5,p7 ,p7)

is replaced by e_384: 

0=p7*q8 + 2*p8*q7


Step 1095: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 41 terms

e_370 is a consequence of e_419.
e_407 is a consequence of e_421.
Substitution of q8 by an expression in 
q7, p8, p7 found in e_384 : 
     - 2*p8*q7
q8=------------
        p7


Step 1096: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_417 and e_429. e_429: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                       2      2      2
 (q26,q17,q11,q10,q7,p8 ,p8,p5 ,p5,p7 ,p7)

is replaced by e_361: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

                   2      2      2
 (q26,q11,q10,q7,p8 ,p8,p5 ,p5,p7 ,p7)


Step 1097: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_376 and e_361. e_361: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

                   2      2      2
 (q26,q11,q10,q7,p8 ,p8,p5 ,p5,p7 ,p7)

is replaced by e_415: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

               2         2
 (q11,q10,q7,p8 ,p8,p5,p7 ,p7)


Step 1098: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_375 and e_442. e_442: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

                   3            2
 (q26,q11,q10,q7,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_329: 

           2     2
0=q7*p8*(p7  + p8 )


Step 1099: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q7

from e_329 and e_410. e_410: 
 4 terms, 20 factors, with derivatives of functions of all variables: 

               4   2         3   2
 (q22,q10,q7,p8 ,p8 ,p8,p6,p7 ,p7 )

is replaced by e_393: 

0=(p7*q22 - 2*p8*q10)*p6


Step 1100: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q7

from e_329 and e_381. e_381: 
 4 terms, 20 factors, with derivatives of functions of all variables: 

               4   2      2      2
 (q26,q10,q7,p8 ,p8 ,p8,p6 ,p6,p7 )

is replaced by e_395: 
(#) 2 terms, 5 factors, with derivatives of functions of all variables: 

               2
 (q26,q10,p8,p6 ,p6)


Step 1101: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q22

from e_393 and e_439. e_439: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                       2      2
 (q26,q22,q11,q10,p8,p6 ,p6,p5 ,p5,p7)

is replaced by e_398: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                   2      2
 (q26,q11,q10,p8,p6 ,p6,p5 ,p5,p7)


Step 1102: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q7

from e_329 and e_430. e_430: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                   3            2
 (q26,q11,q10,q7,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_399: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

 (q26,q11,q10,p8,p6,p5,p7)


Step 1103: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 363  3-Oct-2003 05:30:35, 40 ms (0%), 1137087 occupied, 23862863 free
Eliminate 
q26

from e_334 and e_444. e_444: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

 (q26,q22,q17,q11,q10,p8,p6,p5,p7)

is replaced by e_400: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

 (q22,q17,q11,q10,p8,p6,p5,p7)


Step 1104: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_417 and e_433. e_433: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                       3            2
 (q22,q17,q11,q10,q7,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_401: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

                   3            2
 (q22,q11,q10,q7,p8 ,p8,p6,p5,p7 ,p7)


Step 1105: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q7

from e_329 and e_401. e_401: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

                   3            2
 (q22,q11,q10,q7,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_402: 
 3 terms, 9 factors, with derivatives of functions of all variables: 

 (q22,q11,q10,p8,p6,p5,p7)


Step 1106: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q22

from e_402 and e_400. e_400: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

 (q22,q17,q11,q10,p8,p6,p5,p7)

is replaced by e_358: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

 (q17,q11,q10,p8,p6,p5,p7)


Step 1107: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1108: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_413 and e_437. e_437: 
(#) 6 terms, 19 factors, with derivatives of functions of all variables: 

                        2            2
 (q27,q26,q17,q11,q10,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_246: 
(#) 4 terms, 9 factors, with derivatives of functions of all variables: 

                       2
 (q26,q17,q11,q10,p8,p6 ,p6,p7)


Step 1109: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_411 and e_246. e_246: 
(#) 4 terms, 9 factors, with derivatives of functions of all variables: 

                       2
 (q26,q17,q11,q10,p8,p6 ,p6,p7)

is replaced by e_447: 
(#) 3 terms, 7 factors, with derivatives of functions of all variables: 

                   2
 (q26,q11,q10,p8,p6 ,p6,p7)


Step 1110: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_395 and e_447. e_447: 
(#) 3 terms, 7 factors, with derivatives of functions of all variables: 

                   2
 (q26,q11,q10,p8,p6 ,p6,p7)

is replaced by e_451: 

0=(5*p7*q11 - p8*q10)*p6


Step 1111: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_451 and e_434. e_434: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                       3            2
 (q26,q17,q11,q10,q7,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_454: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                   3   2            2
 (q26,q17,q10,q7,p8 ,p8 ,p8,p6,p5,p7 ,p7)


Step 1112: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q7

from e_329 and e_454. e_454: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                   3   2            2
 (q26,q17,q10,q7,p8 ,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_455: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                2            2
 (q26,q17,q10,p8 ,p8,p6,p5,p7 ,p7)


Step 1113: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_451 and e_438. e_438: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                       3            2
 (q26,q17,q11,q10,q7,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_456: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                   3   2            2
 (q26,q17,q10,q7,p8 ,p8 ,p8,p6,p5,p7 ,p7)


Step 1114: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q7

from e_329 and e_456. e_456: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                   3   2            2
 (q26,q17,q10,q7,p8 ,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_457: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                2            2
 (q26,q17,q10,p8 ,p8,p6,p5,p7 ,p7)


Step 1115: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_457 and e_455. e_457: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                2            2
 (q26,q17,q10,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_458: 

0=(2*q10 - q17)*p6


e_458 is a consequence of e_411.
Step 1116: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_417 and e_436. e_436: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

                       4   2      2         3   2
 (q26,q17,q11,q10,q7,p8 ,p8 ,p8,p6 ,p6,p5,p7 ,p7 )

is replaced by e_459: 
 6 terms, 30 factors, with derivatives of functions of all variables: 

                   4   2      2         3   2
 (q26,q11,q10,q7,p8 ,p8 ,p8,p6 ,p6,p5,p7 ,p7 )


Step 1117: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_451 and e_459. e_459: 
 6 terms, 30 factors, with derivatives of functions of all variables: 

                   4   2      2         3   2
 (q26,q11,q10,q7,p8 ,p8 ,p8,p6 ,p6,p5,p7 ,p7 )

is replaced by e_460: 
 5 terms, 25 factors, with derivatives of functions of all variables: 

               4   2      2         3   2
 (q26,q10,q7,p8 ,p8 ,p8,p6 ,p6,p5,p7 ,p7 )


Step 1118: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_395 and e_460. e_460: 
 5 terms, 25 factors, with derivatives of functions of all variables: 

               4   2      2         3   2
 (q26,q10,q7,p8 ,p8 ,p8,p6 ,p6,p5,p7 ,p7 )

is replaced by e_461: 
 4 terms, 20 factors, with derivatives of functions of all variables: 

           4   2            3   2
 (q10,q7,p8 ,p8 ,p8,p6,p5,p7 ,p7 )


Step 1119: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q7

from e_329 and e_461. e_461: 
 4 terms, 20 factors, with derivatives of functions of all variables: 

           4   2            3   2
 (q10,q7,p8 ,p8 ,p8,p6,p5,p7 ,p7 )

is replaced by e_462: 

0=q10*(5*p5*p7 + p6*p8)


Step 1120: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_417 and e_441. e_441: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

                       4   2      2         4   3   2
 (q26,q17,q11,q10,q7,p8 ,p8 ,p8,p6 ,p6,p5,p7 ,p7 ,p7 )

is replaced by e_464: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

                   4   2      2         4   3   2
 (q26,q11,q10,q7,p8 ,p8 ,p8,p6 ,p6,p5,p7 ,p7 ,p7 )


Step 1121: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_451 and e_464. e_464: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

                   4   2      2         4   3   2
 (q26,q11,q10,q7,p8 ,p8 ,p8,p6 ,p6,p5,p7 ,p7 ,p7 )

is replaced by e_465: 
 6 terms, 30 factors, with derivatives of functions of all variables: 

               4   2      2         4   3   2
 (q26,q10,q7,p8 ,p8 ,p8,p6 ,p6,p5,p7 ,p7 ,p7 )


Step 1122: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_395 and e_465. e_465: 
 6 terms, 30 factors, with derivatives of functions of all variables: 

               4   2      2         4   3   2
 (q26,q10,q7,p8 ,p8 ,p8,p6 ,p6,p5,p7 ,p7 ,p7 )

is replaced by e_466: 
 5 terms, 25 factors, with derivatives of functions of all variables: 

           4   2            4   3   2
 (q10,q7,p8 ,p8 ,p8,p6,p5,p7 ,p7 ,p7 )


Step 1123: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_462 and e_466. e_466: 
 5 terms, 25 factors, with derivatives of functions of all variables: 

           4   2            4   3   2
 (q10,q7,p8 ,p8 ,p8,p6,p5,p7 ,p7 ,p7 )

is replaced by e_467: 

     2     2
0=(p7  + p8 )*q7

e_329 is a consequence of e_467

Step 1124: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q7

from e_467 and e_415. e_415: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

               2         2
 (q11,q10,q7,p8 ,p8,p5,p7 ,p7)

is replaced by e_469: 

0=(p7*q10 + p8*q11)*p5


Step 1125: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_469 and e_376. e_376: 
(#) 3 terms, 7 factors, with derivatives of functions of all variables: 

                   2
 (q26,q11,q10,p8,p5 ,p5,p7)

is replaced by e_473: 

0=p5*(p5*q26 + 2*p7*q10)


Step 1126: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q7

from e_467 and e_445. e_445: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                   2      2      2      2
 (q26,q11,q10,q7,p8 ,p8,p6 ,p6,p5 ,p5,p7 ,p7)

is replaced by e_143: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                   2      2
 (q26,q11,q10,p8,p6 ,p6,p5 ,p5,p7)


Step 1127: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_417 and e_372. e_372: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                      2
 (q26,q17,q11,p8,p6,p5 ,p5,p7)

is replaced by e_161: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                      2
 (q26,q11,q10,p8,p6,p5 ,p5,p7)


Step 1128: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_473 and e_161. e_161: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                      2
 (q26,q11,q10,p8,p6,p5 ,p5,p7)

is replaced by e_278: 
 3 terms, 9 factors, with derivatives of functions of all variables: 

 (q11,q10,p8,p6,p5,p7)


Step 1129: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_375 and e_455. e_455: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                2            2
 (q26,q17,q10,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_371: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                2            2
 (q17,q11,q10,p8 ,p8,p6,p5,p7 ,p7)


Step 1130: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_451 and e_371. e_371: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                2            2
 (q17,q11,q10,p8 ,p8,p6,p5,p7 ,p7)

is replaced by e_416: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

            2            2
 (q17,q10,p8 ,p8,p6,p5,p7 ,p7)


Step 1131: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_413 and e_425. e_425: 
(#) 6 terms, 19 factors, with derivatives of functions of all variables: 

                        2      2      2
 (q27,q26,q17,q11,q10,p8 ,p8,p5 ,p5,p7 ,p7)

is replaced by e_408: 
(#) 4 terms, 9 factors, with derivatives of functions of all variables: 

 (q26,q17,q11,q10,p8,p6,p5,p7)


Step 1132: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1133: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
*** Garbage collection starting 
*** GC 364  3-Oct-2003 05:30:38, 40 ms (0%), 1130053 occupied, 23869897 free

factorizing e_421 we get the alternative equations : 
0=p6


0=q7


New level : 1.1.2.1.1.1.
CRACK is now called with the new equation e_400 : 
0=p6

e_375,e_393,e_395,e_451,e_411 are consequences of e_400

Step 1134: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

g0111*p8 + g0112*p7 + g0114*p5


The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 35 terms

Substitution of p6 found in e_400 : 
p6=0


Step 1135: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 40 terms

Substitution of q10 by an expression in 
q26, q22, q11, p8, p5, p7 found in e_447 : 11 factors in 4 terms

Step 1136: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1137: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1138: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1139: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1140: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1141: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

e_401 is a consequence of e_442.
Step 1142: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1143: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1144: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_375 is a consequence of e_442.
Step 1145: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1146: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

e_461 is a consequence of e_442.
Step 1147: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_430 and e_397. e_430: 
(#) 2 terms, 5 factors, with derivatives of functions of all variables: 

               2
 (q26,q11,p8,p5 ,p5)

is replaced by e_463: 

0=p5*p8*q11


Step 1148: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1149: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_463 and e_397. e_397: 

0=p5*(p5*q26 + 6*p8*q11)

is replaced by e_329: 

0=p5*q26


Step 1150: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

e_415 is a consequence of e_463.
Step 1151: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

e_470 is a consequence of e_463.
Step 1152: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

e_412 is a consequence of e_463.
Step 1153: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term
e_463 is a consequence of e_376

Step 1154: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

e_475 is a consequence of e_446.
Step 1155: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1156: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term
e_446 is a consequence of e_479

Step 1157: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1158: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1159: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1160: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1161: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1162: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1163: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1164: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1165: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1166: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1167: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

e_453 is a consequence of e_483.
Step 1168: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_448 and e_388. e_388: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                2      2
 (q22,q17,q11,p8 ,p8,p7 ,p7)

is replaced by e_429: 

0=(q11 + q22)*p8


Step 1169: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1170: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q22

from e_429 and e_445. e_445: 
 3 terms, 9 factors, with derivatives of functions of all variables: 

            2   2
 (q22,q11,p8 ,p7 )

is replaced by e_482: 

         2     2
0=q11*(p7  + p8 )


Step 1171: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_482 and e_371. e_371: 

                 2     2
0=(q11 - q22)*(p7  + p8 )

is replaced by e_381: 

         2     2
0=q22*(p7  + p8 )

e_185 is a consequence of e_381

Step 1172: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_482 and e_103. e_103: 
 3 terms, 9 factors, with derivatives of functions of all variables: 

            2      2
 (q27,q11,p8 ,p5,p7 ,p7)

is replaced by e_366: 

0=p5*q27


Step 1173: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_437 we get the alternative equations : 
0=p5


0=q22


New level : 1.1.2.1.1.1.1.
CRACK is now called with the new equation e_430 : 
0=p5

e_419,e_329,e_376,e_479,e_366 are consequences of e_430

Step 1174: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

g0111*p8 + g0112*p7


The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 27 terms

Substitution of p5 found in e_430 : 
p5=0


Step 1175: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_429 we get the alternative equations : 
0=p8


0=q11 + q22


New level : 1.1.2.1.1.1.1.1.
CRACK is now called with the new equation e_441 : 
0=p8


Step 1176: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 8 terms

e_394 is a consequence of e_400.
Substitution of p8 found in e_441 : 
p8=0


Step 1177: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 6 terms

e_468 is a consequence of e_465.
Substitution of q22 found in e_400 : 
q22=0


Step 1178: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 

g0058*q17 + g0061*q17 + g0071*q7


Substitution of q11 found in e_465 : 
q11=0


Step 1179: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 

g0003*q26 + g0018*q7 + g0023*p7


The list of inequalities got extended by: 

g0028*q26 + g0043*q7 + g0048*p7


The list of inequalities got extended by: 

g0084*q27 + g0085*q26 + g0104*q7


The list of inequalities got extended by: 

q7


Substitution of q17 found in e_466 : 
q17=0


Step 1180: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
contradiction from the substitution:
q7=0

because of the non-vanishing expression:
q7


Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p8


New level : 1.1.2.1.1.1.1.2.
CRACK is now called with the new equation e_441 : 
0=q11 + q22

e_387 is a consequence of e_441

Step 1181: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 18 terms

e_400 is a consequence of e_482.
e_465 is a consequence of e_482.
Substitution of q22 by an expression in 
q11 found in e_441 : 
q22= - q11


Step 1182: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization : 
factorizing e_467 we get the alternative equations : 
0=q7


    2     2
0=p7  + p8


New level : 1.1.2.1.1.1.1.2.1.
CRACK is now called with the new equation e_466 : 
0=q7


Step 1183: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 12 terms

Substitution of q7 found in e_466 : 
q7=0


Step 1184: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization : 
factorizing e_448 we get the alternative equations : 
0=q17


    2     2
0=p7  + p8


New level : 1.1.2.1.1.1.1.2.1.1.
CRACK is now called with the new equation e_397 : 
0=q17


Step 1185: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 8 terms

q11


Substitution of q17 found in e_397 : 
q17=0


Step 1186: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.2.1.1.1.1.2.1.1. : 
equations : 

e_482 : 
    2     2
0=p7  + p8



Non-vanishing expressions: q11,p7,p8

g0054*p8 - g0055*p7 + g0056*p7 + g0057*p8 + g0062*p8 + g0063*p7 - g0067*p7

 + g0068*p8


g0084*p7*q27 + g0085*p7*q26 - g0087*p8*q11 + g0088*p7*q11 - g0089*p7*q11

 - g0090*p8*q11 - g0095*p8*q11 - g0096*p7*q11 + g0100*p7*q11 - g0101*p8*q11


g0028*p7*q26 - g0030*p8*q11 + g0031*p7*q11 - g0032*p7*q11 - g0036*p7*q11

                                         2
 + g0039*p7*q11 - g0040*p8*q11 + g0048*p7


g0003*p7*q26 - g0005*p8*q11 + g0006*p7*q11 - g0007*p8*q11 - g0011*p8*q11

                                         2
 + g0014*p7*q11 - g0015*p8*q11 + g0023*p7


g0111*p8 + g0112*p7


functions : q27, q26, 
q25=0


      - p8*q11
q24=-----------
        p7


q23=q11


q22= - q11


      - p8*q11
q21=-----------
        p7


q20=0


q19=0


q18=0


q17=0


      - p8*q11
q16=-----------
        p7


q15= - q11


q14=0


q13=0


q12=0

q11, 
      - p8*q11
q10=-----------
        p7


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, 
p6=0


p5=0


p4=0


p3=0


p2=0


p1=0


with 42 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_482(2a)
5 constants : p7,p8,q11,q26,q27
The equation: 

f =D D f  *p7 + f  *p8
 t  1 2 2x       3x
The symmetry: 
f =(D f  *D D f*p7*q11 - D f  *f *p8*q11 + D f*D D f  *p7*q11 - D f*f  *p8*q11
 s   2 2x  1 2            2 2x  x           2   1 2 2x           2   3x

     + D D f  *p7*q26 - D D f  *D f*p8*q11 - D D f*D f  *p8*q11
        1 2 4x           1 2 2x  1            1 2   1 2x

     - D f  *f *p7*q11 - D f*f  *p7*q11 + f  *p7*q27)/p7
        1 2x  x           1   3x           5x
And now in machine readable form:

The system: 

df(f(1),t)=d(1,d(2,df(f(1),x,2)))*p7 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=(d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p7*q11 - d(2,df(f(1),x,2))*df(f(1),
x)*p8*q11 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p7*q11 - d(2,f(1))*df(f(1),x,3)*p8*
q11 + d(1,d(2,df(f(1),x,4)))*p7*q26 - d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p8*q11 - 
d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p8*q11 - d(1,df(f(1),x,2))*df(f(1),x)*p7*q11 - 
d(1,f(1))*df(f(1),x,3)*p7*q11 + df(f(1),x,5)*p7*q27)/p7$

Time: 0 ms

Time: 0 ms

Time: 0 ms

The list of inequalities got extended by: 

q17

The lexicographical ordering of unknowns is changed
because q17 has to be non-zero, giving q17 a low priority.
Old ordering: q27,q26,q17,q11,p8,p7
New ordering: q27,q26,q11,q17,p8,p7

New level : 1.1.2.1.1.1.1.2.1.2.
CRACK is now called with the new equation e_397 : 
    2     2
0=p7  + p8

e_482 is a consequence of e_397

Step 1187: 
Hot list of urgent steps : 
Step 1188: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.2.1.1.1.1.2.1.2. : 
equations : 

e_397 : 
    2     2
0=p7  + p8



Non-vanishing expressions: q17,p8,p7

g0054*p8*q11 - g0055*p7*q11 + g0056*p7*q11 + g0057*p8*q11 - g0058*p7*q17

 + g0059*p8*q17 - g0060*p8*q17 - g0061*p7*q17 + g0062*p8*q11 + g0063*p7*q11

 - g0067*p7*q11 + g0068*p8*q11


g0084*p7*q27 + g0085*p7*q26 - g0087*p8*q11 + g0088*p7*q11 - g0089*p7*q11

 - g0090*p8*q11 + g0091*p7*q17 - g0092*p8*q17 + g0093*p8*q17 + g0094*p7*q17

 - g0095*p8*q11 - g0096*p7*q11 + g0100*p7*q11 - g0101*p8*q11


g0028*p7*q26 - g0030*p8*q11 + g0031*p7*q11 - g0032*p7*q11 - g0033*p8*q17

 + g0034*p8*q17 + g0035*p7*q17 - g0036*p7*q11 + g0039*p7*q11 - g0040*p8*q11

           2
 + g0048*p7


g0003*p7*q26 - g0005*p8*q11 + g0006*p7*q11 - g0007*p8*q11 + g0008*p7*q17

 + g0009*p8*q17 + g0010*p7*q17 - g0011*p8*q11 + g0014*p7*q11 - g0015*p8*q11

           2
 + g0023*p7


g0111*p8 + g0112*p7


functions : q27, q26, 
q25=0


      - p8*q11
q24=-----------
        p7


q23=q11


q22= - q11


      - p8*q11
q21=-----------
        p7


q20=q17


      - p8*q17
q19=-----------
        p7


     p8*q17
q18=--------
       p7

q17, 
      - p8*q11
q16=-----------
        p7


q15= - q11


q14=0


q13=0


q12=0

q11, 
      - p8*q11
q10=-----------
        p7


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, 
p6=0


p5=0


p4=0


p3=0


p2=0


p1=0


with 45 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_397(2a)
6 constants : p7,p8,q11,q17,q26,q27
The equation: 

f =D D f  *p7 + f  *p8
 t  1 2 2x       3x
The symmetry: 
f =(D f  *D D f*p7*q11 - D f  *f *p8*q11 + D f *D D f *p8*q17 + D f *f  *p7*q17
 s   2 2x  1 2            2 2x  x           2 x  1 2 x           2 x  2x

     + D f*D D f  *p7*q11 - D f*f  *p8*q11 + D D f  *p7*q26 - D D f  *D f*p8*q11
        2   1 2 2x           2   3x           1 2 4x           1 2 2x  1

     + D D f *D f *p7*q17 - D D f*D f  *p8*q11 - D f  *f *p7*q11
        1 2 x  1 x           1 2   1 2x           1 2x  x

     - D f *f  *p8*q17 - D f*f  *p7*q11 + f  *p7*q27)/p7
        1 x  2x           1   3x           5x
And now in machine readable form:

The system: 

df(f(1),t)=d(1,d(2,df(f(1),x,2)))*p7 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=(d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p7*q11 - d(2,df(f(1),x,2))*df(f(1),
x)*p8*q11 + d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p8*q17 + d(2,df(f(1),x))*df(f(1
),x,2)*p7*q17 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p7*q11 - d(2,f(1))*df(f(1),x,3)
*p8*q11 + d(1,d(2,df(f(1),x,4)))*p7*q26 - d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p8*
q11 + d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p7*q17 - d(1,d(2,f(1)))*d(1,df(f(1),x
,2))*p8*q11 - d(1,df(f(1),x,2))*df(f(1),x)*p7*q11 - d(1,df(f(1),x))*df(f(1),x,2)
*p8*q17 - d(1,f(1))*df(f(1),x,3)*p7*q11 + df(f(1),x,5)*p7*q27)/p7$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 0 ms

The list of inequalities got extended by: 

q7


New level : 1.1.2.1.1.1.1.2.2.
CRACK is now called with the new equation e_466 : 
    2     2
0=p7  + p8

e_448,e_482 are consequences of e_466

Step 1189: 
Hot list of urgent steps : 
Step 1190: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.2.1.1.1.1.2.2. : 
equations : 

e_466 : 
    2     2
0=p7  + p8



Non-vanishing expressions: q7,p7,p8

        2                  3               3               2
g0054*p7 *p8*q11 - g0055*p7 *q11 + g0056*p7 *q11 + g0057*p7 *p8*q11

           3               2                  2                  3
 - g0058*p7 *q17 + g0059*p7 *p8*q17 - g0060*p7 *p8*q17 - g0061*p7 *q17

           2                  3               3                   2
 + g0062*p7 *p8*q11 + g0063*p7 *q11 + g0064*p8 *q7 - 2*g0065*p7*p8 *q7

           2                 3               2                     2
 + g0066*p7 *p8*q7 - g0067*p7 *q11 + g0068*p7 *p8*q11 - g0069*p7*p8 *q7

             2                 3
 + 2*g0070*p7 *p8*q7 - g0071*p7 *q7


        3               3               2                  3               3
g0084*p7 *q27 + g0085*p7 *q26 - g0087*p7 *p8*q11 + g0088*p7 *q11 - g0089*p7 *q11

           2                  3               2                  2
 - g0090*p7 *p8*q11 + g0091*p7 *q17 - g0092*p7 *p8*q17 + g0093*p7 *p8*q17

           3               2                  3               3
 + g0094*p7 *q17 - g0095*p7 *p8*q11 - g0096*p7 *q11 - g0097*p8 *q7

                2              2                 3               2
 + 2*g0098*p7*p8 *q7 - g0099*p7 *p8*q7 + g0100*p7 *q11 - g0101*p7 *p8*q11

              2                2                 3
 + g0102*p7*p8 *q7 - 2*g0103*p7 *p8*q7 + g0104*p7 *q7


        3               2                  3               3
g0028*p7 *q26 - g0030*p7 *p8*q11 + g0031*p7 *q11 - g0032*p7 *q11

           2                  2                  3               3
 - g0033*p7 *p8*q17 + g0034*p7 *p8*q17 + g0035*p7 *q17 - g0036*p7 *q11

           3                   2              3               2
 - g0037*p8 *q7 + 2*g0038*p7*p8 *q7 + g0039*p7 *q11 - g0040*p7 *p8*q11

              2                2                 3              4
 + g0041*p7*p8 *q7 - 2*g0042*p7 *p8*q7 + g0043*p7 *q7 + g0048*p7


        2                                 2
g0003*p7 *q26 - g0005*p7*p8*q11 + g0006*p7 *q11 - g0007*p7*p8*q11

           2                                 2
 + g0008*p7 *q17 + g0009*p7*p8*q17 + g0010*p7 *q17 - g0011*p7*p8*q11

             2                               2
 + 2*g0012*p8 *q7 - g0013*p7*p8*q7 + g0014*p7 *q11 - g0015*p7*p8*q11

           2                                 2              3
 + g0016*p8 *q7 - 2*g0017*p7*p8*q7 + g0018*p7 *q7 + g0023*p7


g0111*p8 + g0112*p7


functions : q27, q26, 
q25=0


      - p8*q11
q24=-----------
        p7


q23=q11


q22= - q11


      - p8*q11
q21=-----------
        p7


q20=q17


      - p8*q17
q19=-----------
        p7


     p8*q17
q18=--------
       p7

q17, 
      - p8*q11
q16=-----------
        p7


q15= - q11


          3
      - p8 *q7
q14=-----------
          3
        p7


         2
     2*p8 *q7
q13=----------
         2
       p7


      - p8*q7
q12=----------
        p7

q11, 
      - p8*q11
q10=-----------
        p7


      2
    p8 *q7
q9=--------
       2
     p7


     - 2*p8*q7
q8=------------
        p7

q7, 
q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, 
p6=0


p5=0


p4=0


p3=0


p2=0


p1=0


with 50 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_466(2a)
7 constants : p7,p8,q7,q11,q17,q26,q27
The equation: 

f =D D f  *p7 + f  *p8
 t  1 2 2x       3x
The symmetry: 
                  3                  2                        2
f =(D f  *D D f*p7 *q11 - D f  *f *p7 *p8*q11 + D f *D D f *p7 *p8*q17
 s   2 2x  1 2             2 2x  x               2 x  1 2 x

                  3            2         3           2      2
     + D f *f  *p7 *q17 + (D f) *D D f*p7 *q7 - (D f) *f *p7 *p8*q7
        2 x  2x             2     1 2             2     x

                     3                         2                           2
     + D f*D D f  *p7 *q11 - 2*D f*D D f*D f*p7 *p8*q7 + 2*D f*D f*f *p7*p8 *q7
        2   1 2 2x              2   1 2   1                 2   1   x

                 2                    3                     2
     - D f*f  *p7 *p8*q11 + D D f  *p7 *q26 - D D f  *D f*p7 *p8*q11
        2   3x               1 2 4x            1 2 2x  1

                     3                     2                     2      2
     + D D f *D f *p7 *q17 - D D f*D f  *p7 *p8*q11 + D D f*(D f) *p7*p8 *q7
        1 2 x  1 x            1 2   1 2x               1 2    1

                  3                  2               2      3
     - D f  *f *p7 *q11 - D f *f  *p7 *p8*q17 - (D f) *f *p8 *q7
        1 2x  x            1 x  2x                1     x

                 3             3        3
     - D f*f  *p7 *q11 + f  *p7 *q27)/p7
        1   3x            5x
And now in machine readable form:

The system: 

df(f(1),t)=d(1,d(2,df(f(1),x,2)))*p7 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=(d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p7**3*q11 - d(2,df(f(1),x,2))*df(f(
1),x)*p7**2*p8*q11 + d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p7**2*p8*q17 + d(2,df(
f(1),x))*df(f(1),x,2)*p7**3*q17 + d(2,f(1))**2*d(1,d(2,f(1)))*p7**3*q7 - d(2,f(1
))**2*df(f(1),x)*p7**2*p8*q7 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p7**3*q11 - 2*d(
2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p7**2*p8*q7 + 2*d(2,f(1))*d(1,f(1))*df(f(1),x)*
p7*p8**2*q7 - d(2,f(1))*df(f(1),x,3)*p7**2*p8*q11 + d(1,d(2,df(f(1),x,4)))*p7**3
*q26 - d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p7**2*p8*q11 + d(1,d(2,df(f(1),x)))*d(1,
df(f(1),x))*p7**3*q17 - d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p7**2*p8*q11 + d(1,d(2,
f(1)))*d(1,f(1))**2*p7*p8**2*q7 - d(1,df(f(1),x,2))*df(f(1),x)*p7**3*q11 - d(1,
df(f(1),x))*df(f(1),x,2)*p7**2*p8*q17 - d(1,f(1))**2*df(f(1),x)*p8**3*q7 - d(1,f
(1))*df(f(1),x,3)*p7**3*q11 + df(f(1),x,5)*p7**3*q27)/p7**3$

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p5


New level : 1.1.2.1.1.1.2.
CRACK is now called with the new equation e_430 : 
0=q22

e_381 is a consequence of e_430

Step 1191: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 31 terms

e_441 is a consequence of e_376.
e_400 is a consequence of e_376.
e_465 is a consequence of e_376.
Substitution of q22 found in e_430 : 
q22=0


Step 1192: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 25 terms

Substitution of q7 found in e_419 : 
q7=0


Step 1193: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 18 terms

Substitution of q26 found in e_329 : 
q26=0


Step 1194: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 7 terms

Substitution of q11 found in e_376 : 
q11=0


Step 1195: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 3 terms

The list of inequalities got extended by: 
An expression with 2 terms

The list of inequalities got extended by: 

3*g0084*p7 - 5*g0093*p5


q27

The lexicographical ordering of unknowns is changed
because q27 has to be non-zero, giving q27 a low priority.
Old ordering: q27,q17,p8,p5,p7
New ordering: q17,q27,p8,p5,p7

The list of inequalities got extended by: 

5*g0060*q27 - 3*g0079*p7


Substitution of q17 found in e_479 : 
q17=0


Step 1196: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
contradiction from the substitution:
q27=0

because of the non-vanishing expression:
q27


The list of inequalities got extended by: 

p7


This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q27,q26,q22,q17,q11,q10,q7,p8,p6,p5,p7
New ordering: q27,q26,q22,q17,q11,q10,q7,p8,p5,p6,p7

New level : 1.1.2.1.1.2.
CRACK is now called with the new equation e_400 : 
0=q7

e_467,e_419 are consequences of e_400

Step 1197: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 35 terms

Substitution of q7 found in e_400 : 
q7=0


Step 1198: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 32 terms

Substitution of q17 by an expression in 
q10 found in e_411 : 
q17=2*q10


Step 1199: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 32 terms

Substitution of q22 by an expression in 
q10, p8, p7 found in e_393 : 
     2*p8*q10
q22=----------
        p7


Step 1200: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
*** Garbage collection starting 
*** GC 365  3-Oct-2003 05:30:41, 20 ms (0%), 1004820 occupied, 23995130 free

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 30 terms

e_255 is a consequence of e_451.
e_472 is a consequence of e_375.
Substitution of q26 by an expression in 
q10, p8, p6 found in e_395 : 
      12
     ----*p8*q10
      5
q26=-------------
         p6


Step 1201: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 27 terms

e_426 is a consequence of e_334.
Substitution of q11 by an expression in 
q10, p8, p7 found in e_451 : 
      1
     ---*p8*q10
      5
q11=------------
         p7


Step 1202: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 28 terms

q10


The list of inequalities got extended by: 
An expression with 27 terms

Substitution of q27 by an expression in 
q10, p8, p6, p7 found in e_358 : 11 factors in 3 terms

Step 1203: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 20 terms
e_398,e_473,e_469 are consequences of e_334

e_399 is a consequence of e_334.
e_402 is a consequence of e_334.
The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 

p8


e_431 is a consequence of e_416.
Substitution of p8 by an expression in 
p5, p6, p7 found in e_462 : 
     - 5*p5*p7
p8=------------
        p6


Step 1204: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
contradiction from the substitution:
p5=0

because of the non-vanishing expression:
p5


This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 30 ms

The list of inequalities got extended by: 

p3


New level : 1.1.2.1.2.
CRACK is now called with the new equation e_406 : 
0=q17 - q20


Step 1205: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 39 terms

Substitution of q20 by an expression in 
q17 found in e_406 : 
q20=q17


Step 1206: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 39 terms

e_335 is a consequence of e_331.
Substitution of q14 by an expression in 
q8, p6, p3 found in e_328 : 
      1
     ---*p6*q8
      2
q14=-----------
        p3


Step 1207: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 42 terms

The list of inequalities got extended by: 
An expression with 41 terms

Substitution of q27 by an expression in 
q26, q11, q10, p8, p5, p3, p7 found in e_408 : 14 factors in 4 terms

Step 1208: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_362 and e_423. e_423: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                          2      3   2
 (q26,q17,q11,q10,p8,p6,p5 ,p5,p3 ,p3 ,p3,p7)

is replaced by e_161: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                      2      3   2
 (q26,q11,q10,p8,p6,p5 ,p5,p3 ,p3 ,p3,p7)


Step 1209: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 366  3-Oct-2003 05:30:44, 40 ms (0%), 1026139 occupied, 23973810 free
Eliminate 
q17

from e_414 and e_326. e_326: 
 10 terms, 40 factors, with derivatives of functions of all variables: 

                             2         3   2      2
 (q26,q17,q11,q10,q8,q7,p8,p6 ,p6,p5,p3 ,p3 ,p3,p7 ,p7)

is replaced by e_278: 
(#) 10 terms, 17 factors, with derivatives of functions of all variables: 

                     2      3   2      2
 (q26,q11,q8,q7,p8,p6 ,p6,p3 ,p3 ,p3,p7 ,p7)


Step 1210: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 367  3-Oct-2003 05:30:47, 40 ms (0%), 1019880 occupied, 23980070 free
Eliminate 
q17

from e_414 and e_379. e_379: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                              2         2
 (q26,q22,q17,q11,q10,q8,p8,p6 ,p6,p5,p3 ,p3,p7)

is replaced by e_103: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                         2      2      2
 (q26,q22,q11,q8,q7,p8,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1211: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 368  3-Oct-2003 05:30:50, 30 ms (0%), 1023150 occupied, 23976799 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_407 we get the alternative equations : 
0=p6

9 factors in 3 terms

New level : 1.1.2.1.2.1.
CRACK is now called with the new equation e_387 : 
0=p6


Step 1212: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 35 terms
e_327 is a consequence of e_255

e_366 is a consequence of e_255.
Substitution of p6 found in e_387 : 
p6=0


Step 1213: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 32 terms

e_433 is a consequence of e_255.
e_384 is a consequence of e_400.
Substitution of q17 by an expression in 
q10 found in e_378 : 
q17= - q10


Step 1214: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 30 terms

e_432 is a consequence of e_397.
e_434 is a consequence of e_393.
Substitution of q22 by an expression in 
q8, p8, p3 found in e_255 : 
     p8*q8
q22=-------
      p3


Step 1215: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 30 terms

Substitution of q7 by an expression in 
q8, p8, p7 found in e_397 : 
    p8*q8
q7=-------
     p7


Step 1216: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 27 terms

e_403 is a consequence of e_437.
Substitution of q26 by an expression in 
q11, p3, p7 found in e_185 : 
     p7*q11
q26=--------
       p3


Step 1217: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 33 terms
*** Garbage collection starting 
*** GC 369  3-Oct-2003 05:30:54, 40 ms (0%), 1030480 occupied, 23969470 free

Substitution of q11 by an expression in 
q10, p8, p5, p3, p7 found in e_329 : 10 factors in 3 terms

Step 1218: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1219: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1220: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1221: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1222: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1223: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 41 terms

q10

The lexicographical ordering of unknowns is changed
because q10 has to be non-zero, giving q10 a low priority.
Old ordering: q10,q8,p8,p5,p3,p7
New ordering: q8,q10,p8,p5,p3,p7

The list of inequalities got extended by: 

p8

The lexicographical ordering of unknowns is changed
because p8 has to be non-zero, giving p8 a low priority.
Old ordering: q8,q10,p8,p5,p3,p7
New ordering: q8,q10,p5,p8,p3,p7

The list of inequalities got extended by: 
An expression with 37 terms

e_393 is a consequence of e_404.
Substitution of q8 by an expression in 
q10, p5, p3, p7 found in e_459 : 7 factors in 3 terms

Step 1224: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 

g0111*p8 + g0112*p7 + g0116*p3


The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 16 terms

Substitution of p5 found in e_448 : 
p5=0


leads to a contradiction in : 7 factors in 4 terms

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q26,q22,q17,q11,q10,q8,q7,p8,p6,p5,p3,p7
New ordering: q26,q22,q17,q11,q10,q8,q7,p8,p5,p6,p3,p7

New level : 1.1.2.1.2.2.
CRACK is now called with the new equation e_387 : 9 factors in 3 terms

Step 1225: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 45 terms

e_393 is a consequence of e_411.
e_395 is a consequence of e_419.
Substitution of q17 by an expression in 
q26, q10, p5, p7 found in e_387 : 8 factors in 3 terms

Step 1226: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_430 and e_397. e_397: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                   2            2      2
 (q26,q22,q10,q8,p8 ,p8,p5,p6,p3 ,p3,p7 ,p7)

is replaced by e_401: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

               2         2      2
 (q22,q10,q8,p8 ,p8,p6,p3 ,p3,p7 ,p7)


Step 1227: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_411 and e_384. e_384: 
 6 terms, 30 factors, with derivatives of functions of all variables: 

                         2      2      2
 (q26,q22,q10,q8,p8,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_402: 

0=(p3 + p6)*(p3*q22 - p8*q8)


e_402 is a consequence of e_331.
Step 1228: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 370  3-Oct-2003 05:30:56, 30 ms (0%), 1025054 occupied, 23974896 free
Eliminate 
q22

from e_401 and e_398. e_398: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                       2      2         2      3   2
 (q26,q22,q11,q10,q8,p8 ,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7 ,p7)

is replaced by e_403: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                   2      2         2      3   2
 (q26,q11,q10,q8,p8 ,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7 ,p7)


Step 1229: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 371  3-Oct-2003 05:30:59, 40 ms (0%), 1024249 occupied, 23975701 free
*** Garbage collection starting 
*** GC 372  3-Oct-2003 05:31:03, 30 ms (0%), 1020048 occupied, 23979901 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_381 we get the alternative equations : 
0=p5

9 factors in 3 terms

New level : 1.1.2.1.2.2.1.
CRACK is now called with the new equation e_335 : 
0=p5

e_366,e_327 are consequences of e_335

Step 1230: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 30 terms

e_450 is a consequence of e_440.
e_455 is a consequence of e_453.
Substitution of p5 found in e_335 : 
p5=0


Step 1231: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 30 terms

e_439 is a consequence of e_449.e_436 is a consequence of e_448

Substitution of q22 by an expression in 
q11, p6, p3 found in e_432 : 
     p6*q11
q22=--------
       p3


Step 1232: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 31 terms

e_438 is a consequence of e_437.
e_451 is a consequence of e_448.
e_444 is a consequence of e_437.
e_445 is a consequence of e_437.
e_457 is a consequence of e_446.
e_459 is a consequence of e_433.
Substitution of q26 by an expression in 
q11, q10, p8, p6, p3, p7 found in e_434 : 13 factors in 3 terms

Step 1233: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 42 terms

e_453 is a consequence of e_456.
Substitution of q10 by an expression in 
q8, q7, p8, p3, p7 found in e_440 : 7 factors in 3 terms

Step 1234: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 48 terms

The list of inequalities got extended by: 
An expression with 43 terms
e_328 is a consequence of e_464

e_449 is a consequence of e_464.
e_454 is a consequence of e_433.
e_465 is a consequence of e_460.
Substitution of q11 by an expression in 
q8, q7, p8, p6, p7 found in e_456 : 7 factors in 3 terms

Step 1235: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1236: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_406 is a consequence of e_464.
Step 1237: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_381 is a consequence of e_464.
Step 1238: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_327 is a consequence of e_464.
Step 1239: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_366 is a consequence of e_464.
Step 1240: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_450 is a consequence of e_464.
Step 1241: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_455 is a consequence of e_464.
Step 1242: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_335 is a consequence of e_464.
Step 1243: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_462 is a consequence of e_464.
Step 1244: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by -2 terms

e_463 is a consequence of e_464.
Step 1245: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1246: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_436 is a consequence of e_464.
Step 1247: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1248: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_467 is a consequence of e_464.
Step 1249: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1250: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_469 is a consequence of e_464.
Step 1251: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_464 we get the alternative equations : 
0=q7


0=p3 + p6


New level : 1.1.2.1.2.2.1.1.
CRACK is now called with the new equation e_474 : 
0=q7


Step 1252: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 21 terms

q8

The lexicographical ordering of unknowns is changed
because q8 has to be non-zero, giving q8 a low priority.
Old ordering: q8,q7,p8,p6,p3,p7
New ordering: q7,q8,p8,p6,p3,p7

The list of inequalities got extended by: 
An expression with 20 terms

Substitution of q7 found in e_474 : 
q7=0


Step 1253: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 

1


The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 17 terms

Substitution of p6 by an expression in 
p3 found in e_405 : 
p6= - p3



>>>>>>>>> Solution of level 1.1.2.1.2.2.1.1. : 
no equations


Non-vanishing expressions: p6,p7,p3,q8

2*g0054*p7*q8 - 2*g0055*p8*q8 + 2*g0056*p8*q8 + 2*g0057*p7*q8 + 2*g0058*p7*q8

 + 2*g0059*p8*q8 - 2*g0060*p8*q8 + 2*g0061*p7*q8 + 2*g0062*p7*q8 + 2*g0063*p8*q8

 - g0064*p3*q8 + g0066*p3*q8 - 2*g0067*p8*q8 + 2*g0068*p7*q8 + 2*g0070*p3*q8

             2             2
 - 2*g0078*p3  + 2*g0081*p3


          2             2
6*g0084*p7  - 6*g0084*p8  - 12*g0085*p7*p8 + 10*g0087*p3*p7 - 10*g0088*p3*p8

 + 10*g0089*p3*p8 + 10*g0090*p3*p7 + 10*g0091*p3*p7 + 10*g0092*p3*p8

 - 10*g0093*p3*p8 + 10*g0094*p3*p7 + 10*g0095*p3*p7 + 10*g0096*p3*p8

             2             2                                                2
 - 5*g0097*p3  + 5*g0099*p3  - 10*g0100*p3*p8 + 10*g0101*p3*p7 + 10*g0103*p3


12*g0028*p7*p8*q8 - 10*g0030*p3*p7*q8 + 10*g0031*p3*p8*q8 - 10*g0032*p3*p8*q8

 - 10*g0033*p3*p8*q8 + 10*g0034*p3*p8*q8 - 10*g0035*p3*p7*q8 - 10*g0036*p3*p8*q8

             2                                                         2
 + 5*g0037*p3 *q8 + 10*g0039*p3*p8*q8 - 10*g0040*p3*p7*q8 - 10*g0042*p3 *q8

