%------------------------------------------------------------------------------
% File     : CiME---2.01
% Problem  : GRP770-1 : TPTP v6.0.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_cime %s

% Computer : n082.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.11.2.el6.x86_64
% CPULimit : 300s
% DateTime : Tue Jun 10 00:25:03 EDT 2014

% Result   : Timeout 300.05s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP770-1 : TPTP v6.0.0. Released v4.1.0.
% % Command  : tptp2X_and_run_cime %s
% % Computer : n082.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.11.2.el6.x86_64
% % CPULimit : 300
% % DateTime : Sat Jun  7 01:40:53 CDT 2014
% % CPUTime  : 300.05 
% Processing problem /tmp/CiME_20766_n082.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " x2,x1,x0,one : constant;  t : 2;  eta : 1;  j : 1;  i : 1;  quotient : 2;  difference : 2;  product : 2;";
% let X = vars "A B C";
% let Axioms = equations F X "
% product(A,one) = A;
% product(one,A) = A;
% product(A,difference(A,B)) = B;
% difference(A,product(A,B)) = B;
% quotient(product(A,B),B) = A;
% product(quotient(A,B),B) = A;
% difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A);
% difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A);
% i(A) = difference(A,one);
% j(A) = quotient(one,A);
% product(i(A),A) = product(A,j(A));
% eta(A) = product(i(A),A);
% product(i(i(A)),B) = product(eta(A),product(A,B));
% product(A,product(eta(A),B)) = product(j(j(A)),B);
% product(A,product(B,eta(A))) = product(product(A,B),eta(A));
% product(eta(A),product(B,C)) = product(product(eta(A),B),C);
% quotient(j(A),A) = product(j(A),i(A));
% product(product(product(quotient(j(A),A),product(A,A)),B),C) = product(product(quotient(j(A),A),product(A,A)),product(B,C));
% t(A,B) = quotient(product(A,B),A);
% t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C));
% product(i(product(A,B)),i(i(A))) = i(B);
% product(j(j(A)),j(product(B,A))) = j(B);
% product(A,i(product(B,A))) = i(B);
% product(j(product(A,B)),A) = j(B);
% ";
% 
% let s1 = status F "
% x2 lr_lex;
% x1 lr_lex;
% x0 lr_lex;
% t lr_lex;
% eta lr_lex;
% j lr_lex;
% i lr_lex;
% quotient lr_lex;
% difference lr_lex;
% product lr_lex;
% one lr_lex;
% ";
% 
% let p1 = precedence F "
% product > difference > quotient > t > i > j > eta > one > x0 > x1 > x2";
% 
% let s2 = status F "
% x2 mul;
% x1 mul;
% x0 mul;
% t mul;
% eta mul;
% j mul;
% i mul;
% quotient mul;
% difference mul;
% product mul;
% one mul;
% ";
% 
% let p2 = precedence F "
% product > difference > quotient > t > i > j > eta > one = x0 = x1 = x2";
% 
% let o_auto = AUTO Axioms;
% 
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
% 
% let Conjectures = equations F X " product(x0,product(x1,x2)) = product(quotient(product(x0,x1),x0),product(x0,x2));"
% ;
% (*
% let Red_Axioms = normalize_equations Defining_rules Axioms;
% 
% let Red_Conjectures =  normalize_equations Defining_rules Conjectures;
% *)
% #time on;
% 
% let res = prove_conj_by_ordered_completion o Axioms Conjectures;
% 
% #time off;
% 
% 
% let status = if res then "unsatisfiable" else "satisfiable";
% #quit;