              2                 3              3
 - 10*g0048*p3 *p7 + 10*g0049*p3  - 10*g0051*p3


12*g0003*p7*p8*q8 - 10*g0005*p3*p7*q8 + 10*g0006*p3*p8*q8 - 10*g0007*p3*p7*q8

 - 10*g0008*p3*p7*q8 + 10*g0009*p3*p8*q8 - 10*g0010*p3*p7*q8 - 10*g0011*p3*p7*q8

             2                                                         2
 - 5*g0013*p3 *q8 + 10*g0014*p3*p8*q8 - 10*g0015*p3*p7*q8 - 10*g0017*p3 *q8

              2                 3
 - 10*g0023*p3 *p7 - 10*g0026*p3


g0111*p8 + g0112*p7 - g0113*p3 + g0116*p3


functions : 
      3    2       3    2
     ---*p7 *q8 - ---*p8 *q8
      5            5
q27=-------------------------
                 2
               p3


         6
      - ---*p7*p8*q8
         5
q26=-----------------
             2
           p3


q25=0


     p7*q8
q24=-------
      p3


      - p8*q8
q23=----------
        p3


     p8*q8
q22=-------
      p3


     p7*q8
q21=-------
      p3


     p7*q8
q20=-------
      p3


     p8*q8
q19=-------
      p3


      - p8*q8
q18=----------
        p3


     p7*q8
q17=-------
      p3


     p7*q8
q16=-------
      p3


     p8*q8
q15=-------
      p3


        1
q14= - ---*q8
        2


q13=0


     1
q12=---*q8
     2


      - p8*q8
q11=----------
        p3


     p7*q8
q10=-------
      p3


q9=0

q8, 
q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, 
p6= - p3


p5=0


p4=0

p3, 
p2=0


p1=0


with 53 terms
no equations
4 constants : p3,p7,p8,q8
The equation: 

f =D f*D D f*p3 + D D f  *p7 - D f*f *p3 + f  *p8
 t  2   1 2        1 2 2x       1   x       3x
The symmetry: 
f =( - D f  *D D f*p3*p8*q8 + D f  *f *p3*p7*q8 - D f *D D f *p3*p8*q8
 s      2 2x  1 2              2 2x  x             2 x  1 2 x

                            1       2      2
     + D f *f  *p3*p7*q8 + ---*(D f) *f *p3 *q8 - D f*D D f  *p3*p8*q8
        2 x  2x             2    2     x           2   1 2 2x

                       2                          6
     + D f*D D f*D f*p3 *q8 + D f*f  *p3*p7*q8 - ---*D D f  *p7*p8*q8
        2   1 2   1            2   3x             5   1 2 4x

     + D D f  *D f*p3*p7*q8 + D D f *D f *p3*p7*q8 + D D f*D f  *p3*p7*q8
        1 2 2x  1              1 2 x  1 x             1 2   1 2x

                                                1       2      2
     + D f  *f *p3*p8*q8 + D f *f  *p3*p8*q8 - ---*(D f) *f *p3 *q8
        1 2x  x             1 x  2x             2    1     x

                           3        2       3        2       2
     + D f*f  *p3*p8*q8 + ---*f  *p7 *q8 - ---*f  *p8 *q8)/p3
        1   3x             5   5x           5   5x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(1,d(2,df(f(1),x,2)))*p7 - d(1,f(1))*
df(f(1),x)*p3 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=( - d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p3*p8*q8 + d(2,df(f(1),x,2))*df(
f(1),x)*p3*p7*q8 - d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p3*p8*q8 + d(2,df(f(1),x
))*df(f(1),x,2)*p3*p7*q8 + 1/2*d(2,f(1))**2*df(f(1),x)*p3**2*q8 - d(2,f(1))*d(1,
d(2,df(f(1),x,2)))*p3*p8*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p3**2*q8 + d(2,
f(1))*df(f(1),x,3)*p3*p7*q8 - 6/5*d(1,d(2,df(f(1),x,4)))*p7*p8*q8 + d(1,d(2,df(f
(1),x,2)))*d(1,f(1))*p3*p7*q8 + d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p3*p7*q8 + 
d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p3*p7*q8 + d(1,df(f(1),x,2))*df(f(1),x)*p3*p8*
q8 + d(1,df(f(1),x))*df(f(1),x,2)*p3*p8*q8 - 1/2*d(1,f(1))**2*df(f(1),x)*p3**2*
q8 + d(1,f(1))*df(f(1),x,3)*p3*p8*q8 + 3/5*df(f(1),x,5)*p7**2*q8 - 3/5*df(f(1),x
,5)*p8**2*q8)/p3**2$

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

q7


New level : 1.1.2.1.2.2.1.2.
CRACK is now called with the new equation e_474 : 
0=p3 + p6

e_405 is a consequence of e_474

Step 1254: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 32 terms

Substitution of p6 by an expression in 
p3 found in e_474 : 
p6= - p3



>>>>>>>>> Solution of level 1.1.2.1.2.2.1.2. : 
no equations


Non-vanishing expressions: p6,p3,p7,q7
124 factors in 32 terms
170 factors in 36 terms
133 factors in 29 terms
130 factors in 28 terms

g0111*p8 + g0112*p7 - g0113*p3 + g0116*p3


functions : 
      3    2       12              3    2
     ---*p7 *q8 + ----*p7*p8*q7 - ---*p8 *q8
      5            5               5
q27=-----------------------------------------
                         2
                       p3


      6    2       6              6    2
     ---*p7 *q7 - ---*p7*p8*q8 - ---*p8 *q7
      5            5              5
q26=----------------------------------------
                        2
                      p3


q25=0


     p7*q8 + 2*p8*q7
q24=-----------------
           p3


     2*p7*q7 - p8*q8
q23=-----------------
           p3


      - 2*p7*q7 + p8*q8
q22=--------------------
             p3


     p7*q8 + 2*p8*q7
q21=-----------------
           p3


     p7*q8 + 2*p8*q7
q20=-----------------
           p3


      - 2*p7*q7 + p8*q8
q19=--------------------
             p3


     2*p7*q7 - p8*q8
q18=-----------------
           p3


     p7*q8 + 2*p8*q7
q17=-----------------
           p3


     p7*q8 + 2*p8*q7
q16=-----------------
           p3


      - 2*p7*q7 + p8*q8
q15=--------------------
             p3


        1
q14= - ---*q8
        2


q13= - 2*q7


     1
q12=---*q8
     2


     2*p7*q7 - p8*q8
q11=-----------------
           p3


     p7*q8 + 2*p8*q7
q10=-----------------
           p3


q9= - q7

q8, q7, 
q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, 
p6= - p3


p5=0


p4=0

p3, 
p2=0


p1=0


with 70 terms
no equations
5 constants : p3,p7,p8,q7,q8
The equation: 

f =D f*D D f*p3 + D D f  *p7 - D f*f *p3 + f  *p8
 t  2   1 2        1 2 2x       1   x       3x
The symmetry: 
f =(2*D f  *D D f*p3*p7*q7 - D f  *D D f*p3*p8*q8 + D f  *f *p3*p7*q8
 s     2 2x  1 2              2 2x  1 2              2 2x  x

     + 2*D f  *f *p3*p8*q7 + 2*D f *D D f *p3*p7*q7 - D f *D D f *p3*p8*q8
          2 2x  x               2 x  1 2 x             2 x  1 2 x

                                                      2         2
     + D f *f  *p3*p7*q8 + 2*D f *f  *p3*p8*q7 + (D f) *D D f*p3 *q7
        2 x  2x               2 x  2x              2     1 2

        1       2      2
     + ---*(D f) *f *p3 *q8 + 2*D f*D D f  *p3*p7*q7 - D f*D D f  *p3*p8*q8
        2    2     x             2   1 2 2x             2   1 2 2x

                       2                     2
     + D f*D D f*D f*p3 *q8 - 2*D f*D f*f *p3 *q7 + D f*f  *p3*p7*q8
        2   1 2   1              2   1   x           2   3x

                             6            2       6
     + 2*D f*f  *p3*p8*q7 + ---*D D f  *p7 *q7 - ---*D D f  *p7*p8*q8
          2   3x             5   1 2 4x           5   1 2 4x

        6            2
     - ---*D D f  *p8 *q7 + D D f  *D f*p3*p7*q8 + 2*D D f  *D f*p3*p8*q7
        5   1 2 4x           1 2 2x  1                1 2 2x  1

     + D D f *D f *p3*p7*q8 + 2*D D f *D f *p3*p8*q7 + D D f*D f  *p3*p7*q8
        1 2 x  1 x               1 2 x  1 x             1 2   1 2x

                                           2   2
     + 2*D D f*D f  *p3*p8*q7 - D D f*(D f) *p3 *q7 - 2*D f  *f *p3*p7*q7
          1 2   1 2x             1 2    1                1 2x  x

     + D f  *f *p3*p8*q8 - 2*D f *f  *p3*p7*q7 + D f *f  *p3*p8*q8
        1 2x  x               1 x  2x             1 x  2x

        1       2      2
     - ---*(D f) *f *p3 *q8 - 2*D f*f  *p3*p7*q7 + D f*f  *p3*p8*q8
        2    1     x             1   3x             1   3x

        3        2       12                  3        2       2
     + ---*f  *p7 *q8 + ----*f  *p7*p8*q7 - ---*f  *p8 *q8)/p3
        5   5x           5    5x             5   5x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*d(1,d(2,f(1)))*p3 + d(1,d(2,df(f(1),x,2)))*p7 - d(1,f(1))*
df(f(1),x)*p3 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=(2*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p3*p7*q7 - d(2,df(f(1),x,2))*d(1,
d(2,f(1)))*p3*p8*q8 + d(2,df(f(1),x,2))*df(f(1),x)*p3*p7*q8 + 2*d(2,df(f(1),x,2)
)*df(f(1),x)*p3*p8*q7 + 2*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p3*p7*q7 - d(2,df
(f(1),x))*d(1,d(2,df(f(1),x)))*p3*p8*q8 + d(2,df(f(1),x))*df(f(1),x,2)*p3*p7*q8 
+ 2*d(2,df(f(1),x))*df(f(1),x,2)*p3*p8*q7 + d(2,f(1))**2*d(1,d(2,f(1)))*p3**2*q7
 + 1/2*d(2,f(1))**2*df(f(1),x)*p3**2*q8 + 2*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p3*
p7*q7 - d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p3*p8*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1
,f(1))*p3**2*q8 - 2*d(2,f(1))*d(1,f(1))*df(f(1),x)*p3**2*q7 + d(2,f(1))*df(f(1),
x,3)*p3*p7*q8 + 2*d(2,f(1))*df(f(1),x,3)*p3*p8*q7 + 6/5*d(1,d(2,df(f(1),x,4)))*
p7**2*q7 - 6/5*d(1,d(2,df(f(1),x,4)))*p7*p8*q8 - 6/5*d(1,d(2,df(f(1),x,4)))*p8**
2*q7 + d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p3*p7*q8 + 2*d(1,d(2,df(f(1),x,2)))*d(1,
f(1))*p3*p8*q7 + d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p3*p7*q8 + 2*d(1,d(2,df(f(
1),x)))*d(1,df(f(1),x))*p3*p8*q7 + d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p3*p7*q8 + 2
*d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p3*p8*q7 - d(1,d(2,f(1)))*d(1,f(1))**2*p3**2*
q7 - 2*d(1,df(f(1),x,2))*df(f(1),x)*p3*p7*q7 + d(1,df(f(1),x,2))*df(f(1),x)*p3*
p8*q8 - 2*d(1,df(f(1),x))*df(f(1),x,2)*p3*p7*q7 + d(1,df(f(1),x))*df(f(1),x,2)*
p3*p8*q8 - 1/2*d(1,f(1))**2*df(f(1),x)*p3**2*q8 - 2*d(1,f(1))*df(f(1),x,3)*p3*p7
*q7 + d(1,f(1))*df(f(1),x,3)*p3*p8*q8 + 3/5*df(f(1),x,5)*p7**2*q8 + 12/5*df(f(1)
,x,5)*p7*p8*q7 - 3/5*df(f(1),x,5)*p8**2*q8)/p3**2$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p5


New level : 1.1.2.1.2.2.2.
CRACK is now called with the new equation e_335 : 9 factors in 3 terms

Step 1255: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 45 terms

e_432 is a consequence of e_328.
e_448 is a consequence of e_366.
Substitution of q22 by an expression in 
q26, p6, p3, p7 found in e_335 : 8 factors in 3 terms

Step 1256: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_328 and e_445. e_445: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

               2         3   2      3   2
 (q26,q10,q8,p8 ,p8,p6,p3 ,p3 ,p3,p7 ,p7 ,p7)

is replaced by e_456: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

              2
 (q10,q8,p6,p3 ,p3,p7)


Step 1257: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 373  3-Oct-2003 05:31:06, 40 ms (0%), 1019829 occupied, 23980120 free
Eliminate 
q26

from e_328 and e_437. e_437: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                       3   2      2
 (q26,q8,q7,p8,p5,p6,p3 ,p3 ,p3,p7 ,p7)

is replaced by e_457: 

0=p3*q7 + p5*q8 - p6*q7


Step 1258: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 50 terms

The list of inequalities got extended by: 
An expression with 49 terms

Substitution of q8 by an expression in 
q7, p5, p6, p3 found in e_457 : 
     - p3*q7 + p6*q7
q8=------------------
           p5


Step 1259: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_465 is a consequence of e_434.
Step 1260: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_438 and e_461. e_461: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

                      2         2      2
 (q26,q11,q10,q7,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7)

is replaced by e_466: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                  2         2
 (q11,q10,q7,p8,p5 ,p5,p6,p3 ,p3,p7)


Step 1261: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_438 and e_460. e_460: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

                      3   2         2      2
 (q26,q11,q10,q7,p8,p5 ,p5 ,p5,p6,p3 ,p3,p7 ,p7)

is replaced by e_467: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                  2         2
 (q11,q10,q7,p8,p5 ,p5,p6,p3 ,p3,p7)


Step 1262: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 374  3-Oct-2003 05:31:09, 40 ms (0%), 1020109 occupied, 23979839 free
Eliminate 
q26

from e_438 and e_464. e_464: 
 11 terms, 66 factors, with derivatives of functions of all variables: 

                   2      3   2      2      2      3   2
 (q26,q11,q10,q7,p8 ,p8,p5 ,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7 ,p7)

is replaced by e_468: 
 11 terms, 55 factors, with derivatives of functions of all variables: 

               2      2      2      2      2
 (q11,q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1263: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_467 and e_468. e_468: 
 11 terms, 55 factors, with derivatives of functions of all variables: 

               2      2      2      2      2
 (q11,q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_469: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                 2      2
 (q10,q7,p8,p5,p6 ,p6,p3 ,p3,p7)


Step 1264: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_469 and e_466. e_466: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                  2         2
 (q11,q10,q7,p8,p5 ,p5,p6,p3 ,p3,p7)

is replaced by e_470: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

              2      2      2
 (q11,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7)


Step 1265: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_458 we get the alternative equations : 
0=p3 + p6

17 factors in 4 terms

New level : 1.1.2.1.2.2.2.1.
CRACK is now called with the new equation e_475 : 
0=p3 + p6

e_459 is a consequence of e_475

Step 1266: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 

p3


The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 42 terms

The list of inequalities got extended by: 
An expression with 41 terms

Substitution of p3 by an expression in 
p6 found in e_475 : 
p3= - p6


Step 1267: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 26 terms

e_143 is a consequence of e_407.
e_28 is a consequence of e_237.
e_393 is a consequence of e_400.
e_406 is a consequence of e_95.
e_381 is a consequence of e_448.
Substitution of q26 found in e_423 : 
q26=0


Step 1268: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 15 terms

e_326 is a consequence of e_237.
e_379 is a consequence of e_237.
e_23 is a consequence of e_237.
e_371 is a consequence of e_237.
e_95 is a consequence of e_237.
e_370 is a consequence of e_237.e_376 is a consequence of e_395

e_397 is a consequence of e_237.
e_388 is a consequence of e_237.
e_400 is a consequence of e_395.
e_402 is a consequence of e_237.
e_387 is a consequence of e_237.
e_432 is a consequence of e_237.
Substitution of q10 found in e_407 : 
q10=0


Step 1269: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 6 terms

q7


The list of inequalities got extended by: 

q11


The list of inequalities got extended by: 
An expression with 9 terms

Substitution of q11 found in e_237 : 
q11=0


leads to a contradiction in : 
0=2*p6*q11 + p7*q7


Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p3 + p6


New level : 1.1.2.1.2.2.2.2.
CRACK is now called with the new equation e_475 : 17 factors in 4 terms

Step 1270: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 53 terms

The list of inequalities got extended by: 
An expression with 58 terms

The list of inequalities got extended by: 
An expression with 71 terms

The list of inequalities got extended by: 
An expression with 67 terms

e_423 is a consequence of e_456.
Substitution of q26 by an expression in 
q10, q7, p5, p6, p3, p7 found in e_475 : 16 factors in 4 terms

Step 1271: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1272: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1273: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_432. e_432: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

                 2
 (q10,q7,p8,p5,p6 ,p6,p3,p7)

is replaced by e_448: 

0=q7*p8*(3*p3 + 2*p6)


Step 1274: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 375  3-Oct-2003 05:31:12, 40 ms (0%), 1031171 occupied, 23968779 free
Eliminate 
q10

from e_393 and e_143. e_143: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                 2      2
 (q10,q7,p8,p5,p6 ,p6,p3 ,p3,p7)

is replaced by e_449: 

0=q7*p8*(3*p3 + 2*p6)


e_449 is a consequence of e_448.
Step 1275: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_326 and e_371. e_371: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

               3   2      2      3   2
 (q11,q10,q7,p5 ,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7)

is replaced by e_450: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

           3   2      2      3   2
 (q10,q7,p5 ,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7)


Step 1276: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_467. e_467: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                  2         2
 (q11,q10,q7,p8,p5 ,p5,p6,p3 ,p3,p7)

is replaced by e_451: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

              2         2
 (q11,q7,p8,p5 ,p5,p6,p3 ,p3,p7)


Step 1277: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_28. e_28: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

                  2         2      2
 (q11,q10,q7,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7)

is replaced by e_452: 
(#) 3 terms, 10 factors, with derivatives of functions of all variables: 

           2
 (q11,q7,p8 ,p8,p5,p3,p7)


Step 1278: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_399. e_399: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

                  2      2      2
 (q11,q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7)

is replaced by e_455: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

 (q11,q7,p8,p5,p6,p3,p7)


Step 1279: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_451. e_451: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

              2         2
 (q11,q7,p8,p5 ,p5,p6,p3 ,p3,p7)

is replaced by e_445: 
(#) 6 terms, 19 factors, with derivatives of functions of all variables: 

          2      2      2
 (q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7)


Step 1280: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_470. e_470: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

              2      2      2
 (q11,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7)

is replaced by e_437: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

             2      2
 (q7,p8,p5,p6 ,p6,p3 ,p3,p7)


Step 1281: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_452 and e_405. e_405: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

               2      2      2      2      2
 (q11,q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_457: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

           2      2      2      2      2
 (q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1282: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_457. e_457: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

           2      2      2      2      2
 (q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_386: 
(#) 7 terms, 29 factors, with derivatives of functions of all variables: 

       2      2      2      2      2
 (q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1283: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_387. e_387: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                  3   2      2      2
 (q11,q10,q7,p8,p5 ,p5 ,p5,p6 ,p6,p3 ,p3,p7)

is replaced by e_465: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

              3   2      2      2
 (q10,q7,p8,p5 ,p5 ,p5,p6 ,p6,p3 ,p3,p7)


Step 1284: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_465. e_465: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

              3   2      2      2
 (q10,q7,p8,p5 ,p5 ,p5,p6 ,p6,p3 ,p3,p7)

is replaced by e_461: 
(#) 5 terms, 16 factors, with derivatives of functions of all variables: 

          2         2
 (q7,p8,p5 ,p5,p6,p3 ,p3,p7)


Step 1285: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_95. e_95: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                  2      2      2      2
 (q11,q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_460: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

              2      2      2      2
 (q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1286: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_460. e_460: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

              2      2      2      2
 (q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_464: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

       2               2
 (q7,p8 ,p8,p5,p6,p3,p7 ,p7)


Step 1287: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1288: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_23. e_23: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                  2      2      2      2
 (q11,q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_471: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

              2      2      2      2
 (q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1289: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_471. e_471: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

              2      2      2      2
 (q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_472: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

       2               2
 (q7,p8 ,p8,p5,p6,p3,p7 ,p7)


Step 1290: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

e_473 is a consequence of e_468.
Step 1291: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_379. e_379: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                  2      2      2      2
 (q11,q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_474: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

              2      2      2      2
 (q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1292: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_474. e_474: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

              2      2      2      2
 (q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_458: 
(#) 3 terms, 10 factors, with derivatives of functions of all variables: 

       2            2
 (q7,p8 ,p8,p5,p6,p7 ,p7)


e_458 is a consequence of e_468.
Step 1293: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_237. e_237: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                  2      2      2      2
 (q11,q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_476: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

              2      2      2      2
 (q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1294: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_476. e_476: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

              2      2      2      2
 (q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_477: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

       2               2
 (q7,p8 ,p8,p5,p6,p3,p7 ,p7)


Step 1295: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

e_478 is a consequence of e_468.
Step 1296: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_370. e_370: 
 8 terms, 48 factors, with derivatives of functions of all variables: 

                  3   2      2      3   2      2
 (q11,q10,q7,p8,p5 ,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7 ,p7)

is replaced by e_479: 
 6 terms, 30 factors, with derivatives of functions of all variables: 

              2         2      2
 (q11,q7,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7)


Step 1297: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_398. e_398: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

               2      2      2      2      2
 (q11,q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_480: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

           2      2         2
 (q11,q7,p8 ,p8,p5 ,p5,p6,p3 ,p3,p7)


Step 1298: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_480. e_480: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

           2      2         2
 (q11,q7,p8 ,p8,p5 ,p5,p6,p3 ,p3,p7)

is replaced by e_481: 
(#) 7 terms, 29 factors, with derivatives of functions of all variables: 

       2      2      2      2      2
 (q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1299: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_452 and e_406. e_406: 
 11 terms, 55 factors, with derivatives of functions of all variables: 

               2      2      2      2      2
 (q11,q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_482: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

           2      2      2      2      2
 (q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1300: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_482. e_482: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

           2      2      2      2      2
 (q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_483: 
(#) 5 terms, 17 factors, with derivatives of functions of all variables: 

       2      2         2
 (q7,p8 ,p8,p5 ,p5,p6,p3 ,p3,p7)


Step 1301: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_452 and e_404. e_404: 
 10 terms, 60 factors, with derivatives of functions of all variables: 

               2      2      2      2      2
 (q11,q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_484: 
 10 terms, 60 factors, with derivatives of functions of all variables: 

           2      2      2      2      2
 (q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1302: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_484. e_484: 
 10 terms, 60 factors, with derivatives of functions of all variables: 

           2      2      2      2      2
 (q10,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_485: 
(#) 5 terms, 21 factors, with derivatives of functions of all variables: 

       2         2      2      2
 (q7,p8 ,p8,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1303: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_452 and e_397. e_397: 
 10 terms, 60 factors, with derivatives of functions of all variables: 

               2      3   2      2      2      2
 (q11,q10,q7,p8 ,p8,p5 ,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_486: 
 10 terms, 60 factors, with derivatives of functions of all variables: 

           2      3   2      2      2      2
 (q10,q7,p8 ,p8,p5 ,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1304: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_486. e_486: 
 10 terms, 60 factors, with derivatives of functions of all variables: 

           2      3   2      2      2      2
 (q10,q7,p8 ,p8,p5 ,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_487: 
(#) 6 terms, 25 factors, with derivatives of functions of all variables: 

       2      2         2      2
 (q7,p8 ,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7)


Step 1305: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_402. e_402: 
 12 terms, 60 factors, with derivatives of functions of all variables: 

                  2      3   2      3   2
 (q11,q10,q7,p8,p5 ,p5,p6 ,p6 ,p6,p3 ,p3 ,p3,p7)

is replaced by e_488: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

              2      3   2      3   2
 (q10,q7,p8,p5 ,p5,p6 ,p6 ,p6,p3 ,p3 ,p3,p7)


Step 1306: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_488. e_488: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

              2      3   2      3   2
 (q10,q7,p8,p5 ,p5,p6 ,p6 ,p6,p3 ,p3 ,p3,p7)

is replaced by e_489: 

0=q7*(p3*p8 - 2*p5*p7)


Step 1307: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_400. e_400: 
 10 terms, 60 factors, with derivatives of functions of all variables: 

                  3   2         3   2      2
 (q11,q10,q7,p8,p5 ,p5 ,p5,p6,p3 ,p3 ,p3,p7 ,p7)

is replaced by e_491: 
 10 terms, 60 factors, with derivatives of functions of all variables: 

           2      3   2         3   2      2
 (q10,q7,p8 ,p8,p5 ,p5 ,p5,p6,p3 ,p3 ,p3,p7 ,p7)


Step 1308: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_491. e_491: 
 10 terms, 60 factors, with derivatives of functions of all variables: 

           2      3   2         3   2      2
 (q10,q7,p8 ,p8,p5 ,p5 ,p5,p6,p3 ,p3 ,p3,p7 ,p7)

is replaced by e_492: 
(#) 5 terms, 21 factors, with derivatives of functions of all variables: 

       2      2         2      2
 (q7,p8 ,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7)


Step 1309: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 376  3-Oct-2003 05:31:15, 50 ms (0%), 1024090 occupied, 23975858 free
Eliminate 
q10

from e_393 and e_388. e_388: 
 10 terms, 60 factors, with derivatives of functions of all variables: 

                  3   2      2      3   2      2
 (q11,q10,q7,p8,p5 ,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7 ,p7)

is replaced by e_493: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

              2         2      2
 (q11,q7,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7)


Step 1310: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_493. e_493: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

              2         2      2
 (q11,q7,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7)

is replaced by e_494: 
(#) 6 terms, 25 factors, with derivatives of functions of all variables: 

       2      2         2      2
 (q7,p8 ,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7)


Step 1311: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_395. e_395: 
 11 terms, 66 factors, with derivatives of functions of all variables: 

                  3   2      2      3   2      2
 (q11,q10,q7,p8,p5 ,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7 ,p7)

is replaced by e_423: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

           2      2         2      2
 (q11,q7,p8 ,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7)


Step 1312: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_423. e_423: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

           2      2         2      2
 (q11,q7,p8 ,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7)

is replaced by e_475: 
(#) 7 terms, 29 factors, with derivatives of functions of all variables: 

       2      2         2      2
 (q7,p8 ,p8,p5 ,p5,p6,p3 ,p3,p7 ,p7)


Step 1313: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_384. e_384: 
 15 terms, 90 factors, with derivatives of functions of all variables: 

               2      3   2      3   2      3   2      2
 (q11,q10,q7,p8 ,p8,p5 ,p5 ,p5,p6 ,p6 ,p6,p3 ,p3 ,p3,p7 ,p7)

is replaced by e_469: 
 11 terms, 55 factors, with derivatives of functions of all variables: 

           2      2      2      2      2
 (q11,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1314: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_469. e_469: 
 11 terms, 55 factors, with derivatives of functions of all variables: 

           2      2      2      2      2
 (q11,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7 ,p7)

is replaced by e_376: 
(#) 7 terms, 29 factors, with derivatives of functions of all variables: 

       2         2      2      2
 (q7,p8 ,p8,p5,p6 ,p6,p3 ,p3,p7 ,p7)


Step 1315: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_358. e_358: 
 16 terms, 112 factors, with derivatives of functions of all variables: 

                  3   2      2      4   3   2      2
 (q11,q10,q7,p8,p5 ,p5 ,p5,p6 ,p6,p3 ,p3 ,p3 ,p3,p7 ,p7)

is replaced by e_432: 
 14 terms, 84 factors, with derivatives of functions of all variables: 

           2      2      2      3   2      2
 (q11,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7 ,p7)


Step 1316: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_432. e_432: 
 14 terms, 84 factors, with derivatives of functions of all variables: 

           2      2      2      3   2      2
 (q11,q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7 ,p7)

is replaced by e_335: 
(#) 11 terms, 56 factors, with derivatives of functions of all variables: 

       2      2      2      3   2      2
 (q7,p8 ,p8,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7 ,p7)


Step 1317: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_326. e_326: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

               2      2      3   2
 (q11,q10,q7,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7)

is replaced by e_143: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

              2      2      3   2
 (q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7)


Step 1318: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_143. e_143: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

              2      2      3   2
 (q10,q7,p8,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7)

is replaced by e_449: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

             2      2
 (q7,p8,p5,p6 ,p6,p3 ,p3,p7)


Step 1319: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1320: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_393 and e_407. e_407: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

               3   2      2      3   2
 (q11,q10,q7,p5 ,p5 ,p5,p6 ,p6,p3 ,p3 ,p3,p7)

is replaced by e_28: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

              2         2
 (q11,q7,p8,p5 ,p5,p6,p3 ,p3,p7)


Step 1321: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_455 and e_28. e_28: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

              2         2
 (q11,q7,p8,p5 ,p5,p6,p3 ,p3,p7)

is replaced by e_453: 
(#) 6 terms, 19 factors, with derivatives of functions of all variables: 

          2      2      2
 (q7,p8,p5 ,p5,p6 ,p6,p3 ,p3,p7)


Step 1322: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_489 we get the alternative equations : 
0=q7


0=p3*p8 - 2*p5*p7


New level : 1.1.2.1.2.2.2.2.1.
CRACK is now called with the new equation e_498 : 
0=q7

e_335,e_386,e_481,e_475,e_376,e_487,e_494,e_485,e_492,e_445,e_453,e_483,e_461,
e_381,e_437,e_468,e_371,e_448 are consequences of e_498

Step 1323: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 23 terms
e_395 is a consequence of e_423

e_469 is a consequence of e_384.
e_358 is a consequence of e_423.
e_432 is a consequence of e_384.
Substitution of q7 found in e_498 : 
q7=0


Step 1324: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 16 terms

q10


The list of inequalities got extended by: 
An expression with 17 terms

Substitution of q11 found in e_423 : 
q11=0


Step 1325: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
contradiction from the substitution:
q10=0

because of the non-vanishing expression:
q10


The list of inequalities got extended by: 

g0078*p6 + g0079*p5 + g0081*p3


p3


p5


p7

The lexicographical ordering of unknowns is changed
because p5 has to be non-zero, giving p5 a low priority.
Old ordering: q10,p8,p5,p6,p3,p7
New ordering: q10,p8,p6,p5,p3,p7

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p8


The list of inequalities got extended by: 

q7


New level : 1.1.2.1.2.2.2.2.2.
CRACK is now called with the new equation e_498 : 
0=p3*p8 - 2*p5*p7


Step 1326: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 
An expression with 49 terms

The list of inequalities got extended by: 
An expression with 54 terms

The list of inequalities got extended by: 
An expression with 67 terms

The list of inequalities got extended by: 
An expression with 63 terms

The list of inequalities got extended by: 

q11

The lexicographical ordering of unknowns is changed
because q11 has to be non-zero, giving q11 a low priority.
Old ordering: q11,q10,q7,p8,p5,p6,p3,p7
New ordering: q10,q11,q7,p8,p5,p6,p3,p7

Substitution of p5 by an expression in 
p8, p3, p7 found in e_498 : 
     1
    ---*p3*p8
     2
p5=-----------
       p7


Step 1327: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 47 terms

The list of inequalities got extended by: 

q7


The list of inequalities got extended by: 
An expression with 53 terms

The list of inequalities got extended by: 
An expression with 65 terms
*** Garbage collection starting 
*** GC 377  3-Oct-2003 05:31:18, 40 ms (0%), 1039424 occupied, 23960525 free

The list of inequalities got extended by: 
An expression with 61 terms
e_395,e_448 are consequences of e_469

Substitution of q7 by an expression in 
q11, p3, p7 found in e_384 : 
     1
    ---*p3*q11
     4
q7=------------
        p7


Step 1328: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 

p3


The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 38 terms

e_470 is a consequence of e_95.
e_449 is a consequence of e_95.
e_143 is a consequence of e_95.
e_423 is a consequence of e_95.
e_457 is a consequence of e_95.
e_451 is a consequence of e_95.
e_454 is a consequence of e_95.
e_387 is a consequence of e_95.
e_399 is a consequence of e_95.
e_407 is a consequence of e_95.
e_467 is a consequence of e_95.
e_326 is a consequence of e_95.
e_432 is a consequence of e_95.
The list of inequalities got extended by: 

q10


e_405 is a consequence of e_95.
e_464 is a consequence of e_95.
e_465 is a consequence of e_95.
Substitution of p3 by an expression in 
p6 found in e_469 : 
       2
p3= - ---*p6
       3


Step 1329: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 

q10


The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 28 terms

e_358 is a consequence of e_95.
e_460 is a consequence of e_95.
Substitution of q10 by an expression in 
q11, p8, p7 found in e_28 : 
      - p7*q11
q10=-----------
        p8


Step 1330: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.2.1.2.2.2.2.2. : 
equations : 

e_95 : 
    2     2
0=p7  + p8



Non-vanishing expressions: q10,q7,p8,p6,p7,p5,q11,p3
140 factors in 28 terms
128 factors in 28 terms
132 factors in 24 terms
128 factors in 23 terms

                          2
3*g0111*p7*p8 + 3*g0112*p7  + 3*g0113*p6*p7 - g0114*p6*p8 - 2*g0116*p6*p7


functions : 
      3    2        9     2
     ---*p7 *q11 - ----*p8 *q11
      5             10
q27=----------------------------
               p6*p8


      3    3
     ---*p7 *q11
      2
q26=-------------
            2
       p6*p8


q25=0


         5
      - ---*p7*q11
         4
q24=---------------
          p8


      3    2           2
     ---*p7 *q11 + 2*p8 *q11
      4
q23=-------------------------
                 2
               p8


      5    2
     ---*p7 *q11
      4
q22=-------------
           2
         p8


         5
      - ---*p7*q11
         4
q21=---------------
          p8


         5
      - ---*p7*q11
         4
q20=---------------
          p8


      5    2        5    2
     ---*p7 *q11 + ---*p8 *q11
      2             4
q19=---------------------------
                  2
                p8


         5    4        11    2   2        1    4
      - ---*p7 *q11 - ----*p7 *p8 *q11 - ---*p8 *q11
         3             12                 2
q18=-------------------------------------------------
                           2   2
                         p7 *p8


         5
      - ---*p7*q11
         4
q17=---------------
          p8


         3
      - ---*p7*q11
         2
q16=---------------
          p8


      1    2         2
     ---*p7 *q11 - p8 *q11
      2
q15=-----------------------
                2
              p8


         5
      - ---*p6*q11
         8
q14=---------------
          p8


      5
     ----*p6*q11
      12
q13=-------------
         p7


      7        2        1       2
     ----*p6*p7 *q11 - ---*p6*p8 *q11
      24                6
q12=----------------------------------
                    2
                  p7 *p8

q11, 
      - p7*q11
q10=-----------
        p8


        5        2        5        2
     - ----*p6*p7 *q11 - ----*p6*p8 *q11
        12                12
q9=--------------------------------------
                        2
                   p7*p8


     5
    ---*p6*q11
     6
q8=------------
        p8


        1
     - ---*p6*q11
        6
q7=---------------
         p7


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, p6, 
        1
     - ---*p6*p8
        3
p5=--------------
         p7


p4=0


       2
p3= - ---*p6
       3


p2=0


p1=0


with 64 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_95(2a)
4 constants : p6,p7,p8,q11
The equation: 

        2                     1                           2
f =( - ---*D f*D D f*p6*p7 - ---*D f*f *p6*p8 + D D f  *p7  + D f*f *p6*p7
 t      3   2   1 2           3   2   x          1 2 2x        1   x

     + f  *p7*p8)/p7
        3x
The symmetry: 
                     2   2        3                3
f =(D f  *D D f*p6*p7 *p8 *q11 - ---*D f  *f *p6*p7 *p8*q11
 s   2 2x  1 2                    2   2 2x  x

        5                   4        11                   2   2
     - ---*D f *D D f *p6*p7 *q11 - ----*D f *D D f *p6*p7 *p8 *q11
        3   2 x  1 2 x               12   2 x  1 2 x

        1                   4        5                3
     - ---*D f *D D f *p6*p8 *q11 - ---*D f *f  *p6*p7 *p8*q11
        2   2 x  1 2 x               4   2 x  2x

        1       2         2      2        7        2      2   2
     - ---*(D f) *D D f*p6 *p7*p8 *q11 + ----*(D f) *f *p6 *p7 *p8*q11
        6    2     1 2                    24    2     x

        1       2      2   3        3                   4
     - ---*(D f) *f *p6 *p8 *q11 + ---*D f*D D f  *p6*p7 *q11
        6    2     x                4   2   1 2 2x

                          2   2        5                  2   2
     + 2*D f*D D f  *p6*p7 *p8 *q11 + ---*D f*D D f*D f*p6 *p7 *p8*q11
          2   1 2 2x                   6   2   1 2   1

        5                2      2        5               3
     + ----*D f*D f*f *p6 *p7*p8 *q11 - ---*D f*f  *p6*p7 *p8*q11
        12   2   1   x                   4   2   3x

        3            5        5                   3
     + ---*D D f  *p7 *q11 - ---*D D f  *D f*p6*p7 *p8*q11
        2   1 2 4x            4   1 2 2x  1

        5                   3                           3
     - ---*D D f *D f *p6*p7 *p8*q11 - D D f*D f  *p6*p7 *p8*q11
        4   1 2 x  1 x                  1 2   1 2x

        5              2   2   3        5              2   2      2
     - ----*D D f*(D f) *p6 *p7 *q11 - ----*D D f*(D f) *p6 *p7*p8 *q11
        12   1 2    1                   12   1 2    1

        1                4                     2   2
     + ---*D f  *f *p6*p7 *q11 - D f  *f *p6*p7 *p8 *q11
        2   1 2x  x               1 2x  x

        5                4        5                2   2
     + ---*D f *f  *p6*p7 *q11 + ---*D f *f  *p6*p7 *p8 *q11
        2   1 x  2x               4   1 x  2x

        5       2      2   2           5               4
     - ---*(D f) *f *p6 *p7 *p8*q11 + ---*D f*f  *p6*p7 *q11
        8    1     x                   4   1   3x

        3        4           9         2   3            2   2
     + ---*f  *p7 *p8*q11 - ----*f  *p7 *p8 *q11)/(p6*p7 *p8 )
        5   5x               10   5x
And now in machine readable form:

The system: 

df(f(1),t)=( - 2/3*d(2,f(1))*d(1,d(2,f(1)))*p6*p7 - 1/3*d(2,f(1))*df(f(1),x)*p6*
p8 + d(1,d(2,df(f(1),x,2)))*p7**2 + d(1,f(1))*df(f(1),x)*p6*p7 + df(f(1),x,3)*p7
*p8)/p7$
The symmetry: 
df(f(1),s)=(d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p6*p7**2*p8**2*q11 - 3/2*d(2,df(f(1
),x,2))*df(f(1),x)*p6*p7**3*p8*q11 - 5/3*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6
*p7**4*q11 - 11/12*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6*p7**2*p8**2*q11 - 1/2
*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6*p8**4*q11 - 5/4*d(2,df(f(1),x))*df(f(1)
,x,2)*p6*p7**3*p8*q11 - 1/6*d(2,f(1))**2*d(1,d(2,f(1)))*p6**2*p7*p8**2*q11 + 7/
24*d(2,f(1))**2*df(f(1),x)*p6**2*p7**2*p8*q11 - 1/6*d(2,f(1))**2*df(f(1),x)*p6**
2*p8**3*q11 + 3/4*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p6*p7**4*q11 + 2*d(2,f(1))*d(
1,d(2,df(f(1),x,2)))*p6*p7**2*p8**2*q11 + 5/6*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))
*p6**2*p7**2*p8*q11 + 5/12*d(2,f(1))*d(1,f(1))*df(f(1),x)*p6**2*p7*p8**2*q11 - 5
/4*d(2,f(1))*df(f(1),x,3)*p6*p7**3*p8*q11 + 3/2*d(1,d(2,df(f(1),x,4)))*p7**5*q11
 - 5/4*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p6*p7**3*p8*q11 - 5/4*d(1,d(2,df(f(1),x)
))*d(1,df(f(1),x))*p6*p7**3*p8*q11 - d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p6*p7**3*
p8*q11 - 5/12*d(1,d(2,f(1)))*d(1,f(1))**2*p6**2*p7**3*q11 - 5/12*d(1,d(2,f(1)))*
d(1,f(1))**2*p6**2*p7*p8**2*q11 + 1/2*d(1,df(f(1),x,2))*df(f(1),x)*p6*p7**4*q11 
- d(1,df(f(1),x,2))*df(f(1),x)*p6*p7**2*p8**2*q11 + 5/2*d(1,df(f(1),x))*df(f(1),
x,2)*p6*p7**4*q11 + 5/4*d(1,df(f(1),x))*df(f(1),x,2)*p6*p7**2*p8**2*q11 - 5/8*d(
1,f(1))**2*df(f(1),x)*p6**2*p7**2*p8*q11 + 5/4*d(1,f(1))*df(f(1),x,3)*p6*p7**4*
q11 + 3/5*df(f(1),x,5)*p7**4*p8*q11 - 9/10*df(f(1),x,5)*p7**2*p8**3*q11)/(p6*p7
**2*p8**2)$

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 30 ms

The list of inequalities got extended by: 

p4

The lexicographical ordering of unknowns is changed
because p4 has to be non-zero, giving p4 a low priority.
Old ordering: q27,q26,q22,q20,q17,q14,q13,q12,q11,q10,q9,q8,q7,p8,p6,p5,p4,p3,p7
New ordering: q27,q26,q22,q20,q17,q14,q13,q12,q11,q10,q9,q8,q7,p8,p6,p5,p3,p4,p7

New level : 1.1.2.2.
CRACK is now called with the new equation e_326 : 25 factors in 8 terms
e_337 is a consequence of e_326

Step 1331: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 48 terms

The list of inequalities got extended by: 
An expression with 50 terms

e_358 is a consequence of e_333.
Substitution of q22 by an expression in 
q27, q26, q20, q17, q11, p8, p6, p5, p3, p4, p7 found in e_326 : 28 factors in 8
 terms

Step 1332: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 42 terms

The list of inequalities got extended by: 
An expression with 49 terms

The list of inequalities got extended by: 
An expression with 51 terms

Substitution of q13 by an expression in 
q9, p5, p4 found in e_287 : 
     p4*q9 + p5*q9
q13=---------------
          p4


Step 1333: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 51 terms

The list of inequalities got extended by: 
An expression with 53 terms

Substitution of q14 by an expression in 
q9, q8, p6, p3, p4 found in e_157 : 14 factors in 4 terms

Step 1334: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_328 and e_226. e_226: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                             2
 (q27,q26,q20,q17,p8,p6,p5,p3 ,p3,p4,p7)

is replaced by e_382: 

                 2     2
0=(q17 - q20)*(p3  + p4 )


Step 1335: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 378  3-Oct-2003 05:31:21, 40 ms (0%), 1046554 occupied, 23953396 free
*** Garbage collection starting 
*** GC 379  3-Oct-2003 05:31:24, 40 ms (0%), 1035074 occupied, 23964876 free
Eliminate 
q27

from e_330 and e_365. e_365: 
 19 terms, 57 factors, with derivatives of functions of all variables: 

                                  2         2
 (q27,q26,q20,q17,q11,q10,p8,p6,p5 ,p5,p3,p4 ,p4,p7)

is replaced by e_385: 
(#) 10 terms, 14 factors, with derivatives of functions of all variables: 

                       2         2
 (q26,q20,q17,q10,p6,p5 ,p5,p3,p4 ,p4,p7)


Step 1336: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_328 and e_372. e_372: 
 16 terms, 64 factors, with derivatives of functions of all variables: 

                                 2         2      2      2
 (q27,q26,q20,q17,q11,q9,q7,p8,p6 ,p6,p5,p3 ,p3,p4 ,p4,p7 ,p7)

is replaced by e_386: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                          2         2         2
 (q26,q20,q17,q11,q9,q7,p6 ,p6,p5,p3 ,p3,p4,p7 ,p7)