% Verbose level is now 1
% 
% F : signature = <signature>
% X : variable_set = <variable set>
% 
% Axioms : (F,X) equations = { product(A,one) = A,
% product(one,A) = A,
% product(A,difference(A,B)) = B,
% difference(A,product(A,B)) = B,
% quotient(product(A,B),B) = A,
% product(quotient(A,B),B) = A,
% difference(A,product(product(A,B),C)) =
% quotient(product(B,product(C,A)),A),
% difference(product(A,B),product(A,product(B,C)))
% =
% quotient(quotient(product(C,product(A,B)),B),A),
% i(A) = difference(A,one),
% j(A) = quotient(one,A),
% product(i(A),A) = product(A,j(A)),
% eta(A) = product(i(A),A),
% product(i(i(A)),B) =
% product(eta(A),product(A,B)),
% product(A,product(eta(A),B)) =
% product(j(j(A)),B),
% product(A,product(B,eta(A))) =
% product(product(A,B),eta(A)),
% product(eta(A),product(B,C)) =
% product(product(eta(A),B),C),
% quotient(j(A),A) = product(j(A),i(A)),
% product(product(product(quotient(j(A),A),
% product(A,A)),B),C) =
% product(product(quotient(j(A),A),product(A,A)),
% product(B,C)),
% t(A,B) = quotient(product(A,B),A),
% t(eta(A),product(B,C)) =
% product(t(eta(A),B),t(eta(A),C)),
% product(i(product(A,B)),i(i(A))) = i(B),
% product(j(j(A)),j(product(B,A))) = j(B),
% product(A,i(product(B,A))) = i(B),
% product(j(product(A,B)),A) = j(B) }
% (24 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { product(x0,product(x1,x2)) =
% product(quotient(product(x0,x1),x0),
% product(x0,x2)) } (1 equation(s))
% time is now on
% 
% Initializing completion ...
% New rule produced : [1] product(A,one) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 25
% Current number of rules: 1
% New rule produced : [2] product(one,A) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 24
% Current number of rules: 2
% New rule produced : [3] quotient(one,A) -> j(A)
% Current number of equations to process: 0
% Current number of ordered equations: 23
% Current number of rules: 3
% New rule produced : [4] difference(A,one) -> i(A)
% Current number of equations to process: 0
% Current number of ordered equations: 22
% Current number of rules: 4
% New rule produced : [5] product(i(A),A) -> eta(A)
% Current number of equations to process: 1
% Current number of ordered equations: 20
% Current number of rules: 5
% New rule produced : [6] quotient(product(A,B),B) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 20
% Current number of rules: 6
% New rule produced : [7] difference(A,product(A,B)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 19
% Current number of rules: 7
% New rule produced : [8] product(A,difference(A,B)) -> B
% Current number of equations to process: 0
% Current number of ordered equations: 18
% Current number of rules: 8
% New rule produced : [9] product(quotient(A,B),B) -> A
% Current number of equations to process: 0
% Current number of ordered equations: 17
% Current number of rules: 9
% New rule produced : [10] product(A,j(A)) -> eta(A)
% Current number of equations to process: 0
% Current number of ordered equations: 16
% Current number of rules: 10
% New rule produced : [11] quotient(product(A,B),A) -> t(A,B)
% The conjecture has been reduced. 
% Conjecture is now:
% product(x0,product(x1,x2)) = product(t(x0,x1),product(x0,x2))
% 
% Current number of equations to process: 0
% Current number of ordered equations: 15
% Current number of rules: 11
% New rule produced : [12] product(A,i(product(B,A))) -> i(B)
% Current number of equations to process: 0
% Current number of ordered equations: 14
% Current number of rules: 12
% New rule produced : [13] product(j(A),i(A)) -> quotient(j(A),A)
% Current number of equations to process: 0
% Current number of ordered equations: 13
% Current number of rules: 13
% New rule produced : [14] product(j(product(A,B)),A) -> j(B)
% Current number of equations to process: 0
% Current number of ordered equations: 12
% Current number of rules: 14
% New rule produced : [15] product(i(i(A)),B) -> product(eta(A),product(A,B))
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 15
% New rule produced : [16] product(j(j(A)),B) -> product(A,product(eta(A),B))
% Current number of equations to process: 1
% Current number of ordered equations: 9
% Current number of rules: 16
% New rule produced : [17] product(A,product(eta(A),j(product(B,A)))) -> j(B)
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 17
% New rule produced :
% [18] product(product(A,B),eta(A)) -> product(A,product(B,eta(A)))
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 18
% New rule produced :
% [19] product(product(eta(A),B),C) -> product(eta(A),product(B,C))
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 19
% New rule produced : [20] product(i(product(A,B)),i(i(A))) -> i(B)
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 20
% New rule produced :
% [21]
% quotient(product(B,product(C,A)),A) <-> difference(A,product(product(A,B),C))
% Current number of equations to process: 70
% Current number of ordered equations: 74
% Current number of rules: 21
% New rule produced :
% [22]
% difference(A,product(product(A,B),C)) <-> quotient(product(B,product(C,A)),A)
% Current number of equations to process: 70
% Current number of ordered equations: 73
% Current number of rules: 22
% New rule produced :
% [23] product(t(eta(A),B),t(eta(A),C)) -> t(eta(A),product(B,C))
% Current number of equations to process: 70
% Current number of ordered equations: 72
% Current number of rules: 23
% New rule produced :
% [24]
% quotient(quotient(product(C,product(A,B)),B),A) <->
% difference(product(A,B),product(A,product(B,C)))
% Current number of equations to process: 51
% Current number of ordered equations: 139
% Current number of rules: 24
% New rule produced :
% [25]
% difference(product(A,B),product(A,product(B,C))) <->
% quotient(quotient(product(C,product(A,B)),B),A)
% Current number of equations to process: 51
% Current number of ordered equations: 138
% Current number of rules: 25
% New rule produced :
% [26]
% product(product(product(quotient(j(A),A),product(A,A)),B),C) ->
% product(product(quotient(j(A),A),product(A,A)),product(B,C))
% Current number of equations to process: 51
% Current number of ordered equations: 137
% Current number of rules: 26
% New rule produced : [27] i(one) -> eta(one)
% Current number of equations to process: 54
% Current number of ordered equations: 133
% Current number of rules: 27
% New rule produced : [28] j(one) -> eta(one)
% Current number of equations to process: 56
% Current number of ordered equations: 130
% Current number of rules: 28
% New rule produced : [29] quotient(A,one) -> A
% Current number of equations to process: 59
% Current number of ordered equations: 125
% Current number of rules: 29
% New rule produced : [30] quotient(A,A) -> one
% Current number of equations to process: 60
% Current number of ordered equations: 123
% Current number of rules: 30
% New rule produced : [31] difference(A,A) -> one
% Current number of equations to process: 60
% Current number of ordered equations: 122
% Current number of rules: 31
% New rule produced : [32] difference(one,A) -> A
% Current number of equations to process: 60
% Current number of ordered equations: 120
% Current number of rules: 32
% New rule produced : [33] t(A,A) -> A
% Current number of equations to process: 60
% Current number of ordered equations: 119
% Current number of rules: 33
% New rule produced : [34] product(A,i(A)) -> one
% Current number of equations to process: 61
% Current number of ordered equations: 117