Step 1337: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 380  3-Oct-2003 05:31:26, 30 ms (0%), 1042612 occupied, 23957337 free
Eliminate 
q27

from e_328 and e_371. e_371: 
 16 terms, 64 factors, with derivatives of functions of all variables: 

                                              3   2      2
 (q27,q26,q20,q17,q11,q10,q9,q8,p8,p6,p5,p3,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_387: 
 11 terms, 44 factors, with derivatives of functions of all variables: 

                                          2      2
 (q26,q20,q17,q11,q10,q9,q8,p8,p6,p5,p3,p4 ,p4,p7 ,p7)


Step 1338: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_378 and e_387. e_387: 
 11 terms, 44 factors, with derivatives of functions of all variables: 

                                          2      2
 (q26,q20,q17,q11,q10,q9,q8,p8,p6,p5,p3,p4 ,p4,p7 ,p7)

is replaced by e_388: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

 (q20,q17,q9,p8,p6,p5,p3,p4,p7)


Step 1339: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_328 and e_374. e_374: 
 18 terms, 72 factors, with derivatives of functions of all variables: 

                                        2         3   2      2
 (q27,q26,q20,q17,q11,q10,q9,q8,p8,p6,p5 ,p5,p3,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_389: 
 11 terms, 44 factors, with derivatives of functions of all variables: 

                                          2      2
 (q26,q20,q17,q11,q10,q9,q8,p8,p6,p5,p3,p4 ,p4,p7 ,p7)


Step 1340: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_328 and e_381. e_381: 
 19 terms, 76 factors, with derivatives of functions of all variables: 

                                     2         2      3   2      2
 (q27,q26,q20,q17,q11,q10,q9,q8,p8,p6 ,p6,p5,p3 ,p3,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_390: 
 17 terms, 68 factors, with derivatives of functions of all variables: 

                                 2         2      3   2      2
 (q26,q20,q17,q11,q10,q9,q8,p8,p6 ,p6,p5,p3 ,p3,p4 ,p4 ,p4,p7 ,p7)


Step 1341: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 381  3-Oct-2003 05:31:29, 30 ms (0%), 1033786 occupied, 23966162 free
Eliminate 
q27

from e_328 and e_380. e_380: 
 20 terms, 80 factors, with derivatives of functions of all variables: 

                                     2         2      2      2
 (q27,q26,q20,q17,q11,q10,q9,q8,p8,p6 ,p6,p5,p3 ,p3,p4 ,p4,p7 ,p7)

is replaced by e_391: 
 16 terms, 64 factors, with derivatives of functions of all variables: 

                                 2      2      2      2
 (q26,q20,q17,q11,q10,q9,q8,p8,p6 ,p6,p3 ,p3,p4 ,p4,p7 ,p7)


Step 1342: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 382  3-Oct-2003 05:31:32, 40 ms (0%), 1050218 occupied, 23949730 free
*** Garbage collection starting 
*** GC 383  3-Oct-2003 05:31:35, 30 ms (0%), 1034924 occupied, 23965025 free
*** Garbage collection starting 
*** GC 384  3-Oct-2003 05:31:39, 40 ms (0%), 1037014 occupied, 23962935 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_385 we get the alternative equations : 
0=p3*p4 + p5*p6

12 factors in 5 terms

New level : 1.1.2.2.1.
CRACK is now called with the new equation e_396 : 
0=p3*p4 + p5*p6


Step 1343: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 51 terms

The list of inequalities got extended by: 
An expression with 53 terms

Substitution of p3 by an expression in 
p6, p5, p4 found in e_396 : 
     - p5*p6
p3=----------
       p4


Step 1344: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_408 and e_415. e_415: 
 10 terms, 40 factors, with derivatives of functions of all variables: 

                    2            2      2
 (q27,q26,q20,q17,p8 ,p8,p6,p5,p4 ,p4,p7 ,p7)

is replaced by e_441: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

                         3   2      2
 (q26,q20,q17,p8,p6,p5,p4 ,p4 ,p4,p7 ,p7)


Step 1345: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_65 and e_411. e_411: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

                               3   2
 (q17,q11,q10,q9,q8,p8,p6,p5,p4 ,p4 ,p4,p7)

is replaced by e_442: 
 7 terms, 21 factors, with derivatives of functions of all variables: 

                     2      2
 (q11,q10,q9,q8,p8,p6 ,p6,p4 ,p4,p7)


Step 1346: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 385  3-Oct-2003 05:31:43, 40 ms (0%), 1055571 occupied, 23944379 free
*** Garbage collection starting 
*** GC 386  3-Oct-2003 05:31:46, 30 ms (0%), 1053453 occupied, 23946497 free
Eliminate 
q27

from e_417 and e_424. e_424: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                                  2      3   2
 (q27,q26,q20,q17,q11,q10,p8,p6,p5 ,p5,p4 ,p4 ,p4,p7)

is replaced by e_443: 
(#) 4 terms, 8 factors, with derivatives of functions of all variables: 

                     2
 (q20,q17,p8,p6,p5,p4 ,p4,p7)


Step 1347: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_417 and e_422. e_422: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                            2            2      2
 (q27,q26,q20,q17,q11,q10,p8 ,p8,p6,p5,p4 ,p4,p7 ,p7)

is replaced by e_446: 
(#) 10 terms, 14 factors, with derivatives of functions of all variables: 

                             2      2
 (q26,q20,q17,q10,p8,p6,p5,p4 ,p4,p7 ,p7)


Step 1348: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_402 and e_419. e_419: 
 11 terms, 55 factors, with derivatives of functions of all variables: 

                               2      2      3   2
 (q27,q26,q20,q17,q11,q10,p8,p6 ,p6,p5 ,p5,p4 ,p4 ,p4,p7)

is replaced by e_28: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

                           2      2      3   2
 (q26,q20,q17,q11,q10,p8,p6 ,p6,p5 ,p5,p4 ,p4 ,p4,p7)


Step 1349: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_420 and e_431. e_431: 
 12 terms, 60 factors, with derivatives of functions of all variables: 

                                2      3   2      2
 (q26,q20,q11,q10,q9,q8,p8,p6,p5 ,p5,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_237: 
(#) 12 terms, 26 factors, with derivatives of functions of all variables: 

                         2      3   2      2
 (q26,q20,q10,q9,p8,p6,p5 ,p5,p4 ,p4 ,p4,p7 ,p7)


Step 1350: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_417 and e_435. e_435: 
 20 terms, 100 factors, with derivatives of functions of all variables: 

                               2      2      4   3   2
 (q27,q26,q20,q17,q11,q10,p8,p6 ,p6,p5 ,p5,p4 ,p4 ,p4 ,p4,p7)

is replaced by e_246: 
 20 terms, 100 factors, with derivatives of functions of all variables: 

                       2      2      4   3   2
 (q26,q20,q17,q10,p8,p6 ,p6,p5 ,p5,p4 ,p4 ,p4 ,p4,p7)


Step 1351: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 387  3-Oct-2003 05:31:48, 40 ms (0%), 1055105 occupied, 23944845 free
Eliminate 
q27

from e_408 and e_429. e_429: 
 14 terms, 56 factors, with derivatives of functions of all variables: 

                                     2      3   2      2
 (q27,q26,q20,q17,q12,q11,q8,p8,p6,p5 ,p5,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_161: 
 11 terms, 55 factors, with derivatives of functions of all variables: 

                              2      3   2      2
 (q26,q20,q17,q12,q11,q8,p6,p5 ,p5,p4 ,p4 ,p4,p7 ,p7)


Step 1352: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_408 and e_425. e_425: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                                         2      2      2
 (q27,q26,q20,q17,q12,q11,q10,q7,p8,p6,p5 ,p5,p4 ,p4,p7 ,p7)

is replaced by e_278: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                                 2      2
 (q20,q17,q12,q11,q10,q7,p8,p6,p5 ,p5,p4 ,p4,p7)


Step 1353: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 388  3-Oct-2003 05:31:51, 40 ms (0%), 1059103 occupied, 23940847 free
*** Garbage collection starting 
*** GC 389  3-Oct-2003 05:31:55, 30 ms (0%), 1053519 occupied, 23946430 free
Eliminate 
q20

from e_278 and e_428. e_278: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                                 2      2
 (q20,q17,q12,q11,q10,q7,p8,p6,p5 ,p5,p4 ,p4,p7)

is replaced by e_103: 
 7 terms, 21 factors, with derivatives of functions of all variables: 

 (q12,q11,q10,q9,q8,q7,p8,p6,p5,p4,p7)


Step 1354: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 390  3-Oct-2003 05:31:58, 40 ms (0%), 1059899 occupied, 23940051 free
Eliminate 
q27

from e_432 and e_426. e_426: 
 13 terms, 65 factors, with derivatives of functions of all variables: 

                                  2      2      3   2      2
 (q27,q26,q20,q12,q11,q10,q7,p8,p6 ,p6,p5 ,p5,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_23: 
 12 terms, 60 factors, with derivatives of functions of all variables: 

                                2      2      3   2      2
 (q26,q12,q11,q10,q9,q8,q7,p8,p6 ,p6,p5 ,p5,p4 ,p4 ,p4,p7 ,p7)


Step 1355: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_443 we get the alternative equations : 
0=p4*q20 - p5*q17


0=p4*p8 - p6*p7


New level : 1.1.2.2.1.1.
CRACK is now called with the new equation e_325 : 
0=p4*q20 - p5*q17


Step 1356: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 51 terms

The list of inequalities got extended by: 
An expression with 53 terms

Substitution of q20 by an expression in 
q17, p5, p4 found in e_325 : 
     p5*q17
q20=--------
       p4


Step 1357: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 391  3-Oct-2003 05:32:03, 30 ms (0%), 1067410 occupied, 23932539 free
*** Garbage collection starting 
*** GC 392  3-Oct-2003 05:32:05, 40 ms (0%), 1072252 occupied, 23927698 free
Eliminate 
q27

from e_374 and e_380. e_380: 
 11 terms, 55 factors, with derivatives of functions of all variables: 

                              2      3   2
 (q27,q26,q17,q11,q10,p8,p6,p5 ,p5,p4 ,p4 ,p4,p7)

is replaced by e_422: 
 9 terms, 54 factors, with derivatives of functions of all variables: 

                          2      3   2      2
 (q26,q17,q11,q10,p8,p6,p5 ,p5,p4 ,p4 ,p4,p7 ,p7)


Step 1358: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 393  3-Oct-2003 05:32:08, 30 ms (0%), 1080271 occupied, 23919679 free
Eliminate 
q27

from e_384 and e_385. e_385: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                                    2      2      2
 (q27,q26,q17,q11,q10,q9,q8,p8,p6,p5 ,p5,p4 ,p4,p7 ,p7)

is replaced by e_447: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

                            3   2      4   3   2
 (q17,q11,q10,q9,q8,p8,p6,p5 ,p5 ,p5,p4 ,p4 ,p4 ,p4,p7)


Step 1359: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_396 and e_440. e_440: 
 14 terms, 70 factors, with derivatives of functions of all variables: 

                                 2      2      4   3   2      2
 (q27,q26,q17,q11,q10,q9,q8,p8,p6 ,p6,p5 ,p5,p4 ,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_448: 
 14 terms, 70 factors, with derivatives of functions of all variables: 

                             2      2      4   3   2      2
 (q26,q17,q11,q10,q9,q8,p8,p6 ,p6,p5 ,p5,p4 ,p4 ,p4 ,p4,p7 ,p7)


Step 1360: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 394  3-Oct-2003 05:32:12, 30 ms (0%), 1079835 occupied, 23920114 free
*** Garbage collection starting 
*** GC 395  3-Oct-2003 05:32:15, 40 ms (0%), 1070614 occupied, 23929336 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_400 we get the alternative equations : 
0=p6


0=p4 + p5


0=p4*q7 + p5*q9


New level : 1.1.2.2.1.1.1.
CRACK is now called with the new equation e_468 : 
0=p6


Step 1361: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 41 terms
e_424 is a consequence of e_476

e_483 is a consequence of e_471.
e_506 is a consequence of e_489.
Substitution of p6 found in e_468 : 
p6=0


Step 1362: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 34 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 41 terms

Substitution of q12 by an expression in 
q8, p5, p4 found in e_473 : 
      1
     ---*p5*q8
      2
q12=-----------
        p4


Step 1363: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 42 terms

The list of inequalities got extended by: 
An expression with 42 terms

Substitution of q7 by an expression in 
q17, q8, p8, p5, p4, p7 found in e_498 : 12 factors in 3 terms

Step 1364: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 46 terms

e_503 is a consequence of e_471.
e_484 is a consequence of e_471.
Substitution of q11 by an expression in 
q9, q8, p8, p4, p7 found in e_479 : 7 factors in 3 terms

Step 1365: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 37 terms

The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 46 terms

e_486 is a consequence of e_469.
e_491 is a consequence of e_469.
e_504 is a consequence of e_480.
Substitution of q10 by an expression in 
q17, p5, p4 found in e_497 : 10 factors in 3 terms

Step 1366: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 55 terms

The list of inequalities got extended by: 
An expression with 55 terms

e_507 is a consequence of e_469.
*** Garbage collection starting 
*** GC 396  3-Oct-2003 05:32:19, 40 ms (0%), 1078217 occupied, 23921733 free

Substitution of q9 by an expression in 
q17, q8, p8, p5, p4, p7 found in e_499 : 14 factors in 4 terms

Step 1367: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1368: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_452 is a consequence of e_469.
Step 1369: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1370: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1371: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1372: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1373: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1374: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1375: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1376: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1377: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1378: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1379: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1380: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1381: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1382: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1383: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_512 is a consequence of e_469.
Step 1384: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1385: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1386: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1387: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1388: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1389: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1390: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_503 is a consequence of e_435.
Step 1391: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1392: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_425 is a consequence of e_435.
Step 1393: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1394: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_491 is a consequence of e_435.
Step 1395: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1396: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_95 is a consequence of e_435.
Step 1397: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1398: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_255 is a consequence of e_435.
Step 1399: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1400: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_499 is a consequence of e_435.
Step 1401: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_494 and e_490. e_494: 
(#) 8 terms, 14 factors, with derivatives of functions of all variables: 

           2      2      2      2
 (q17,q8,p8 ,p8,p5 ,p5,p4 ,p4,p7 )

is replaced by e_216: 

0=q8*(p4 - p5)

e_435 is a consequence of e_216

Step 1402: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q8

from e_216 and e_466. e_466: 
(#) 8 terms, 14 factors, with derivatives of functions of all variables: 

           2      2      2      2
 (q17,q8,p8 ,p8,p5 ,p5,p4 ,p4,p7 )

is replaced by e_322: 
(#) 4 terms, 6 factors, with derivatives of functions of all variables: 

           2      2
 (q17,p8,p5 ,p5,p4 ,p4)


e_322 is a consequence of e_469.
Step 1403: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q8

from e_216 and e_478. e_478: 
(#) 8 terms, 14 factors, with derivatives of functions of all variables: 

           2      2      2      2
 (q17,q8,p8 ,p8,p5 ,p5,p4 ,p4,p7 )

is replaced by e_323: 
(#) 4 terms, 6 factors, with derivatives of functions of all variables: 

           2      2
 (q17,p8,p5 ,p5,p4 ,p4)


e_323 is a consequence of e_469.
Step 1404: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q8

from e_216 and e_490. e_490: 
(#) 8 terms, 14 factors, with derivatives of functions of all variables: 

           2      2      2      2
 (q17,q8,p8 ,p8,p5 ,p5,p4 ,p4,p7 )

is replaced by e_324: 
(#) 4 terms, 6 factors, with derivatives of functions of all variables: 

           2      2
 (q17,p8,p5 ,p5,p4 ,p4)


e_324 is a consequence of e_469.
Step 1405: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_431 and e_419. e_431: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

               2            2
 (q27,q17,q8,p8 ,p8,p5,p4,p7 )

is replaced by e_443: 

0=q17*p8*(p4 - p5)


e_443 is a consequence of e_469.
Step 1406: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_419 and e_473. e_419: 
 5 terms, 15 factors, with derivatives of functions of all variables: 

               2            2
 (q27,q17,q8,p8 ,p8,p5,p4,p7 )

is replaced by e_325: 

0=q17*p8*(p4 - p5)


e_325 is a consequence of e_469.
Step 1407: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : A length reducing simplification (27
) was prevented
to avoid a cycle.
A length reducing simplification (27) was prevented
to avoid a cycle.
A length reducing simplification (27) was prevented
to avoid a cycle.
Eliminate 
q27

from e_488 and e_473. e_488: 
(#) 4 terms, 13 factors, with derivatives of functions of all variables: 

               2      2         2
 (q27,q17,q8,p8 ,p8,p5 ,p5,p4,p7 )

is replaced by e_445: 

0=q17*p8*p5*(p4 - p5)


e_445 is a consequence of e_469.
Step 1408: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_467 and e_506. e_506: 
(#) 7 terms, 29 factors, with derivatives of functions of all variables: 

               3   2      2         2
 (q26,q17,q8,p8 ,p8 ,p8,p5 ,p5,p4,p7 ,p7)

is replaced by e_380: 

0=q17*p5*(p4 - p5)


e_380 is a consequence of e_469.
Step 1409: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_467 and e_509. e_509: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

               3   2      2      2      2
 (q26,q17,q8,p8 ,p8 ,p8,p5 ,p5,p4 ,p4,p7 ,p7)

is replaced by e_385: 

0=q17*(p4 - p5)*(3*p4 - p5)


e_385 is a consequence of e_469.
Step 1410: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_469 we get the alternative equations : 
0=q17


0=p4 - p5


New level : 1.1.2.2.1.1.1.1.
CRACK is now called with the new equation e_455 : 
0=q17


Step 1411: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 29 terms

e_458 is a consequence of e_457.
e_508 is a consequence of e_457.
Substitution of q17 found in e_455 : 
q17=0


Step 1412: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 29 terms

e_496 is a consequence of e_510.
e_460 is a consequence of e_457.
Substitution of q26 by an expression in 
q27, p8, p7 found in e_472 : 
      - p8*q27
q26=-----------
        p7


Step 1413: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_510 we get the alternative equations : 
0=q27


0=p4 - p5


New level : 1.1.2.2.1.1.1.1.1.
CRACK is now called with the new equation e_492 : 
0=q27


Step 1414: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 15 terms

q8


The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 

p8


e_461 is a consequence of e_493.
Substitution of q27 found in e_492 : 
q27=0


Step 1415: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 16 terms

Substitution of p5 by an expression in 
p4 found in e_216 : 
p5=p4


Step 1416: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.2.2.1.1.1.1.1. : 
equations : 

e_493 : 
    2     2
0=p7  + p8



Non-vanishing expressions: p5,p7,p4,q8,p8

          2                2                2                2
2*g0055*p7 *q8 + 2*g0055*p8 *q8 - 2*g0056*p7 *q8 - 2*g0056*p8 *q8

             2                2
 - 2*g0063*p7 *q8 - 2*g0063*p8 *q8 - g0064*p4*p7*q8 - 2*g0065*p4*p8*q8

                              2                2
 + g0066*p4*p7*q8 + 2*g0067*p7 *q8 + 2*g0067*p8 *q8 - g0069*p4*p8*q8

                                                 2                2
 + 2*g0070*p4*p7*q8 + g0071*p4*p8*q8 + 2*g0079*p4 *p7 + 2*g0080*p4 *p7


          2             2             2             2             2
2*g0088*p7  + 2*g0088*p8  - 2*g0089*p7  - 2*g0089*p8  - 2*g0096*p7

             2                                                         2
 - 2*g0096*p8  - g0097*p4*p7 - 2*g0098*p4*p8 + g0099*p4*p7 + 2*g0100*p7

             2
 + 2*g0100*p8  - g0102*p4*p8 + 2*g0103*p4*p7 + g0104*p4*p8


          2                2
2*g0006*p7 *q8 + 2*g0006*p8 *q8 - 2*g0012*p4*p8*q8 + g0013*p4*p7*q8

             2                2
 + 2*g0014*p7 *q8 + 2*g0014*p8 *q8 - g0016*p4*p8*q8 + 2*g0017*p4*p7*q8

                                 2             2                2
 + g0018*p4*p8*q8 + 2*g0023*p4*p7  + 2*g0024*p4 *p7 + 2*g0025*p4 *p7


          2                2                2                2
2*g0031*p7 *q8 + 2*g0031*p8 *q8 - 2*g0032*p7 *q8 - 2*g0032*p8 *q8

             2                2
 - 2*g0036*p7 *q8 - 2*g0036*p8 *q8 - g0037*p4*p7*q8 - 2*g0038*p4*p8*q8

             2                2
 + 2*g0039*p7 *q8 + 2*g0039*p8 *q8 - g0041*p4*p8*q8 + 2*g0042*p4*p7*q8

                                 2             2
 + g0043*p4*p8*q8 + 2*g0048*p4*p7  + 2*g0050*p4 *p7


g0111*p8 + g0112*p7 + g0114*p4 + g0115*p4


functions : 
q27=0


q26=0


q25=0


q24=0


       2        2
     p7 *q8 + p8 *q8
q23=-----------------
          p4*p7


          2        2
      - p7 *q8 - p8 *q8
q22=--------------------
           p4*p7


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


          2        2
      - p7 *q8 - p8 *q8
q15=--------------------
           p4*p7


        1
q14= - ---*q8
        2


      - p8*q8
q13=----------
        p7


     1
q12=---*q8
     2


       2        2
     p7 *q8 + p8 *q8
q11=-----------------
          p4*p7


q10=0


        1
     - ---*p8*q8
        2
q9=--------------
         p7

q8, 
     1
    ---*p8*q8
     2
q7=-----------
       p7


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, 
p6=0


p5=p4

p4, 
p3=0


p2=0


p1=0


with 49 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_493(2a)
4 constants : p4,p7,p8,q8
The equation: 

f =D f*f *p4 + D D f  *p7 + D D f*D f*p4 + f  *p8
 t  2   x       1 2 2x       1 2   1        3x
The symmetry: 
                  2                    2       1       2
f =(D f  *D D f*p7 *q8 + D f  *D D f*p8 *q8 + ---*(D f) *D D f*p4*p8*q8
 s   2 2x  1 2            2 2x  1 2            2    2     1 2

        1       2                             2                    2
     + ---*(D f) *f *p4*p7*q8 + D f*D D f  *p7 *q8 + D f*D D f  *p8 *q8
        2    2     x             2   1 2 2x           2   1 2 2x

                                                       1             2
     + D f*D D f*D f*p4*p7*q8 - D f*D f*f *p4*p8*q8 - ---*D D f*(D f) *p4*p8*q8
        2   1 2   1              2   1   x             2   1 2    1

                  2                 2       1       2
     - D f  *f *p7 *q8 - D f  *f *p8 *q8 - ---*(D f) *f *p4*p7*q8
        1 2x  x           1 2x  x           2    1     x

                 2                2
     - D f*f  *p7 *q8 - D f*f  *p8 *q8)/(p4*p7)
        1   3x           1   3x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*df(f(1),x)*p4 + d(1,d(2,df(f(1),x,2)))*p7 + d(1,d(2,f(1)))*
d(1,f(1))*p4 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=(d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p7**2*q8 + d(2,df(f(1),x,2))*d(1,d(
2,f(1)))*p8**2*q8 + 1/2*d(2,f(1))**2*d(1,d(2,f(1)))*p4*p8*q8 + 1/2*d(2,f(1))**2*
df(f(1),x)*p4*p7*q8 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p7**2*q8 + d(2,f(1))*d(1,
d(2,df(f(1),x,2)))*p8**2*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p4*p7*q8 - d(2,
f(1))*d(1,f(1))*df(f(1),x)*p4*p8*q8 - 1/2*d(1,d(2,f(1)))*d(1,f(1))**2*p4*p8*q8 -
 d(1,df(f(1),x,2))*df(f(1),x)*p7**2*q8 - d(1,df(f(1),x,2))*df(f(1),x)*p8**2*q8 -
 1/2*d(1,f(1))**2*df(f(1),x)*p4*p7*q8 - d(1,f(1))*df(f(1),x,3)*p7**2*q8 - d(1,f(
1))*df(f(1),x,3)*p8**2*q8)/(p4*p7)$

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 

q27

The lexicographical ordering of unknowns is changed
because q27 has to be non-zero, giving q27 a low priority.
Old ordering: q27,q8,p8,p5,p4,p7
New ordering: q8,q27,p8,p5,p4,p7

New level : 1.1.2.2.1.1.1.1.2.
CRACK is now called with the new equation e_492 : 
0=p4 - p5

e_216 is a consequence of e_492

Step 1417: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 

1


The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 14 terms

The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 18 terms

e_500 is a consequence of e_493.
Substitution of p4 by an expression in 
p5 found in e_492 : 
p4=p5


Step 1418: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 

  2     2
p7  + p8


q8

The lexicographical ordering of unknowns is changed
because q8 has to be non-zero, giving q8 a low priority.
Old ordering: q8,q27,p8,p5,p7
New ordering: q27,q8,p8,p5,p7

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 20 terms

Substitution of q27 by an expression in 
q8, p8, p5, p7 found in e_493 : 10 factors in 3 terms


>>>>>>>>> Solution of level 1.1.2.2.1.1.1.1.2. : 
no equations


Non-vanishing expressions: q8,p5,p7,p4

          2                2                2                2
2*g0055*p7 *q8 + 2*g0055*p8 *q8 - 2*g0056*p7 *q8 - 2*g0056*p8 *q8

             2                2                2                2
 - 2*g0059*p7 *q8 - 2*g0059*p8 *q8 + 2*g0060*p7 *q8 + 2*g0060*p8 *q8

             2                2
 - 2*g0063*p7 *q8 - 2*g0063*p8 *q8 - g0064*p5*p7*q8 - 2*g0065*p5*p8*q8

                              2                2
 + g0066*p5*p7*q8 + 2*g0067*p7 *q8 + 2*g0067*p8 *q8 - g0069*p5*p8*q8

                                                 2                2
 + 2*g0070*p5*p7*q8 + g0071*p5*p8*q8 + 2*g0079*p5 *p7 + 2*g0080*p5 *p7


          3                2             2                3                 2
6*g0084*p7  + 6*g0084*p7*p8  - 6*g0085*p7 *p8 - 6*g0085*p8  - 10*g0088*p5*p7

                 2                 2                 2                 2
 - 10*g0088*p5*p8  + 10*g0089*p5*p7  + 10*g0089*p5*p8  + 10*g0092*p5*p7

                 2                 2                 2                 2
 + 10*g0092*p5*p8  - 10*g0093*p5*p7  - 10*g0093*p5*p8  + 10*g0096*p5*p7

                 2             2                 2                2
 + 10*g0096*p5*p8  + 5*g0097*p5 *p7 + 10*g0098*p5 *p8 - 5*g0099*p5 *p7

                 2                 2             2                 2
 - 10*g0100*p5*p7  - 10*g0100*p5*p8  + 5*g0102*p5 *p8 - 10*g0103*p5 *p7

             2
 - 5*g0104*p5 *p8


          2                   3                    2                    2
6*g0003*p7 *p8*q8 + 6*g0003*p8 *q8 + 10*g0006*p5*p7 *q8 + 10*g0006*p5*p8 *q8

                 2                    2                 2
 + 10*g0009*p5*p7 *q8 + 10*g0009*p5*p8 *q8 - 10*g0012*p5 *p8*q8

             2                       2                    2
 + 5*g0013*p5 *p7*q8 + 10*g0014*p5*p7 *q8 + 10*g0014*p5*p8 *q8

             2                    2                   2                    2   2
 - 5*g0016*p5 *p8*q8 + 10*g0017*p5 *p7*q8 + 5*g0018*p5 *p8*q8 + 10*g0023*p5 *p7

              3                 3
 + 10*g0024*p5 *p7 + 10*g0025*p5 *p7

102 factors in 21 terms

  2     2
p7  + p8


g0111*p8 + g0112*p7 + g0114*p5 + g0115*p5


functions : 
         3    2       3    2
      - ---*p7 *q8 - ---*p8 *q8
         5            5
q27=----------------------------
                  2
                p5


      3    2          3    3
     ---*p7 *p8*q8 + ---*p8 *q8
      5               5
q26=----------------------------
                 2
               p5 *p7


q25=0


q24=0


       2        2
     p7 *q8 + p8 *q8
q23=-----------------
          p5*p7


          2        2
      - p7 *q8 - p8 *q8
q22=--------------------
           p5*p7


q21=0


q20=0


          2        2
      - p7 *q8 - p8 *q8
q19=--------------------
           p5*p7


       2        2
     p7 *q8 + p8 *q8
q18=-----------------
          p5*p7


q17=0


q16=0


          2        2
      - p7 *q8 - p8 *q8
q15=--------------------
           p5*p7


        1
q14= - ---*q8
        2


      - p8*q8
q13=----------
        p7


     1
q12=---*q8
     2


       2        2
     p7 *q8 + p8 *q8
q11=-----------------
          p5*p7


q10=0


        1
     - ---*p8*q8
        2
q9=--------------
         p7

q8, 
     1
    ---*p8*q8
     2
q7=-----------
       p7


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, 
p6=0

p5, 
p4=p5


p3=0


p2=0


p1=0


with 57 terms
no equations
4 constants : p5,p7,p8,q8
The equation: 

f =D f*f *p5 + D D f  *p7 + D D f*D f*p5 + f  *p8
 t  2   x       1 2 2x       1 2   1        3x
The symmetry: 
                     2                       2                       2
f =(D f  *D D f*p5*p7 *q8 + D f  *D D f*p5*p8 *q8 + D f *D D f *p5*p7 *q8
 s   2 2x  1 2               2 2x  1 2               2 x  1 2 x

                        2       1       2         2
     + D f *D D f *p5*p8 *q8 + ---*(D f) *D D f*p5 *p8*q8
        2 x  1 2 x              2    2     1 2

        1       2      2                          2                       2
     + ---*(D f) *f *p5 *p7*q8 + D f*D D f  *p5*p7 *q8 + D f*D D f  *p5*p8 *q8
        2    2     x              2   1 2 2x              2   1 2 2x

                       2                      2          3            2
     + D f*D D f*D f*p5 *p7*q8 - D f*D f*f *p5 *p8*q8 + ---*D D f  *p7 *p8*q8
        2   1 2   1               2   1   x              5   1 2 4x

        3            3       1             2   2                       2
     + ---*D D f  *p8 *q8 - ---*D D f*(D f) *p5 *p8*q8 - D f  *f *p5*p7 *q8
        5   1 2 4x           2   1 2    1                 1 2x  x

                     2                    2                    2
     - D f  *f *p5*p8 *q8 - D f *f  *p5*p7 *q8 - D f *f  *p5*p8 *q8
        1 2x  x              1 x  2x              1 x  2x

        1       2      2                      2                   2
     - ---*(D f) *f *p5 *p7*q8 - D f*f  *p5*p7 *q8 - D f*f  *p5*p8 *q8
        2    1     x              1   3x              1   3x

        3        3       3           2        2
     - ---*f  *p7 *q8 - ---*f  *p7*p8 *q8)/(p5 *p7)
        5   5x           5   5x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,df(f(1),x,2)))*p7 + d(1,d(2,f(1)))*
d(1,f(1))*p5 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=(d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5*p7**2*q8 + d(2,df(f(1),x,2))*d(1
,d(2,f(1)))*p5*p8**2*q8 + d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5*p7**2*q8 + d(2
,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5*p8**2*q8 + 1/2*d(2,f(1))**2*d(1,d(2,f(1)))*
p5**2*p8*q8 + 1/2*d(2,f(1))**2*df(f(1),x)*p5**2*p7*q8 + d(2,f(1))*d(1,d(2,df(f(1
),x,2)))*p5*p7**2*q8 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p5*p8**2*q8 + d(2,f(1))*
d(1,d(2,f(1)))*d(1,f(1))*p5**2*p7*q8 - d(2,f(1))*d(1,f(1))*df(f(1),x)*p5**2*p8*
q8 + 3/5*d(1,d(2,df(f(1),x,4)))*p7**2*p8*q8 + 3/5*d(1,d(2,df(f(1),x,4)))*p8**3*
q8 - 1/2*d(1,d(2,f(1)))*d(1,f(1))**2*p5**2*p8*q8 - d(1,df(f(1),x,2))*df(f(1),x)*
p5*p7**2*q8 - d(1,df(f(1),x,2))*df(f(1),x)*p5*p8**2*q8 - d(1,df(f(1),x))*df(f(1)
,x,2)*p5*p7**2*q8 - d(1,df(f(1),x))*df(f(1),x,2)*p5*p8**2*q8 - 1/2*d(1,f(1))**2*
df(f(1),x)*p5**2*p7*q8 - d(1,f(1))*df(f(1),x,3)*p5*p7**2*q8 - d(1,f(1))*df(f(1),
x,3)*p5*p8**2*q8 - 3/5*df(f(1),x,5)*p7**3*q8 - 3/5*df(f(1),x,5)*p7*p8**2*q8)/(p5
**2*p7)$

This completes the investigation of all cases of a factorization.

Time: 10 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 

q17

The lexicographical ordering of unknowns is changed
because q17 has to be non-zero, giving q17 a low priority.
Old ordering: q27,q26,q17,q8,p8,p5,p4,p7
New ordering: q27,q26,q8,q17,p8,p5,p4,p7

New level : 1.1.2.2.1.1.1.2.
CRACK is now called with the new equation e_455 : 
0=p4 - p5

e_450,e_510,e_216 are consequences of e_455

Step 1419: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 

1


The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 33 terms

e_458 is a consequence of e_457.
e_508 is a consequence of e_457.
e_461 is a consequence of e_457.
Substitution of p4 by an expression in 
p5 found in e_455 : 
p4=p5


Step 1420: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 35 terms

e_460 is a consequence of e_457.
Substitution of q26 by an expression in 
q27, q17, p8, p5, p7 found in e_472 : 14 factors in 4 terms

Step 1421: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 40 terms

Substitution of q27 by an expression in 
q8, q17, p8, p5, p7 found in e_457 : 15 factors in 4 terms


>>>>>>>>> Solution of level 1.1.2.2.1.1.1.2. : 
no equations


Non-vanishing expressions: p4,p7,p5,q17
196 factors in 40 terms
143 factors in 30 terms
169 factors in 35 terms
152 factors in 35 terms

g0111*p8 + g0112*p7 + g0114*p5 + g0115*p5


functions : 
      6               3    2       3    2
     ---*p5*p8*q17 - ---*p7 *q8 - ---*p8 *q8
      5               5            5
q27=-----------------------------------------
                         2
                       p5


      3       2        3       2        3    2          3    3
     ---*p5*p7 *q17 - ---*p5*p8 *q17 + ---*p7 *p8*q8 + ---*p8 *q8
      5                5                5               5
q26=--------------------------------------------------------------
                                  2
                                p5 *p7


q25=0


q24=q17


                      2        2
      - p5*p8*q17 + p7 *q8 + p8 *q8
q23=--------------------------------
                 p5*p7


                   2        2
     p5*p8*q17 - p7 *q8 - p8 *q8
q22=-----------------------------
                p5*p7


q21=q17


q20=q17


                   2        2
     p5*p8*q17 - p7 *q8 - p8 *q8
q19=-----------------------------
                p5*p7


                      2        2
      - p5*p8*q17 + p7 *q8 + p8 *q8
q18=--------------------------------
                 p5*p7

q17, 
q16=q17


                   2        2
     p5*p8*q17 - p7 *q8 - p8 *q8
q15=-----------------------------
                p5*p7


        1
q14= - ---*q8
        2


     p5*q17 - p8*q8
q13=----------------
           p7


     1
q12=---*q8
     2


                      2        2
      - p5*p8*q17 + p7 *q8 + p8 *q8
q11=--------------------------------
                 p5*p7


q10=q17


     1            1
    ---*p5*q17 - ---*p8*q8
     2            2
q9=------------------------
              p7

q8, 
        1            1
     - ---*p5*q17 + ---*p8*q8
        2            2
q7=---------------------------
               p7


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, 
p6=0

p5, 
p4=p5


p3=0


p2=0


p1=0


with 74 terms
no equations
5 constants : p5,p7,p8,q8,q17
The equation: 

f =D f*f *p5 + D D f  *p7 + D D f*D f*p5 + f  *p8
 t  2   x       1 2 2x       1 2   1        3x
The symmetry: 
                     2                           2                       2
f =( - D f  *D D f*p5 *p8*q17 + D f  *D D f*p5*p7 *q8 + D f  *D D f*p5*p8 *q8
 s      2 2x  1 2                2 2x  1 2               2 2x  1 2

                  2                        2                           2
     + D f  *f *p5 *p7*q17 - D f *D D f *p5 *p8*q17 + D f *D D f *p5*p7 *q8
        2 2x  x               2 x  1 2 x               2 x  1 2 x

                        2                 2           1       2         3
     + D f *D D f *p5*p8 *q8 + D f *f  *p5 *p7*q17 - ---*(D f) *D D f*p5 *q17
        2 x  1 2 x              2 x  2x               2    2     1 2

        1       2         2          1       2      2
     + ---*(D f) *D D f*p5 *p8*q8 + ---*(D f) *f *p5 *p7*q8
        2    2     1 2               2    2     x

                     2                           2                       2
     - D f*D D f  *p5 *p8*q17 + D f*D D f  *p5*p7 *q8 + D f*D D f  *p5*p8 *q8
        2   1 2 2x               2   1 2 2x              2   1 2 2x

                       2                      3                    2
     + D f*D D f*D f*p5 *p7*q8 + D f*D f*f *p5 *q17 - D f*D f*f *p5 *p8*q8
        2   1 2   1               2   1   x            2   1   x

                 2           3               2        3               2
     + D f*f  *p5 *p7*q17 + ---*D D f  *p5*p7 *q17 - ---*D D f  *p5*p8 *q17
        2   3x               5   1 2 4x               5   1 2 4x

        3            2          3            3                    2
     + ---*D D f  *p7 *p8*q8 + ---*D D f  *p8 *q8 + D D f  *D f*p5 *p7*q17
        5   1 2 4x              5   1 2 4x           1 2 2x  1

                     2                        2
     + D D f *D f *p5 *p7*q17 + D D f*D f  *p5 *p7*q17
        1 2 x  1 x               1 2   1 2x

        1             2   3        1             2   2
     + ---*D D f*(D f) *p5 *q17 - ---*D D f*(D f) *p5 *p8*q8
        2   1 2    1               2   1 2    1

                  2                        2                    2
     + D f  *f *p5 *p8*q17 - D f  *f *p5*p7 *q8 - D f  *f *p5*p8 *q8
        1 2x  x               1 2x  x              1 2x  x

                  2                        2                    2
     + D f *f  *p5 *p8*q17 - D f *f  *p5*p7 *q8 - D f *f  *p5*p8 *q8
        1 x  2x               1 x  2x              1 x  2x

        1       2      2                   2                       2
     - ---*(D f) *f *p5 *p7*q8 + D f*f  *p5 *p8*q17 - D f*f  *p5*p7 *q8
        2    1     x              1   3x               1   3x

                    2       6                      3        3
     - D f*f  *p5*p8 *q8 + ---*f  *p5*p7*p8*q17 - ---*f  *p7 *q8
        1   3x              5   5x                 5   5x

        3           2        2
     - ---*f  *p7*p8 *q8)/(p5 *p7)
        5   5x
And now in machine readable form:

The system: 

df(f(1),t)=d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,df(f(1),x,2)))*p7 + d(1,d(2,f(1)))*
d(1,f(1))*p5 + df(f(1),x,3)*p8$
The symmetry: 
df(f(1),s)=( - d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5**2*p8*q17 + d(2,df(f(1),x,2))
*d(1,d(2,f(1)))*p5*p7**2*q8 + d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5*p8**2*q8 + d(2
,df(f(1),x,2))*df(f(1),x)*p5**2*p7*q17 - d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5
**2*p8*q17 + d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5*p7**2*q8 + d(2,df(f(1),x))*
d(1,d(2,df(f(1),x)))*p5*p8**2*q8 + d(2,df(f(1),x))*df(f(1),x,2)*p5**2*p7*q17 - 1
/2*d(2,f(1))**2*d(1,d(2,f(1)))*p5**3*q17 + 1/2*d(2,f(1))**2*d(1,d(2,f(1)))*p5**2
*p8*q8 + 1/2*d(2,f(1))**2*df(f(1),x)*p5**2*p7*q8 - d(2,f(1))*d(1,d(2,df(f(1),x,2
)))*p5**2*p8*q17 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p5*p7**2*q8 + d(2,f(1))*d(1,
d(2,df(f(1),x,2)))*p5*p8**2*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p5**2*p7*q8 
+ d(2,f(1))*d(1,f(1))*df(f(1),x)*p5**3*q17 - d(2,f(1))*d(1,f(1))*df(f(1),x)*p5**
2*p8*q8 + d(2,f(1))*df(f(1),x,3)*p5**2*p7*q17 + 3/5*d(1,d(2,df(f(1),x,4)))*p5*p7
**2*q17 - 3/5*d(1,d(2,df(f(1),x,4)))*p5*p8**2*q17 + 3/5*d(1,d(2,df(f(1),x,4)))*
p7**2*p8*q8 + 3/5*d(1,d(2,df(f(1),x,4)))*p8**3*q8 + d(1,d(2,df(f(1),x,2)))*d(1,f
(1))*p5**2*p7*q17 + d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p5**2*p7*q17 + d(1,d(2,
f(1)))*d(1,df(f(1),x,2))*p5**2*p7*q17 + 1/2*d(1,d(2,f(1)))*d(1,f(1))**2*p5**3*
q17 - 1/2*d(1,d(2,f(1)))*d(1,f(1))**2*p5**2*p8*q8 + d(1,df(f(1),x,2))*df(f(1),x)
*p5**2*p8*q17 - d(1,df(f(1),x,2))*df(f(1),x)*p5*p7**2*q8 - d(1,df(f(1),x,2))*df(
f(1),x)*p5*p8**2*q8 + d(1,df(f(1),x))*df(f(1),x,2)*p5**2*p8*q17 - d(1,df(f(1),x)
)*df(f(1),x,2)*p5*p7**2*q8 - d(1,df(f(1),x))*df(f(1),x,2)*p5*p8**2*q8 - 1/2*d(1,
f(1))**2*df(f(1),x)*p5**2*p7*q8 + d(1,f(1))*df(f(1),x,3)*p5**2*p8*q17 - d(1,f(1)
)*df(f(1),x,3)*p5*p7**2*q8 - d(1,f(1))*df(f(1),x,3)*p5*p8**2*q8 + 6/5*df(f(1),x,
5)*p5*p7*p8*q17 - 3/5*df(f(1),x,5)*p7**3*q8 - 3/5*df(f(1),x,5)*p7*p8**2*q8)/(p5
**2*p7)$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 30 ms

The list of inequalities got extended by: 

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q27,q26,q17,q12,q11,q10,q9,q8,q7,p8,p6,p5,p4,p7
New ordering: q27,q26,q17,q12,q11,q10,q9,q8,q7,p8,p5,p6,p4,p7

The list of inequalities got extended by: 

p5


New level : 1.1.2.2.1.1.2.
CRACK is now called with the new equation e_468 : 
0=p4 + p5


Step 1422: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 

1


The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 38 terms

Substitution of p4 by an expression in 
p5 found in e_468 : 
p4= - p5


Step 1423: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 38 terms

Substitution of q11 by an expression in 
q10, p5, p6 found in e_496 : 
      - p6*q10
q11=-----------
        p5


Step 1424: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 38 terms

e_471 is a consequence of e_485.
*** Garbage collection starting 
*** GC 397  3-Oct-2003 05:32:22, 40 ms (0%), 1031419 occupied, 23968530 free

Substitution of q17 by an expression in 
q8, p6, p7 found in e_495 : 
      3
     ---*p7*q8
      4
q17=-----------
        p6


Step 1425: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 
An expression with 31 terms

The list of inequalities got extended by: 
An expression with 33 terms

The list of inequalities got extended by: 
An expression with 35 terms

e_492 is a consequence of e_474.
Substitution of q10 by an expression in 
q8, p6, p7 found in e_491 : 
      3
     ---*p7*q8
      4
q10=-----------
        p6


Step 1426: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 30 terms

e_477 is a consequence of e_469.
e_498 is a consequence of e_469.
e_501 is a consequence of e_488.
e_474 is a consequence of e_482.
e_481 is a consequence of e_476.
Substitution of q26 by an expression in 
q8, p5, p6, p7 found in e_487 : 7 factors in 2 terms

Step 1427: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 29 terms
e_508 is a consequence of e_473

e_470 is a consequence of e_506.
Substitution of q12 found in e_503 : 
q12=0


Step 1428: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 25 terms

e_494 is a consequence of e_488.
e_493 is a consequence of e_488.
e_482 is a consequence of e_488.
Substitution of q27 by an expression in 
q8, p5, p7 found in e_472 : 
      2    2
     ---*p7 *q8
      5
q27=------------
          2
        p5


Step 1429: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 25 terms

e_476 is a consequence of e_479.
e_504 is a consequence of e_469.
e_490 is a consequence of e_473.
Substitution of q8 by an expression in 
q7, p5, p6 found in e_506 : 
     - 2*p5*q7
q8=------------
        p6


Step 1430: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 21 terms

q7


The list of inequalities got extended by: 

p8


The list of inequalities got extended by: 

q9


The list of inequalities got extended by: 
An expression with 23 terms

e_485 is a consequence of e_488.
e_484 is a consequence of e_488.
e_497 is a consequence of e_483.
e_480 is a consequence of e_469.
e_500 is a consequence of e_507.
Substitution of q9 by an expression in 
q7, p5, p6 found in e_473 : 
      2
    p5 *q7
q9=--------
       2
     p6


Step 1431: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

p8


The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 23 terms

e_488 is a consequence of e_469.
e_507 is a consequence of e_469.
e_505 is a consequence of e_469.
e_499 is a consequence of e_469.
e_483 is a consequence of e_469.
e_502 is a consequence of e_469.
e_478 is a consequence of e_469.
e_396 is a consequence of e_469.
e_486 is a consequence of e_469.
e_489 is a consequence of e_469.
e_475 is a consequence of e_469.
Substitution of p8 by an expression in 
p5, p6, p7 found in e_479 : 
    p5*p7
p8=-------
     p6


Step 1432: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.2.2.1.1.2. : 
equations : 

e_469 : 
    2     2
0=p5  + p6



Non-vanishing expressions: p8,p5,p6,p7,p4,q7,q9
112 factors in 23 terms

          2   2                    2              2                    3
8*g0084*p6 *p7  - 10*g0085*p5*p6*p7  + 20*g0087*p5 *p6*p7 - 15*g0088*p5 *p7

                 2                 3                    2
 - 35*g0088*p5*p6 *p7 - 15*g0089*p5 *p7 - 25*g0089*p5*p6 *p7

              2                    2                    3
 - 10*g0090*p5 *p6*p7 - 15*g0091*p5 *p6*p7 - 15*g0092*p5 *p7

                 2                 3                    2
 - 30*g0092*p5*p6 *p7 - 15*g0093*p5 *p7 - 30*g0093*p5*p6 *p7

              2                   2                      2
 + 15*g0094*p5 *p6*p7 - 5*g0095*p5 *p6*p7 - 5*g0096*p5*p6 *p7

                 2                 2                    3                 2   2
 - 15*g0100*p5*p6 *p7 + 15*g0101*p5 *p6*p7 - 10*g0102*p5 *p6 + 20*g0103*p5 *p6

                 3
 - 10*g0104*p5*p6


             2                                      2                   2
2*g0003*p6*p7 *q7 - 4*g0005*p5*p6*p7*q7 + 3*g0006*p5 *p7*q7 + 7*g0006*p6 *p7*q7

                                                         2
 + 2*g0007*p5*p6*p7*q7 + 3*g0008*p5*p6*p7*q7 + 3*g0009*p5 *p7*q7

             2
 + 6*g0009*p6 *p7*q7 - 3*g0010*p5*p6*p7*q7 + g0011*p5*p6*p7*q7

             2                                         2
 + 3*g0014*p6 *p7*q7 - 3*g0015*p5*p6*p7*q7 + 2*g0016*p5 *p6*q7

                2                3                3                   3
 - 4*g0017*p5*p6 *q7 + 2*g0018*p6 *q7 + 2*g0023*p6 *p7 + 2*g0024*p5*p6

                3             4
 - 2*g0025*p5*p6  + 2*g0026*p6


             2                                      2                   2
2*g0028*p6*p7 *q7 - 4*g0030*p5*p6*p7*q7 + 3*g0031*p5 *p7*q7 + 7*g0031*p6 *p7*q7

             2                   2                   2                   2
 + 3*g0032*p5 *p7*q7 + 5*g0032*p6 *p7*q7 + 3*g0033*p5 *p7*q7 + 6*g0033*p6 *p7*q7

             2                   2                                       2
 + 3*g0034*p5 *p7*q7 + 6*g0034*p6 *p7*q7 - 3*g0035*p5*p6*p7*q7 + g0036*p6 *p7*q7

             2                                         2
 + 3*g0039*p6 *p7*q7 - 3*g0040*p5*p6*p7*q7 + 2*g0041*p5 *p6*q7

                2                3                3                4
 - 4*g0042*p5*p6 *q7 + 2*g0043*p6 *q7 + 2*g0048*p6 *p7 + 2*g0049*p6

                3             4
 - 2*g0050*p5*p6  + 2*g0051*p6


                                    2                                       2
g0111*p5*p7 + g0112*p6*p7 + g0113*p6  + g0114*p5*p6 - g0115*p5*p6 + g0116*p6


functions : 
         4    2
      - ---*p7 *q7
         5
q27=---------------
         p5*p6


       2
     p7 *q7
q26=--------
        2
      p6


q25=0


      - 2*p5*p7*q7
q24=---------------
            2
          p6


      3    2          7    2
     ---*p5 *p7*q7 + ---*p6 *p7*q7
      2               2
q23=-------------------------------
                    3
                  p6


      3    2          5    2
     ---*p5 *p7*q7 + ---*p6 *p7*q7
      2               2
q22=-------------------------------
                    3
                  p6


     p5*p7*q7
q21=----------
         2
       p6


      3
     ---*p5*p7*q7
      2
q20=--------------
           2
         p6


      3    2             2
     ---*p5 *p7*q7 + 3*p6 *p7*q7
      2
q19=-----------------------------
                   3
                 p6


      3    2             2
     ---*p5 *p7*q7 + 3*p6 *p7*q7
      2
q18=-----------------------------
                   3
                 p6


         3
      - ---*p5*p7*q7
         2
q17=-----------------
             2
           p6


      1
     ---*p5*p7*q7
      2
q16=--------------
           2
         p6


      1
     ---*p7*q7
      2
q15=-----------
        p6


q14=0


q13=0


q12=0


      3
     ---*p7*q7
      2
q11=-----------
        p6


         3
      - ---*p5*p7*q7
         2
q10=-----------------
             2
           p6


      2
    p5 *q7
q9=--------
       2
     p6


     - 2*p5*q7
q8=------------
        p6

q7, 
q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


    p5*p7
p8=-------
     p6

p7, p6, p5, 
p4= - p5


p3=p6


p2=0


p1=0


with 58 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_469(2a)
4 constants : p5,p6,p7,q7
The equation: 

                2                                                             2
f =(D f*D D f*p6  + D f*f *p5*p6 + D D f  *p6*p7 - D D f*D f*p5*p6 + D f*f *p6
 t   2   1 2         2   x          1 2 2x          1 2   1           1   x

     + f  *p5*p7)/p6
        3x
The symmetry: 
     3                   2          1             2
f =(---*D f  *D D f*p5*p6 *p7*q7 + ---*D f  *f *p5 *p6*p7*q7
 s   2   2 2x  1 2                  2   2 2x  x

        3                3                            2
     + ---*D f *D D f *p5 *p7*q7 + 3*D f *D D f *p5*p6 *p7*q7
        2   2 x  1 2 x                2 x  1 2 x

        3             2                 2            3
     + ---*D f *f  *p5 *p6*p7*q7 + (D f) *D D f*p5*p6 *q7
        2   2 x  2x                  2     1 2

        3                3          7                   2
     + ---*D f*D D f  *p5 *p7*q7 + ---*D f*D D f  *p5*p6 *p7*q7
        2   2   1 2 2x              2   2   1 2 2x

                         2   2                2                            2
     - 2*D f*D D f*D f*p5 *p6 *q7 + D f*f  *p5 *p6*p7*q7 + D D f  *p5*p6*p7 *q7
          2   1 2   1                2   3x                 1 2 4x

                       2             3                2
     - 2*D D f  *D f*p5 *p6*p7*q7 - ---*D D f *D f *p5 *p6*p7*q7
          1 2 2x  1                  2   1 2 x  1 x

        3                2                       2   3
     - ---*D D f*D f  *p5 *p6*p7*q7 + D D f*(D f) *p5 *p6*q7
        2   1 2   1 2x                 1 2    1

        1                2          3             3
     + ---*D f  *f *p5*p6 *p7*q7 + ---*D f *f  *p5 *p7*q7
        2   1 2x  x                 2   1 x  2x

                       2          3            3
     + 3*D f *f  *p5*p6 *p7*q7 + ---*D f*f  *p5 *p7*q7
          1 x  2x                 2   1   3x

        5               2          4        2   2           3
     + ---*D f*f  *p5*p6 *p7*q7 - ---*f  *p6 *p7 *q7)/(p5*p6 )
        2   1   3x                 5   5x
And now in machine readable form:

The system: 

df(f(1),t)=(d(2,f(1))*d(1,d(2,f(1)))*p6**2 + d(2,f(1))*df(f(1),x)*p5*p6 + d(1,d(
2,df(f(1),x,2)))*p6*p7 - d(1,d(2,f(1)))*d(1,f(1))*p5*p6 + d(1,f(1))*df(f(1),x)*
p6**2 + df(f(1),x,3)*p5*p7)/p6$
The symmetry: 
df(f(1),s)=(3/2*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5*p6**2*p7*q7 + 1/2*d(2,df(f(1
),x,2))*df(f(1),x)*p5**2*p6*p7*q7 + 3/2*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5
**3*p7*q7 + 3*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5*p6**2*p7*q7 + 3/2*d(2,df(f
(1),x))*df(f(1),x,2)*p5**2*p6*p7*q7 + d(2,f(1))**2*d(1,d(2,f(1)))*p5*p6**3*q7 + 
3/2*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p5**3*p7*q7 + 7/2*d(2,f(1))*d(1,d(2,df(f(1)
,x,2)))*p5*p6**2*p7*q7 - 2*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p5**2*p6**2*q7 + d
(2,f(1))*df(f(1),x,3)*p5**2*p6*p7*q7 + d(1,d(2,df(f(1),x,4)))*p5*p6*p7**2*q7 - 2
*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p5**2*p6*p7*q7 - 3/2*d(1,d(2,df(f(1),x)))*d(1,
df(f(1),x))*p5**2*p6*p7*q7 - 3/2*d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p5**2*p6*p7*q7
 + d(1,d(2,f(1)))*d(1,f(1))**2*p5**3*p6*q7 + 1/2*d(1,df(f(1),x,2))*df(f(1),x)*p5
*p6**2*p7*q7 + 3/2*d(1,df(f(1),x))*df(f(1),x,2)*p5**3*p7*q7 + 3*d(1,df(f(1),x))*
df(f(1),x,2)*p5*p6**2*p7*q7 + 3/2*d(1,f(1))*df(f(1),x,3)*p5**3*p7*q7 + 5/2*d(1,f
(1))*df(f(1),x,3)*p5*p6**2*p7*q7 - 4/5*df(f(1),x,5)*p6**2*p7**2*q7)/(p5*p6**3)$

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q27,q26,q17,q12,q11,q10,q9,q8,q7,p8,p6,p5,p4,p7
New ordering: q27,q26,q17,q12,q11,q10,q9,q8,q7,p8,p5,p6,p4,p7

The list of inequalities got extended by: 

p4 + p5


New level : 1.1.2.2.1.1.3.
CRACK is now called with the new equation e_468 : 
0=p4*q7 + p5*q9


Step 1433: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 51 terms

The list of inequalities got extended by: 
An expression with 53 terms

Substitution of q7 by an expression in 
q9, p5, p4 found in e_468 : 
     - p5*q9
q7=----------
       p4


Step 1434: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 398  3-Oct-2003 05:32:25, 40 ms (0%), 1027486 occupied, 23972459 free
*** Garbage collection starting 
*** GC 399  3-Oct-2003 05:32:27, 40 ms (0%), 1030333 occupied, 23969612 free
Eliminate 
q26

from e_287 and e_392. e_392: 
 11 terms, 44 factors, with derivatives of functions of all variables: 

                             2         3   2      2
 (q26,q17,q11,q10,q9,q8,p8,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_479: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                        2      2
 (q11,q10,q9,q8,p8,p5,p6 ,p6,p4 ,p4,p7)


Step 1435: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 400  3-Oct-2003 05:32:30, 30 ms (0%), 1035749 occupied, 23964195 free
Eliminate 
q26

from e_475 and e_438. e_438: 
 10 terms, 60 factors, with derivatives of functions of all variables: 

                       3   2         4   3   2      2
 (q26,q17,q12,q11,q8,p5 ,p5 ,p5,p6,p4 ,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_419: 
 4 terms, 8 factors, with derivatives of functions of all variables: 

 (q12,q9,q8,p5,p6,p4)

e_469 is a consequence of e_419

Step 1436: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 53 terms

The list of inequalities got extended by: 
An expression with 55 terms

e_431 is a consequence of e_472.
Substitution of q12 by an expression in 
q9, q8, p5, p6, p4 found in e_419 : 14 factors in 4 terms

Step 1437: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1438: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_470 and e_474. e_474: 
 14 terms, 84 factors, with derivatives of functions of all variables: 

                         2      3   2      3   2      2
 (q26,q11,q10,q9,q8,p8,p5 ,p5,p6 ,p6 ,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_429: 
 13 terms, 78 factors, with derivatives of functions of all variables: 

                     2      3   2      3   2      2
 (q26,q10,q9,q8,p8,p5 ,p5,p6 ,p6 ,p6,p4 ,p4 ,p4,p7 ,p7)


Step 1439: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 401  3-Oct-2003 05:32:33, 30 ms (0%), 1031837 occupied, 23968107 free
*** Garbage collection starting 
*** GC 402  3-Oct-2003 05:32:36, 40 ms (0%), 1029045 occupied, 23970900 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_365 we get the alternative equations : 
0=p4 - p5

17 factors in 4 terms

The list of inequalities got extended by: 

p5


New level : 1.1.2.2.1.1.3.1.
CRACK is now called with the new equation e_95 : 
0=p4 - p5

e_475,e_287,e_387,e_424,e_384,e_372,e_472,e_338 are consequences of e_95

Step 1440: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

1


The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 24 terms

The list of inequalities got extended by: 
An expression with 26 terms

e_238 is a consequence of e_274.
e_322 is a consequence of e_216.
e_443 is a consequence of e_313.
e_325 is a consequence of e_216.
e_380 is a consequence of e_313.
e_385 is a consequence of e_313.
e_440 is a consequence of e_216.
e_450 is a consequence of e_191.
e_453 is a consequence of e_324.
e_454 is a consequence of e_274.
e_455 is a consequence of e_451.
e_458 is a consequence of e_274.
e_459 is a consequence of e_274.
Substitution of p4 by an expression in 
p5 found in e_95 : 
p4=p5


Step 1441: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 30 terms

The list of inequalities got extended by: 
An expression with 30 terms

e_445 is a consequence of e_396.
e_53 is a consequence of e_323.
Substitution of q27 by an expression in 
q26, q11, q10, p8, p5, p6, p7 found in e_315 : 12 factors in 4 terms

Step 1442: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 42 terms

e_216 is a consequence of e_457.
e_255 is a consequence of e_457.
e_451 is a consequence of e_396.
e_456 is a consequence of e_396.
Substitution of q11 by an expression in 
q10, q9, q8, p8, p5, p6, p7 found in e_274 : 9 factors in 4 terms

Step 1443: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_191 and e_396. e_396: 
 10 terms, 40 factors, with derivatives of functions of all variables: 

                      2      2      3   2      2
 (q26,q17,q10,q9,q8,p8 ,p8,p5 ,p5,p6 ,p6 ,p6,p7 ,p7)

is replaced by e_464: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

                  2      2      3   2      2
 (q26,q10,q9,q8,p8 ,p8,p5 ,p5,p6 ,p6 ,p6,p7 ,p7)


e_464 is a consequence of e_313.
Step 1444: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_465 is a consequence of e_313.
Step 1445: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_324 and e_452. e_452: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

                      2      3   2      3   2      2
 (q26,q17,q10,q9,q8,p8 ,p8,p5 ,p5 ,p5,p6 ,p6 ,p6,p7 ,p7)

is replaced by e_466: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

                  2      3   2      3   2      2
 (q26,q10,q9,q8,p8 ,p8,p5 ,p5 ,p5,p6 ,p6 ,p6,p7 ,p7)


Step 1446: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_313 and e_466. e_466: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

                  2      3   2      3   2      2
 (q26,q10,q9,q8,p8 ,p8,p5 ,p5 ,p5,p6 ,p6 ,p6,p7 ,p7)

is replaced by e_467: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                 2      2
 (q10,q9,q8,p8,p5 ,p5,p6 ,p6,p7)


e_467 is a consequence of e_457.
Step 1447: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_313 and e_323. e_323: 
 11 terms, 55 factors, with derivatives of functions of all variables: 

                      3   2      2      3   2      2
 (q26,q17,q10,q9,q8,p8 ,p8 ,p8,p5 ,p5,p6 ,p6 ,p6,p7 ,p7)

is replaced by e_400: 

                 2     2
0=(q10 - q17)*(p7  + p8 )


Step 1448: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 3 terms

Step 1449: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_191 we get the alternative equations : 
0=q10 - q17


0=p5*p7 + p6*p8


New level : 1.1.2.2.1.1.3.1.1.
CRACK is now called with the new equation e_484 : 
0=q10 - q17

e_324,e_400 are consequences of e_484

Step 1450: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 42 terms

Substitution of q17 by an expression in 
q10 found in e_484 : 
q17=q10


Step 1451: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q10

from e_457 and e_477. e_425 is added: 
 12 terms, 60 factors, with derivatives of functions of all variables: 

              2      4   2      4   2      2
 (q26,q9,q8,p8 ,p8,p5 ,p5 ,p5,p6 ,p6 ,p6,p7 ,p7)


Step 1452: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q26

from e_477 and e_425. e_365 is added: 
(#) 12 terms, 22 factors, with derivatives of functions of all variables: 

              2      3   2      3   2      2
 (q10,q9,q8,p8 ,p8,p5 ,p5 ,p5,p6 ,p6 ,p6,p7 ,p7)


e_365 is a consequence of e_457.
Step 1453: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms : 
The list of inequalities got extended by: 

p8


for the substitution of q9 by e_457 we have to consider the case 0=e_338: 
0=2*( - p5*p7 - p6*p8)

The coefficient to be set = 0 in the first subcase is:

e_338 : 
0=p5*p7 + p6*p8


New level : 1.1.2.2.1.1.3.1.1.1.
Step 1454: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 
An expression with 35 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 38 terms

e_425 is a consequence of e_372.
Substitution of p5 by an expression in 
p8, p6, p7 found in e_338 : 
     - p6*p8
p5=----------
       p7


Step 1455: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization : 
factorizing e_472 we get the alternative equations : 
    2     2
0=p7  + p8


0=p6*q10 + p7*q8


New level : 1.1.2.2.1.1.3.1.1.1.1.
CRACK is now called with the new equation e_322 : 
    2     2
0=p7  + p8

e_372 is a consequence of e_322

Step 1456: 
Hot list of urgent steps : 
Step 1457: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.2.2.1.1.3.1.1.1.1. : 
equations : 

e_322 : 
    2     2
0=p7  + p8



Non-vanishing expressions: p5,p4,p7,p6,p8
188 factors in 38 terms
214 factors in 40 terms
133 factors in 27 terms
172 factors in 35 terms

                      2
g0111*p7*p8 + g0112*p7  + g0113*p6*p7 - g0114*p6*p8 - g0115*p6*p8 - g0116*p6*p7


functions : 
          2           3       2        3       2        6    2
q27=( - p6 *p8*q26 - ---*p6*p7 *q10 - ---*p6*p8 *q10 - ---*p7 *p8*q9
                      5                5                5

         3       2        2
      - ---*p7*p8 *q8)/(p6 *p7)
         5

q26, 
q25=0


q24=q10


                     2
     p6*p8*q10 + 2*p7 *q9 + p7*p8*q8
q23=---------------------------------
                  p6*p7


                        2
      - p6*p8*q10 - 2*p7 *q9 - p7*p8*q8
q22=------------------------------------
                   p6*p7


q21=q10


q20=q10


      5    2   2        5    2   2            3           2   2           3
     ---*p6 *p7 *q26 + ---*p6 *p8 *q26 + p6*p8 *q10 + 2*p7 *p8 *q9 + p7*p8 *q8
      3                 3
q19=---------------------------------------------------------------------------
                                           3
                                      p6*p7


q18

      5    2   2        5    2   2            3           2   2           3
   - ---*p6 *p7 *q26 - ---*p6 *p8 *q26 - p6*p8 *q10 - 2*p7 *p8 *q9 - p7*p8 *q8
      3                 3
=------------------------------------------------------------------------------
                                          3
                                     p6*p7


q17=q10


q16=q10


                        2
      - p6*p8*q10 - 2*p7 *q9 - p7*p8*q8
q15=------------------------------------
                   p6*p7


        1
q14= - ---*q8
        2


q13=2*q9


     1
q12=---*q8
     2


                     2
     p6*p8*q10 + 2*p7 *q9 + p7*p8*q8
q11=---------------------------------
                  p6*p7

q10, q9, q8, 
q7= - q9


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, p6, 
     - p6*p8
p5=----------
       p7


     - p6*p8
p4=----------
       p7


p3= - p6


p2=0


p1=0


with 74 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_322(2a)
7 constants : p6,p7,p8,q8,q9,q10,q26
The equation: 

                                                  2
f =( - D f*D D f*p6*p7 - D f*f *p6*p8 + D D f  *p7  - D D f*D f*p6*p8
 t      2   1 2           2   x          1 2 2x        1 2   1

     + D f*f *p6*p7 + f  *p7*p8)/p7
        1   x          3x
The symmetry: 
                  2   2                             4
f =(D f  *D D f*p6 *p7 *p8*q10 + 2*D f  *D D f*p6*p7 *q9
 s   2 2x  1 2                      2 2x  1 2

                        3                    2   3
     + D f  *D D f*p6*p7 *p8*q8 + D f  *f *p6 *p7 *q10
        2 2x  1 2                  2 2x  x

        5                3   2        5                3   2
     - ---*D f *D D f *p6 *p7 *q26 - ---*D f *D D f *p6 *p8 *q26
        3   2 x  1 2 x                3   2 x  1 2 x

                     2   3                          2   2
     - D f *D D f *p6 *p8 *q10 - 2*D f *D D f *p6*p7 *p8 *q9
        2 x  1 2 x                  2 x  1 2 x

                           3                 2   3            2         2   3
     - D f *D D f *p6*p7*p8 *q8 + D f *f  *p6 *p7 *q10 - (D f) *D D f*p6 *p7 *q9
        2 x  1 2 x                 2 x  2x                 2     1 2

        1       2      2   3                    2   2
     + ---*(D f) *f *p6 *p7 *q8 + D f*D D f  *p6 *p7 *p8*q10
        2    2     x               2   1 2 2x

                          4                       3
     + 2*D f*D D f  *p6*p7 *q9 + D f*D D f  *p6*p7 *p8*q8
          2   1 2 2x              2   1 2 2x

                       2   3                     2   3                2   3
     + D f*D D f*D f*p6 *p7 *q8 + 2*D f*D f*f *p6 *p7 *q9 + D f*f  *p6 *p7 *q10
        2   1 2   1                  2   1   x               2   3x

                 2   3                     2   3                     2   3
     + D D f  *p6 *p7 *q26 + D D f  *D f*p6 *p7 *q10 + D D f *D f *p6 *p7 *q10
        1 2 4x                1 2 2x  1                 1 2 x  1 x

                     2   3                  2   2   3
     + D D f*D f  *p6 *p7 *q10 + D D f*(D f) *p6 *p7 *q9
        1 2   1 2x                1 2    1

                  2   2                          4                    3
     - D f  *f *p6 *p7 *p8*q10 - 2*D f  *f *p6*p7 *q9 - D f  *f *p6*p7 *p8*q8
        1 2x  x                     1 2x  x              1 2x  x

        5             3   2        5             3   2
     + ---*D f *f  *p6 *p7 *q26 + ---*D f *f  *p6 *p8 *q26
        3   1 x  2x                3   1 x  2x

                  2   3                       2   2                       3
     + D f *f  *p6 *p8 *q10 + 2*D f *f  *p6*p7 *p8 *q9 + D f *f  *p6*p7*p8 *q8
        1 x  2x                  1 x  2x                  1 x  2x

        1       2      2   3                2   2                         4
     - ---*(D f) *f *p6 *p7 *q8 - D f*f  *p6 *p7 *p8*q10 - 2*D f*f  *p6*p7 *q9
        2    1     x               1   3x                     1   3x

                    3               2   2           3           4
     - D f*f  *p6*p7 *p8*q8 - f  *p6 *p7 *p8*q26 - ---*f  *p6*p7 *q10
        1   3x                 5x                   5   5x

        3           2   2        6        4          3        3   2        2   3
     - ---*f  *p6*p7 *p8 *q10 - ---*f  *p7 *p8*q9 - ---*f  *p7 *p8 *q8)/(p6 *p7
        5   5x                   5   5x              5   5x

   )
And now in machine readable form:

The system: 

df(f(1),t)=( - d(2,f(1))*d(1,d(2,f(1)))*p6*p7 - d(2,f(1))*df(f(1),x)*p6*p8 + d(1
,d(2,df(f(1),x,2)))*p7**2 - d(1,d(2,f(1)))*d(1,f(1))*p6*p8 + d(1,f(1))*df(f(1),x
)*p6*p7 + df(f(1),x,3)*p7*p8)/p7$
The symmetry: 
df(f(1),s)=(d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p6**2*p7**2*p8*q10 + 2*d(2,df(f(1),
x,2))*d(1,d(2,f(1)))*p6*p7**4*q9 + d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p6*p7**3*p8*
q8 + d(2,df(f(1),x,2))*df(f(1),x)*p6**2*p7**3*q10 - 5/3*d(2,df(f(1),x))*d(1,d(2,
df(f(1),x)))*p6**3*p7**2*q26 - 5/3*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6**3*p8
**2*q26 - d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6**2*p8**3*q10 - 2*d(2,df(f(1),x
))*d(1,d(2,df(f(1),x)))*p6*p7**2*p8**2*q9 - d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))
*p6*p7*p8**3*q8 + d(2,df(f(1),x))*df(f(1),x,2)*p6**2*p7**3*q10 - d(2,f(1))**2*d(
1,d(2,f(1)))*p6**2*p7**3*q9 + 1/2*d(2,f(1))**2*df(f(1),x)*p6**2*p7**3*q8 + d(2,f
(1))*d(1,d(2,df(f(1),x,2)))*p6**2*p7**2*p8*q10 + 2*d(2,f(1))*d(1,d(2,df(f(1),x,2
)))*p6*p7**4*q9 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p6*p7**3*p8*q8 + d(2,f(1))*d(
1,d(2,f(1)))*d(1,f(1))*p6**2*p7**3*q8 + 2*d(2,f(1))*d(1,f(1))*df(f(1),x)*p6**2*
p7**3*q9 + d(2,f(1))*df(f(1),x,3)*p6**2*p7**3*q10 + d(1,d(2,df(f(1),x,4)))*p6**2
*p7**3*q26 + d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p6**2*p7**3*q10 + d(1,d(2,df(f(1),
x)))*d(1,df(f(1),x))*p6**2*p7**3*q10 + d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p6**2*p7
**3*q10 + d(1,d(2,f(1)))*d(1,f(1))**2*p6**2*p7**3*q9 - d(1,df(f(1),x,2))*df(f(1)
,x)*p6**2*p7**2*p8*q10 - 2*d(1,df(f(1),x,2))*df(f(1),x)*p6*p7**4*q9 - d(1,df(f(1
),x,2))*df(f(1),x)*p6*p7**3*p8*q8 + 5/3*d(1,df(f(1),x))*df(f(1),x,2)*p6**3*p7**2
*q26 + 5/3*d(1,df(f(1),x))*df(f(1),x,2)*p6**3*p8**2*q26 + d(1,df(f(1),x))*df(f(1
),x,2)*p6**2*p8**3*q10 + 2*d(1,df(f(1),x))*df(f(1),x,2)*p6*p7**2*p8**2*q9 + d(1,
df(f(1),x))*df(f(1),x,2)*p6*p7*p8**3*q8 - 1/2*d(1,f(1))**2*df(f(1),x)*p6**2*p7**
3*q8 - d(1,f(1))*df(f(1),x,3)*p6**2*p7**2*p8*q10 - 2*d(1,f(1))*df(f(1),x,3)*p6*
p7**4*q9 - d(1,f(1))*df(f(1),x,3)*p6*p7**3*p8*q8 - df(f(1),x,5)*p6**2*p7**2*p8*
q26 - 3/5*df(f(1),x,5)*p6*p7**4*q10 - 3/5*df(f(1),x,5)*p6*p7**2*p8**2*q10 - 6/5*
df(f(1),x,5)*p7**4*p8*q9 - 3/5*df(f(1),x,5)*p7**3*p8**2*q8)/(p6**2*p7**3)$

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

  2     2
p7  + p8


New level : 1.1.2.2.1.1.3.1.1.1.2.
CRACK is now called with the new equation e_322 : 
0=p6*q10 + p7*q8


Step 1458: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 26 terms

The list of inequalities got extended by: 
An expression with 26 terms

Substitution of q10 by an expression in 
q8, p6, p7 found in e_322 : 
      - p7*q8
q10=----------
        p6


Step 1459: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 20 terms

The list of inequalities got extended by: 
An expression with 22 terms

Substitution of q26 by an expression in 
q9, p6, p7 found in e_372 : 
         6    2
      - ---*p7 *q9
         5
q26=---------------
            2
          p6



>>>>>>>>> Solution of level 1.1.2.2.1.1.3.1.1.1.2. : 
no equations


Non-vanishing expressions: p5,p4,p7,p6,p8

          2                2                2                2
2*g0054*p7 *q8 - 4*g0055*p7 *q9 + 4*g0056*p7 *q9 + 2*g0057*p7 *q8

             2                2                2                2
 + 2*g0058*p7 *q8 + 4*g0059*p7 *q9 - 4*g0060*p7 *q9 + 2*g0061*p7 *q8

             2                2
 + 2*g0062*p7 *q8 + 4*g0063*p7 *q9 + g0064*p6*p7*q8 - 4*g0065*p6*p7*q9

                              2                2
 - g0066*p6*p7*q8 - 4*g0067*p7 *q9 + 2*g0068*p7 *q8 - 2*g0069*p6*p7*q9

                                                   2                2
 - 2*g0070*p6*p7*q8 + 2*g0071*p6*p7*q9 - 2*g0078*p6 *p7 + 2*g0079*p6 *p8

             2                2
 + 2*g0080*p6 *p8 + 2*g0081*p6 *p7


          2                 2
6*g0084*p7 *q8 - 12*g0085*p7 *q9 - 10*g0087*p6*p7*q8 + 20*g0088*p6*p7*q9

 - 20*g0089*p6*p7*q9 - 10*g0090*p6*p7*q8 - 10*g0091*p6*p7*q8 - 20*g0092*p6*p7*q9

 + 20*g0093*p6*p7*q9 - 10*g0094*p6*p7*q8 - 10*g0095*p6*p7*q8 - 20*g0096*p6*p7*q9

             2                 2                2
 - 5*g0097*p6 *q8 + 20*g0098*p6 *q9 + 5*g0099*p6 *q8 + 20*g0100*p6*p7*q9

                                  2                 2                 2
 - 10*g0101*p6*p7*q8 + 10*g0102*p6 *q9 + 10*g0103*p6 *q8 - 10*g0104*p6 *q9


           3                    2                    2                    2
12*g0003*p7 *q9 + 10*g0005*p6*p7 *q8 - 20*g0006*p6*p7 *q9 + 10*g0007*p6*p7 *q8

                 2                    2                    2
 + 10*g0008*p6*p7 *q8 - 20*g0009*p6*p7 *q9 + 10*g0010*p6*p7 *q8

                 2                 2                   2
 + 10*g0011*p6*p7 *q8 - 20*g0012*p6 *p7*q9 - 5*g0013*p6 *p7*q8

                 2                    2                 2
 - 20*g0014*p6*p7 *q9 + 10*g0015*p6*p7 *q8 - 10*g0016*p6 *p7*q9

              2                    2                    2   2              3
 - 10*g0017*p6 *p7*q8 + 10*g0018*p6 *p7*q9 - 10*g0023*p6 *p7  + 10*g0024*p6 *p8

              3                 3
 + 10*g0025*p6 *p8 + 10*g0026*p6 *p7


           3                    2                    2                    2
12*g0028*p7 *q9 + 10*g0030*p6*p7 *q8 - 20*g0031*p6*p7 *q9 + 20*g0032*p6*p7 *q9

                 2                    2                    2
 + 20*g0033*p6*p7 *q9 - 20*g0034*p6*p7 *q9 + 10*g0035*p6*p7 *q8

                 2                2                    2
 + 20*g0036*p6*p7 *q9 + 5*g0037*p6 *p7*q8 - 20*g0038*p6 *p7*q9

                 2                    2                 2
 - 20*g0039*p6*p7 *q9 + 10*g0040*p6*p7 *q8 - 10*g0041*p6 *p7*q9

              2                    2                    2   2              3
 - 10*g0042*p6 *p7*q8 + 10*g0043*p6 *p7*q9 - 10*g0048*p6 *p7  - 10*g0049*p6 *p7

              3                 3
 + 10*g0050*p6 *p8 + 10*g0051*p6 *p7


  2     2
p7  + p8


                      2
g0111*p7*p8 + g0112*p7  + g0113*p6*p7 - g0114*p6*p8 - g0115*p6*p8 - g0116*p6*p7


functions : 
      3    2
     ---*p7 *q8
      5
q27=------------
          2
        p6


         6    2
      - ---*p7 *q9
         5
q26=---------------
            2
          p6


q25=0


      - p7*q8
q24=----------
        p6


     2*p7*q9
q23=---------
       p6


      - 2*p7*q9
q22=------------
         p6


      - p7*q8
q21=----------
        p6


      - p7*q8
q20=----------
        p6


      - 2*p7*q9
q19=------------
         p6


     2*p7*q9
q18=---------
       p6


      - p7*q8
q17=----------
        p6


      - p7*q8
q16=----------
        p6


      - 2*p7*q9
q15=------------
         p6


        1
q14= - ---*q8
        2


q13=2*q9


     1
q12=---*q8
     2


     2*p7*q9
q11=---------
       p6


      - p7*q8
q10=----------
        p6

q9, q8, 
q7= - q9


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, p6, 
     - p6*p8
p5=----------
       p7


     - p6*p8
p4=----------
       p7


p3= - p6


p2=0


p1=0


with 56 terms
no equations
5 constants : p6,p7,p8,q8,q9
The equation: 

                                                  2
f =( - D f*D D f*p6*p7 - D f*f *p6*p8 + D D f  *p7  - D D f*D f*p6*p8
 t      2   1 2           2   x          1 2 2x        1 2   1

     + D f*f *p6*p7 + f  *p7*p8)/p7
        1   x          3x
The symmetry: 
f =(2*D f  *D D f*p6*p7*q9 - D f  *f *p6*p7*q8 + 2*D f *D D f *p6*p7*q9
 s     2 2x  1 2              2 2x  x               2 x  1 2 x

                                2         2       1       2      2
     - D f *f  *p6*p7*q8 - (D f) *D D f*p6 *q9 + ---*(D f) *f *p6 *q8
        2 x  2x              2     1 2            2    2     x

                                                2                     2
     + 2*D f*D D f  *p6*p7*q9 + D f*D D f*D f*p6 *q8 + 2*D f*D f*f *p6 *q9
          2   1 2 2x             2   1 2   1              2   1   x

                           6            2
     - D f*f  *p6*p7*q8 - ---*D D f  *p7 *q9 - D D f  *D f*p6*p7*q8
        2   3x             5   1 2 4x           1 2 2x  1

                                                                2   2
     - D D f *D f *p6*p7*q8 - D D f*D f  *p6*p7*q8 + D D f*(D f) *p6 *q9
        1 2 x  1 x             1 2   1 2x             1 2    1

                                                    1       2      2
     - 2*D f  *f *p6*p7*q9 - 2*D f *f  *p6*p7*q9 - ---*(D f) *f *p6 *q8
          1 2x  x               1 x  2x             2    1     x

                             3        2       2
     - 2*D f*f  *p6*p7*q9 + ---*f  *p7 *q8)/p6
          1   3x             5   5x
And now in machine readable form:

The system: 

df(f(1),t)=( - d(2,f(1))*d(1,d(2,f(1)))*p6*p7 - d(2,f(1))*df(f(1),x)*p6*p8 + d(1
,d(2,df(f(1),x,2)))*p7**2 - d(1,d(2,f(1)))*d(1,f(1))*p6*p8 + d(1,f(1))*df(f(1),x
)*p6*p7 + df(f(1),x,3)*p7*p8)/p7$
The symmetry: 
df(f(1),s)=(2*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p6*p7*q9 - d(2,df(f(1),x,2))*df(f
(1),x)*p6*p7*q8 + 2*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6*p7*q9 - d(2,df(f(1),
x))*df(f(1),x,2)*p6*p7*q8 - d(2,f(1))**2*d(1,d(2,f(1)))*p6**2*q9 + 1/2*d(2,f(1))
**2*df(f(1),x)*p6**2*q8 + 2*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p6*p7*q9 + d(2,f(1)
)*d(1,d(2,f(1)))*d(1,f(1))*p6**2*q8 + 2*d(2,f(1))*d(1,f(1))*df(f(1),x)*p6**2*q9 
- d(2,f(1))*df(f(1),x,3)*p6*p7*q8 - 6/5*d(1,d(2,df(f(1),x,4)))*p7**2*q9 - d(1,d(
2,df(f(1),x,2)))*d(1,f(1))*p6*p7*q8 - d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p6*p7
*q8 - d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p6*p7*q8 + d(1,d(2,f(1)))*d(1,f(1))**2*p6
**2*q9 - 2*d(1,df(f(1),x,2))*df(f(1),x)*p6*p7*q9 - 2*d(1,df(f(1),x))*df(f(1),x,2
)*p6*p7*q9 - 1/2*d(1,f(1))**2*df(f(1),x)*p6**2*q8 - 2*d(1,f(1))*df(f(1),x,3)*p6*
p7*q9 + 3/5*df(f(1),x,5)*p7**2*q8)/p6**2$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 10 ms

New level : 1.1.2.2.1.1.3.1.1.2.
now back to the substitution of q9 by e_457
The list of inequalities got extended by: 

p5*p7 + p6*p8


Step 1460: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms : 
contradiction : 7 factors in 2 terms
Therefore no special investigation whether the 
coefficient of a function to be substituted is zero.
The list of inequalities got extended by: 
An expression with 68 terms

The list of inequalities got extended by: 
An expression with 56 terms

The list of inequalities got extended by: 
An expression with 75 terms

The list of inequalities got extended by: 
An expression with 74 terms

e_475 is a consequence of e_477.
Substitution of q9 by an expression in 
q10, q8, p8, p5, p6, p7 found in e_457 : 23 factors in 5 terms

Step 1461: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms : 
for the substitution of q26 by e_477 we have to consider the case 0=e_325: 8
 factors in 4 terms
The coefficient to be set = 0 in the first subcase is:

e_325 : 
    2     2
0=p5  + p6


New level : 1.1.2.2.1.1.3.1.1.2.1.
Step 1462: 
Hot list of urgent steps : 
Step 1463: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p5

from e_325 and e_380. e_380: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

           3   2      2      2      3   2
 (q10,q8,p8 ,p8 ,p8,p5 ,p5,p6 ,p6,p7 ,p7 ,p7)

is replaced by e_385: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

           3   2         2      3   2
 (q10,q8,p8 ,p8 ,p8,p5,p6 ,p6,p7 ,p7 ,p7)


Step 1464: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms : 
for the substitution of q10 by e_385 we have to consider the case 0=e_453: 11
 factors in 3 terms
The coefficient to be set = 0 in the first subcase is:

e_453 : 
                    2        2
0=2*p5*p7*p8 - p6*p7  + p6*p8


New level : 1.1.2.2.1.1.3.1.1.2.1.1.
Step 1465: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

  2     2
p7  + p8


The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 

p7 + p8


p7 - p8


The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 
An expression with 48 terms

The list of inequalities got extended by: 
An expression with 48 terms

Substitution of p5 by an expression in 
p8, p6, p7 found in e_453 : 11 factors in 3 terms

leads to a contradiction in : 
    2     2
0=p5  + p6


Time: 0 ms

Time: 0 ms

Time: 10 ms

New level : 1.1.2.2.1.1.3.1.1.2.1.2.
now back to the substitution of q10 by e_385
The list of inequalities got extended by: 
An expression with 3 terms
*** Garbage collection starting 
*** GC 403  3-Oct-2003 05:32:39, 40 ms (0%), 1099592 occupied, 23900355 free

The list of inequalities got extended by: 
An expression with 141 terms

The list of inequalities got extended by: 
An expression with 127 terms

The list of inequalities got extended by: 
An expression with 156 terms

The list of inequalities got extended by: 
An expression with 159 terms

Substitution of q10 by an expression in 
q8, p8, p5, p6, p7 found in e_385 : 35 factors in 5 terms

Step 1466: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.2.2.1.1.3.1.1.2.1.2. : 
equations : 

e_325 : 
    2     2
0=p5  + p6



Non-vanishing expressions: p8,p5,p6,p7,p4
1004 factors in 159 terms
1002 factors in 156 terms
801 factors in 127 terms
885 factors in 141 terms

p5*p7 + p6*p8


g0111*p8 + g0112*p7 + g0113*p6 + g0114*p5 + g0115*p5 - g0116*p6


                  2        2
2*p5*p7*p8 - p6*p7  + p6*p8


functions : 
       3      2           1    2   2   3        3    2   2      2
q27=(p5 *p6*p7 *p8*q26 - ---*p5 *p6 *p7 *q26 + ---*p5 *p6 *p7*p8 *q26
                          2                     2

         3     2   4          3     2   5       1       3   2
      + ----*p5 *p7 *p8*q8 - ----*p5 *p8 *q8 - ---*p5*p6 *p7 *p8*q26
         20                   20                2

         1       3   3        3           5       3           3   2
      + ---*p5*p6 *p8 *q26 - ----*p5*p6*p7 *q8 - ----*p5*p6*p7 *p8 *q8
         2                    20                  10

         3              4       3     2   2   3       3     2   5
      - ----*p5*p6*p7*p8 *q8 - ----*p6 *p7 *p8 *q8 - ----*p6 *p8 *q8)/(
         20                     10                    10

     2   2   2       1       3   3    3       3      2    1    4   2
   p5 *p6 *p7 *p8 - ---*p5*p6 *p7  + ---*p5*p6 *p7*p8  - ---*p6 *p7 *p8
                     2                2                   2

       1    4   3
    + ---*p6 *p8 )
       2

q26, 
q25=0


         1       2          1       3       1       3       1          2
      - ---*p5*p7 *p8*q8 - ---*p5*p8 *q8 + ---*p6*p7 *q8 + ---*p6*p7*p8 *q8
         4                  4               4               4
q24=------------------------------------------------------------------------
                                   1    2   2    1    2   2
                    p5*p6*p7*p8 - ---*p6 *p7  + ---*p6 *p8
                                   2             2


      1    2   2   2       1    2   4       1          3
q23=(---*p5 *p7 *p8 *q8 + ---*p5 *p8 *q8 + ---*p5*p6*p7 *p8*q8
      4                    4                2

         1             3       1    2   4       1    2   2   2
      + ---*p5*p6*p7*p8 *q8 - ---*p6 *p7 *q8 + ---*p6 *p7 *p8 *q8
         2                     4                4

         1    2   4        2      2       1       2   3    3       2      2
      + ---*p6 *p8 *q8)/(p5 *p6*p7 *p8 - ---*p5*p6 *p7  + ---*p5*p6 *p7*p8
         2                                2                2