% Current number of rules: 34
% New rule produced : [35] product(j(A),A) -> one
% Current number of equations to process: 61
% Current number of ordered equations: 116
% Current number of rules: 35
% New rule produced : [36] t(A,one) -> one
% Current number of equations to process: 60
% Current number of ordered equations: 116
% Current number of rules: 36
% New rule produced : [37] t(one,A) -> A
% Current number of equations to process: 59
% Current number of ordered equations: 116
% Current number of rules: 37
% New rule produced : [38] quotient(eta(A),A) -> i(A)
% Current number of equations to process: 60
% Current number of ordered equations: 114
% Current number of rules: 38
% New rule produced : [39] difference(A,eta(A)) -> j(A)
% Current number of equations to process: 60
% Current number of ordered equations: 113
% Current number of rules: 39
% Rule [28] j(one) -> eta(one) is composed into [28] j(one) -> one
% Rule [27] i(one) -> eta(one) is composed into [27] i(one) -> one
% New rule produced : [40] eta(one) -> one
% Current number of equations to process: 59
% Current number of ordered equations: 112
% Current number of rules: 40
% New rule produced : [41] difference(i(A),eta(A)) -> A
% Current number of equations to process: 58
% Current number of ordered equations: 111
% Current number of rules: 41
% New rule produced : [42] quotient(A,difference(B,A)) -> B
% Current number of equations to process: 58
% Current number of ordered equations: 110
% Current number of rules: 42
% New rule produced : [43] difference(quotient(A,B),A) -> B
% Current number of equations to process: 58
% Current number of ordered equations: 109
% Current number of rules: 43
% New rule produced : [44] quotient(eta(A),j(A)) -> A
% Current number of equations to process: 58
% Current number of ordered equations: 108
% Current number of rules: 44
% New rule produced : [45] product(eta(A),A) -> i(i(A))
% Current number of equations to process: 59
% Current number of ordered equations: 106
% Current number of rules: 45
% New rule produced : [46] product(A,eta(A)) -> j(j(A))
% Current number of equations to process: 59
% Current number of ordered equations: 105
% Current number of rules: 46
% New rule produced : [47] t(A,j(A)) -> i(A)
% Current number of equations to process: 58
% Current number of ordered equations: 105
% Current number of rules: 47
% New rule produced : [48] i(product(B,A)) -> difference(A,i(B))
% Rule [12] product(A,i(product(B,A))) -> i(B) collapsed.
% Rule [20] product(i(product(A,B)),i(i(A))) -> i(B) collapsed.
% Current number of equations to process: 59
% Current number of ordered equations: 70
% Current number of rules: 46
% New rule produced : [49] product(difference(B,i(A)),i(i(A))) -> i(B)
% Current number of equations to process: 58
% Current number of ordered equations: 70
% Current number of rules: 47
% New rule produced : [50] j(product(B,A)) -> quotient(j(A),B)
% Rule [14] product(j(product(A,B)),A) -> j(B) collapsed.
% Rule [17] product(A,product(eta(A),j(product(B,A)))) -> j(B) collapsed.
% Current number of equations to process: 60
% Current number of ordered equations: 46
% Current number of rules: 46
% New rule produced : [51] product(A,product(eta(A),quotient(j(A),B))) -> j(B)
% Current number of equations to process: 59
% Current number of ordered equations: 46
% Current number of rules: 47
% New rule produced : [52] t(B,difference(B,A)) -> quotient(A,B)
% Current number of equations to process: 59
% Current number of ordered equations: 45
% Current number of rules: 48
% New rule produced : [53] product(t(A,B),A) -> product(A,B)
% Current number of equations to process: 59
% Current number of ordered equations: 44
% Current number of rules: 49
% New rule produced : [54] quotient(eta(A),i(A)) -> t(i(A),A)
% Current number of equations to process: 59
% Current number of ordered equations: 43
% Current number of rules: 50
% New rule produced : [55] quotient(A,quotient(A,B)) -> t(quotient(A,B),B)
% Current number of equations to process: 57
% Current number of ordered equations: 42
% Current number of rules: 51
% New rule produced : [56] quotient(quotient(j(A),A),i(A)) -> j(A)
% Current number of equations to process: 55
% Current number of ordered equations: 41
% Current number of rules: 52
% New rule produced : [57] difference(j(A),quotient(j(A),A)) -> i(A)