       1    3   2       1    3   3
    - ---*p6 *p7 *p8 + ---*p6 *p8 )
       2                2


         1    2   2   2       1    2   4       1          3
q22=( - ---*p5 *p7 *p8 *q8 - ---*p5 *p8 *q8 - ---*p5*p6*p7 *p8*q8
         4                    4                2

         1             3       1    2   4       1    2   2   2
      - ---*p5*p6*p7*p8 *q8 + ---*p6 *p7 *q8 - ---*p6 *p7 *p8 *q8
         2                     4                4

         1    2   4        2      2       1       2   3    3       2      2
      - ---*p6 *p8 *q8)/(p5 *p6*p7 *p8 - ---*p5*p6 *p7  + ---*p5*p6 *p7*p8
         2                                2                2

       1    3   2       1    3   3
    - ---*p6 *p7 *p8 + ---*p6 *p8 )
       2                2


         1       2          1       3       1       3       1          2
      - ---*p5*p7 *p8*q8 - ---*p5*p8 *q8 + ---*p6*p7 *q8 + ---*p6*p7*p8 *q8
         4                  4               4               4
q21=------------------------------------------------------------------------
                                   1    2   2    1    2   2
                    p5*p6*p7*p8 - ---*p6 *p7  + ---*p6 *p8
                                   2             2


         1       2          1       3       1       3       1          2
      - ---*p5*p7 *p8*q8 - ---*p5*p8 *q8 + ---*p6*p7 *q8 + ---*p6*p7*p8 *q8
         4                  4               4               4
q20=------------------------------------------------------------------------
                                   1    2   2    1    2   2
                    p5*p6*p7*p8 - ---*p6 *p7  + ---*p6 *p8
                                   2             2


      5    4      2           5    3   2   3        5    3   2      2
q19=(---*p5 *p6*p7 *p8*q26 - ---*p5 *p6 *p7 *q26 + ---*p5 *p6 *p7*p8 *q26
      3                       6                     2

         1    3   4          1    3   5       5    2   3   2
      + ---*p5 *p7 *p8*q8 - ---*p5 *p8 *q8 + ---*p5 *p6 *p7 *p8*q26
         4                   4                6

         5    2   3   3        1    2      5       1    2      3   2
      + ---*p5 *p6 *p8 *q26 - ---*p5 *p6*p7 *q8 - ---*p5 *p6*p7 *p8 *q8
         6                     4                   4

         5       4   3        5       4      2        1       2   4
      - ---*p5*p6 *p7 *q26 + ---*p5*p6 *p7*p8 *q26 - ---*p5*p6 *p7 *p8*q8
         6                    2                       4

         1       2   2   3       1       2   5       5    5   2
      - ---*p5*p6 *p7 *p8 *q8 - ---*p5*p6 *p8 *q8 - ---*p6 *p7 *p8*q26
         2                       4                   6

         5    5   3        1    3   3   2       1    3      4
      + ---*p6 *p8 *q26 - ---*p6 *p7 *p8 *q8 - ---*p6 *p7*p8 *q8)/(
         6                 4                    4

     2   2   3       1       3   4    3       3   2   2    1    4   3
   p5 *p6 *p7 *p8 - ---*p5*p6 *p7  + ---*p5*p6 *p7 *p8  - ---*p6 *p7 *p8
                     2                2                    2

       1    4      3
    + ---*p6 *p7*p8 )
       2


         5    4      2           5    3   2   3        5    3   2      2
q18=( - ---*p5 *p6*p7 *p8*q26 + ---*p5 *p6 *p7 *q26 - ---*p5 *p6 *p7*p8 *q26
         3                       6                     2

         1    3   4          1    3   5       5    2   3   2
      - ---*p5 *p7 *p8*q8 + ---*p5 *p8 *q8 - ---*p5 *p6 *p7 *p8*q26
         4                   4                6

         5    2   3   3        1    2      5       1    2      3   2
      - ---*p5 *p6 *p8 *q26 + ---*p5 *p6*p7 *q8 + ---*p5 *p6*p7 *p8 *q8
         6                     4                   4

         5       4   3        5       4      2        1       2   4
      + ---*p5*p6 *p7 *q26 - ---*p5*p6 *p7*p8 *q26 + ---*p5*p6 *p7 *p8*q8
         6                    2                       4

         1       2   2   3       1       2   5       5    5   2
      + ---*p5*p6 *p7 *p8 *q8 + ---*p5*p6 *p8 *q8 + ---*p6 *p7 *p8*q26
         2                       4                   6

         5    5   3        1    3   3   2       1    3      4
      - ---*p6 *p8 *q26 + ---*p6 *p7 *p8 *q8 + ---*p6 *p7*p8 *q8)/(
         6                 4                    4

     2   2   3       1       3   4    3       3   2   2    1    4   3
   p5 *p6 *p7 *p8 - ---*p5*p6 *p7  + ---*p5*p6 *p7 *p8  - ---*p6 *p7 *p8
                     2                2                    2

       1    4      3
    + ---*p6 *p7*p8 )
       2


         1       2          1       3       1       3       1          2
      - ---*p5*p7 *p8*q8 - ---*p5*p8 *q8 + ---*p6*p7 *q8 + ---*p6*p7*p8 *q8
         4                  4               4               4
q17=------------------------------------------------------------------------
                                   1    2   2    1    2   2
                    p5*p6*p7*p8 - ---*p6 *p7  + ---*p6 *p8
                                   2             2


         1       2          1       3       1       3       1          2
      - ---*p5*p7 *p8*q8 - ---*p5*p8 *q8 + ---*p6*p7 *q8 + ---*p6*p7*p8 *q8
         4                  4               4               4
q16=------------------------------------------------------------------------
                                   1    2   2    1    2   2
                    p5*p6*p7*p8 - ---*p6 *p7  + ---*p6 *p8
                                   2             2


         1    2   2   2       1    2   4       1          3
q15=( - ---*p5 *p7 *p8 *q8 - ---*p5 *p8 *q8 - ---*p5*p6*p7 *p8*q8
         4                    4                2

         1             3       1    2   4       1    2   2   2
      - ---*p5*p6*p7*p8 *q8 + ---*p6 *p7 *q8 - ---*p6 *p7 *p8 *q8
         2                     4                4

         1    2   4        2      2       1       2   3    3       2      2
      - ---*p6 *p8 *q8)/(p5 *p6*p7 *p8 - ---*p5*p6 *p7  + ---*p5*p6 *p7*p8
         2                                2                2

       1    3   2       1    3   3
    - ---*p6 *p7 *p8 + ---*p6 *p8 )
       2                2


        1
q14= - ---*q8
        2


         1    3   2          1    3   3       1    2      3
q13=( - ---*p5 *p7 *p8*q8 - ---*p5 *p8 *q8 + ---*p5 *p6*p7 *q8
         4                   4                4

         3    2         2       5       2   2          3       2   3
      - ---*p5 *p6*p7*p8 *q8 + ---*p5*p6 *p7 *p8*q8 - ---*p5*p6 *p8 *q8
         4                      4                      4

         1    3   3       3    3      2        2      2       1       2   3
      - ---*p6 *p7 *q8 + ---*p6 *p7*p8 *q8)/(p5 *p6*p7 *p8 - ---*p5*p6 *p7
         4                4                                   2

       3       2      2    1    3   2       1    3   3
    + ---*p5*p6 *p7*p8  - ---*p6 *p7 *p8 + ---*p6 *p8 )
       2                   2                2


     1
q12=---*q8
     2


      1    2   2   2       1    2   4       1          3
q11=(---*p5 *p7 *p8 *q8 + ---*p5 *p8 *q8 + ---*p5*p6*p7 *p8*q8
      4                    4                2

         1             3       1    2   4       1    2   2   2
      + ---*p5*p6*p7*p8 *q8 - ---*p6 *p7 *q8 + ---*p6 *p7 *p8 *q8
         2                     4                4

         1    2   4        2      2       1       2   3    3       2      2
      + ---*p6 *p8 *q8)/(p5 *p6*p7 *p8 - ---*p5*p6 *p7  + ---*p5*p6 *p7*p8
         2                                2                2

       1    3   2       1    3   3
    - ---*p6 *p7 *p8 + ---*p6 *p8 )
       2                2


         1       2          1       3       1       3       1          2
      - ---*p5*p7 *p8*q8 - ---*p5*p8 *q8 + ---*p6*p7 *q8 + ---*p6*p7*p8 *q8
         4                  4               4               4
q10=------------------------------------------------------------------------
                                   1    2   2    1    2   2
                    p5*p6*p7*p8 - ---*p6 *p7  + ---*p6 *p8
                                   2             2


        1    3   2          1    3   3       1    2      3
q9=( - ---*p5 *p7 *p8*q8 - ---*p5 *p8 *q8 + ---*p5 *p6*p7 *q8
        8                   8                8

        3    2         2       5       2   2          3       2   3
     - ---*p5 *p6*p7*p8 *q8 + ---*p5*p6 *p7 *p8*q8 - ---*p5*p6 *p8 *q8
        8                      8                      8

        1    3   3       3    3      2        2      2       1       2   3
     - ---*p6 *p7 *q8 + ---*p6 *p7*p8 *q8)/(p5 *p6*p7 *p8 - ---*p5*p6 *p7
        8                8                                   2

       3       2      2    1    3   2       1    3   3
    + ---*p5*p6 *p7*p8  - ---*p6 *p7 *p8 + ---*p6 *p8 )
       2                   2                2

q8, 
     1    3   2          1    3   3       1    2      3
q7=(---*p5 *p7 *p8*q8 + ---*p5 *p8 *q8 - ---*p5 *p6*p7 *q8
     8                   8                8

        3    2         2       5       2   2          3       2   3
     + ---*p5 *p6*p7*p8 *q8 - ---*p5*p6 *p7 *p8*q8 + ---*p5*p6 *p8 *q8
        8                      8                      8

        1    3   3       3    3      2        2      2       1       2   3
     + ---*p6 *p7 *q8 - ---*p6 *p7*p8 *q8)/(p5 *p6*p7 *p8 - ---*p5*p6 *p7
        8                8                                   2

       3       2      2    1    3   2       1    3   3
    + ---*p5*p6 *p7*p8  - ---*p6 *p7 *p8 + ---*p6 *p8 )
       2                   2                2


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, p6, p5, 
p4=p5


p3= - p6


p2=0


p1=0


with 163 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_325(2a)
6 constants : p5,p6,p7,p8,q8,q26
The equation: 

f = - D f*D D f*p6 + D f*f *p5 + D D f  *p7 + D D f*D f*p5 + D f*f *p6 + f  *p8
 t     2   1 2        2   x       1 2 2x       1 2   1        1   x       3x
The symmetry: 
     1                2      3   2       1                2         4
f =(---*D f  *D D f*p5 *p6*p7 *p8 *q8 + ---*D f  *D D f*p5 *p6*p7*p8 *q8
 s   4   2 2x  1 2                       4   2 2x  1 2

        1                   2   4          1                   2   2   3
     + ---*D f  *D D f*p5*p6 *p7 *p8*q8 + ---*D f  *D D f*p5*p6 *p7 *p8 *q8
        2   2 2x  1 2                      2   2 2x  1 2

        1                3   5       1                3   3   2
     - ---*D f  *D D f*p6 *p7 *q8 + ---*D f  *D D f*p6 *p7 *p8 *q8
        4   2 2x  1 2                4   2 2x  1 2

        1                3      4       1             2      4
     + ---*D f  *D D f*p6 *p7*p8 *q8 - ---*D f  *f *p5 *p6*p7 *p8*q8
        2   2 2x  1 2                   4   2 2x  x

        1             2      2   3       1                2   5
     - ---*D f  *f *p5 *p6*p7 *p8 *q8 + ---*D f  *f *p5*p6 *p7 *q8
        4   2 2x  x                      4   2 2x  x

        1                2      4       1             3   4
     - ---*D f  *f *p5*p6 *p7*p8 *q8 + ---*D f  *f *p6 *p7 *p8*q8
        4   2 2x  x                     4   2 2x  x

        1             3   2   3       5                4      2
     + ---*D f  *f *p6 *p7 *p8 *q8 - ---*D f *D D f *p5 *p6*p7 *p8*q26
        4   2 2x  x                   3   2 x  1 2 x

        5                3   2   3        5                3   2      2
     + ---*D f *D D f *p5 *p6 *p7 *q26 - ---*D f *D D f *p5 *p6 *p7*p8 *q26
        6   2 x  1 2 x                    2   2 x  1 2 x

        1                3   4          1                3   5
     - ---*D f *D D f *p5 *p7 *p8*q8 + ---*D f *D D f *p5 *p8 *q8
        4   2 x  1 2 x                  4   2 x  1 2 x

        5                2   3   2           5                2   3   3
     - ---*D f *D D f *p5 *p6 *p7 *p8*q26 - ---*D f *D D f *p5 *p6 *p8 *q26
        6   2 x  1 2 x                       6   2 x  1 2 x

        1                2      5       1                2      3   2
     + ---*D f *D D f *p5 *p6*p7 *q8 + ---*D f *D D f *p5 *p6*p7 *p8 *q8
        4   2 x  1 2 x                  4   2 x  1 2 x

        5                   4   3        5                   4      2
     + ---*D f *D D f *p5*p6 *p7 *q26 - ---*D f *D D f *p5*p6 *p7*p8 *q26
        6   2 x  1 2 x                   2   2 x  1 2 x

        1                   2   4          1                   2   2   3
     + ---*D f *D D f *p5*p6 *p7 *p8*q8 + ---*D f *D D f *p5*p6 *p7 *p8 *q8
        4   2 x  1 2 x                     2   2 x  1 2 x

        1                   2   5       5                5   2
     + ---*D f *D D f *p5*p6 *p8 *q8 + ---*D f *D D f *p6 *p7 *p8*q26
        4   2 x  1 2 x                  6   2 x  1 2 x

        5                5   3        1                3   3   2
     - ---*D f *D D f *p6 *p8 *q26 + ---*D f *D D f *p6 *p7 *p8 *q8
        6   2 x  1 2 x                4   2 x  1 2 x

        1                3      4       1             2      4
     + ---*D f *D D f *p6 *p7*p8 *q8 - ---*D f *f  *p5 *p6*p7 *p8*q8
        4   2 x  1 2 x                  4   2 x  2x

        1             2      2   3       1                2   5
     - ---*D f *f  *p5 *p6*p7 *p8 *q8 + ---*D f *f  *p5*p6 *p7 *q8
        4   2 x  2x                      4   2 x  2x

        1                2      4       1             3   4
     - ---*D f *f  *p5*p6 *p7*p8 *q8 + ---*D f *f  *p6 *p7 *p8*q8
        4   2 x  2x                     4   2 x  2x

        1             3   2   3       1       2         3      3
     + ---*D f *f  *p6 *p7 *p8 *q8 + ---*(D f) *D D f*p5 *p6*p7 *p8*q8
        4   2 x  2x                   8    2     1 2

        1       2         3         3       1       2         2   2   4
     + ---*(D f) *D D f*p5 *p6*p7*p8 *q8 - ---*(D f) *D D f*p5 *p6 *p7 *q8
        8    2     1 2                      8    2     1 2

        3       2         2   2   2   2       5       2            3   3
     + ---*(D f) *D D f*p5 *p6 *p7 *p8 *q8 - ---*(D f) *D D f*p5*p6 *p7 *p8*q8
        8    2     1 2                        8    2     1 2

        3       2            3      3       1       2         4   4
     + ---*(D f) *D D f*p5*p6 *p7*p8 *q8 + ---*(D f) *D D f*p6 *p7 *q8
        8    2     1 2                      8    2     1 2

        3       2         4   2   2       1       2      2   2   3
     - ---*(D f) *D D f*p6 *p7 *p8 *q8 + ---*(D f) *f *p5 *p6 *p7 *p8*q8
        8    2     1 2                    2    2     x

        1       2         3   4       3       2         3   2   2
     - ---*(D f) *f *p5*p6 *p7 *q8 + ---*(D f) *f *p5*p6 *p7 *p8 *q8
        4    2     x                  4    2     x

        1       2      4   3          1       2      4      3
     - ---*(D f) *f *p6 *p7 *p8*q8 + ---*(D f) *f *p6 *p7*p8 *q8
        4    2     x                  4    2     x

        1                2      3   2       1                2         4
     + ---*D f*D D f  *p5 *p6*p7 *p8 *q8 + ---*D f*D D f  *p5 *p6*p7*p8 *q8
        4   2   1 2 2x                      4   2   1 2 2x

        1                   2   4          1                   2   2   3
     + ---*D f*D D f  *p5*p6 *p7 *p8*q8 + ---*D f*D D f  *p5*p6 *p7 *p8 *q8
        2   2   1 2 2x                     2   2   1 2 2x

        1                3   5       1                3   3   2
     - ---*D f*D D f  *p6 *p7 *q8 + ---*D f*D D f  *p6 *p7 *p8 *q8
        4   2   1 2 2x               4   2   1 2 2x

        1                3      4                      2   2   3
     + ---*D f*D D f  *p6 *p7*p8 *q8 + D f*D D f*D f*p5 *p6 *p7 *p8*q8
        2   2   1 2 2x                  2   1 2   1

        1                     3   4       3                     3   2   2
     - ---*D f*D D f*D f*p5*p6 *p7 *q8 + ---*D f*D D f*D f*p5*p6 *p7 *p8 *q8
        2   2   1 2   1                   2   2   1 2   1

        1                  4   3          1                  4      3
     - ---*D f*D D f*D f*p6 *p7 *p8*q8 + ---*D f*D D f*D f*p6 *p7*p8 *q8
        2   2   1 2   1                   2   2   1 2   1

        1               3      3          1               3         3
     - ---*D f*D f*f *p5 *p6*p7 *p8*q8 - ---*D f*D f*f *p5 *p6*p7*p8 *q8
        4   2   1   x                     4   2   1   x

        1               2   2   4       3               2   2   2   2
     + ---*D f*D f*f *p5 *p6 *p7 *q8 - ---*D f*D f*f *p5 *p6 *p7 *p8 *q8
        4   2   1   x                   4   2   1   x

        5                  3   3          3                  3      3
     + ---*D f*D f*f *p5*p6 *p7 *p8*q8 - ---*D f*D f*f *p5*p6 *p7*p8 *q8
        4   2   1   x                     4   2   1   x

        1               4   4       3               4   2   2
     - ---*D f*D f*f *p6 *p7 *q8 + ---*D f*D f*f *p6 *p7 *p8 *q8
        4   2   1   x               4   2   1   x

        1            2      4          1            2      2   3
     - ---*D f*f  *p5 *p6*p7 *p8*q8 - ---*D f*f  *p5 *p6*p7 *p8 *q8
        4   2   3x                     4   2   3x

        1               2   5       1               2      4
     + ---*D f*f  *p5*p6 *p7 *q8 - ---*D f*f  *p5*p6 *p7*p8 *q8
        4   2   3x                  4   2   3x

        1            3   4          1            3   2   3
     + ---*D f*f  *p6 *p7 *p8*q8 + ---*D f*f  *p6 *p7 *p8 *q8
        4   2   3x                  4   2   3x

                 2   2   3           1               3   4
     + D D f  *p5 *p6 *p7 *p8*q26 - ---*D D f  *p5*p6 *p7 *q26
        1 2 4x                       2   1 2 4x

        3               3   2   2        1            4   3
     + ---*D D f  *p5*p6 *p7 *p8 *q26 - ---*D D f  *p6 *p7 *p8*q26
        2   1 2 4x                       2   1 2 4x

        1            4      3        1                2      4
     + ---*D D f  *p6 *p7*p8 *q26 - ---*D D f  *D f*p5 *p6*p7 *p8*q8
        2   1 2 4x                   4   1 2 2x  1

        1                2      2   3       1                   2   5
     - ---*D D f  *D f*p5 *p6*p7 *p8 *q8 + ---*D D f  *D f*p5*p6 *p7 *q8
        4   1 2 2x  1                       4   1 2 2x  1

        1                   2      4       1                3   4
     - ---*D D f  *D f*p5*p6 *p7*p8 *q8 + ---*D D f  *D f*p6 *p7 *p8*q8
        4   1 2 2x  1                      4   1 2 2x  1

        1                3   2   3       1                2      4
     + ---*D D f  *D f*p6 *p7 *p8 *q8 - ---*D D f *D f *p5 *p6*p7 *p8*q8
        4   1 2 2x  1                    4   1 2 x  1 x

        1                2      2   3       1                   2   5
     - ---*D D f *D f *p5 *p6*p7 *p8 *q8 + ---*D D f *D f *p5*p6 *p7 *q8
        4   1 2 x  1 x                      4   1 2 x  1 x

        1                   2      4       1                3   4
     - ---*D D f *D f *p5*p6 *p7*p8 *q8 + ---*D D f *D f *p6 *p7 *p8*q8
        4   1 2 x  1 x                     4   1 2 x  1 x

        1                3   2   3       1                2      4
     + ---*D D f *D f *p6 *p7 *p8 *q8 - ---*D D f*D f  *p5 *p6*p7 *p8*q8
        4   1 2 x  1 x                   4   1 2   1 2x

        1                2      2   3       1                   2   5
     - ---*D D f*D f  *p5 *p6*p7 *p8 *q8 + ---*D D f*D f  *p5*p6 *p7 *q8
        4   1 2   1 2x                      4   1 2   1 2x

        1                   2      4       1                3   4
     - ---*D D f*D f  *p5*p6 *p7*p8 *q8 + ---*D D f*D f  *p6 *p7 *p8*q8
        4   1 2   1 2x                     4   1 2   1 2x

        1                3   2   3       1             2   3      3
     + ---*D D f*D f  *p6 *p7 *p8 *q8 - ---*D D f*(D f) *p5 *p6*p7 *p8*q8
        4   1 2   1 2x                   8   1 2    1

        1             2   3         3       1             2   2   2   4
     - ---*D D f*(D f) *p5 *p6*p7*p8 *q8 + ---*D D f*(D f) *p5 *p6 *p7 *q8
        8   1 2    1                        8   1 2    1

        3             2   2   2   2   2       5             2      3   3
     - ---*D D f*(D f) *p5 *p6 *p7 *p8 *q8 + ---*D D f*(D f) *p5*p6 *p7 *p8*q8
        8   1 2    1                          8   1 2    1

        3             2      3      3       1             2   4   4
     - ---*D D f*(D f) *p5*p6 *p7*p8 *q8 - ---*D D f*(D f) *p6 *p7 *q8
        8   1 2    1                        8   1 2    1

        3             2   4   2   2       1             2      3   2
     + ---*D D f*(D f) *p6 *p7 *p8 *q8 - ---*D f  *f *p5 *p6*p7 *p8 *q8
        8   1 2    1                      4   1 2x  x

        1             2         4       1                2   4
     - ---*D f  *f *p5 *p6*p7*p8 *q8 - ---*D f  *f *p5*p6 *p7 *p8*q8
        4   1 2x  x                     2   1 2x  x

        1                2   2   3       1             3   5
     - ---*D f  *f *p5*p6 *p7 *p8 *q8 + ---*D f  *f *p6 *p7 *q8
        2   1 2x  x                      4   1 2x  x

        1             3   3   2       1             3      4
     - ---*D f  *f *p6 *p7 *p8 *q8 - ---*D f  *f *p6 *p7*p8 *q8
        4   1 2x  x                   2   1 2x  x

        5             4      2           5             3   2   3
     + ---*D f *f  *p5 *p6*p7 *p8*q26 - ---*D f *f  *p5 *p6 *p7 *q26
        3   1 x  2x                      6   1 x  2x

        5             3   2      2        1             3   4
     + ---*D f *f  *p5 *p6 *p7*p8 *q26 + ---*D f *f  *p5 *p7 *p8*q8
        2   1 x  2x                       4   1 x  2x

        1             3   5       5             2   3   2
     - ---*D f *f  *p5 *p8 *q8 + ---*D f *f  *p5 *p6 *p7 *p8*q26
        4   1 x  2x               6   1 x  2x

        5             2   3   3        1             2      5
     + ---*D f *f  *p5 *p6 *p8 *q26 - ---*D f *f  *p5 *p6*p7 *q8
        6   1 x  2x                    4   1 x  2x

        1             2      3   2       5                4   3
     - ---*D f *f  *p5 *p6*p7 *p8 *q8 - ---*D f *f  *p5*p6 *p7 *q26
        4   1 x  2x                      6   1 x  2x

        5                4      2        1                2   4
     + ---*D f *f  *p5*p6 *p7*p8 *q26 - ---*D f *f  *p5*p6 *p7 *p8*q8
        2   1 x  2x                      4   1 x  2x

        1                2   2   3       1                2   5
     - ---*D f *f  *p5*p6 *p7 *p8 *q8 - ---*D f *f  *p5*p6 *p8 *q8
        2   1 x  2x                      4   1 x  2x

        5             5   2           5             5   3
     - ---*D f *f  *p6 *p7 *p8*q26 + ---*D f *f  *p6 *p8 *q26
        6   1 x  2x                   6   1 x  2x

        1             3   3   2       1             3      4
     - ---*D f *f  *p6 *p7 *p8 *q8 - ---*D f *f  *p6 *p7*p8 *q8
        4   1 x  2x                   4   1 x  2x

        1       2      2   2   3          1       2         3   4
     - ---*(D f) *f *p5 *p6 *p7 *p8*q8 + ---*(D f) *f *p5*p6 *p7 *q8
        2    1     x                      4    1     x

        3       2         3   2   2       1       2      4   3
     - ---*(D f) *f *p5*p6 *p7 *p8 *q8 + ---*(D f) *f *p6 *p7 *p8*q8
        4    1     x                      4    1     x

        1       2      4      3       1            2      3   2
     - ---*(D f) *f *p6 *p7*p8 *q8 - ---*D f*f  *p5 *p6*p7 *p8 *q8
        4    1     x                  4   1   3x

        1            2         4       1               2   4
     - ---*D f*f  *p5 *p6*p7*p8 *q8 - ---*D f*f  *p5*p6 *p7 *p8*q8
        4   1   3x                     2   1   3x

        1               2   2   3       1            3   5
     - ---*D f*f  *p5*p6 *p7 *p8 *q8 + ---*D f*f  *p6 *p7 *q8
        2   1   3x                      4   1   3x

        1            3   3   2       1            3      4
     - ---*D f*f  *p6 *p7 *p8 *q8 - ---*D f*f  *p6 *p7*p8 *q8
        4   1   3x                   2   1   3x

             3      3           1        2   2   4
     + f  *p5 *p6*p7 *p8*q26 - ---*f  *p5 *p6 *p7 *q26
        5x                      2   5x

        3        2   2   2   2        3         2   5
     + ---*f  *p5 *p6 *p7 *p8 *q26 + ----*f  *p5 *p7 *p8*q8
        2   5x                        20   5x

        3         2      5       1           3   3
     - ----*f  *p5 *p7*p8 *q8 - ---*f  *p5*p6 *p7 *p8*q26
        20   5x                  2   5x

        1           3      3        3               6
     + ---*f  *p5*p6 *p7*p8 *q26 - ----*f  *p5*p6*p7 *q8
        2   5x                      20   5x

        3               4   2       3               2   4
     - ----*f  *p5*p6*p7 *p8 *q8 - ----*f  *p5*p6*p7 *p8 *q8
        10   5x                     20   5x

        3         2   3   3       3         2      5        2   2   3
     - ----*f  *p6 *p7 *p8 *q8 - ----*f  *p6 *p7*p8 *q8)/(p5 *p6 *p7 *p8
        10   5x                   10   5x

       1       3   4    3       3   2   2    1    4   3       1    4      3
    - ---*p5*p6 *p7  + ---*p5*p6 *p7 *p8  - ---*p6 *p7 *p8 + ---*p6 *p7*p8 )
       2                2                    2                2
And now in machine readable form:

The system: 

df(f(1),t)= - d(2,f(1))*d(1,d(2,f(1)))*p6 + d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,df
(f(1),x,2)))*p7 + d(1,d(2,f(1)))*d(1,f(1))*p5 + d(1,f(1))*df(f(1),x)*p6 + df(f(1
),x,3)*p8$
The symmetry: 
df(f(1),s)=(1/4*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5**2*p6*p7**3*p8**2*q8 + 1/4*d
(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5**2*p6*p7*p8**4*q8 + 1/2*d(2,df(f(1),x,2))*d(1
,d(2,f(1)))*p5*p6**2*p7**4*p8*q8 + 1/2*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5*p6**2
*p7**2*p8**3*q8 - 1/4*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p6**3*p7**5*q8 + 1/4*d(2,
df(f(1),x,2))*d(1,d(2,f(1)))*p6**3*p7**3*p8**2*q8 + 1/2*d(2,df(f(1),x,2))*d(1,d(
2,f(1)))*p6**3*p7*p8**4*q8 - 1/4*d(2,df(f(1),x,2))*df(f(1),x)*p5**2*p6*p7**4*p8*
q8 - 1/4*d(2,df(f(1),x,2))*df(f(1),x)*p5**2*p6*p7**2*p8**3*q8 + 1/4*d(2,df(f(1),
x,2))*df(f(1),x)*p5*p6**2*p7**5*q8 - 1/4*d(2,df(f(1),x,2))*df(f(1),x)*p5*p6**2*
p7*p8**4*q8 + 1/4*d(2,df(f(1),x,2))*df(f(1),x)*p6**3*p7**4*p8*q8 + 1/4*d(2,df(f(
1),x,2))*df(f(1),x)*p6**3*p7**2*p8**3*q8 - 5/3*d(2,df(f(1),x))*d(1,d(2,df(f(1),x
)))*p5**4*p6*p7**2*p8*q26 + 5/6*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**3*p6**2
*p7**3*q26 - 5/2*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**3*p6**2*p7*p8**2*q26 -
 1/4*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**3*p7**4*p8*q8 + 1/4*d(2,df(f(1),x)
)*d(1,d(2,df(f(1),x)))*p5**3*p8**5*q8 - 5/6*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))
*p5**2*p6**3*p7**2*p8*q26 - 5/6*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**2*p6**3
*p8**3*q26 + 1/4*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**2*p6*p7**5*q8 + 1/4*d(
2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**2*p6*p7**3*p8**2*q8 + 5/6*d(2,df(f(1),x))
*d(1,d(2,df(f(1),x)))*p5*p6**4*p7**3*q26 - 5/2*d(2,df(f(1),x))*d(1,d(2,df(f(1),x
)))*p5*p6**4*p7*p8**2*q26 + 1/4*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5*p6**2*p7
**4*p8*q8 + 1/2*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5*p6**2*p7**2*p8**3*q8 + 1
/4*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5*p6**2*p8**5*q8 + 5/6*d(2,df(f(1),x))*
d(1,d(2,df(f(1),x)))*p6**5*p7**2*p8*q26 - 5/6*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)
))*p6**5*p8**3*q26 + 1/4*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6**3*p7**3*p8**2*
q8 + 1/4*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6**3*p7*p8**4*q8 - 1/4*d(2,df(f(1
),x))*df(f(1),x,2)*p5**2*p6*p7**4*p8*q8 - 1/4*d(2,df(f(1),x))*df(f(1),x,2)*p5**2
*p6*p7**2*p8**3*q8 + 1/4*d(2,df(f(1),x))*df(f(1),x,2)*p5*p6**2*p7**5*q8 - 1/4*d(
2,df(f(1),x))*df(f(1),x,2)*p5*p6**2*p7*p8**4*q8 + 1/4*d(2,df(f(1),x))*df(f(1),x,
2)*p6**3*p7**4*p8*q8 + 1/4*d(2,df(f(1),x))*df(f(1),x,2)*p6**3*p7**2*p8**3*q8 + 1
/8*d(2,f(1))**2*d(1,d(2,f(1)))*p5**3*p6*p7**3*p8*q8 + 1/8*d(2,f(1))**2*d(1,d(2,f
(1)))*p5**3*p6*p7*p8**3*q8 - 1/8*d(2,f(1))**2*d(1,d(2,f(1)))*p5**2*p6**2*p7**4*
q8 + 3/8*d(2,f(1))**2*d(1,d(2,f(1)))*p5**2*p6**2*p7**2*p8**2*q8 - 5/8*d(2,f(1))
**2*d(1,d(2,f(1)))*p5*p6**3*p7**3*p8*q8 + 3/8*d(2,f(1))**2*d(1,d(2,f(1)))*p5*p6
**3*p7*p8**3*q8 + 1/8*d(2,f(1))**2*d(1,d(2,f(1)))*p6**4*p7**4*q8 - 3/8*d(2,f(1))
**2*d(1,d(2,f(1)))*p6**4*p7**2*p8**2*q8 + 1/2*d(2,f(1))**2*df(f(1),x)*p5**2*p6**
2*p7**3*p8*q8 - 1/4*d(2,f(1))**2*df(f(1),x)*p5*p6**3*p7**4*q8 + 3/4*d(2,f(1))**2
*df(f(1),x)*p5*p6**3*p7**2*p8**2*q8 - 1/4*d(2,f(1))**2*df(f(1),x)*p6**4*p7**3*p8
*q8 + 1/4*d(2,f(1))**2*df(f(1),x)*p6**4*p7*p8**3*q8 + 1/4*d(2,f(1))*d(1,d(2,df(f
(1),x,2)))*p5**2*p6*p7**3*p8**2*q8 + 1/4*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p5**2*
p6*p7*p8**4*q8 + 1/2*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p5*p6**2*p7**4*p8*q8 + 1/2
*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p5*p6**2*p7**2*p8**3*q8 - 1/4*d(2,f(1))*d(1,d(
2,df(f(1),x,2)))*p6**3*p7**5*q8 + 1/4*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p6**3*p7
**3*p8**2*q8 + 1/2*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p6**3*p7*p8**4*q8 + d(2,f(1)
)*d(1,d(2,f(1)))*d(1,f(1))*p5**2*p6**2*p7**3*p8*q8 - 1/2*d(2,f(1))*d(1,d(2,f(1))
)*d(1,f(1))*p5*p6**3*p7**4*q8 + 3/2*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p5*p6**3*
p7**2*p8**2*q8 - 1/2*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p6**4*p7**3*p8*q8 + 1/2*
d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p6**4*p7*p8**3*q8 - 1/4*d(2,f(1))*d(1,f(1))*
df(f(1),x)*p5**3*p6*p7**3*p8*q8 - 1/4*d(2,f(1))*d(1,f(1))*df(f(1),x)*p5**3*p6*p7
*p8**3*q8 + 1/4*d(2,f(1))*d(1,f(1))*df(f(1),x)*p5**2*p6**2*p7**4*q8 - 3/4*d(2,f(
1))*d(1,f(1))*df(f(1),x)*p5**2*p6**2*p7**2*p8**2*q8 + 5/4*d(2,f(1))*d(1,f(1))*df
(f(1),x)*p5*p6**3*p7**3*p8*q8 - 3/4*d(2,f(1))*d(1,f(1))*df(f(1),x)*p5*p6**3*p7*
p8**3*q8 - 1/4*d(2,f(1))*d(1,f(1))*df(f(1),x)*p6**4*p7**4*q8 + 3/4*d(2,f(1))*d(1
,f(1))*df(f(1),x)*p6**4*p7**2*p8**2*q8 - 1/4*d(2,f(1))*df(f(1),x,3)*p5**2*p6*p7
**4*p8*q8 - 1/4*d(2,f(1))*df(f(1),x,3)*p5**2*p6*p7**2*p8**3*q8 + 1/4*d(2,f(1))*
df(f(1),x,3)*p5*p6**2*p7**5*q8 - 1/4*d(2,f(1))*df(f(1),x,3)*p5*p6**2*p7*p8**4*q8
 + 1/4*d(2,f(1))*df(f(1),x,3)*p6**3*p7**4*p8*q8 + 1/4*d(2,f(1))*df(f(1),x,3)*p6
**3*p7**2*p8**3*q8 + d(1,d(2,df(f(1),x,4)))*p5**2*p6**2*p7**3*p8*q26 - 1/2*d(1,d
(2,df(f(1),x,4)))*p5*p6**3*p7**4*q26 + 3/2*d(1,d(2,df(f(1),x,4)))*p5*p6**3*p7**2
*p8**2*q26 - 1/2*d(1,d(2,df(f(1),x,4)))*p6**4*p7**3*p8*q26 + 1/2*d(1,d(2,df(f(1)
,x,4)))*p6**4*p7*p8**3*q26 - 1/4*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p5**2*p6*p7**4
*p8*q8 - 1/4*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p5**2*p6*p7**2*p8**3*q8 + 1/4*d(1,
d(2,df(f(1),x,2)))*d(1,f(1))*p5*p6**2*p7**5*q8 - 1/4*d(1,d(2,df(f(1),x,2)))*d(1,
f(1))*p5*p6**2*p7*p8**4*q8 + 1/4*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p6**3*p7**4*p8
*q8 + 1/4*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p6**3*p7**2*p8**3*q8 - 1/4*d(1,d(2,df
(f(1),x)))*d(1,df(f(1),x))*p5**2*p6*p7**4*p8*q8 - 1/4*d(1,d(2,df(f(1),x)))*d(1,
df(f(1),x))*p5**2*p6*p7**2*p8**3*q8 + 1/4*d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*
p5*p6**2*p7**5*q8 - 1/4*d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p5*p6**2*p7*p8**4*
q8 + 1/4*d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p6**3*p7**4*p8*q8 + 1/4*d(1,d(2,df
(f(1),x)))*d(1,df(f(1),x))*p6**3*p7**2*p8**3*q8 - 1/4*d(1,d(2,f(1)))*d(1,df(f(1)
,x,2))*p5**2*p6*p7**4*p8*q8 - 1/4*d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p5**2*p6*p7**
2*p8**3*q8 + 1/4*d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p5*p6**2*p7**5*q8 - 1/4*d(1,d(
2,f(1)))*d(1,df(f(1),x,2))*p5*p6**2*p7*p8**4*q8 + 1/4*d(1,d(2,f(1)))*d(1,df(f(1)
,x,2))*p6**3*p7**4*p8*q8 + 1/4*d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p6**3*p7**2*p8**
3*q8 - 1/8*d(1,d(2,f(1)))*d(1,f(1))**2*p5**3*p6*p7**3*p8*q8 - 1/8*d(1,d(2,f(1)))
*d(1,f(1))**2*p5**3*p6*p7*p8**3*q8 + 1/8*d(1,d(2,f(1)))*d(1,f(1))**2*p5**2*p6**2
*p7**4*q8 - 3/8*d(1,d(2,f(1)))*d(1,f(1))**2*p5**2*p6**2*p7**2*p8**2*q8 + 5/8*d(1
,d(2,f(1)))*d(1,f(1))**2*p5*p6**3*p7**3*p8*q8 - 3/8*d(1,d(2,f(1)))*d(1,f(1))**2*
p5*p6**3*p7*p8**3*q8 - 1/8*d(1,d(2,f(1)))*d(1,f(1))**2*p6**4*p7**4*q8 + 3/8*d(1,
d(2,f(1)))*d(1,f(1))**2*p6**4*p7**2*p8**2*q8 - 1/4*d(1,df(f(1),x,2))*df(f(1),x)*
p5**2*p6*p7**3*p8**2*q8 - 1/4*d(1,df(f(1),x,2))*df(f(1),x)*p5**2*p6*p7*p8**4*q8 
- 1/2*d(1,df(f(1),x,2))*df(f(1),x)*p5*p6**2*p7**4*p8*q8 - 1/2*d(1,df(f(1),x,2))*
df(f(1),x)*p5*p6**2*p7**2*p8**3*q8 + 1/4*d(1,df(f(1),x,2))*df(f(1),x)*p6**3*p7**
5*q8 - 1/4*d(1,df(f(1),x,2))*df(f(1),x)*p6**3*p7**3*p8**2*q8 - 1/2*d(1,df(f(1),x
,2))*df(f(1),x)*p6**3*p7*p8**4*q8 + 5/3*d(1,df(f(1),x))*df(f(1),x,2)*p5**4*p6*p7
**2*p8*q26 - 5/6*d(1,df(f(1),x))*df(f(1),x,2)*p5**3*p6**2*p7**3*q26 + 5/2*d(1,df
(f(1),x))*df(f(1),x,2)*p5**3*p6**2*p7*p8**2*q26 + 1/4*d(1,df(f(1),x))*df(f(1),x,
2)*p5**3*p7**4*p8*q8 - 1/4*d(1,df(f(1),x))*df(f(1),x,2)*p5**3*p8**5*q8 + 5/6*d(1
,df(f(1),x))*df(f(1),x,2)*p5**2*p6**3*p7**2*p8*q26 + 5/6*d(1,df(f(1),x))*df(f(1)
,x,2)*p5**2*p6**3*p8**3*q26 - 1/4*d(1,df(f(1),x))*df(f(1),x,2)*p5**2*p6*p7**5*q8
 - 1/4*d(1,df(f(1),x))*df(f(1),x,2)*p5**2*p6*p7**3*p8**2*q8 - 5/6*d(1,df(f(1),x)
)*df(f(1),x,2)*p5*p6**4*p7**3*q26 + 5/2*d(1,df(f(1),x))*df(f(1),x,2)*p5*p6**4*p7
*p8**2*q26 - 1/4*d(1,df(f(1),x))*df(f(1),x,2)*p5*p6**2*p7**4*p8*q8 - 1/2*d(1,df(
f(1),x))*df(f(1),x,2)*p5*p6**2*p7**2*p8**3*q8 - 1/4*d(1,df(f(1),x))*df(f(1),x,2)
*p5*p6**2*p8**5*q8 - 5/6*d(1,df(f(1),x))*df(f(1),x,2)*p6**5*p7**2*p8*q26 + 5/6*d
(1,df(f(1),x))*df(f(1),x,2)*p6**5*p8**3*q26 - 1/4*d(1,df(f(1),x))*df(f(1),x,2)*
p6**3*p7**3*p8**2*q8 - 1/4*d(1,df(f(1),x))*df(f(1),x,2)*p6**3*p7*p8**4*q8 - 1/2*
d(1,f(1))**2*df(f(1),x)*p5**2*p6**2*p7**3*p8*q8 + 1/4*d(1,f(1))**2*df(f(1),x)*p5
*p6**3*p7**4*q8 - 3/4*d(1,f(1))**2*df(f(1),x)*p5*p6**3*p7**2*p8**2*q8 + 1/4*d(1,
f(1))**2*df(f(1),x)*p6**4*p7**3*p8*q8 - 1/4*d(1,f(1))**2*df(f(1),x)*p6**4*p7*p8
**3*q8 - 1/4*d(1,f(1))*df(f(1),x,3)*p5**2*p6*p7**3*p8**2*q8 - 1/4*d(1,f(1))*df(f
(1),x,3)*p5**2*p6*p7*p8**4*q8 - 1/2*d(1,f(1))*df(f(1),x,3)*p5*p6**2*p7**4*p8*q8 
- 1/2*d(1,f(1))*df(f(1),x,3)*p5*p6**2*p7**2*p8**3*q8 + 1/4*d(1,f(1))*df(f(1),x,3
)*p6**3*p7**5*q8 - 1/4*d(1,f(1))*df(f(1),x,3)*p6**3*p7**3*p8**2*q8 - 1/2*d(1,f(1
))*df(f(1),x,3)*p6**3*p7*p8**4*q8 + df(f(1),x,5)*p5**3*p6*p7**3*p8*q26 - 1/2*df(
f(1),x,5)*p5**2*p6**2*p7**4*q26 + 3/2*df(f(1),x,5)*p5**2*p6**2*p7**2*p8**2*q26 +
 3/20*df(f(1),x,5)*p5**2*p7**5*p8*q8 - 3/20*df(f(1),x,5)*p5**2*p7*p8**5*q8 - 1/2
*df(f(1),x,5)*p5*p6**3*p7**3*p8*q26 + 1/2*df(f(1),x,5)*p5*p6**3*p7*p8**3*q26 - 3
/20*df(f(1),x,5)*p5*p6*p7**6*q8 - 3/10*df(f(1),x,5)*p5*p6*p7**4*p8**2*q8 - 3/20*
df(f(1),x,5)*p5*p6*p7**2*p8**4*q8 - 3/10*df(f(1),x,5)*p6**2*p7**3*p8**3*q8 - 3/
10*df(f(1),x,5)*p6**2*p7*p8**5*q8)/(p5**2*p6**2*p7**3*p8 - 1/2*p5*p6**3*p7**4 + 
3/2*p5*p6**3*p7**2*p8**2 - 1/2*p6**4*p7**3*p8 + 1/2*p6**4*p7*p8**3)$

Time: 0 ms

Time: 0 ms

Time: 10 ms

New level : 1.1.2.2.1.1.3.1.1.2.2.
now back to the substitution of q26 by e_477
The list of inequalities got extended by: 

  2     2
p5  + p6


Step 1467: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 114 terms

The list of inequalities got extended by: 
An expression with 102 terms

The list of inequalities got extended by: 
An expression with 122 terms

The list of inequalities got extended by: 
An expression with 62 terms

Substitution of q26 by an expression in 
q10, q8, p8, p5, p6, p7 found in e_477 : 60 factors in 10 terms


>>>>>>>>> Solution of level 1.1.2.2.1.1.3.1.1.2.2. : 
no equations


Non-vanishing expressions: p8,p5,p6,p7,p4
276 factors in 62 terms
650 factors in 122 terms
533 factors in 102 terms
593 factors in 114 terms

p5*p7 + p6*p8


g0111*p8 + g0112*p7 + g0113*p6 + g0114*p5 + g0115*p5 - g0116*p6


  2     2
p5  + p6


functions : 
      6    2              6          2        6          2        3       3
q27=(---*p5 *p7*p8*q10 - ---*p5*p6*p7 *q10 + ---*p5*p6*p8 *q10 - ---*p5*p7 *q8
      5                   5                   5                   5

         3          2       6    2              3       2          3       3
      - ---*p5*p7*p8 *q8 - ---*p6 *p7*p8*q10 - ---*p6*p7 *p8*q8 - ---*p6*p8 *q8)
         5                  5                   5                  5

    3        2              2        3
/(p5 *p7 + p5 *p6*p8 + p5*p6 *p7 + p6 *p8)


      3    2   2        3    2   2        12                     3       2
q26=(---*p5 *p7 *q10 - ---*p5 *p8 *q10 + ----*p5*p6*p7*p8*q10 + ---*p5*p7 *p8*q8
      5                 5                 5                      5

         3       3       3    2   2        3    2   2        3       3
      + ---*p5*p8 *q8 - ---*p6 *p7 *q10 + ---*p6 *p8 *q10 - ---*p6*p7 *q8
         5               5                 5                 5

         3          2        3        2              2        3
      - ---*p6*p7*p8 *q8)/(p5 *p7 + p5 *p6*p8 + p5*p6 *p7 + p6 *p8)
         5


q25=0


q24=q10


                                  2        2
      - p5*p8*q10 + p6*p7*q10 + p7 *q8 + p8 *q8
q23=--------------------------------------------
                   p5*p7 + p6*p8


                               2        2
     p5*p8*q10 - p6*p7*q10 - p7 *q8 - p8 *q8
q22=-----------------------------------------
                  p5*p7 + p6*p8


q21=q10


q20=q10


                               2        2
     p5*p8*q10 - p6*p7*q10 - p7 *q8 - p8 *q8
q19=-----------------------------------------
                  p5*p7 + p6*p8


                                  2        2
      - p5*p8*q10 + p6*p7*q10 + p7 *q8 + p8 *q8
q18=--------------------------------------------
                   p5*p7 + p6*p8


q17=q10


q16=q10


                               2        2
     p5*p8*q10 - p6*p7*q10 - p7 *q8 - p8 *q8
q15=-----------------------------------------
                  p5*p7 + p6*p8


        1
q14= - ---*q8
        2


       2                    2
     p5 *q10 - p5*p8*q8 + p6 *q10 + p6*p7*q8
q13=-----------------------------------------
                  p5*p7 + p6*p8


     1
q12=---*q8
     2


                                  2        2
      - p5*p8*q10 + p6*p7*q10 + p7 *q8 + p8 *q8
q11=--------------------------------------------
                   p5*p7 + p6*p8

q10, 
     1    2        1              1    2        1
    ---*p5 *q10 - ---*p5*p8*q8 + ---*p6 *q10 + ---*p6*p7*q8
     2             2              2             2
q9=---------------------------------------------------------
                         p5*p7 + p6*p8

q8, 
        1    2        1              1    2        1
     - ---*p5 *q10 + ---*p5*p8*q8 - ---*p6 *q10 - ---*p6*p7*q8
        2             2              2             2
q7=------------------------------------------------------------
                          p5*p7 + p6*p8


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, p6, p5, 
p4=p5


p3= - p6


p2=0


p1=0


with 97 terms
no equations
6 constants : p5,p6,p7,p8,q8,q10
The equation: 

f = - D f*D D f*p6 + D f*f *p5 + D D f  *p7 + D D f*D f*p5 + D f*f *p6 + f  *p8
 t     2   1 2        2   x       1 2 2x       1 2   1        1   x       3x
The symmetry: 
                     3                        2
f =( - D f  *D D f*p5 *p8*q10 + D f  *D D f*p5 *p6*p7*q10
 s      2 2x  1 2                2 2x  1 2

                     2   2                    2   2
     + D f  *D D f*p5 *p7 *q8 + D f  *D D f*p5 *p8 *q8
        2 2x  1 2                2 2x  1 2

                        2                        3
     - D f  *D D f*p5*p6 *p8*q10 + D f  *D D f*p6 *p7*q10
        2 2x  1 2                   2 2x  1 2

                     2   2                    2   2                 3
     + D f  *D D f*p6 *p7 *q8 + D f  *D D f*p6 *p8 *q8 + D f  *f *p5 *p7*q10
        2 2x  1 2                2 2x  1 2                2 2x  x

                  2                           2                     3
     + D f  *f *p5 *p6*p8*q10 + D f  *f *p5*p6 *p7*q10 + D f  *f *p6 *p8*q10
        2 2x  x                  2 2x  x                  2 2x  x

                     3                        2
     - D f *D D f *p5 *p8*q10 + D f *D D f *p5 *p6*p7*q10
        2 x  1 2 x               2 x  1 2 x

                     2   2                    2   2
     + D f *D D f *p5 *p7 *q8 + D f *D D f *p5 *p8 *q8
        2 x  1 2 x               2 x  1 2 x

                        2                        3
     - D f *D D f *p5*p6 *p8*q10 + D f *D D f *p6 *p7*q10
        2 x  1 2 x                  2 x  1 2 x

                     2   2                    2   2                 3
     + D f *D D f *p6 *p7 *q8 + D f *D D f *p6 *p8 *q8 + D f *f  *p5 *p7*q10
        2 x  1 2 x               2 x  1 2 x               2 x  2x

                  2                           2                     3
     + D f *f  *p5 *p6*p8*q10 + D f *f  *p5*p6 *p7*q10 + D f *f  *p6 *p8*q10
        2 x  2x                  2 x  2x                  2 x  2x

        1       2         4        1       2         3
     - ---*(D f) *D D f*p5 *q10 + ---*(D f) *D D f*p5 *p8*q8
        2    2     1 2             2    2     1 2

            2         2   2        1       2         2
     - (D f) *D D f*p5 *p6 *q10 - ---*(D f) *D D f*p5 *p6*p7*q8
         2     1 2                 2    2     1 2

        1       2            2          1       2         4
     + ---*(D f) *D D f*p5*p6 *p8*q8 - ---*(D f) *D D f*p6 *q10
        2    2     1 2                  2    2     1 2

        1       2         3          1       2      3
     - ---*(D f) *D D f*p6 *p7*q8 + ---*(D f) *f *p5 *p7*q8
        2    2     1 2               2    2     x

        1       2      2             1       2         2
     + ---*(D f) *f *p5 *p6*p8*q8 + ---*(D f) *f *p5*p6 *p7*q8
        2    2     x                 2    2     x

        1       2      3                       3
     + ---*(D f) *f *p6 *p8*q8 - D f*D D f  *p5 *p8*q10
        2    2     x              2   1 2 2x

                     2                           2   2
     + D f*D D f  *p5 *p6*p7*q10 + D f*D D f  *p5 *p7 *q8
        2   1 2 2x                  2   1 2 2x

                     2   2                       2
     + D f*D D f  *p5 *p8 *q8 - D f*D D f  *p5*p6 *p8*q10
        2   1 2 2x               2   1 2 2x

                     3                        2   2                    2   2
     + D f*D D f  *p6 *p7*q10 + D f*D D f  *p6 *p7 *q8 + D f*D D f  *p6 *p8 *q8
        2   1 2 2x               2   1 2 2x               2   1 2 2x

                       3                         2
     + D f*D D f*D f*p5 *p7*q8 + D f*D D f*D f*p5 *p6*p8*q8
        2   1 2   1               2   1 2   1

                          2                         3                      4
     + D f*D D f*D f*p5*p6 *p7*q8 + D f*D D f*D f*p6 *p8*q8 + D f*D f*f *p5 *q10
        2   1 2   1                  2   1 2   1               2   1   x

                    3                        2   2                    2
     - D f*D f*f *p5 *p8*q8 + 2*D f*D f*f *p5 *p6 *q10 + D f*D f*f *p5 *p6*p7*q8
        2   1   x                2   1   x                2   1   x

                       2                      4                    3
     - D f*D f*f *p5*p6 *p8*q8 + D f*D f*f *p6 *q10 + D f*D f*f *p6 *p7*q8
        2   1   x                 2   1   x            2   1   x

                 3                    2                          2
     + D f*f  *p5 *p7*q10 + D f*f  *p5 *p6*p8*q10 + D f*f  *p5*p6 *p7*q10
        2   3x               2   3x                  2   3x

                 3           3            2   2        3            2   2
     + D f*f  *p6 *p8*q10 + ---*D D f  *p5 *p7 *q10 - ---*D D f  *p5 *p8 *q10
        2   3x               5   1 2 4x                5   1 2 4x

        12                             3               2
     + ----*D D f  *p5*p6*p7*p8*q10 + ---*D D f  *p5*p7 *p8*q8
        5    1 2 4x                    5   1 2 4x

        3               3       3            2   2        3            2   2
     + ---*D D f  *p5*p8 *q8 - ---*D D f  *p6 *p7 *q10 + ---*D D f  *p6 *p8 *q10
        5   1 2 4x              5   1 2 4x                5   1 2 4x

        3               3       3                  2                    3
     - ---*D D f  *p6*p7 *q8 - ---*D D f  *p6*p7*p8 *q8 + D D f  *D f*p5 *p7*q10
        5   1 2 4x              5   1 2 4x                 1 2 2x  1

                     2                              2
     + D D f  *D f*p5 *p6*p8*q10 + D D f  *D f*p5*p6 *p7*q10
        1 2 2x  1                   1 2 2x  1

                     3                        3
     + D D f  *D f*p6 *p8*q10 + D D f *D f *p5 *p7*q10
        1 2 2x  1                1 2 x  1 x

                     2                              2
     + D D f *D f *p5 *p6*p8*q10 + D D f *D f *p5*p6 *p7*q10
        1 2 x  1 x                  1 2 x  1 x

                     3                        3
     + D D f *D f *p6 *p8*q10 + D D f*D f  *p5 *p7*q10
        1 2 x  1 x               1 2   1 2x

                     2                              2
     + D D f*D f  *p5 *p6*p8*q10 + D D f*D f  *p5*p6 *p7*q10
        1 2   1 2x                  1 2   1 2x

                     3           1             2   4
     + D D f*D f  *p6 *p8*q10 + ---*D D f*(D f) *p5 *q10
        1 2   1 2x               2   1 2    1

        1             2   3                    2   2   2
     - ---*D D f*(D f) *p5 *p8*q8 + D D f*(D f) *p5 *p6 *q10
        2   1 2    1                 1 2    1

        1             2   2             1             2      2
     + ---*D D f*(D f) *p5 *p6*p7*q8 - ---*D D f*(D f) *p5*p6 *p8*q8
        2   1 2    1                    2   1 2    1

        1             2   4        1             2   3
     + ---*D D f*(D f) *p6 *q10 + ---*D D f*(D f) *p6 *p7*q8
        2   1 2    1               2   1 2    1

                  3                     2                        2   2
     + D f  *f *p5 *p8*q10 - D f  *f *p5 *p6*p7*q10 - D f  *f *p5 *p7 *q8
        1 2x  x               1 2x  x                  1 2x  x

                  2   2                    2                     3
     - D f  *f *p5 *p8 *q8 + D f  *f *p5*p6 *p8*q10 - D f  *f *p6 *p7*q10
        1 2x  x               1 2x  x                  1 2x  x

                  2   2                 2   2                 3
     - D f  *f *p6 *p7 *q8 - D f  *f *p6 *p8 *q8 + D f *f  *p5 *p8*q10
        1 2x  x               1 2x  x               1 x  2x

                  2                        2   2                 2   2
     - D f *f  *p5 *p6*p7*q10 - D f *f  *p5 *p7 *q8 - D f *f  *p5 *p8 *q8
        1 x  2x                  1 x  2x               1 x  2x

                     2                     3                     2   2
     + D f *f  *p5*p6 *p8*q10 - D f *f  *p6 *p7*q10 - D f *f  *p6 *p7 *q8
        1 x  2x                  1 x  2x               1 x  2x

                  2   2       1       2      3
     - D f *f  *p6 *p8 *q8 - ---*(D f) *f *p5 *p7*q8
        1 x  2x               2    1     x

        1       2      2             1       2         2
     - ---*(D f) *f *p5 *p6*p8*q8 - ---*(D f) *f *p5*p6 *p7*q8
        2    1     x                 2    1     x

        1       2      3                   3                    2
     - ---*(D f) *f *p6 *p8*q8 + D f*f  *p5 *p8*q10 - D f*f  *p5 *p6*p7*q10
        2    1     x              1   3x               1   3x

                 2   2                2   2                   2
     - D f*f  *p5 *p7 *q8 - D f*f  *p5 *p8 *q8 + D f*f  *p5*p6 *p8*q10
        1   3x               1   3x               1   3x

                 3                    2   2                2   2
     - D f*f  *p6 *p7*q10 - D f*f  *p6 *p7 *q8 - D f*f  *p6 *p8 *q8
        1   3x               1   3x               1   3x

        6        2              6              2        6              2
     + ---*f  *p5 *p7*p8*q10 - ---*f  *p5*p6*p7 *q10 + ---*f  *p5*p6*p8 *q10
        5   5x                  5   5x                  5   5x

        3           3       3              2       6        2
     - ---*f  *p5*p7 *q8 - ---*f  *p5*p7*p8 *q8 - ---*f  *p6 *p7*p8*q10
        5   5x              5   5x                 5   5x

        3           2          3           3        3        2              2
     - ---*f  *p6*p7 *p8*q8 - ---*f  *p6*p8 *q8)/(p5 *p7 + p5 *p6*p8 + p5*p6 *p7
        5   5x                 5   5x

        3
    + p6 *p8)
And now in machine readable form:

The system: 

df(f(1),t)= - d(2,f(1))*d(1,d(2,f(1)))*p6 + d(2,f(1))*df(f(1),x)*p5 + d(1,d(2,df
(f(1),x,2)))*p7 + d(1,d(2,f(1)))*d(1,f(1))*p5 + d(1,f(1))*df(f(1),x)*p6 + df(f(1
),x,3)*p8$
The symmetry: 
df(f(1),s)=( - d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5**3*p8*q10 + d(2,df(f(1),x,2))
*d(1,d(2,f(1)))*p5**2*p6*p7*q10 + d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5**2*p7**2*
q8 + d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5**2*p8**2*q8 - d(2,df(f(1),x,2))*d(1,d(2
,f(1)))*p5*p6**2*p8*q10 + d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p6**3*p7*q10 + d(2,df
(f(1),x,2))*d(1,d(2,f(1)))*p6**2*p7**2*q8 + d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p6
**2*p8**2*q8 + d(2,df(f(1),x,2))*df(f(1),x)*p5**3*p7*q10 + d(2,df(f(1),x,2))*df(
f(1),x)*p5**2*p6*p8*q10 + d(2,df(f(1),x,2))*df(f(1),x)*p5*p6**2*p7*q10 + d(2,df(
f(1),x,2))*df(f(1),x)*p6**3*p8*q10 - d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**3*
p8*q10 + d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**2*p6*p7*q10 + d(2,df(f(1),x))*
d(1,d(2,df(f(1),x)))*p5**2*p7**2*q8 + d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**2
*p8**2*q8 - d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5*p6**2*p8*q10 + d(2,df(f(1),x
))*d(1,d(2,df(f(1),x)))*p6**3*p7*q10 + d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6**
2*p7**2*q8 + d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6**2*p8**2*q8 + d(2,df(f(1),x
))*df(f(1),x,2)*p5**3*p7*q10 + d(2,df(f(1),x))*df(f(1),x,2)*p5**2*p6*p8*q10 + d(
2,df(f(1),x))*df(f(1),x,2)*p5*p6**2*p7*q10 + d(2,df(f(1),x))*df(f(1),x,2)*p6**3*
p8*q10 - 1/2*d(2,f(1))**2*d(1,d(2,f(1)))*p5**4*q10 + 1/2*d(2,f(1))**2*d(1,d(2,f(
1)))*p5**3*p8*q8 - d(2,f(1))**2*d(1,d(2,f(1)))*p5**2*p6**2*q10 - 1/2*d(2,f(1))**
2*d(1,d(2,f(1)))*p5**2*p6*p7*q8 + 1/2*d(2,f(1))**2*d(1,d(2,f(1)))*p5*p6**2*p8*q8
 - 1/2*d(2,f(1))**2*d(1,d(2,f(1)))*p6**4*q10 - 1/2*d(2,f(1))**2*d(1,d(2,f(1)))*
p6**3*p7*q8 + 1/2*d(2,f(1))**2*df(f(1),x)*p5**3*p7*q8 + 1/2*d(2,f(1))**2*df(f(1)
,x)*p5**2*p6*p8*q8 + 1/2*d(2,f(1))**2*df(f(1),x)*p5*p6**2*p7*q8 + 1/2*d(2,f(1))
**2*df(f(1),x)*p6**3*p8*q8 - d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p5**3*p8*q10 + d(2
,f(1))*d(1,d(2,df(f(1),x,2)))*p5**2*p6*p7*q10 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))
*p5**2*p7**2*q8 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p5**2*p8**2*q8 - d(2,f(1))*d(
1,d(2,df(f(1),x,2)))*p5*p6**2*p8*q10 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p6**3*p7
*q10 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p6**2*p7**2*q8 + d(2,f(1))*d(1,d(2,df(f(
1),x,2)))*p6**2*p8**2*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p5**3*p7*q8 + d(2,
f(1))*d(1,d(2,f(1)))*d(1,f(1))*p5**2*p6*p8*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1
))*p5*p6**2*p7*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p6**3*p8*q8 + d(2,f(1))*d
(1,f(1))*df(f(1),x)*p5**4*q10 - d(2,f(1))*d(1,f(1))*df(f(1),x)*p5**3*p8*q8 + 2*d
(2,f(1))*d(1,f(1))*df(f(1),x)*p5**2*p6**2*q10 + d(2,f(1))*d(1,f(1))*df(f(1),x)*
p5**2*p6*p7*q8 - d(2,f(1))*d(1,f(1))*df(f(1),x)*p5*p6**2*p8*q8 + d(2,f(1))*d(1,f
(1))*df(f(1),x)*p6**4*q10 + d(2,f(1))*d(1,f(1))*df(f(1),x)*p6**3*p7*q8 + d(2,f(1
))*df(f(1),x,3)*p5**3*p7*q10 + d(2,f(1))*df(f(1),x,3)*p5**2*p6*p8*q10 + d(2,f(1)
)*df(f(1),x,3)*p5*p6**2*p7*q10 + d(2,f(1))*df(f(1),x,3)*p6**3*p8*q10 + 3/5*d(1,d
(2,df(f(1),x,4)))*p5**2*p7**2*q10 - 3/5*d(1,d(2,df(f(1),x,4)))*p5**2*p8**2*q10 +
 12/5*d(1,d(2,df(f(1),x,4)))*p5*p6*p7*p8*q10 + 3/5*d(1,d(2,df(f(1),x,4)))*p5*p7
**2*p8*q8 + 3/5*d(1,d(2,df(f(1),x,4)))*p5*p8**3*q8 - 3/5*d(1,d(2,df(f(1),x,4)))*
p6**2*p7**2*q10 + 3/5*d(1,d(2,df(f(1),x,4)))*p6**2*p8**2*q10 - 3/5*d(1,d(2,df(f(
1),x,4)))*p6*p7**3*q8 - 3/5*d(1,d(2,df(f(1),x,4)))*p6*p7*p8**2*q8 + d(1,d(2,df(f
(1),x,2)))*d(1,f(1))*p5**3*p7*q10 + d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p5**2*p6*p8
*q10 + d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p5*p6**2*p7*q10 + d(1,d(2,df(f(1),x,2)))
*d(1,f(1))*p6**3*p8*q10 + d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p5**3*p7*q10 + d(
1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p5**2*p6*p8*q10 + d(1,d(2,df(f(1),x)))*d(1,df
(f(1),x))*p5*p6**2*p7*q10 + d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p6**3*p8*q10 + 
d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p5**3*p7*q10 + d(1,d(2,f(1)))*d(1,df(f(1),x,2))
*p5**2*p6*p8*q10 + d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p5*p6**2*p7*q10 + d(1,d(2,f(
1)))*d(1,df(f(1),x,2))*p6**3*p8*q10 + 1/2*d(1,d(2,f(1)))*d(1,f(1))**2*p5**4*q10 
- 1/2*d(1,d(2,f(1)))*d(1,f(1))**2*p5**3*p8*q8 + d(1,d(2,f(1)))*d(1,f(1))**2*p5**
2*p6**2*q10 + 1/2*d(1,d(2,f(1)))*d(1,f(1))**2*p5**2*p6*p7*q8 - 1/2*d(1,d(2,f(1))
)*d(1,f(1))**2*p5*p6**2*p8*q8 + 1/2*d(1,d(2,f(1)))*d(1,f(1))**2*p6**4*q10 + 1/2*
d(1,d(2,f(1)))*d(1,f(1))**2*p6**3*p7*q8 + d(1,df(f(1),x,2))*df(f(1),x)*p5**3*p8*
q10 - d(1,df(f(1),x,2))*df(f(1),x)*p5**2*p6*p7*q10 - d(1,df(f(1),x,2))*df(f(1),x
)*p5**2*p7**2*q8 - d(1,df(f(1),x,2))*df(f(1),x)*p5**2*p8**2*q8 + d(1,df(f(1),x,2
))*df(f(1),x)*p5*p6**2*p8*q10 - d(1,df(f(1),x,2))*df(f(1),x)*p6**3*p7*q10 - d(1,
df(f(1),x,2))*df(f(1),x)*p6**2*p7**2*q8 - d(1,df(f(1),x,2))*df(f(1),x)*p6**2*p8
**2*q8 + d(1,df(f(1),x))*df(f(1),x,2)*p5**3*p8*q10 - d(1,df(f(1),x))*df(f(1),x,2
)*p5**2*p6*p7*q10 - d(1,df(f(1),x))*df(f(1),x,2)*p5**2*p7**2*q8 - d(1,df(f(1),x)
)*df(f(1),x,2)*p5**2*p8**2*q8 + d(1,df(f(1),x))*df(f(1),x,2)*p5*p6**2*p8*q10 - d
(1,df(f(1),x))*df(f(1),x,2)*p6**3*p7*q10 - d(1,df(f(1),x))*df(f(1),x,2)*p6**2*p7
**2*q8 - d(1,df(f(1),x))*df(f(1),x,2)*p6**2*p8**2*q8 - 1/2*d(1,f(1))**2*df(f(1),
x)*p5**3*p7*q8 - 1/2*d(1,f(1))**2*df(f(1),x)*p5**2*p6*p8*q8 - 1/2*d(1,f(1))**2*
df(f(1),x)*p5*p6**2*p7*q8 - 1/2*d(1,f(1))**2*df(f(1),x)*p6**3*p8*q8 + d(1,f(1))*
df(f(1),x,3)*p5**3*p8*q10 - d(1,f(1))*df(f(1),x,3)*p5**2*p6*p7*q10 - d(1,f(1))*
df(f(1),x,3)*p5**2*p7**2*q8 - d(1,f(1))*df(f(1),x,3)*p5**2*p8**2*q8 + d(1,f(1))*
df(f(1),x,3)*p5*p6**2*p8*q10 - d(1,f(1))*df(f(1),x,3)*p6**3*p7*q10 - d(1,f(1))*
df(f(1),x,3)*p6**2*p7**2*q8 - d(1,f(1))*df(f(1),x,3)*p6**2*p8**2*q8 + 6/5*df(f(1
),x,5)*p5**2*p7*p8*q10 - 6/5*df(f(1),x,5)*p5*p6*p7**2*q10 + 6/5*df(f(1),x,5)*p5*
p6*p8**2*q10 - 3/5*df(f(1),x,5)*p5*p7**3*q8 - 3/5*df(f(1),x,5)*p5*p7*p8**2*q8 - 
6/5*df(f(1),x,5)*p6**2*p7*p8*q10 - 3/5*df(f(1),x,5)*p6*p7**2*p8*q8 - 3/5*df(f(1)
,x,5)*p6*p8**3*q8)/(p5**3*p7 + p5**2*p6*p8 + p5*p6**2*p7 + p6**3*p8)$

Time: 0 ms

Time: 0 ms

Time: 10 ms

The list of inequalities got extended by: 

p8


The list of inequalities got extended by: 

q10 - q17


New level : 1.1.2.2.1.1.3.1.2.
CRACK is now called with the new equation e_484 : 
0=p5*p7 + p6*p8


Step 1468: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 42 terms

e_438 is a consequence of e_400.
e_469 is a consequence of e_400.
e_431 is a consequence of e_400.
Substitution of p5 by an expression in 
p8, p6, p7 found in e_484 : 
     - p6*p8
p5=----------
       p7


Step 1469: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.2.2.1.1.3.1.2. : 
equations : 

e_400 : 
    2     2
0=p7  + p8



Non-vanishing expressions: p5,p6,p7,p4,p8
212 factors in 42 terms
238 factors in 44 terms
145 factors in 29 terms
196 factors in 39 terms

                      2
g0111*p7*p8 + g0112*p7  + g0113*p6*p7 - g0114*p6*p8 - g0115*p6*p8 - g0116*p6*p7


q10 - q17


functions : 
          2           3       2        3       2        6    2
q27=( - p6 *p8*q26 - ---*p6*p7 *q10 - ---*p6*p8 *q10 - ---*p7 *p8*q9
                      5                5                5

         3       2        2
      - ---*p7*p8 *q8)/(p6 *p7)
         5

q26, 
q25=0


q24=q10


                     2
     p6*p8*q10 + 2*p7 *q9 + p7*p8*q8
q23=---------------------------------
                  p6*p7


                        2
      - p6*p8*q10 - 2*p7 *q9 - p7*p8*q8
q22=------------------------------------
                   p6*p7


q21=q10


q20=q17


      5    2   2        5    2   2            2               2
q19=(---*p6 *p7 *q26 + ---*p6 *p8 *q26 + p6*p7 *p8*q10 - p6*p7 *p8*q17
      3                 3

             3           2   2           3           3
      + p6*p8 *q10 + 2*p7 *p8 *q9 + p7*p8 *q8)/(p6*p7 )


         5    2   2        5    2   2            2               2
q18=( - ---*p6 *p7 *q26 - ---*p6 *p8 *q26 - p6*p7 *p8*q10 + p6*p7 *p8*q17
         3                 3

             3           2   2           3           3
      - p6*p8 *q10 - 2*p7 *p8 *q9 - p7*p8 *q8)/(p6*p7 )

q17, 
q16=q10


                        2
      - p6*p8*q10 - 2*p7 *q9 - p7*p8*q8
q15=------------------------------------
                   p6*p7


        1
q14= - ---*q8
        2


q13=2*q9


     1
q12=---*q8
     2


                     2
     p6*p8*q10 + 2*p7 *q9 + p7*p8*q8
q11=---------------------------------
                  p6*p7

q10, q9, q8, 
q7= - q9


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0

p8, p7, p6, 
     - p6*p8
p5=----------
       p7


     - p6*p8
p4=----------
       p7


p3= - p6


p2=0


p1=0


with 77 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_400(2a)
8 constants : p6,p7,p8,q8,q9,q10,q17,q26
The equation: 

*** Garbage collection starting 
*** GC 404  3-Oct-2003 05:32:42, 30 ms (0%), 1004370 occupied, 23995580 free
                                                  2
f =( - D f*D D f*p6*p7 - D f*f *p6*p8 + D D f  *p7  - D D f*D f*p6*p8
 t      2   1 2           2   x          1 2 2x        1 2   1

     + D f*f *p6*p7 + f  *p7*p8)/p7
        1   x          3x
The symmetry: 
                  2   2                             4
f =(D f  *D D f*p6 *p7 *p8*q10 + 2*D f  *D D f*p6*p7 *q9
 s   2 2x  1 2                      2 2x  1 2

                        3                    2   3
     + D f  *D D f*p6*p7 *p8*q8 + D f  *f *p6 *p7 *q10
        2 2x  1 2                  2 2x  x

        5                3   2        5                3   2
     - ---*D f *D D f *p6 *p7 *q26 - ---*D f *D D f *p6 *p8 *q26
        3   2 x  1 2 x                3   2 x  1 2 x

                     2   2                        2   2
     - D f *D D f *p6 *p7 *p8*q10 + D f *D D f *p6 *p7 *p8*q17
        2 x  1 2 x                   2 x  1 2 x

                     2   3                          2   2
     - D f *D D f *p6 *p8 *q10 - 2*D f *D D f *p6*p7 *p8 *q9
        2 x  1 2 x                  2 x  1 2 x

                           3                 2   3            2         2   3
     - D f *D D f *p6*p7*p8 *q8 + D f *f  *p6 *p7 *q17 - (D f) *D D f*p6 *p7 *q9
        2 x  1 2 x                 2 x  2x                 2     1 2

        1       2      2   3                    2   2
     + ---*(D f) *f *p6 *p7 *q8 + D f*D D f  *p6 *p7 *p8*q10
        2    2     x               2   1 2 2x

                          4                       3
     + 2*D f*D D f  *p6*p7 *q9 + D f*D D f  *p6*p7 *p8*q8
          2   1 2 2x              2   1 2 2x

                       2   3                     2   3                2   3
     + D f*D D f*D f*p6 *p7 *q8 + 2*D f*D f*f *p6 *p7 *q9 + D f*f  *p6 *p7 *q10
        2   1 2   1                  2   1   x               2   3x

                 2   3                     2   3                     2   3
     + D D f  *p6 *p7 *q26 + D D f  *D f*p6 *p7 *q10 + D D f *D f *p6 *p7 *q17
        1 2 4x                1 2 2x  1                 1 2 x  1 x

                     2   3                  2   2   3
     + D D f*D f  *p6 *p7 *q10 + D D f*(D f) *p6 *p7 *q9
        1 2   1 2x                1 2    1

                  2   2                          4                    3
     - D f  *f *p6 *p7 *p8*q10 - 2*D f  *f *p6*p7 *q9 - D f  *f *p6*p7 *p8*q8
        1 2x  x                     1 2x  x              1 2x  x

        5             3   2        5             3   2
     + ---*D f *f  *p6 *p7 *q26 + ---*D f *f  *p6 *p8 *q26
        3   1 x  2x                3   1 x  2x

                  2   2                     2   2                     2   3
     + D f *f  *p6 *p7 *p8*q10 - D f *f  *p6 *p7 *p8*q17 + D f *f  *p6 *p8 *q10
        1 x  2x                   1 x  2x                   1 x  2x

                       2   2                       3
     + 2*D f *f  *p6*p7 *p8 *q9 + D f *f  *p6*p7*p8 *q8
          1 x  2x                  1 x  2x

        1       2      2   3                2   2                         4
     - ---*(D f) *f *p6 *p7 *q8 - D f*f  *p6 *p7 *p8*q10 - 2*D f*f  *p6*p7 *q9
        2    1     x               1   3x                     1   3x

                    3               2   2           3           4
     - D f*f  *p6*p7 *p8*q8 - f  *p6 *p7 *p8*q26 - ---*f  *p6*p7 *q10
        1   3x                 5x                   5   5x

        3           2   2        6        4          3        3   2        2   3
     - ---*f  *p6*p7 *p8 *q10 - ---*f  *p7 *p8*q9 - ---*f  *p7 *p8 *q8)/(p6 *p7
        5   5x                   5   5x              5   5x

   )
And now in machine readable form:

The system: 

df(f(1),t)=( - d(2,f(1))*d(1,d(2,f(1)))*p6*p7 - d(2,f(1))*df(f(1),x)*p6*p8 + d(1
,d(2,df(f(1),x,2)))*p7**2 - d(1,d(2,f(1)))*d(1,f(1))*p6*p8 + d(1,f(1))*df(f(1),x
)*p6*p7 + df(f(1),x,3)*p7*p8)/p7$
The symmetry: 
df(f(1),s)=(d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p6**2*p7**2*p8*q10 + 2*d(2,df(f(1),
x,2))*d(1,d(2,f(1)))*p6*p7**4*q9 + d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p6*p7**3*p8*
q8 + d(2,df(f(1),x,2))*df(f(1),x)*p6**2*p7**3*q10 - 5/3*d(2,df(f(1),x))*d(1,d(2,
df(f(1),x)))*p6**3*p7**2*q26 - 5/3*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6**3*p8
**2*q26 - d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6**2*p7**2*p8*q10 + d(2,df(f(1),
x))*d(1,d(2,df(f(1),x)))*p6**2*p7**2*p8*q17 - d(2,df(f(1),x))*d(1,d(2,df(f(1),x)
))*p6**2*p8**3*q10 - 2*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6*p7**2*p8**2*q9 - 
d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p6*p7*p8**3*q8 + d(2,df(f(1),x))*df(f(1),x,
2)*p6**2*p7**3*q17 - d(2,f(1))**2*d(1,d(2,f(1)))*p6**2*p7**3*q9 + 1/2*d(2,f(1))
**2*df(f(1),x)*p6**2*p7**3*q8 + d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p6**2*p7**2*p8*
q10 + 2*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p6*p7**4*q9 + d(2,f(1))*d(1,d(2,df(f(1)
,x,2)))*p6*p7**3*p8*q8 + d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p6**2*p7**3*q8 + 2*d
(2,f(1))*d(1,f(1))*df(f(1),x)*p6**2*p7**3*q9 + d(2,f(1))*df(f(1),x,3)*p6**2*p7**
3*q10 + d(1,d(2,df(f(1),x,4)))*p6**2*p7**3*q26 + d(1,d(2,df(f(1),x,2)))*d(1,f(1)
)*p6**2*p7**3*q10 + d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*p6**2*p7**3*q17 + d(1,d
(2,f(1)))*d(1,df(f(1),x,2))*p6**2*p7**3*q10 + d(1,d(2,f(1)))*d(1,f(1))**2*p6**2*
p7**3*q9 - d(1,df(f(1),x,2))*df(f(1),x)*p6**2*p7**2*p8*q10 - 2*d(1,df(f(1),x,2))
*df(f(1),x)*p6*p7**4*q9 - d(1,df(f(1),x,2))*df(f(1),x)*p6*p7**3*p8*q8 + 5/3*d(1,
df(f(1),x))*df(f(1),x,2)*p6**3*p7**2*q26 + 5/3*d(1,df(f(1),x))*df(f(1),x,2)*p6**
3*p8**2*q26 + d(1,df(f(1),x))*df(f(1),x,2)*p6**2*p7**2*p8*q10 - d(1,df(f(1),x))*
df(f(1),x,2)*p6**2*p7**2*p8*q17 + d(1,df(f(1),x))*df(f(1),x,2)*p6**2*p8**3*q10 +
 2*d(1,df(f(1),x))*df(f(1),x,2)*p6*p7**2*p8**2*q9 + d(1,df(f(1),x))*df(f(1),x,2)
*p6*p7*p8**3*q8 - 1/2*d(1,f(1))**2*df(f(1),x)*p6**2*p7**3*q8 - d(1,f(1))*df(f(1)
,x,3)*p6**2*p7**2*p8*q10 - 2*d(1,f(1))*df(f(1),x,3)*p6*p7**4*q9 - d(1,f(1))*df(f
(1),x,3)*p6*p7**3*p8*q8 - df(f(1),x,5)*p6**2*p7**2*p8*q26 - 3/5*df(f(1),x,5)*p6*
p7**4*q10 - 3/5*df(f(1),x,5)*p6*p7**2*p8**2*q10 - 6/5*df(f(1),x,5)*p7**4*p8*q9 -
 3/5*df(f(1),x,5)*p7**3*p8**2*q8)/(p6**2*p7**3)$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p4 - p5


New level : 1.1.2.2.1.1.3.2.
CRACK is now called with the new equation e_95 : 17 factors in 4 terms

Step 1470: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 55 terms

The list of inequalities got extended by: 
An expression with 55 terms

e_274 is a consequence of e_255.
e_238 is a consequence of e_255.
e_322 is a consequence of e_255.
Substitution of q27 by an expression in 
q26, q17, p8, p6, p4, p7 found in e_95 : 18 factors in 4 terms

Step 1471: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_53 and e_216. e_216: 
 8 terms, 48 factors, with derivatives of functions of all variables: 

                       2      2      3   2      2
 (q26,q17,q11,q10,p8,p5 ,p5,p6 ,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_385: 
 6 terms, 36 factors, with derivatives of functions of all variables: 

                3      2      5   4   3
 (q17,q11,q10,p5 ,p5,p6 ,p6,p4 ,p4 ,p4 )


Step 1472: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_53 and e_323. e_323: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

                             3   2      2
 (q26,q17,q11,q10,p8,p5,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_440: 
 4 terms, 16 factors, with derivatives of functions of all variables: 

                2      3   2
 (q17,q11,q10,p5 ,p6,p4 ,p4 )


Step 1473: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_53 and e_324. e_324: 
 9 terms, 54 factors, with derivatives of functions of all variables: 

                        2      3   2      3   2
 (q26,q17,q9,q8,p8,p5,p6 ,p6,p4 ,p4 ,p4,p7 ,p7 ,p7)

is replaced by e_449: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                    2      3   2
 (q17,q9,q8,p8,p5,p6 ,p6,p4 ,p4 ,p4,p7)


Step 1474: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_53 and e_325. e_325: 
 9 terms, 63 factors, with derivatives of functions of all variables: 

                     2      2      3   2      3   2
 (q26,q17,q9,q8,p8,p5 ,p5,p6 ,p6,p4 ,p4 ,p4,p7 ,p7 ,p7)

is replaced by e_450: 
 7 terms, 42 factors, with derivatives of functions of all variables: 

                 3   2      2      4   3   2
 (q17,q9,q8,p8,p5 ,p5 ,p5,p6 ,p6,p4 ,p4 ,p4 ,p4,p7)


Step 1475: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_53 and e_445. e_445: 
 11 terms, 77 factors, with derivatives of functions of all variables: 

                     2      3   2      3   2      3   2
 (q26,q17,q9,q8,p8,p5 ,p5,p6 ,p6 ,p6,p4 ,p4 ,p4,p7 ,p7 ,p7)

is replaced by e_451: 
 7 terms, 49 factors, with derivatives of functions of all variables: 

                 3   2      3      5   4   3
 (q17,q9,q8,p8,p5 ,p5 ,p5,p6 ,p6,p4 ,p4 ,p4 ,p4,p7)


Step 1476: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 405  3-Oct-2003 05:32:45, 50 ms (0%), 1026569 occupied, 23973380 free
Eliminate 
q26

from e_424 and e_439. e_439: 
 12 terms, 60 factors, with derivatives of functions of all variables: 

                             2      2      3   2      2
 (q26,q17,q11,q10,q9,q8,p8,p5 ,p5,p6 ,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_452: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                         2      2      4   3   2
 (q17,q11,q10,q9,q8,p8,p5 ,p5,p6 ,p6,p4 ,p4 ,p4 ,p4,p7)


Step 1477: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 406  3-Oct-2003 05:32:49, 40 ms (0%), 1026403 occupied, 23973542 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_337 we get the alternative equations : 
0=p4*p7 + p6*p8

16 factors in 5 terms

The list of inequalities got extended by: 

p8

The lexicographical ordering of unknowns is changed
because p8 has to be non-zero, giving p8 a low priority.
Old ordering: q26,q17,q11,q10,q9,q8,p8,p5,p6,p4,p7
New ordering: q26,q17,q11,q10,q9,q8,p5,p8,p6,p4,p7

New level : 1.1.2.2.1.1.3.2.1.
CRACK is now called with the new equation e_458 : 
0=p4*p7 + p6*p8


Step 1478: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

p6


The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 55 terms

The list of inequalities got extended by: 
An expression with 55 terms

Substitution of p6 by an expression in 
p8, p4, p7 found in e_458 : 
     - p4*p7
p6=----------
       p8


Step 1479: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 47 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 59 terms

The list of inequalities got extended by: 
An expression with 57 terms

Substitution of q26 by an expression in 
q17, p5, p4, p7 found in e_466 : 12 factors in 3 terms

Step 1480: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 407  3-Oct-2003 05:32:52, 40 ms (0%), 1041854 occupied, 23958094 free
Eliminate 
q11

from e_476 and e_486. e_486: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

                      3   2      2      2
 (q17,q11,q10,q9,q8,p5 ,p5 ,p5,p8 ,p8,p4 ,p4,p7)

is replaced by e_499: 
 3 terms, 12 factors, with derivatives of functions of all variables: 

           2      2
 (q17,q9,p5 ,p5,p8 ,p4,p7)


Step 1481: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_499 and e_495. e_495: 
(#) 14 terms, 39 factors, with derivatives of functions of all variables: 

                  3   2      4   3   2      2      3   2
 (q17,q10,q9,q8,p5 ,p5 ,p5,p8 ,p8 ,p8 ,p8,p4 ,p4,p7 ,p7 ,p7)

is replaced by e_500: 

     2     2
0=(p7  + p8 )*(p5*q10 - p8*q8)


Step 1482: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_476 and e_488. e_488: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                      2      3   2      2      2
 (q17,q11,q10,q9,q8,p5 ,p5,p8 ,p8 ,p8,p4 ,p4,p7 ,p7)

is replaced by e_503: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

              2      3   2      2      2
 (q17,q9,q8,p5 ,p5,p8 ,p8 ,p8,p4 ,p4,p7 ,p7)


Step 1483: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_500 and e_492. e_492: 
 9 terms, 54 factors, with derivatives of functions of all variables: 

                3   2      2      3   2      2
 (q17,q11,q10,p5 ,p5 ,p5,p8 ,p8,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_504: 
 9 terms, 54 factors, with derivatives of functions of all variables: 

               3   2      3   2      3   2      2
 (q17,q11,q8,p5 ,p5 ,p5,p8 ,p8 ,p8,p4 ,p4 ,p4,p7 ,p7)


Step 1484: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 408  3-Oct-2003 05:32:55, 30 ms (0%), 1044882 occupied, 23955065 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 47 terms

The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 58 terms

The list of inequalities got extended by: 
An expression with 56 terms

Substitution of q8 by an expression in 
q9, p5, p8, p4, p7 found in e_460 : 10 factors in 3 terms

Step 1485: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_477 and e_467. e_467: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

                      3      2      2
 (q17,q11,q10,q9,p5,p8 ,p8,p4 ,p4,p7 ,p7)

is replaced by e_514: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

               2      2
 (q17,q10,q9,p8 ,p4,p7 ,p7)


Step 1486: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 409  3-Oct-2003 05:32:58, 50 ms (0%), 1049335 occupied, 23950613 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 54 terms

The list of inequalities got extended by: 
An expression with 48 terms

The list of inequalities got extended by: 
An expression with 67 terms

The list of inequalities got extended by: 
An expression with 65 terms

Substitution of q9 by an expression in 
q17, p5, p8, p4, p7 found in e_499 : 14 factors in 3 terms

Step 1487: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1488: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1489: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 410  3-Oct-2003 05:33:02, 40 ms (0%), 1044046 occupied, 23955901 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_476 we get the alternative equations : 
0=p5

32 factors in 7 terms

New level : 1.1.2.2.1.1.3.2.1.1.
CRACK is now called with the new equation e_324 : 
0=p5

e_469,e_493,e_491,e_438 are consequences of e_324

Step 1490: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 

1


The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 21 terms
e_503,e_461,e_468,e_392,e_464 are consequences of e_325

e_498 is a consequence of e_453.
e_506 is a consequence of e_501.
Substitution of p5 found in e_324 : 
p5=0