% Current number of equations to process: 55
% Current number of ordered equations: 40
% Current number of rules: 53
% New rule produced : [58] product(A,product(eta(A),j(A))) -> one
% Current number of equations to process: 54
% Current number of ordered equations: 40
% Current number of rules: 54
% New rule produced :
% [59] quotient(eta(product(A,B)),B) -> difference(B,eta(A))
% Current number of equations to process: 54
% Current number of ordered equations: 39
% Current number of rules: 55
% New rule produced :
% [60] difference(A,eta(product(A,B))) -> quotient(eta(B),A)
% Current number of equations to process: 54
% Current number of ordered equations: 38
% Current number of rules: 56
% New rule produced : [61] eta(i(A)) -> eta(A)
% Current number of equations to process: 55
% Current number of ordered equations: 36
% Current number of rules: 57
% New rule produced : [62] quotient(quotient(j(A),A),j(A)) -> t(j(A),i(A))
% Current number of equations to process: 60
% Current number of ordered equations: 35
% Current number of rules: 58
% New rule produced : [63] quotient(product(eta(A),product(A,B)),B) -> i(i(A))
% Current number of equations to process: 60
% Current number of ordered equations: 34
% Current number of rules: 59
% New rule produced : [64] quotient(product(A,product(eta(A),B)),B) -> j(j(A))
% Current number of equations to process: 60
% Current number of ordered equations: 33
% Current number of rules: 60
% New rule produced :
% [65] product(A,product(j(A),eta(A))) -> product(eta(A),eta(A))
% Current number of equations to process: 60
% Current number of ordered equations: 32
% Current number of rules: 61
% New rule produced :
% [66] t(A,product(B,A)) <-> difference(A,product(product(A,A),B))
% Current number of equations to process: 60
% Current number of ordered equations: 31
% Current number of rules: 62
% New rule produced :
% [67] difference(A,product(product(A,A),B)) <-> t(A,product(B,A))
% Current number of equations to process: 60
% Current number of ordered equations: 30
% Current number of rules: 63
% New rule produced :
% [68] product(B,product(difference(B,A),eta(B))) -> product(A,eta(B))
% Current number of equations to process: 62
% Current number of ordered equations: 29
% Current number of rules: 64
% New rule produced :
% [69] quotient(product(eta(A),product(B,C)),C) -> product(eta(A),B)
% Rule [63] quotient(product(eta(A),product(A,B)),B) -> i(i(A)) collapsed.
% Current number of equations to process: 62
% Current number of ordered equations: 28
% Current number of rules: 64
% New rule produced : [70] quotient(product(A,i(i(B))),B) -> product(A,eta(B))
% Current number of equations to process: 61
% Current number of ordered equations: 28
% Current number of rules: 65
% New rule produced :
% [71] difference(i(i(A)),product(eta(A),product(A,B))) -> B
% Current number of equations to process: 62
% Current number of ordered equations: 27
% Current number of rules: 66
% New rule produced :
% [72] product(eta(B),product(B,difference(i(i(B)),A))) -> A
% Current number of equations to process: 62
% Current number of ordered equations: 26
% Current number of rules: 67
% New rule produced :
% [73] difference(j(j(A)),product(A,product(eta(A),B))) -> B
% Current number of equations to process: 62
% Current number of ordered equations: 25
% Current number of rules: 68
% New rule produced :
% [74] product(B,product(eta(B),difference(j(j(B)),A))) -> A
% Current number of equations to process: 62
% Current number of ordered equations: 24
% Current number of rules: 69
% New rule produced :
% [75] quotient(product(A,product(B,eta(A))),eta(A)) -> product(A,B)
% Current number of equations to process: 62
% Current number of ordered equations: 23
% Current number of rules: 70
% New rule produced :
% [76] product(eta(C),product(difference(eta(C),A),B)) -> product(A,B)
% Current number of equations to process: 62
% Current number of ordered equations: 22
% Current number of rules: 71
% New rule produced :
% [77] product(eta(A),product(j(eta(A)),B)) -> product(eta(eta(A)),B)
% Current number of equations to process: 62
% Current number of ordered equations: 21
% Current number of rules: 72
% New rule produced :
% [78] quotient(product(A,product(B,eta(C))),eta(C)) -> product(A,B)
% Rule [75] quotient(product(A,product(B,eta(A))),eta(A)) -> product(A,B)
% collapsed.