Step 1491: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 10 terms

e_458 is a consequence of e_505.
e_456 is a consequence of e_505.
e_455 is a consequence of e_505.
e_445 is a consequence of e_501.
e_453 is a consequence of e_488.
e_439 is a consequence of e_505.
e_466 is a consequence of e_486.
e_337 is a consequence of e_505.
e_457 is a consequence of e_488.
Substitution of q17 found in e_325 : 
q17=0


Step 1492: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

q10


The list of inequalities got extended by: 

q11


The list of inequalities got extended by: 
An expression with 6 terms

Substitution of q11 found in e_501 : 
q11=0


leads to a contradiction in : 
0=2*p7*q11 - p8*q10


Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p5


New level : 1.1.2.2.1.1.3.2.1.2.
CRACK is now called with the new equation e_324 : 32 factors in 7 terms

Step 1493: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 63 terms

The list of inequalities got extended by: 
An expression with 54 terms

The list of inequalities got extended by: 
An expression with 76 terms

The list of inequalities got extended by: 
An expression with 74 terms
*** Garbage collection starting 
*** GC 411  3-Oct-2003 05:33:05, 30 ms (0%), 1035372 occupied, 23964578 free

Substitution of q11 by an expression in 
q17, q10, p5, p8, p4, p7 found in e_324 : 35 factors in 7 terms

Step 1494: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1495: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1496: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1497: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1498: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1499: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1500: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 412  3-Oct-2003 05:33:08, 30 ms (0%), 1039675 occupied, 23960274 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_486 we get the alternative equations : 
0=q17


0=p4 - 3*p5

8 factors in 3 terms

New level : 1.1.2.2.1.1.3.2.1.2.1.
CRACK is now called with the new equation e_522 : 
0=q17

e_506,e_492,e_461,e_468,e_445,e_456,e_392,e_491,e_438,e_464,e_459
 are consequences of e_522

Step 1501: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 8 terms

q10


The list of inequalities got extended by: 
An expression with 12 terms

Substitution of q17 found in e_522 : 
q17=0


leads to a contradiction in : 25 factors in 6 terms

Time: 0 ms

Time: 0 ms

Time: 40 ms

The list of inequalities got extended by: 

q17

The lexicographical ordering of unknowns is changed
because q17 has to be non-zero, giving q17 a low priority.
Old ordering: q17,q10,p5,p8,p4,p7
New ordering: q10,q17,p5,p8,p4,p7

New level : 1.1.2.2.1.1.3.2.1.2.2.
CRACK is now called with the new equation e_522 : 
0=p4 - 3*p5


Step 1502: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 16 terms

The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 20 terms

e_524 is a consequence of e_523.e_527 is a consequence of e_528

Substitution of p4 by an expression in 
p5 found in e_522 : 
p4=3*p5


leads to a contradiction in : 17 factors in 5 terms

Time: 0 ms

Time: 0 ms

Time: 30 ms

The list of inequalities got extended by: 

q17

The lexicographical ordering of unknowns is changed
because q17 has to be non-zero, giving q17 a low priority.
Old ordering: q17,q10,p5,p8,p4,p7
New ordering: q10,q17,p5,p8,p4,p7

The list of inequalities got extended by: 

p4 - 3*p5


New level : 1.1.2.2.1.1.3.2.1.2.3.
CRACK is now called with the new equation e_522 : 8 factors in 3 terms

Step 1503: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

p7 + p8


p7 - p8


The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 

  2     2
p7  + p8


The list of inequalities got extended by: 

  2       2
p7  - 3*p8


The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 72 terms

The list of inequalities got extended by: 
An expression with 71 terms

The list of inequalities got extended by: 
An expression with 78 terms

The list of inequalities got extended by: 
An expression with 87 terms

The list of inequalities got extended by: 

  2       2
p7  - 7*p8


Substitution of p4 by an expression in 
p5, p8, p7 found in e_522 : 10 factors in 3 terms

leads to a contradiction in : 
    2   2     2   2
0=p4 *p8  + p5 *p7


This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p4*p7 + p6*p8


New level : 1.1.2.2.1.1.3.2.2.
CRACK is now called with the new equation e_458 : 16 factors in 5 terms
e_424 is a consequence of e_458

Step 1504: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 68 terms

The list of inequalities got extended by: 
An expression with 55 terms

The list of inequalities got extended by: 
An expression with 79 terms

The list of inequalities got extended by: 
An expression with 78 terms

Substitution of q26 by an expression in 
q17, q10, p5, p4, p7 found in e_458 : 14 factors in 4 terms

Step 1505: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_464 and e_468. e_468: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

                   2         3   2
 (q17,q11,q10,p8,p5 ,p5,p6,p4 ,p4 ,p4,p7)

is replaced by e_481: 

    2
0=p4 *q11 + p5*p6*q10


Step 1506: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 65 terms

The list of inequalities got extended by: 
An expression with 54 terms

The list of inequalities got extended by: 
An expression with 76 terms

The list of inequalities got extended by: 
An expression with 75 terms

e_463 is a consequence of e_464.
Substitution of q11 by an expression in 
q10, p5, p6, p4 found in e_481 : 
      - p5*p6*q10
q11=--------------
           2
         p4


Step 1507: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 62 terms

The list of inequalities got extended by: 
An expression with 58 terms

The list of inequalities got extended by: 
An expression with 67 terms

The list of inequalities got extended by: 
An expression with 75 terms

e_459 is a consequence of e_464.
e_490 is a consequence of e_489.
Substitution of q17 by an expression in 
q10, p5, p4 found in e_482 : 
     2*p4*q10
q17=----------
     p4 - p5


Step 1508: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 413  3-Oct-2003 05:33:11, 40 ms (0%), 1033315 occupied, 23966635 free
Eliminate 
q10

from e_489 and e_495. e_495: 
 6 terms, 30 factors, with derivatives of functions of all variables: 

                 2      2      3   2
 (q10,q9,q8,p8,p5 ,p5,p6 ,p6,p4 ,p4 ,p4,p7)

is replaced by e_498: 
 6 terms, 30 factors, with derivatives of functions of all variables: 

             2         3   2
 (q9,q8,p8,p5 ,p5,p6,p4 ,p4 ,p4,p7)


Step 1509: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_489 and e_485. e_485: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

                 2      2      3   2
 (q10,q9,q8,p8,p5 ,p5,p6 ,p6,p4 ,p4 ,p4,p7)

is replaced by e_499: 
 6 terms, 30 factors, with derivatives of functions of all variables: 

             2         3   2
 (q9,q8,p8,p5 ,p5,p6,p4 ,p4 ,p4,p7)


e_499 is a consequence of e_498.
Step 1510: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_489 and e_478. e_478: 
 15 terms, 90 factors, with derivatives of functions of all variables: 

                 2      3   2      4   3   2
 (q10,q9,q8,p8,p5 ,p5,p6 ,p6 ,p6,p4 ,p4 ,p4 ,p4,p7)

is replaced by e_500: 
 14 terms, 84 factors, with derivatives of functions of all variables: 

             2      2      4   3   2
 (q9,q8,p8,p5 ,p5,p6 ,p6,p4 ,p4 ,p4 ,p4,p7)


Step 1511: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 414  3-Oct-2003 05:33:15, 30 ms (0%), 1039898 occupied, 23960052 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_464 we get the alternative equations : 
0=q10

16 factors in 4 terms

New level : 1.1.2.2.1.1.3.2.2.1.
CRACK is now called with the new equation e_520 : 
0=q10

e_476,e_466,e_400,e_462,e_467,e_460,e_488,e_492 are consequences of e_520

Step 1512: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 15 terms
e_431 is a consequence of e_411

e_278 is a consequence of e_411.
e_426 is a consequence of e_469.
Substitution of q10 found in e_520 : 
q10=0


Step 1513: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

q8


The list of inequalities got extended by: 
An expression with 7 terms

e_469 is a consequence of e_322.
Substitution of q9 found in e_411 : 
q9=0


leads to a contradiction in : 10 factors in 3 terms

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p5


The list of inequalities got extended by: 

q10

The lexicographical ordering of unknowns is changed
because q10 has to be non-zero, giving q10 a low priority.
Old ordering: q10,q9,q8,p8,p5,p6,p4,p7
New ordering: q9,q8,q10,p8,p5,p6,p4,p7

New level : 1.1.2.2.1.1.3.2.2.2.
CRACK is now called with the new equation e_520 : 16 factors in 4 terms

Step 1514: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 54 terms

The list of inequalities got extended by: 
An expression with 54 terms

The list of inequalities got extended by: 
An expression with 68 terms

The list of inequalities got extended by: 
An expression with 42 terms

e_322 is a consequence of e_469.
e_216 is a consequence of e_426.
Substitution of p8 by an expression in 
p5, p6, p4, p7 found in e_520 : 15 factors in 3 terms

Step 1515: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p5

from e_492 and e_426. e_426: 
 4 terms, 20 factors, with derivatives of functions of all variables: 

    3   2      2   5   4
 (p5 ,p5 ,p5,p6 ,p4 ,p4 ,p4)

is replaced by e_439: 

    2     2
0=p4  + p6


Step 1516: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
contradiction : 
       4     2   2
0= - p4  + p4 *p5

Eliminate 
p6

from e_439 and e_492. e_492: 

    4     2   2
0=p4  + p5 *p6

is replaced by e_453: 

0=1


This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 30 ms

The list of inequalities got extended by: 

p4*q20 - p5*q17


New level : 1.1.2.2.1.2.
CRACK is now called with the new equation e_325 : 
0=p4*p8 - p6*p7


Step 1517: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 51 terms

The list of inequalities got extended by: 
An expression with 53 terms

e_380 is a consequence of e_372.
Substitution of p8 by an expression in 
p6, p4, p7 found in e_325 : 
    p6*p7
p8=-------
     p4


Step 1518: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_384 and e_326. e_326: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

                  2      3   2
 (q11,q10,q9,q8,p6 ,p6,p4 ,p4 ,p4,p7)

is replaced by e_455: 
(#) 4 terms, 9 factors, with derivatives of functions of all variables: 

           3   2      3   2
 (q10,q9,p6 ,p6 ,p6,p4 ,p4 ,p4,p7)


Step 1519: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
The list of inequalities got extended by: 

p6

The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q27,q26,q20,q17,q12,q11,q10,q9,q8,q7,p6,p5,p4,p7
New ordering: q27,q26,q20,q17,q12,q11,q10,q9,q8,q7,p5,p6,p4,p7
Eliminate 
q26

from e_338 and e_448. e_448: 
(#) 18 terms, 31 factors, with derivatives of functions of all variables: 

                    2      2   4   3   2
 (q26,q20,q17,q10,p5 ,p5,p6 ,p4 ,p4 ,p4 ,p4,p7)

is replaced by e_458: 

    2     2
0=p4  + p6

e_338,e_455,e_337 are consequences of e_458

Step 1520: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_403. e_403: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

             2      2      4   3   2
 (q9,q8,q7,p5 ,p5,p6 ,p6,p4 ,p4 ,p4 ,p4)

is replaced by e_464: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

             2         2
 (q9,q8,q7,p5 ,p5,p6,p4 ,p4)


Step 1521: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_394. e_394: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

                   2   4   3   2
 (q26,q20,q17,p5,p6 ,p4 ,p4 ,p4 ,p4,p7)

is replaced by e_465: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                   2
 (q26,q20,q17,p5,p4 ,p4,p7)


Step 1522: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_411. e_411: 
(#) 10 terms, 41 factors, with derivatives of functions of all variables: 

                    2      2      3   2
 (q27,q26,q20,q17,p5 ,p5,p6 ,p6,p4 ,p4 ,p4,p7)

is replaced by e_466: 
(#) 6 terms, 19 factors, with derivatives of functions of all variables: 

                    2         2
 (q27,q26,q20,q17,p5 ,p5,p6,p4 ,p4,p7)


Step 1523: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_387 and e_465. e_465: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                   2
 (q26,q20,q17,p5,p4 ,p4,p7)

is replaced by e_467: 
 6 terms, 12 factors, with derivatives of functions of all variables: 

 (q20,q17,q10,p5,p4)


Step 1524: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_424. e_424: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

                        2      2      3   2
 (q26,q20,q17,q11,q10,p5 ,p5,p6 ,p6,p4 ,p4 ,p4,p7)

is replaced by e_468: 
(#) 8 terms, 14 factors, with derivatives of functions of all variables: 

                    2         2
 (q26,q17,q11,q10,p5 ,p5,p6,p4 ,p4,p7)


Step 1525: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 415  3-Oct-2003 05:33:18, 40 ms (0%), 1040571 occupied, 23959379 free
Eliminate 
p6

from e_458 and e_371. e_371: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                               2      2
 (q27,q26,q20,q17,q11,q10,p5,p6 ,p6,p4 ,p4,p7)

is replaced by e_469: 
 7 terms, 21 factors, with derivatives of functions of all variables: 

                                  2
 (q27,q26,q20,q17,q11,q10,p5,p6,p4 ,p4,p7)


Step 1526: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_384 and e_358. e_358: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                               2
 (q12,q11,q10,q9,q8,q7,p5,p6,p4 ,p4,p7)

is replaced by e_470: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                       2
 (q12,q9,q8,q7,p5,p6,p4 ,p4)


Step 1527: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q20

from e_467 and e_393. e_393: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

                          2         2
 (q20,q17,q11,q10,q9,q8,p5 ,p5,p6,p4 ,p4,p7)

is replaced by e_471: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                      2         2
 (q17,q11,q10,q9,q8,p5 ,p5,p6,p4 ,p4,p7)


Step 1528: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_384 and e_471. e_471: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                      2         2
 (q17,q11,q10,q9,q8,p5 ,p5,p6,p4 ,p4,p7)

is replaced by e_472: 
(#) 8 terms, 14 factors, with derivatives of functions of all variables: 

                  2         2
 (q17,q10,q9,q8,p5 ,p5,p6,p4 ,p4,p7)


Step 1529: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_440. e_440: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                           2      2      2      2
 (q27,q26,q20,q17,q12,q7,p5 ,p5,p6 ,p6,p4 ,p4,p7 ,p7)

is replaced by e_473: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                           2         2      2
 (q27,q26,q20,q17,q12,q7,p5 ,p5,p6,p4 ,p4,p7 ,p7)


Step 1530: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_439. e_439: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                            2      2      3   2
 (q27,q26,q20,q17,q11,q10,p5 ,p5,p6 ,p6,p4 ,p4 ,p4,p7)

is replaced by e_474: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

                            2         2
 (q27,q26,q20,q17,q11,q10,p5 ,p5,p6,p4 ,p4,p7)


Step 1531: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_287 and e_474. e_474: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

                            2         2
 (q27,q26,q20,q17,q11,q10,p5 ,p5,p6,p4 ,p4,p7)

is replaced by e_419: 
(#) 8 terms, 10 factors, with derivatives of functions of all variables: 

                    2
 (q26,q20,q17,q10,p5 ,p5,p4,p7)


Step 1532: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_438. e_438: 
 9 terms, 54 factors, with derivatives of functions of all variables: 

                             2      4   3   2      2
 (q27,q26,q20,q17,q9,q8,p5,p6 ,p6,p4 ,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_278: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                                3   2      2
 (q27,q26,q20,q17,q9,q8,p5,p6,p4 ,p4 ,p4,p7 ,p7)


Step 1533: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_395 and e_396. e_396: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

                            2         2
 (q27,q26,q20,q17,q11,q10,p5 ,p5,p6,p4 ,p4,p7)

is replaced by e_426: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                    2         2
 (q26,q20,q17,q11,p5 ,p5,p6,p4 ,p4,p7)


Step 1534: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_383 and e_437. e_437: 
 11 terms, 44 factors, with derivatives of functions of all variables: 

                          2         3   2      2
 (q26,q20,q11,q10,q9,q8,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_101: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

                     2
 (q11,q10,q9,q8,p6,p4 ,p4,p7)


Step 1535: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_101 and e_226. e_226: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                            2
 (q17,q11,q10,q9,q8,p5,p6,p4 ,p4,p7)

is replaced by e_95: 
(#) 6 terms, 8 factors, with derivatives of functions of all variables: 

                  2
 (q17,q10,q9,p5,p4 ,p4,p7)


Step 1536: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_430. e_430: 
 12 terms, 72 factors, with derivatives of functions of all variables: 

                          2      2      3   2      2
 (q26,q20,q17,q11,q9,q7,p5 ,p5,p6 ,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_255: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                          2         3   2      2
 (q26,q20,q17,q11,q9,q7,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)


Step 1537: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 416  3-Oct-2003 05:33:21, 40 ms (0%), 1041827 occupied, 23958122 free
Eliminate 
p6

from e_458 and e_445. e_445: 
 13 terms, 65 factors, with derivatives of functions of all variables: 

                              2      2      3   2      2
 (q26,q20,q17,q11,q10,q9,q8,p5 ,p5,p6 ,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_313: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                                2
 (q20,q17,q11,q10,q9,q8,p5,p6,p4 ,p4,p7)


Step 1538: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q20

from e_467 and e_313. e_313: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                                2
 (q20,q17,q11,q10,q9,q8,p5,p6,p4 ,p4,p7)

is replaced by e_274: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                            2
 (q17,q11,q10,q9,q8,p5,p6,p4 ,p4,p7)


Step 1539: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_95 and e_274. e_274: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                            2
 (q17,q11,q10,q9,q8,p5,p6,p4 ,p4,p7)

is replaced by e_216: 
 4 terms, 12 factors, with derivatives of functions of all variables: 

 (q11,q10,q9,q8,p5,p6,p4,p7)


Step 1540: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_384 and e_415. e_415: 
 12 terms, 60 factors, with derivatives of functions of all variables: 

                              2         3   2      2
 (q27,q26,q20,q11,q10,q9,q8,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_238: 
(#) 12 terms, 26 factors, with derivatives of functions of all variables: 

                          2         3   2      2
 (q27,q26,q20,q10,q9,q8,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)


Step 1541: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_444. e_444: 
 12 terms, 72 factors, with derivatives of functions of all variables: 

                             2      2      4   3   2      2
 (q26,q12,q11,q10,q9,q8,q7,p5 ,p5,p6 ,p6,p4 ,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_322: 
 7 terms, 21 factors, with derivatives of functions of all variables: 

 (q12,q11,q10,q9,q8,q7,p5,p6,p4,p7)


Step 1542: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_216 and e_322. e_322: 
 7 terms, 21 factors, with derivatives of functions of all variables: 

 (q12,q11,q10,q9,q8,q7,p5,p6,p4,p7)

is replaced by e_323: 
 5 terms, 10 factors, with derivatives of functions of all variables: 

 (q12,q9,q8,q7,p5,p6,p4)


Step 1543: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 54 terms

The list of inequalities got extended by: 
An expression with 56 terms

Substitution of q12 by an expression in 
q9, q8, q7, p5, p6, p4 found in e_323 : 16 factors in 5 terms

Step 1544: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_470. e_470: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                2      3   2
 (q9,q8,q7,p5,p6 ,p6,p4 ,p4 ,p4)

is replaced by e_325: 
(#) 4 terms, 6 factors, with derivatives of functions of all variables: 

                2
 (q9,q8,p5,p6,p4 ,p4)


Step 1545: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_443. e_443: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

             2      2      4   3   2
 (q9,q8,q7,p5 ,p5,p6 ,p6,p4 ,p4 ,p4 ,p4)

is replaced by e_452: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

             2         2
 (q9,q8,q7,p5 ,p5,p6,p4 ,p4)


Step 1546: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_380. e_380: 
 12 terms, 72 factors, with derivatives of functions of all variables: 

                          2      2      3   2      2
 (q26,q20,q17,q11,q9,q7,p5 ,p5,p6 ,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_453: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                          2         3   2      2
 (q26,q20,q17,q11,q9,q7,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)


Step 1547: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_453 and e_255. e_453: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                          2         3   2      2
 (q26,q20,q17,q11,q9,q7,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_454: 

0=q7 + q9


Step 1548: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 53 terms

The list of inequalities got extended by: 
An expression with 55 terms

e_324 is a consequence of e_400.
e_464 is a consequence of e_452.
Substitution of q9 by an expression in 
q7 found in e_454 : 
q9= - q7


Step 1549: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q8

from e_325 and e_452. e_452: 
(#) 6 terms, 8 factors, with derivatives of functions of all variables: 

          2         2
 (q8,q7,p5 ,p5,p6,p4 ,p4)

is replaced by e_460: 

0=q7*(p4 - p5)*(p4 + p5)


e_460 is a consequence of e_400.
Step 1550: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_365. e_365: 
 8 terms, 40 factors, with derivatives of functions of all variables: 

                          2      2      2      2
 (q27,q26,q20,q17,q8,q7,p5 ,p5,p6 ,p6,p4 ,p4,p7 ,p7)

is replaced by e_461: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                          2            2
 (q27,q26,q20,q17,q8,q7,p5 ,p5,p6,p4,p7 ,p7)


Step 1551: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_447. e_447: 
 16 terms, 96 factors, with derivatives of functions of all variables: 

                              2      2      4   3   2      2
 (q26,q20,q17,q11,q10,q8,q7,p5 ,p5,p6 ,p6,p4 ,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_462: 
 15 terms, 60 factors, with derivatives of functions of all variables: 

                              2         3   2      2
 (q26,q20,q17,q11,q10,q8,q7,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)


Step 1552: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_387 and e_462. e_462: 
 15 terms, 60 factors, with derivatives of functions of all variables: 

                              2         3   2      2
 (q26,q20,q17,q11,q10,q8,q7,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_463: 
 14 terms, 42 factors, with derivatives of functions of all variables: 

                          2         2
 (q20,q17,q11,q10,q8,q7,p5 ,p5,p6,p4 ,p4,p7)


Step 1553: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 417  3-Oct-2003 05:33:23, 30 ms (0%), 1033009 occupied, 23966941 free
Eliminate 
p6

from e_458 and e_449. e_449: 
 17 terms, 102 factors, with derivatives of functions of all variables: 

                              2      2      5   4   3   2      2
 (q26,q20,q17,q11,q10,q8,q7,p5 ,p5,p6 ,p6,p4 ,p4 ,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_403: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                              2         3   2      2
 (q26,q20,q17,q11,q10,q8,q7,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)


Step 1554: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_387 and e_403. e_403: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                              2         3   2      2
 (q26,q20,q17,q11,q10,q8,q7,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_394: 
 12 terms, 36 factors, with derivatives of functions of all variables: 

                          2         2
 (q20,q17,q11,q10,q8,q7,p5 ,p5,p6,p4 ,p4,p7)


Step 1555: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_458 and e_422. e_422: 
 14 terms, 70 factors, with derivatives of functions of all variables: 

                                  2      2      4   3   2      2
 (q27,q26,q20,q17,q11,q10,q8,q7,p5 ,p5,p6 ,p6,p4 ,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_411: 
 13 terms, 52 factors, with derivatives of functions of all variables: 

                                  2         3   2      2
 (q27,q26,q20,q17,q11,q10,q8,q7,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)


Step 1556: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_387 and e_411. e_411: 
 13 terms, 52 factors, with derivatives of functions of all variables: 

                                  2         3   2      2
 (q27,q26,q20,q17,q11,q10,q8,q7,p5 ,p5,p6,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_465: 
 13 terms, 52 factors, with derivatives of functions of all variables: 

                              2         2      2
 (q27,q20,q17,q11,q10,q8,q7,p5 ,p5,p6,p4 ,p4,p7 ,p7)


Step 1557: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q11

from e_216 and e_465. e_465: 
 13 terms, 52 factors, with derivatives of functions of all variables: 

                              2         2      2
 (q27,q20,q17,q11,q10,q8,q7,p5 ,p5,p6,p4 ,p4,p7 ,p7)

is replaced by e_424: 
 10 terms, 40 factors, with derivatives of functions of all variables: 

                    2         2
 (q27,q20,q17,q10,p5 ,p5,p6,p4 ,p4,p7)


Step 1558: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_325 we get the alternative equations : 
0=p4 - p5


0=2*p4*q7 - p6*q8


The list of inequalities got extended by: 

p5


New level : 1.1.2.2.1.2.1.
CRACK is now called with the new equation e_494 : 
0=p4 - p5

e_238,e_255,e_383,e_374,e_468,e_472,e_419,e_387,e_95,e_400 are consequences of 
e_494

Step 1559: 
Hot list of urgent steps : 
The list of inequalities got extended by: 

q17 - q20


The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 

1


The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 29 terms

The list of inequalities got extended by: 
An expression with 27 terms

The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 34 terms

e_397 is a consequence of e_474.
e_429 is a consequence of e_435.
Substitution of p4 by an expression in 
p5 found in e_494 : 
p4=p5


leads to a contradiction in : 16 factors in 6 terms

Time: 0 ms

Time: 0 ms

Time: 20 ms

The list of inequalities got extended by: 

p4 - p5


New level : 1.1.2.2.1.2.2.
CRACK is now called with the new equation e_494 : 
0=2*p4*q7 - p6*q8


Step 1560: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 52 terms

The list of inequalities got extended by: 
An expression with 54 terms

e_435 is a consequence of e_431.
Substitution of q8 by an expression in 
q7, p6, p4 found in e_494 : 
    2*p4*q7
q8=---------
      p6


Step 1561: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
*** Garbage collection starting 
*** GC 418  3-Oct-2003 05:33:27, 40 ms (0%), 1024590 occupied, 23975358 free

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 52 terms

The list of inequalities got extended by: 
An expression with 54 terms

e_474 is a consequence of e_458.
Substitution of q11 by an expression in 
q10, p6, p4 found in e_431 : 
      - p4*q10
q11=-----------
        p6


Step 1562: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 50 terms

The list of inequalities got extended by: 
An expression with 43 terms

The list of inequalities got extended by: 
An expression with 59 terms

The list of inequalities got extended by: 
An expression with 60 terms

Substitution of q26 by an expression in 
q17, q10, p4, p7 found in e_387 : 10 factors in 3 terms

Step 1563: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 3 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 51 terms

The list of inequalities got extended by: 
An expression with 53 terms

e_470 is a consequence of e_400.
e_453 is a consequence of e_450.
Substitution of q17 by an expression in 
q10, q7, p4, p7 found in e_95 : 7 factors in 3 terms

Step 1564: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 

p4*q20 - p5*q10 - p5*q20


p4 + p5


The list of inequalities got extended by: 
An expression with 73 terms

The list of inequalities got extended by: 
An expression with 63 terms

The list of inequalities got extended by: 
An expression with 87 terms

The list of inequalities got extended by: 
An expression with 87 terms

e_459 is a consequence of e_365.
Substitution of q7 by an expression in 
q20, q10, p5, p4, p7 found in e_443 : 14 factors in 4 terms

Step 1565: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 

q20

The lexicographical ordering of unknowns is changed
because q20 has to be non-zero, giving q20 a low priority.
Old ordering: q27,q20,q10,p5,p6,p4,p7
New ordering: q27,q10,q20,p5,p6,p4,p7

The list of inequalities got extended by: 
An expression with 50 terms

The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 50 terms

The list of inequalities got extended by: 
An expression with 55 terms

Substitution of q10 by an expression in 
q20, p5, p4 found in e_383 : 8 factors in 3 terms

leads to a contradiction in : 8 factors in 3 terms

This completes the investigation of all cases of a factorization.

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 30 ms

The list of inequalities got extended by: 

p3*p4 + p5*p6


New level : 1.1.2.2.2.
CRACK is now called with the new equation e_396 : 12 factors in 5 terms

Step 1566: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 41 terms

The list of inequalities got extended by: 
An expression with 47 terms

The list of inequalities got extended by: 
An expression with 56 terms

The list of inequalities got extended by: 
An expression with 58 terms

e_410 is a consequence of e_333.
e_414 is a consequence of e_333.
Substitution of q20 by an expression in 
q26, q17, q10, p5, p4, p7 found in e_396 : 11 factors in 5 terms

Step 1567: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_398 and e_406. e_406: 
 13 terms, 52 factors, with derivatives of functions of all variables: 

                              2      2      2
 (q27,q26,q17,q11,q10,p8,p5,p3 ,p3,p4 ,p4,p7 ,p7)

is replaced by e_430: 
 13 terms, 52 factors, with derivatives of functions of all variables: 

                       2      2      2      2
 (q26,q17,q11,q10,p8,p5 ,p5,p3 ,p3,p4 ,p4,p7 ,p7)


Step 1568: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_402 and e_403. e_403: 
 11 terms, 44 factors, with derivatives of functions of all variables: 

                                2      2
 (q27,q26,q17,q10,p8,p6,p5,p3,p4 ,p4,p7 ,p7)

is replaced by e_431: 
 7 terms, 21 factors, with derivatives of functions of all variables: 

 (q26,q17,q10,p8,p6,p5,p3,p4,p7)


Step 1569: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_402 and e_408. e_408: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                    2                  3   2
 (q27,q26,q17,q10,p8 ,p8,p6,p5,p3,p4,p7 ,p7 ,p7)

is replaced by e_432: 
 8 terms, 24 factors, with derivatives of functions of all variables: 

                2                  2
 (q26,q17,q10,p8 ,p8,p6,p5,p3,p4,p7 ,p7)


Step 1570: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 419  3-Oct-2003 05:33:29, 30 ms (0%), 1039305 occupied, 23960645 free
Eliminate 
q17

from e_65 and e_421. e_421: 
 10 terms, 40 factors, with derivatives of functions of all variables: 

                                   3   2      2
 (q26,q17,q11,q10,q9,q8,p8,p6,p5,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_433: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                               3   2      2
 (q26,q11,q10,q9,q8,p8,p6,p5,p4 ,p4 ,p4,p7 ,p7)


Step 1571: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_227 and e_424. e_424: 
 11 terms, 44 factors, with derivatives of functions of all variables: 

                                   2      2
 (q26,q17,q11,q10,q9,q8,p8,p6,p3,p4 ,p4,p7 ,p7)

is replaced by e_434: 
 11 terms, 44 factors, with derivatives of functions of all variables: 

                               2      2
 (q17,q11,q10,q9,q8,p8,p6,p3,p4 ,p4,p7 ,p7)


Step 1572: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_402 and e_415. e_415: 
 13 terms, 52 factors, with derivatives of functions of all variables: 

                              2      2         2
 (q27,q26,q17,q11,q10,p8,p6,p5 ,p5,p3 ,p3,p4,p7 ,p7)

is replaced by e_435: 
 12 terms, 48 factors, with derivatives of functions of all variables: 

                          2      2         2
 (q26,q17,q11,q10,p8,p6,p5 ,p5,p3 ,p3,p4,p7 ,p7)


Step 1573: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_402 and e_416. e_416: 
 15 terms, 60 factors, with derivatives of functions of all variables: 

                              2         2      2
 (q27,q26,q17,q11,q10,p8,p6,p5 ,p5,p3,p4 ,p4,p7 ,p7)

is replaced by e_28: 
 15 terms, 60 factors, with derivatives of functions of all variables: 

                                2      2
 (q26,q17,q11,q10,p8,p6,p5,p3,p4 ,p4,p7 ,p7)


Step 1574: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_402 and e_428. e_428: 
 22 terms, 88 factors, with derivatives of functions of all variables: 

                           2         2      2      2
 (q27,q26,q17,q11,q10,p8,p6 ,p6,p5,p3 ,p3,p4 ,p4,p7 ,p7)

is replaced by e_237: 
 14 terms, 42 factors, with derivatives of functions of all variables: 

                       2         2      2
 (q26,q17,q11,q10,p8,p6 ,p6,p5,p3 ,p3,p4 ,p4,p7)


Step 1575: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 420  3-Oct-2003 05:33:32, 30 ms (0%), 1040021 occupied, 23959928 free
*** Garbage collection starting 
*** GC 421  3-Oct-2003 05:33:35, 40 ms (0%), 1039119 occupied, 23960831 free
Eliminate 
q27

from e_402 and e_417. e_417: 
 14 terms, 56 factors, with derivatives of functions of all variables: 

                                     2            3   2
 (q27,q26,q17,q12,q11,q10,q7,p8,p6,p5 ,p5,p3,p4,p7 ,p7 ,p7)

is replaced by e_246: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                                          2
 (q26,q17,q12,q11,q10,q7,p8,p6,p5,p3,p4,p7 ,p7)


Step 1576: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_402 and e_419. e_419: 
 15 terms, 60 factors, with derivatives of functions of all variables: 

                                       2      2      3   2
 (q27,q26,q17,q11,q10,q9,q8,p8,p6,p5,p3 ,p3,p4 ,p4,p7 ,p7 ,p7)

is replaced by e_161: 
 11 terms, 33 factors, with derivatives of functions of all variables: 

                                   2      2      2
 (q26,q17,q11,q10,q9,q8,p8,p6,p5,p3 ,p3,p4 ,p4,p7 ,p7)


Step 1577: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_161 and e_426. e_426: 
 11 terms, 44 factors, with derivatives of functions of all variables: 

                                   2      3   2      2
 (q26,q17,q11,q10,q9,q8,p8,p6,p5,p3 ,p3,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_278: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

                               2      2
 (q17,q11,q10,q9,q8,p8,p5,p3,p4 ,p4,p7 ,p7)


Step 1578: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_402 and e_422. e_422: 
 18 terms, 72 factors, with derivatives of functions of all variables: 

                                     2         2      3   2
 (q27,q26,q17,q12,q11,q10,q8,p8,p6,p5 ,p5,p3,p4 ,p4,p7 ,p7 ,p7)

is replaced by e_103: 
 10 terms, 30 factors, with derivatives of functions of all variables: 

                                       2
 (q26,q17,q12,q11,q10,q8,p8,p6,p5,p4,p7 ,p7)


Step 1579: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_402 and e_425. e_425: 
 18 terms, 90 factors, with derivatives of functions of all variables: 

                                    2         3   2      3   2
 (q27,q26,q17,q11,q10,q9,q8,p8,p6,p5 ,p5,p3,p4 ,p4 ,p4,p7 ,p7 ,p7)

is replaced by e_23: 
 15 terms, 75 factors, with derivatives of functions of all variables: 

                                      3   2      3   2
 (q26,q17,q11,q10,q9,q8,p8,p6,p5,p3,p4 ,p4 ,p4,p7 ,p7 ,p7)


Step 1580: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 422  3-Oct-2003 05:33:38, 30 ms (0%), 1041435 occupied, 23958513 free
Eliminate 
q27

from e_409 and e_405. e_405: 
 14 terms, 56 factors, with derivatives of functions of all variables: 

                                 2      2         3   2
 (q27,q26,q17,q12,q10,q7,p8,p6,p5 ,p5,p3 ,p3,p4,p7 ,p7 ,p7)

is replaced by e_101: 
 9 terms, 27 factors, with derivatives of functions of all variables: 

                              2            2
 (q26,q17,q12,q11,q10,q7,p8,p5 ,p5,p3,p4,p7 ,p7)


Step 1581: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 423  3-Oct-2003 05:33:41, 30 ms (0%), 1034591 occupied, 23965359 free
*** Garbage collection starting 
*** GC 424  3-Oct-2003 05:33:45, 30 ms (0%), 1039511 occupied, 23960438 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 43 terms

The list of inequalities got extended by: 
An expression with 58 terms

The list of inequalities got extended by: 
An expression with 60 terms

Substitution of q12 by an expression in 
q9, q8, p5, p3, p4 found in e_367 : 17 factors in 4 terms

Step 1582: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 425  3-Oct-2003 05:33:49, 30 ms (0%), 1049177 occupied, 23950772 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_191 we get the alternative equations : 
0=p4 - p5

8 factors in 3 terms

The list of inequalities got extended by: 

p5

The lexicographical ordering of unknowns is changed
because p5 has to be non-zero, giving p5 a low priority.
Old ordering: q27,q26,q17,q11,q10,q9,q8,q7,p8,p6,p5,p3,p4,p7
New ordering: q27,q26,q17,q11,q10,q9,q8,q7,p8,p6,p3,p5,p4,p7

New level : 1.1.2.2.2.1.
CRACK is now called with the new equation e_358 : 
0=p4 - p5

e_255 is a consequence of e_358

Step 1583: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 36 terms

The list of inequalities got extended by: 

p4


The list of inequalities got extended by: 

1


The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

p3 + p6


The list of inequalities got extended by: 
An expression with 28 terms

The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 41 terms

e_395 is a consequence of e_371.
Substitution of p4 by an expression in 
p5 found in e_358 : 
p4=p5


Step 1584: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 56 terms

The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 62 terms

The list of inequalities got extended by: 
An expression with 66 terms

e_393 is a consequence of e_387.
e_380 is a consequence of e_387.
e_381 is a consequence of e_387.e_287 is a consequence of e_365

e_383 is a consequence of e_365.
Substitution of q26 by an expression in 
q17, q10, p8, p6, p3 found in e_372 : 9 factors in 3 terms

Step 1585: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 22 terms

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 
An expression with 23 terms

The list of inequalities got extended by: 
An expression with 26 terms

e_374 is a consequence of e_439.
e_421 is a consequence of e_443.
e_410 is a consequence of e_385.
e_392 is a consequence of e_387.
e_440 is a consequence of e_387.
e_415 is a consequence of e_408.
Substitution of q17 by an expression in 
q10 found in e_365 : 
q17=q10


Step 1586: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 17 terms

The list of inequalities got extended by: 
An expression with 12 terms

The list of inequalities got extended by: 
An expression with 15 terms

The list of inequalities got extended by: 
An expression with 18 terms

e_408 is a consequence of e_396.
Substitution of q10 found in e_439 : 
q10=0


Step 1587: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 13 terms

The list of inequalities got extended by: 
An expression with 10 terms

The list of inequalities got extended by: 
An expression with 11 terms

The list of inequalities got extended by: 
An expression with 14 terms
e_226 is a consequence of e_387

e_326 is a consequence of e_387.
e_385 is a consequence of e_371.
e_442 is a consequence of e_387.
Substitution of q11 found in e_396 : 
q11=0


Step 1588: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 8 terms

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 10 terms

e_371 is a consequence of e_443.
e_157 is a consequence of e_437.
e_444 is a consequence of e_443.
e_441 is a consequence of e_443.
e_414 is a consequence of e_443.
e_406 is a consequence of e_443.
e_394 is a consequence of e_443.
Substitution of q9 found in e_424 : 
q9=0


Step 1589: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 7 terms

The list of inequalities got extended by: 
An expression with 4 terms

The list of inequalities got extended by: 
An expression with 8 terms

e_403 is a consequence of e_443.
e_445 is a consequence of e_438.
e_446 is a consequence of e_436.
Substitution of q27 found in e_387 : 
q27=0


Step 1590: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

q8

The lexicographical ordering of unknowns is changed
because q8 has to be non-zero, giving q8 a low priority.
Old ordering: q8,q7,p8,p6,p3,p5,p7
New ordering: q7,q8,p8,p6,p3,p5,p7

The list of inequalities got extended by: 

p8


q7

The lexicographical ordering of unknowns is changed
because p8 has to be non-zero, giving p8 a low priority.
Old ordering: q7,q8,p8,p6,p3,p5,p7
New ordering: q7,q8,p6,p3,p8,p5,p7

The list of inequalities got extended by: 
An expression with 7 terms

Substitution of q7 found in e_437 : 
q7=0


leads to a contradiction in : 
0=2*p7*q7 - p8*q8


Time: 0 ms

Time: 0 ms
*** Garbage collection starting 
*** GC 426  3-Oct-2003 05:33:52, 30 ms (0%), 981383 occupied, 24018566 free

Time: 30 ms  plus GC time: 30 ms

The list of inequalities got extended by: 

p4 - p5


New level : 1.1.2.2.2.2.
CRACK is now called with the new equation e_358 : 8 factors in 3 terms

Step 1591: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 48 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 59 terms

The list of inequalities got extended by: 
An expression with 61 terms
e_326 is a consequence of e_287

Substitution of q7 by an expression in 
q9, q8, p3, p4 found in e_358 : 7 factors in 3 terms

Step 1592: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_376 and e_226. e_226: 
 15 terms, 75 factors, with derivatives of functions of all variables: 

                          2         2      2      2
 (q26,q17,q11,q10,q9,q8,p6 ,p6,p5,p3 ,p3,p4 ,p4,p7 ,p7)

is replaced by e_372: 
 15 terms, 75 factors, with derivatives of functions of all variables: 

                         2         2      2      2
 (q26,q11,q10,q9,q8,p8,p6 ,p6,p5,p3 ,p3,p4 ,p4,p7 ,p7)


Step 1593: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 427  3-Oct-2003 05:33:55, 40 ms (0%), 1038544 occupied, 23961397 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 57 terms

The list of inequalities got extended by: 
An expression with 49 terms

The list of inequalities got extended by: 
An expression with 68 terms

The list of inequalities got extended by: 
An expression with 70 terms

Substitution of q11 by an expression in 
q26, q17, q10, q9, q8, p8, p6, p3, p4, p7 found in e_255 : 20 factors in 6 terms

Step 1594: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_374 and e_434. e_374: 
 9 terms, 36 factors, with derivatives of functions of all variables: 

                            2      2
 (q26,q17,q10,q9,p8,p6,p3,p4 ,p4,p7 ,p7)

is replaced by e_395: 
 8 terms, 32 factors, with derivatives of functions of all variables: 

                        2      2
 (q17,q10,q9,p8,p6,p3,p4 ,p4,p7 ,p7)


Step 1595: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 428  3-Oct-2003 05:33:58, 30 ms (0%), 1053835 occupied, 23946106 free
*** Garbage collection starting 
*** GC 429  3-Oct-2003 05:34:01, 40 ms (0%), 1064812 occupied, 23935131 free
*** Garbage collection starting 
*** GC 430  3-Oct-2003 05:34:04, 40 ms (0%), 1056803 occupied, 23943136 free
Eliminate 
q27

from e_409 and e_411. e_411: 
 19 terms, 114 factors, with derivatives of functions of all variables: 

                                2         4   3   2      3   2
 (q27,q26,q17,q10,q9,q8,p8,p6,p5 ,p5,p3,p4 ,p4 ,p4 ,p4,p7 ,p7 ,p7)

is replaced by e_385: 
 16 terms, 96 factors, with derivatives of functions of all variables: 

                                  4   3   2      3   2
 (q26,q17,q10,q9,q8,p8,p6,p5,p3,p4 ,p4 ,p4 ,p4,p7 ,p7 ,p7)


Step 1596: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 431  3-Oct-2003 05:34:08, 30 ms (0%), 1056566 occupied, 23943377 free
*** Garbage collection starting 
*** GC 432  3-Oct-2003 05:34:11, 40 ms (0%), 1056390 occupied, 23943554 free
 --- 
Factorization to subcases leading to substitutions : 
factorizing e_392 we get the alternative equations : 
0=p3

29 factors in 7 terms

New level : 1.1.2.2.2.2.1.
CRACK is now called with the new equation e_396 : 
0=p3


Step 1597: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 5 terms

The list of inequalities got extended by: 

p5


p6

The lexicographical ordering of unknowns is changed
because p5 has to be non-zero, giving p5 a low priority.
Old ordering: q27,q26,q17,q10,q9,q8,p8,p6,p5,p3,p4,p7
New ordering: q27,q26,q17,q10,q9,q8,p8,p6,p3,p5,p4,p7
The lexicographical ordering of unknowns is changed
because p6 has to be non-zero, giving p6 a low priority.
Old ordering: q27,q26,q17,q10,q9,q8,p8,p6,p3,p5,p4,p7
New ordering: q27,q26,q17,q10,q9,q8,p8,p3,p6,p5,p4,p7

The list of inequalities got extended by: 
An expression with 45 terms

The list of inequalities got extended by: 
An expression with 40 terms

The list of inequalities got extended by: 
An expression with 55 terms

The list of inequalities got extended by: 
An expression with 56 terms

e_457 is a consequence of e_445.
Substitution of p3 found in e_396 : 
p3=0


Step 1598: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 51 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 62 terms

The list of inequalities got extended by: 
An expression with 63 terms

e_455 is a consequence of e_408.
Substitution of q8 by an expression in 
q9, p6, p5, p4 found in e_403 : 
    p4*q9 + p5*q9
q8=---------------
         p6


Step 1599: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 54 terms

The list of inequalities got extended by: 
An expression with 53 terms

The list of inequalities got extended by: 
An expression with 71 terms

The list of inequalities got extended by: 
An expression with 71 terms

Substitution of q26 by an expression in 
q17, q10, p8, p6 found in e_408 : 8 factors in 3 terms

Step 1600: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 6 terms

Step 1601: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_406 and e_462. e_462: 
 11 terms, 55 factors, with derivatives of functions of all variables: 

                  2         3   2      2
 (q17,q10,q9,p8,p6 ,p6,p5,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_471: 
 6 terms, 24 factors, with derivatives of functions of all variables: 

              2         2
 (q10,q9,p8,p6 ,p6,p5,p4 ,p4,p7)


Step 1602: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q10

from e_471 and e_446. e_446: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

                        2
 (q17,q10,q9,p8,p6,p5,p4 ,p4,p7)

is replaced by e_472: 
 7 terms, 28 factors, with derivatives of functions of all variables: 

              2         2
 (q17,q9,p8,p6 ,p6,p5,p4 ,p4,p7)


Step 1603: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 433  3-Oct-2003 05:34:14, 40 ms (0%), 1073221 occupied, 23926723 free
Eliminate 
q17

from e_438 and e_450. e_450: 
 12 terms, 60 factors, with derivatives of functions of all variables: 

                  2         3   2      2
 (q17,q10,q9,p8,p6 ,p6,p5,p4 ,p4 ,p4,p7 ,p7)

is replaced by e_473: 
 10 terms, 50 factors, with derivatives of functions of all variables: 

              3   2      2      2
 (q10,q9,p8,p6 ,p6 ,p6,p5 ,p5,p4 ,p4,p7)


Step 1604: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_456 and e_458. e_458: 
 11 terms, 66 factors, with derivatives of functions of all variables: 

               2         2      3   2      3   2
 (q17,q10,q9,p8 ,p8,p6,p5 ,p5,p4 ,p4 ,p4,p7 ,p7 ,p7)

is replaced by e_474: 
(#) 6 terms, 9 factors, with derivatives of functions of all variables: 

             2      2
 (q9,p8,p6,p5 ,p5,p4 ,p4,p7)


e_474 is a consequence of e_453.
Step 1605: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_448 and e_454. e_454: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

                   2            2      3
 (q27,q17,q10,q9,p8 ,p8,p6,p5,p4 ,p4,p7 ,p7)

is replaced by e_475: 
 5 terms, 20 factors, with derivatives of functions of all variables: 

           2            2
 (q27,q9,p8 ,p6,p5,p4,p7 )


Step 1606: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 434  3-Oct-2003 05:34:18, 40 ms (0%), 1067942 occupied, 23932001 free
Eliminate 
q17

from e_438 and e_464. e_464: 
 15 terms, 90 factors, with derivatives of functions of all variables: 

                   2      2      2      2      3   2
 (q27,q17,q10,q9,p8 ,p8,p6 ,p6,p5 ,p5,p4 ,p4,p7 ,p7 ,p7)

is replaced by e_476: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

               2      2            2
 (q27,q10,q9,p8 ,p8,p6 ,p6,p5,p4,p7 ,p7)


Step 1607: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_475 and e_476. e_476: 
 9 terms, 45 factors, with derivatives of functions of all variables: 

               2      2            2
 (q27,q10,q9,p8 ,p8,p6 ,p6,p5,p4,p7 ,p7)

is replaced by e_477: 
 7 terms, 35 factors, with derivatives of functions of all variables: 

           2      2            2
 (q10,q9,p8 ,p8,p6 ,p6,p5,p4,p7 ,p7)


Step 1608: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions : 
factorizing e_469 we get the alternative equations : 
0=q9

7 factors in 3 terms

New level : 1.1.2.2.2.2.1.1.
CRACK is now called with the new equation e_487 : 
0=q9

e_453 is a consequence of e_487

Step 1609: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 38 terms

The list of inequalities got extended by: 
An expression with 42 terms

The list of inequalities got extended by: 
An expression with 53 terms

The list of inequalities got extended by: 
An expression with 53 terms

e_95 is a consequence of e_417.
e_238 is a consequence of e_417.
Substitution of q9 found in e_487 : 
q9=0


Step 1610: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 32 terms

The list of inequalities got extended by: 
An expression with 39 terms

The list of inequalities got extended by: 
An expression with 46 terms

The list of inequalities got extended by: 
An expression with 47 terms

Substitution of q27 found in e_416 : 
q27=0


Step 1611: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases : 
The list of inequalities got extended by: 
An expression with 18 terms

The list of inequalities got extended by: 
An expression with 21 terms

The list of inequalities got extended by: 
An expression with 23 terms

q17

The lexicographical ordering of unknowns is changed
because q17 has to be non-zero, giving q17 a low priority.
Old ordering: q17,q10,p8,p6,p5,p4,p7
New ordering: q10,q17,p8,p6,p5,p4,p7

The list of inequalities got extended by: 
An expression with 25 terms

The list of inequalities got extended by: 

p8


Substitution of q10 found in e_417 : 
q10=0


leads to a contradiction in : 16 factors in 5 terms

Time: 0 ms

Time: 0 ms

Time: 30 ms

The list of inequalities got extended by: 

q9


New level : 1.1.2.2.2.2.1.2.
CRACK is now called with the new equation e_487 : 7 factors in 3 terms
e_406 is a consequence of e_487

Step 1612: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 9 terms

The list of inequalities got extended by: 
An expression with 53 terms

The list of inequalities got extended by: 
An expression with 44 terms

The list of inequalities got extended by: 
An expression with 59 terms

The list of inequalities got extended by: 
An expression with 61 terms

e_238 is a consequence of e_367.
e_325 is a consequence of e_367.
Substitution of p8 by an expression in 
p6, p5, p4, p7 found in e_487 : 
     - p6*p7
p8=----------
    p4 - p5


Step 1613: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1614: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_367 and e_324. e_324: 
 6 terms, 18 factors, with derivatives of functions of all variables: 

                  2
 (q17,q10,q9,p5,p4 ,p4,p7)

is replaced by e_467: 
 3 terms, 6 factors, with derivatives of functions of all variables: 

 (q10,q9,p5,p4,p7)


Step 1615: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
*** Garbage collection starting 
*** GC 435  3-Oct-2003 05:34:21, 40 ms (0%), 1051825 occupied, 23948124 free

The list of inequalities got extended by: 
An expression with 85 terms

The list of inequalities got extended by: 
An expression with 69 terms

The list of inequalities got extended by: 
An expression with 94 terms

The list of inequalities got extended by: 
An expression with 97 terms
e_416 is a consequence of e_422

Substitution of q10 by an expression in 
q9, p5, p4, p7 found in e_467 : 
      - 2*p7*q9
q10=------------
      p4 - p5


Step 1616: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 6 terms

The list of inequalities got extended by: 

  2       2
p5  + 3*p6


The list of inequalities got extended by: 
An expression with 62 terms

The list of inequalities got extended by: 
An expression with 50 terms

The list of inequalities got extended by: 
An expression with 67 terms

The list of inequalities got extended by: 
An expression with 68 terms

e_422 is a consequence of e_323.
e_53 is a consequence of e_367.
Substitution of p4 by an expression in 
p6, p5 found in e_338 : 
      2       2
    p5  + 3*p6
p4=-------------
        p5


Step 1617: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1618: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_323 and e_428. e_428: 
 4 terms, 20 factors, with derivatives of functions of all variables: 

           4   2   3   2
 (q17,q9,p6 ,p6 ,p5 ,p5 ,p5,p7)

is replaced by e_440: 
 3 terms, 12 factors, with derivatives of functions of all variables: 

           2   2
 (q17,q9,p6 ,p5 ,p5,p7)


Step 1619: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1620: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 

  2        2
p5  + 27*p6


q17

The lexicographical ordering of unknowns is changed
because q17 has to be non-zero, giving q17 a low priority.
Old ordering: q27,q17,q9,p6,p5,p7
New ordering: q27,q9,q17,p6,p5,p7

The list of inequalities got extended by: 
An expression with 61 terms

The list of inequalities got extended by: 
An expression with 51 terms

The list of inequalities got extended by: 
An expression with 66 terms

The list of inequalities got extended by: 
An expression with 68 terms

e_440 is a consequence of e_323.
e_466 is a consequence of e_323.
e_405 is a consequence of e_323.
e_337 is a consequence of e_323.
e_425 is a consequence of e_323.
e_426 is a consequence of e_323.
e_374 is a consequence of e_323.
e_414 is a consequence of e_323.
e_255 is a consequence of e_323.
e_392 is a consequence of e_323.
Substitution of q9 by an expression in 
q17, p6, p5, p7 found in e_470 : 11 factors in 3 terms

Step 1621: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
p6

from e_323 and e_468. e_468: 
 4 terms, 16 factors, with derivatives of functions of all variables: 

            3   2      2
 (q27,q17,p6 ,p6 ,p6,p5 ,p7)

is replaced by e_462: 
 3 terms, 12 factors, with derivatives of functions of all variables: 

            2      2
 (q27,q17,p6 ,p6,p5 ,p7)


Step 1622: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
The list of inequalities got extended by: 

q27

Eliminate 
p6

from e_323 and e_462. e_462: 
 3 terms, 12 factors, with derivatives of functions of all variables: 

            2      2
 (q27,q17,p6 ,p6,p5 ,p7)

is replaced by e_446: 

0=5*p6*q27 + 2*p7*q17


Step 1623: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases : 
The list of inequalities got extended by: 
An expression with 53 terms

The list of inequalities got extended by: 

q27


The list of inequalities got extended by: 
An expression with 47 terms

The list of inequalities got extended by: 
An expression with 58 terms

The list of inequalities got extended by: 
An expression with 60 terms

e_322 is a consequence of e_323.
e_457 is a consequence of e_323.
e_419 is a consequence of e_323.
e_410 is a consequence of e_323.
e_411 is a consequence of e_323.
e_326 is a consequence of e_323.
e_226 is a consequence of e_323.
e_358 is a consequence of e_323.
e_191 is a consequence of e_323.
Substitution of q27 by an expression in 
q17, p6, p7 found in e_446 : 
         2
      - ---*p7*q17
         5
q27=---------------
          p6


Step 1624: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step :  --- 
Any factorization :  --- 
Substitution of <=1000 terms :  --- 


>>>>>>>>> Solution of level 1.1.2.2.2.2.1.2. : 
equations : 

e_323 : 
    2       2
0=p5  + 9*p6



Non-vanishing expressions: q27,p7,p6,p5,q17
329 factors in 60 terms
270 factors in 58 terms
260 factors in 47 terms
294 factors in 53 terms

  2       2
p5  + 3*p6


        2                                      2             2
g0111*p5 *p7 - 3*g0112*p5*p6*p7 - 3*g0113*p5*p6  - 3*g0114*p5 *p6

             2                3
 - 3*g0115*p5 *p6 - 9*g0115*p6


  2        2
p5  + 27*p6


functions : 
         2
      - ---*p7*q17
         5
q27=---------------
          p6


       4     3           2        2
     -----*p5 *p7*q17 + ----*p5*p6 *p7*q17
      135                15
q26=---------------------------------------
                        4
                      p6


q25=0


q24=q17


      2     6         7     4   2        67    2   4        42    6
     ----*p5 *q17 + -----*p5 *p6 *q17 - ----*p5 *p6 *q17 - ----*p6 *q17
      81             135                 15                 5
q23=--------------------------------------------------------------------
                               3   3          5
                             p5 *p6  + 3*p5*p6


      2     6        43     4   2        47    2   4        12    6
     ----*p5 *q17 + -----*p5 *p6 *q17 + ----*p5 *p6 *q17 + ----*p6 *q17
      81             135                 15                 5
q22=--------------------------------------------------------------------
                               3   3          5
                             p5 *p6  + 3*p5*p6


q21=q17


q20=q17


      4     4        1    2   2           4
     ----*p5 *q17 - ---*p5 *p6 *q17 - 2*p6 *q17
      81             9
q19=--------------------------------------------
                            3
                       p5*p6


      1
     ---*p5*q17
      3
q18=------------
         p6

q17, 
         2     2        4    2
      - ----*p5 *q17 + ---*p6 *q17
         45             5
q16=-------------------------------
                    2
                  p6


       2     6        11    4   2           2   4        27    6
     -----*p5 *q17 + ----*p5 *p6 *q17 + 4*p5 *p6 *q17 + ----*p6 *q17
      135             45                                 5
q15=-----------------------------------------------------------------
                             3   3          5
                           p5 *p6  + 3*p5*p6


      1     6        31    4   2        15    2   4        81    6
     ----*p5 *q17 + ----*p5 *p6 *q17 + ----*p5 *p6 *q17 + ----*p6 *q17
      15             15                 2                  10
q14=-------------------------------------------------------------------
                           4             2   3
                         p5 *p6*p7 + 3*p5 *p6 *p7


         2     4        19    2   2        27    4
      - ----*p5 *q17 - ----*p5 *p6 *q17 - ----*p6 *q17
         15             5                  5
q13=---------------------------------------------------
                     3             2
                   p5 *p7 + 3*p5*p6 *p7


         1     4        19    2   2        27    4
      - ----*p5 *q17 - ----*p5 *p6 *q17 - ----*p6 *q17
         15             10                 10
q12=---------------------------------------------------
                     2             3
                   p5 *p6*p7 + 3*p6 *p7


       2     6        1     4   2        18    2   4        27    6
     -----*p5 *q17 - ----*p5 *p6 *q17 - ----*p5 *p6 *q17 - ----*p6 *q17
      135             45                 5                  5
q11=--------------------------------------------------------------------
                               3   3          5
                             p5 *p6  + 3*p5*p6


      2     2        6    2
     ----*p5 *q17 + ---*p6 *q17
      45             5
q10=----------------------------
                  2
                p6


        1     2        9    2
     - ----*p5 *q17 - ---*p6 *q17
        15             5
q9=-------------------------------
                p5*p7


        2     4        19    2   2        27    4
     - ----*p5 *q17 - ----*p5 *p6 *q17 - ----*p6 *q17
        15             5                  5
q8=---------------------------------------------------
                          2
                        p5 *p6*p7


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


        1
     - ---*p5*p7
        3
p8=--------------
         p6

p7, p6, p5, 
      2       2
    p5  + 3*p6
p4=-------------
        p5


p3=0


p2=0


p1=0


with 83 terms
number of equations : 1
total no of terms   : 2
total no of factors :  4
1 equation in 0 variables: 
e_323(2a)
4 constants : p5,p6,p7,q17
The equation: 

             2                                     2                    3
f =(D f*f *p5 *p6 + D D f  *p5*p6*p7 + D D f*D f*p5 *p6 + 3*D D f*D f*p6
 t   2   x           1 2 2x             1 2   1              1 2   1

                   2    1        2
     + D f*f *p5*p6  - ---*f  *p5 *p7)/(p5*p6)
        1   x           3   3x
The symmetry: 
      2                 7              1                 5   3
f =(-----*D f  *D D f*p5 *p6*p7*q17 - ----*D f  *D D f*p5 *p6 *p7*q17
 s   135   2 2x  1 2                   45   2 2x  1 2

        18                3   5           27                   7
     - ----*D f  *D D f*p5 *p6 *p7*q17 - ----*D f  *D D f*p5*p6 *p7*q17
        5    2 2x  1 2                    5    2 2x  1 2

        2              6   2           2             4   4
     - ----*D f  *f *p5 *p6 *p7*q17 + ---*D f  *f *p5 *p6 *p7*q17
        45   2 2x  x                   3   2 2x  x

        12             2   6           1                5   3
     + ----*D f  *f *p5 *p6 *p7*q17 + ---*D f *D D f *p5 *p6 *p7*q17
        5    2 2x  x                   3   2 x  1 2 x

                     3   5                     4   4
     + D f *D D f *p5 *p6 *p7*q17 + D f *f  *p5 *p6 *p7*q17
        2 x  1 2 x                   2 x  2x

                    2   6           1        2      6   3
     + 3*D f *f  *p5 *p6 *p7*q17 - ----*(D f) *f *p5 *p6 *q17
          2 x  2x                   15    2     x

        19       2      4   5        27       2      2   7
     - ----*(D f) *f *p5 *p6 *q17 - ----*(D f) *f *p5 *p6 *q17
        10    2     x                10    2     x

        2                 7               7                 5   3
     + ----*D f*D D f  *p5 *p6*p7*q17 + -----*D f*D D f  *p5 *p6 *p7*q17
        81   2   1 2 2x                  135   2   1 2 2x

        67                3   5           42                   7
     - ----*D f*D D f  *p5 *p6 *p7*q17 - ----*D f*D D f  *p5*p6 *p7*q17
        15   2   1 2 2x                   5    2   1 2 2x

        2                   6   3        21                  4   5
     - ----*D f*D D f*D f*p5 *p6 *q17 - ----*D f*D D f*D f*p5 *p6 *q17
        15   2   1 2   1                 5    2   1 2   1

        84                  2   7        81                  9
     - ----*D f*D D f*D f*p5 *p6 *q17 - ----*D f*D D f*D f*p6 *q17
        5    2   1 2   1                 5    2   1 2   1

        2                5   4        19               3   6
     - ----*D f*D f*f *p5 *p6 *q17 - ----*D f*D f*f *p5 *p6 *q17
        15   2   1   x                5    2   1   x

        27                  8                 4   4
     - ----*D f*D f*f *p5*p6 *q17 + D f*f  *p5 *p6 *p7*q17
        5    2   1   x               2   3x

                   2   6            4             7   2
     + 3*D f*f  *p5 *p6 *p7*q17 + -----*D D f  *p5 *p7 *q17
          2   3x                   135   1 2 4x

        2            5   2   2        2            3   4   2
     + ---*D D f  *p5 *p6 *p7 *q17 + ---*D D f  *p5 *p6 *p7 *q17
        9   1 2 4x                    5   1 2 4x

                     4   4                          2   6
     + D D f  *D f*p5 *p6 *p7*q17 + 3*D D f  *D f*p5 *p6 *p7*q17
        1 2 2x  1                      1 2 2x  1

                     4   4                          2   6
     + D D f *D f *p5 *p6 *p7*q17 + 3*D D f *D f *p5 *p6 *p7*q17
        1 2 x  1 x                     1 2 x  1 x

        2                 6   2           4                4   4
     + ----*D D f*D f  *p5 *p6 *p7*q17 + ---*D D f*D f  *p5 *p6 *p7*q17
        45   1 2   1 2x                   3   1 2   1 2x

        18                2   6           1              2   5   4
     + ----*D D f*D f  *p5 *p6 *p7*q17 - ----*D D f*(D f) *p5 *p6 *q17
        5    1 2   1 2x                   15   1 2    1

                    2   3   6        27             2      8
     - 2*D D f*(D f) *p5 *p6 *q17 - ----*D D f*(D f) *p5*p6 *q17
          1 2    1                   5    1 2    1

         2              7              11             5   3
     + -----*D f  *f *p5 *p6*p7*q17 + ----*D f  *f *p5 *p6 *p7*q17
        135   1 2x  x                  45   1 2x  x

                    3   5           27                7
     + 4*D f  *f *p5 *p6 *p7*q17 + ----*D f  *f *p5*p6 *p7*q17
          1 2x  x                   5    1 2x  x

        4              7              1              5   3
     + ----*D f *f  *p5 *p6*p7*q17 + ----*D f *f  *p5 *p6 *p7*q17
        81   1 x  2x                  27   1 x  2x

        7             3   5                          7
     - ---*D f *f  *p5 *p6 *p7*q17 - 6*D f *f  *p5*p6 *p7*q17
        3   1 x  2x                     1 x  2x

        1        2      6   3        31       2      4   5
     + ----*(D f) *f *p5 *p6 *q17 + ----*(D f) *f *p5 *p6 *q17
        15    1     x                15    1     x

        15       2      2   7        81       2      9
     + ----*(D f) *f *p5 *p6 *q17 + ----*(D f) *f *p6 *q17
        2     1     x                10    1     x

        2             7              43             5   3
     + ----*D f*f  *p5 *p6*p7*q17 + -----*D f*f  *p5 *p6 *p7*q17
        81   1   3x                  135   1   3x

        47            3   5           12               7
     + ----*D f*f  *p5 *p6 *p7*q17 + ----*D f*f  *p5*p6 *p7*q17
        15   1   3x                   5    1   3x

        2        4   3   2        6        2   5   2         4   4
     - ---*f  *p5 *p6 *p7 *q17 - ---*f  *p5 *p6 *p7 *q17)/(p5 *p6 *p7
        5   5x                    5   5x

          2   6
    + 3*p5 *p6 *p7)
And now in machine readable form:

The system: 

df(f(1),t)=(d(2,f(1))*df(f(1),x)*p5**2*p6 + d(1,d(2,df(f(1),x,2)))*p5*p6*p7 + d(
1,d(2,f(1)))*d(1,f(1))*p5**2*p6 + 3*d(1,d(2,f(1)))*d(1,f(1))*p6**3 + d(1,f(1))*
df(f(1),x)*p5*p6**2 - 1/3*df(f(1),x,3)*p5**2*p7)/(p5*p6)$
The symmetry: 
df(f(1),s)=(2/135*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5**7*p6*p7*q17 - 1/45*d(2,df
(f(1),x,2))*d(1,d(2,f(1)))*p5**5*p6**3*p7*q17 - 18/5*d(2,df(f(1),x,2))*d(1,d(2,f
(1)))*p5**3*p6**5*p7*q17 - 27/5*d(2,df(f(1),x,2))*d(1,d(2,f(1)))*p5*p6**7*p7*q17
 - 2/45*d(2,df(f(1),x,2))*df(f(1),x)*p5**6*p6**2*p7*q17 + 2/3*d(2,df(f(1),x,2))*
df(f(1),x)*p5**4*p6**4*p7*q17 + 12/5*d(2,df(f(1),x,2))*df(f(1),x)*p5**2*p6**6*p7
*q17 + 1/3*d(2,df(f(1),x))*d(1,d(2,df(f(1),x)))*p5**5*p6**3*p7*q17 + d(2,df(f(1)
,x))*d(1,d(2,df(f(1),x)))*p5**3*p6**5*p7*q17 + d(2,df(f(1),x))*df(f(1),x,2)*p5**
4*p6**4*p7*q17 + 3*d(2,df(f(1),x))*df(f(1),x,2)*p5**2*p6**6*p7*q17 - 1/15*d(2,f(
1))**2*df(f(1),x)*p5**6*p6**3*q17 - 19/10*d(2,f(1))**2*df(f(1),x)*p5**4*p6**5*
q17 - 27/10*d(2,f(1))**2*df(f(1),x)*p5**2*p6**7*q17 + 2/81*d(2,f(1))*d(1,d(2,df(
f(1),x,2)))*p5**7*p6*p7*q17 + 7/135*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p5**5*p6**3
*p7*q17 - 67/15*d(2,f(1))*d(1,d(2,df(f(1),x,2)))*p5**3*p6**5*p7*q17 - 42/5*d(2,f
(1))*d(1,d(2,df(f(1),x,2)))*p5*p6**7*p7*q17 - 2/15*d(2,f(1))*d(1,d(2,f(1)))*d(1,
f(1))*p5**6*p6**3*q17 - 21/5*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p5**4*p6**5*q17 
- 84/5*d(2,f(1))*d(1,d(2,f(1)))*d(1,f(1))*p5**2*p6**7*q17 - 81/5*d(2,f(1))*d(1,d
(2,f(1)))*d(1,f(1))*p6**9*q17 - 2/15*d(2,f(1))*d(1,f(1))*df(f(1),x)*p5**5*p6**4*
q17 - 19/5*d(2,f(1))*d(1,f(1))*df(f(1),x)*p5**3*p6**6*q17 - 27/5*d(2,f(1))*d(1,f
(1))*df(f(1),x)*p5*p6**8*q17 + d(2,f(1))*df(f(1),x,3)*p5**4*p6**4*p7*q17 + 3*d(2
,f(1))*df(f(1),x,3)*p5**2*p6**6*p7*q17 + 4/135*d(1,d(2,df(f(1),x,4)))*p5**7*p7**
2*q17 + 2/9*d(1,d(2,df(f(1),x,4)))*p5**5*p6**2*p7**2*q17 + 2/5*d(1,d(2,df(f(1),x
,4)))*p5**3*p6**4*p7**2*q17 + d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p5**4*p6**4*p7*
q17 + 3*d(1,d(2,df(f(1),x,2)))*d(1,f(1))*p5**2*p6**6*p7*q17 + d(1,d(2,df(f(1),x)
))*d(1,df(f(1),x))*p5**4*p6**4*p7*q17 + 3*d(1,d(2,df(f(1),x)))*d(1,df(f(1),x))*
p5**2*p6**6*p7*q17 + 2/45*d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p5**6*p6**2*p7*q17 + 
4/3*d(1,d(2,f(1)))*d(1,df(f(1),x,2))*p5**4*p6**4*p7*q17 + 18/5*d(1,d(2,f(1)))*d(
1,df(f(1),x,2))*p5**2*p6**6*p7*q17 - 1/15*d(1,d(2,f(1)))*d(1,f(1))**2*p5**5*p6**
4*q17 - 2*d(1,d(2,f(1)))*d(1,f(1))**2*p5**3*p6**6*q17 - 27/5*d(1,d(2,f(1)))*d(1,
f(1))**2*p5*p6**8*q17 + 2/135*d(1,df(f(1),x,2))*df(f(1),x)*p5**7*p6*p7*q17 + 11/
45*d(1,df(f(1),x,2))*df(f(1),x)*p5**5*p6**3*p7*q17 + 4*d(1,df(f(1),x,2))*df(f(1)
,x)*p5**3*p6**5*p7*q17 + 27/5*d(1,df(f(1),x,2))*df(f(1),x)*p5*p6**7*p7*q17 + 4/
81*d(1,df(f(1),x))*df(f(1),x,2)*p5**7*p6*p7*q17 + 1/27*d(1,df(f(1),x))*df(f(1),x
,2)*p5**5*p6**3*p7*q17 - 7/3*d(1,df(f(1),x))*df(f(1),x,2)*p5**3*p6**5*p7*q17 - 6
*d(1,df(f(1),x))*df(f(1),x,2)*p5*p6**7*p7*q17 + 1/15*d(1,f(1))**2*df(f(1),x)*p5
**6*p6**3*q17 + 31/15*d(1,f(1))**2*df(f(1),x)*p5**4*p6**5*q17 + 15/2*d(1,f(1))**
2*df(f(1),x)*p5**2*p6**7*q17 + 81/10*d(1,f(1))**2*df(f(1),x)*p6**9*q17 + 2/81*d(
1,f(1))*df(f(1),x,3)*p5**7*p6*p7*q17 + 43/135*d(1,f(1))*df(f(1),x,3)*p5**5*p6**3
*p7*q17 + 47/15*d(1,f(1))*df(f(1),x,3)*p5**3*p6**5*p7*q17 + 12/5*d(1,f(1))*df(f(
1),x,3)*p5*p6**7*p7*q17 - 2/5*df(f(1),x,5)*p5**4*p6**3*p7**2*q17 - 6/5*df(f(1),x
,5)*p5**2*p6**5*p7**2*q17)/(p5**4*p6**4*p7 + 3*p5**2*p6**6*p7)$

This completes the investigation of all cases of a factorization.

Time: 0 ms

Time: 0 ms

Time: 30 ms

The list of inequalities got extended by: 

p3


New level : 1.1.2.2.2.2.2.
CRACK is now called with the new equation e_396 : 29 factors in 7 terms

Step 1625: 
Hot list of urgent steps : 
The list of inequalities got extended by: 
An expression with 86 terms

The list of inequalities got extended by: 
An expression with 71 terms

The list of inequalities got extended by: 
An expression with 101 terms

The list of inequalities got extended by: 
An expression with 103 terms

Substitution of q17 by an expression in 
q26, q10, q9, q8, p8, p5, p3, p4, p7 found in e_396 : 28 factors in 7 terms

Step 1626: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1627: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1628: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1629: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1630: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

Step 1631: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1632: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 5 terms

Step 1633: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 4 terms

Step 1634: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 3 terms

Step 1635: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1636: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1637: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 3 terms

Step 1638: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 1 term

Step 1639: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 3 terms

Step 1640: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_479 is a consequence of e_424.
Step 1641: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_480 is a consequence of e_424.
Step 1642: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 2 terms

e_481 is a consequence of e_424.
Step 1643: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 436  3-Oct-2003 05:34:24, 30 ms (0%), 1059820 occupied, 23940127 free
*** Garbage collection starting 
*** GC 437  3-Oct-2003 05:34:27, 40 ms (0%), 1068554 occupied, 23931392 free
*** Garbage collection starting 
*** GC 438  3-Oct-2003 05:34:30, 40 ms (0%), 1071853 occupied, 23928093 free
*** Garbage collection starting 
*** GC 439  3-Oct-2003 05:34:34, 40 ms (0%), 1066198 occupied, 23933749 free
*** Garbage collection starting 
*** GC 440  3-Oct-2003 05:34:38, 40 ms (0%), 1064614 occupied, 23935332 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
The list of inequalities got extended by: 
An expression with 203 terms

The list of inequalities got extended by: 
An expression with 177 terms

The list of inequalities got extended by: 
An expression with 248 terms

The list of inequalities got extended by: 
An expression with 250 terms

e_454 is a consequence of e_424.
*** Garbage collection starting 
*** GC 441  3-Oct-2003 05:34:41, 50 ms (0%), 1096102 occupied, 23903846 free

Substitution of q9 by an expression in 
q27, q26, q10, q8, p8, p6, p5, p3, p4, p7 found in e_478 : 44 factors in 9 terms

Step 1644: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 442  3-Oct-2003 05:34:44, 40 ms (0%), 1105805 occupied, 23894142 free
*** Garbage collection starting 
*** GC 443  3-Oct-2003 05:34:47, 40 ms (0%), 1109462 occupied, 23890486 free
*** Garbage collection starting 
*** GC 444  3-Oct-2003 05:34:51, 40 ms (0%), 1111442 occupied, 23888508 free
*** Garbage collection starting 
*** GC 445  3-Oct-2003 05:34:54, 40 ms (0%), 1105598 occupied, 23894352 free
*** Garbage collection starting 
*** GC 446  3-Oct-2003 05:34:58, 40 ms (0%), 1106814 occupied, 23893136 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases : 
*** Garbage collection starting 
*** GC 447  3-Oct-2003 05:35:01, 40 ms (0%), 1105667 occupied, 23894282 free
 --- 
Do one decoupling step : Eliminate 
q27

from e_406 and e_424. e_374 is added: 
(#) 40 terms, 124 factors, with derivatives of functions of all variables: 

               2         2      4   3   2      5   4   3   2      4   3   2
 (q26,q10,q8,p8 ,p8,p6,p5 ,p5,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4 ,p4,p7 ,p7 ,p7 ,p7)


Step 1645: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 448  3-Oct-2003 05:35:05, 40 ms (0%), 1126629 occupied, 23873321 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q26

from e_374 and e_424. e_396 is added: 
(#) 324 terms, 190 factors, with derivatives of functions of all variables: 

               5   4   3   2         3   2      5   4   3   2      7   6   5   4
 (q27,q10,q8,p8 ,p8 ,p8 ,p8 ,p8,p6,p5 ,p5 ,p5,p3 ,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4

     3   2      6   5   4   3   2
  ,p4 ,p4 ,p4,p7 ,p7 ,p7 ,p7 ,p7 ,p7)


Step 1646: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 449  3-Oct-2003 05:35:24, 40 ms (0%), 1134309 occupied, 23865641 free
*** Garbage collection starting 
*** GC 450  3-Oct-2003 05:36:03, 60 ms (0%), 1283309 occupied, 23716639 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
*** Garbage collection starting 
*** GC 451  3-Oct-2003 05:36:21, 50 ms (0%), 1199225 occupied, 23800583 free
*** Garbage collection starting 
*** GC 452  3-Oct-2003 05:36:26, 50 ms (0%), 1195217 occupied, 23804701 free
*** Garbage collection starting 
*** GC 453  3-Oct-2003 05:36:32, 50 ms (0%), 1201958 occupied, 23797961 free
*** Garbage collection starting 
*** GC 454  3-Oct-2003 05:36:38, 50 ms (0%), 1195684 occupied, 23804181 free
*** Garbage collection starting 
*** GC 455  3-Oct-2003 05:36:44, 50 ms (0%), 1206919 occupied, 23793000 free
*** Garbage collection starting 
*** GC 456  3-Oct-2003 05:36:51, 50 ms (0%), 1218634 occupied, 23781284 free
*** Garbage collection starting 
*** GC 457  3-Oct-2003 05:36:57, 50 ms (0%), 1207196 occupied, 23792723 free
*** Garbage collection starting 
*** GC 458  3-Oct-2003 05:37:02, 50 ms (0%), 1224379 occupied, 23775142 free
*** Garbage collection starting 
*** GC 459  3-Oct-2003 05:37:09, 50 ms (0%), 1209972 occupied, 23789947 free
*** Garbage collection starting 
*** GC 460  3-Oct-2003 05:37:17, 50 ms (0%), 1224676 occupied, 23775242 free
*** Garbage collection starting 
*** GC 461  3-Oct-2003 05:37:24, 50 ms (0%), 1221371 occupied, 23778547 free
*** Garbage collection starting 
*** GC 462  3-Oct-2003 05:37:29, 50 ms (0%), 1218071 occupied, 23781847 free
*** Garbage collection starting 
*** GC 463  3-Oct-2003 05:37:34, 50 ms (0%), 1212416 occupied, 23787503 free
*** Garbage collection starting 
*** GC 464  3-Oct-2003 05:37:38, 50 ms (0%), 1221399 occupied, 23778355 free
*** Garbage collection starting 
*** GC 465  3-Oct-2003 05:37:44, 50 ms (0%), 1301544 occupied, 23697750 free
*** Garbage collection starting 
*** GC 466  3-Oct-2003 05:37:57, 50 ms (0%), 1311088 occupied, 23688206 free
Stop of a subroutine.
Number of garbage collections exceeds max_gc_fac.
Eliminate 
q26

from e_374 and e_492. e_452 is added: 
 203 terms, 2436 factors, with derivatives of functions of all variables: 

               3   2      2      4   3   2      6   5   4   3   2      8   7   6
 (q27,q10,q8,p8 ,p8 ,p8,p6 ,p6,p5 ,p5 ,p5 ,p5,p3 ,p3 ,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4

     5   4   3   2      5   4   3   2
  ,p4 ,p4 ,p4 ,p4 ,p4,p7 ,p7 ,p7 ,p7 ,p7)


Step 1647: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 467  3-Oct-2003 05:39:00, 80 ms (0%), 1291171 occupied, 23708774 free
*** Garbage collection starting 
*** GC 468  3-Oct-2003 05:39:55, 50 ms (0%), 1190723 occupied, 23809225 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q27

from e_424 and e_492. e_463 is added: 
 36 terms, 216 factors, with derivatives of functions of all variables: 

               2      2      3   2      3   2      4   3   2      3   2
 (q26,q10,q8,p8 ,p8,p6 ,p6,p5 ,p5 ,p5,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4,p7 ,p7 ,p7)


Step 1648: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 469  3-Oct-2003 05:40:22, 50 ms (0%), 1170217 occupied, 23829732 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
*** Garbage collection starting 
*** GC 470  3-Oct-2003 05:40:27, 50 ms (0%), 1260090 occupied, 23738681 free
*** Garbage collection starting 
*** GC 471  3-Oct-2003 05:40:37, 50 ms (0%), 1258070 occupied, 23741295 free
*** Garbage collection starting 
*** GC 472  3-Oct-2003 05:40:43, 50 ms (0%), 1269211 occupied, 23730481 free
*** Garbage collection starting 
*** GC 473  3-Oct-2003 05:40:55, 50 ms (0%), 1269851 occupied, 23729841 free
*** Garbage collection starting 
*** GC 474  3-Oct-2003 05:41:07, 50 ms (0%), 1301934 occupied, 23697757 free
*** Garbage collection starting 
*** GC 475  3-Oct-2003 05:41:20, 50 ms (0%), 1273367 occupied, 23726325 free
*** Garbage collection starting 
*** GC 476  3-Oct-2003 05:41:32, 50 ms (0%), 1271991 occupied, 23727701 free
*** Garbage collection starting 
*** GC 477  3-Oct-2003 05:41:39, 60 ms (0%), 1332910 occupied, 23666078 free
*** Garbage collection starting 
*** GC 478  3-Oct-2003 05:41:49, 50 ms (0%), 1365043 occupied, 23634644 free
*** Garbage collection starting 
*** GC 479  3-Oct-2003 05:42:04, 60 ms (0%), 1326857 occupied, 23672835 free
*** Garbage collection starting 
*** GC 480  3-Oct-2003 05:42:21, 50 ms (0%), 1340409 occupied, 23659284 free
*** Garbage collection starting 
*** GC 481  3-Oct-2003 05:42:40, 50 ms (0%), 1320147 occupied, 23679546 free
*** Garbage collection starting 
*** GC 482  3-Oct-2003 05:42:56, 50 ms (0%), 1354199 occupied, 23645494 free
*** Garbage collection starting 
*** GC 483  3-Oct-2003 05:43:12, 50 ms (0%), 1405279 occupied, 23594392 free
*** Garbage collection starting 
*** GC 484  3-Oct-2003 05:43:32, 50 ms (0%), 1327642 occupied, 23672051 free
*** Garbage collection starting 
*** GC 485  3-Oct-2003 05:43:51, 50 ms (0%), 1468552 occupied, 23531131 free
Stop of a subroutine.
Number of garbage collections exceeds max_gc_fac.
Eliminate 
q26

from e_374 and e_463. e_462 is added: 
 198 terms, 2574 factors, with derivatives of functions of all variables: 

           4   3   2      2      4   3   2      6   5   4   3   2      7   6   5
 (q10,q8,p8 ,p8 ,p8 ,p8,p6 ,p6,p5 ,p5 ,p5 ,p5,p3 ,p3 ,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4

     4   3   2      5   4   3   2
  ,p4 ,p4 ,p4 ,p4,p7 ,p7 ,p7 ,p7 ,p7)


Step 1649: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 486  3-Oct-2003 05:45:29, 60 ms (0%), 1354257 occupied, 23645684 free
*** Garbage collection starting 
*** GC 487  3-Oct-2003 05:47:10, 40 ms (0%), 1176123 occupied, 23823824 free
*** Garbage collection starting 
*** GC 488  3-Oct-2003 05:48:35, 70 ms (0%), 1278393 occupied, 23721555 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q26

from e_374 and e_406. e_474 is added: 
(#) 216 terms, 172 factors, with derivatives of functions of all variables: 

               4   3   2         3   2      5   4   3   2      7   6   5   4   3
 (q27,q10,q8,p8 ,p8 ,p8 ,p8,p6,p5 ,p5 ,p5,p3 ,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4 ,p4

     2      5   4   3   2
  ,p4 ,p4,p7 ,p7 ,p7 ,p7 ,p7)


Step 1650: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 489  3-Oct-2003 05:48:53, 50 ms (0%), 1265393 occupied, 23734554 free
*** Garbage collection starting 
*** GC 490  3-Oct-2003 05:49:29, 60 ms (0%), 1425027 occupied, 23574917 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
 An identity 0=0 results.Eliminate 
q27

from e_474 and e_396. 
Step 1651: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q27

from e_406 and e_447. e_479 is added: 
(#) 52 terms, 186 factors, with derivatives of functions of all variables: 

               3   2         2      4   3   2      5   4   3   2      4   3   2
 (q26,q10,q8,p8 ,p8 ,p8,p6,p5 ,p5,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4 ,p4,p7 ,p7 ,p7 ,

  p7)


Step 1652: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : shortening by 4 terms

Step 1653: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 491  3-Oct-2003 05:49:43, 70 ms (0%), 1153133 occupied, 23846816 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q26

from e_442 and e_374. e_484 is added: 
(#) 192 terms, 44 factors, with derivatives of functions of all variables: 

           5   4   3   2         2      5   4   3   2      6   5   4   3   2
 (q10,q8,p8 ,p8 ,p8 ,p8 ,p8,p6,p5 ,p5,p3 ,p3 ,p3 ,p3 ,p3,p4 ,p4 ,p4 ,p4 ,p4 ,p4,

    6   5   4   3   2
  p7 ,p7 ,p7 ,p7 ,p7 ,p7)


Step 1654: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 492  3-Oct-2003 05:49:55, 40 ms (0%), 1182833 occupied, 23817115 free
*** Garbage collection starting 
*** GC 493  3-Oct-2003 05:50:33, 70 ms (0%), 1244561 occupied, 23755385 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q10

from e_484 and e_374. e_488 is added: 
(#) 576 terms, 89 factors, with derivatives of functions of all variables: 

        5   4   3   2      2      4   3   2      6   5   4   3   2      8   7
 (q26,p8 ,p8 ,p8 ,p8 ,p8,p6 ,p6,p5 ,p5 ,p5 ,p5,p3 ,p3 ,p3 ,p3 ,p3 ,p3,p4 ,p4 ,

    6   5   4   3   2      5   4   3   2
  p4 ,p4 ,p4 ,p4 ,p4 ,p4,p7 ,p7 ,p7 ,p7 ,p7)


e_488 is a consequence of e_442.
Step 1655: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps :  --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : Eliminate 
q10

from e_484 and e_474. e_489 is added: 
(#) 1728 terms, 98 factors, with derivatives of functions of all variables: 

        7   6   5   4   3   2      2      4   3   2      7   6   5   4   3   2
 (q27,p8 ,p8 ,p8 ,p8 ,p8 ,p8 ,p8,p6 ,p6,p5 ,p5 ,p5 ,p5,p3 ,p3 ,p3 ,p3 ,p3 ,p3 ,

       9   8   7   6   5   4   3   2      7   6   5   4   3   2
  p3,p4 ,p4 ,p4 ,p4 ,p4 ,p4 ,p4 ,p4 ,p4,p7 ,p7 ,p7 ,p7 ,p7 ,p7 ,p7)


Step 1656: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : 
*** Garbage collection starting 
*** GC 494  3-Oct-2003 05:50:57, 40 ms (0%), 1173261 occupied, 23826688 free
*** Garbage collection starting 
*** GC 495  3-Oct-2003 05:53:11, 70 ms (0%), 1366891 occupied, 23633052 free
*** Garbage collection starting 
*** GC 496  3-Oct-2003 05:55:55, 60 ms (0%), 1283687 occupied, 23716262 free
*** Garbage collection starting 
*** GC 497  3-Oct-2003 05:58:48, 70 ms (0%), 1511093 occupied, 23488852 free
*** Garbage collection starting 
*** GC 498  3-Oct-2003 06:01:40, 70 ms (0%), 1269005 occupied, 23730942 free
*** Garbage collection starting 
*** GC 499  3-Oct-2003 06:04:58, 70 ms (0%), 1464045 occupied, 23535900 free
 --- 
Factorization to subcases leading to substitutions :  --- 
Substitution of <=1000 terms, no cases :  --- 
Do one decoupling step : 
*** Garbage collection starting 
*** GC 500  3-Oct-2003 06:06:59, 50 ms (0%), 1258021 occupied, 23741922 free
Eliminate 
q10

from e_484 and e_396. e_478 is added: 
(#) 10368 terms, 122 factors, with derivatives of functions of all variables: 

        9   8   7   6   5   4   3   2      2      5   4   3   2      8   7   6
 (q27,p8 ,p8 ,p8 ,p8 ,p8 ,p8 ,p8 ,p8 ,p8,p6 ,p6,p5 ,p5 ,p5 ,p5 ,p5,p3 ,p3 ,p3 ,

    5   4   3   2      11   10   9   8   7   6   5   4   3   2      9   8   7
  p3 ,p3 ,p3 ,p3 ,p3,p4  ,p4  ,p4 ,p4 ,p4 ,p4 ,p4 ,p4 ,p4 ,p4 ,p4,p7 ,p7 ,p7 ,

    6   5   4   3   2
  p7 ,p7 ,p7 ,p7 ,p7 ,p7)


e_478 is a consequence of e_489.
***** PREMATURE STOP DUE TO TIME CONSTRAINT! 

Time: 1952510 ms  plus GC time: 3310 ms

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7: Do you want to merge solutions computed in this session,
i.e. since loading CRACK the last time?  (Y or N) ***** `bu498-3-Oct-sol_list' cannot be open for input

Time: 0 ms

8: This is a reminder for you to read in any file CRACK_OUT.RED
with a procedure CRACK_OUT() in case that is necessary to display
results following from solutions to be printed.

Do you want to print solutions computed in this session,
i.e. since loading CRACK the last time?  (Y or N) 
***** `bu498-3-Oct-sol_list' cannot be open for input

Time: 0 ms

9: 9: 9: 9: 
y /home/twolf/public_html/htdocs/susy/N2t6s10f3/N2t6s10f3 N2t6s10f3 bye$$$$

***** Missing operator 

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*** End-of-file read 

Quitting