% Current number of equations to process: 62
% Current number of ordered equations: 20
% Current number of rules: 72
% New rule produced : [79] product(eta(A),product(A,j(i(i(A))))) -> eta(A)
% Current number of equations to process: 65
% Current number of ordered equations: 20
% Current number of rules: 73
% New rule produced :
% [80] product(A,product(eta(A),j(j(j(A))))) -> eta(j(j(A)))
% Current number of equations to process: 65
% Current number of ordered equations: 19
% Current number of rules: 74
% New rule produced :
% [81] product(A,product(eta(A),i(j(A)))) -> quotient(j(j(A)),j(A))
% Current number of equations to process: 65
% Current number of ordered equations: 18
% Current number of rules: 75
% New rule produced : [82] product(i(A),j(j(A))) -> product(eta(A),eta(A))
% Current number of equations to process: 64
% Current number of ordered equations: 18
% Current number of rules: 76
% New rule produced :
% [83] difference(product(A,B),product(A,product(B,eta(A)))) -> eta(A)
% Current number of equations to process: 64
% Current number of ordered equations: 17
% Current number of rules: 77
% New rule produced :
% [84]
% quotient(product(j(A),product(B,A)),A) -> difference(A,product(eta(A),B))
% Current number of equations to process: 64
% Current number of ordered equations: 16
% Current number of rules: 78
% New rule produced :
% [85] difference(product(eta(A),B),product(eta(A),product(B,C))) -> C
% Current number of equations to process: 67
% Current number of ordered equations: 15
% Current number of rules: 79
% New rule produced :
% [86] product(eta(B),product(C,difference(product(eta(B),C),A))) -> A
% Current number of equations to process: 67
% Current number of ordered equations: 14
% Current number of rules: 80
% New rule produced :
% [87]
% difference(C,product(product(C,A),quotient(B,C))) -> quotient(product(A,B),C)
% Current number of equations to process: 67
% Current number of ordered equations: 13
% Current number of rules: 81
% New rule produced :
% [88]
% product(difference(A,product(product(A,B),C)),A) -> product(B,product(C,A))
% Current number of equations to process: 67
% Current number of ordered equations: 12
% Current number of rules: 82
% New rule produced :
% [89]
% product(A,quotient(product(B,product(C,A)),A)) <-> product(product(A,B),C)
% Current number of equations to process: 67
% Current number of ordered equations: 11
% Current number of rules: 83
% New rule produced :
% [90]
% product(product(A,B),C) <-> product(A,quotient(product(B,product(C,A)),A))
% Rule [18] product(product(A,B),eta(A)) -> product(A,product(B,eta(A)))
% collapsed.
% Current number of equations to process: 67
% Current number of ordered equations: 7
% Current number of rules: 83
% New rule produced :
% [91]
% quotient(product(difference(A,B),product(C,A)),A) ->
% difference(A,product(B,C))
% Current number of equations to process: 67
% Current number of ordered equations: 6
% Current number of rules: 84
% New rule produced :
% [92] quotient(product(eta(A),product(A,B)),i(i(A))) -> t(i(i(A)),B)
% Current number of equations to process: 68
% Current number of ordered equations: 5
% Current number of rules: 85
% New rule produced :
% [93] quotient(product(A,product(eta(A),B)),j(j(A))) -> t(j(j(A)),B)
% Current number of equations to process: 68
% Current number of ordered equations: 4
% Current number of rules: 86
% New rule produced :
% [94]
% product(eta(A),product(B,quotient(j(B),eta(A)))) -> eta(product(eta(A),B))
% Current number of equations to process: 67
% Current number of ordered equations: 4
% Current number of rules: 87
% New rule produced :
% [95]
% difference(i(A),product(eta(A),B)) <->
% quotient(product(A,product(B,i(A))),i(A))
% Current number of equations to process: 67
% Current number of ordered equations: 3
% Current number of rules: 88
% New rule produced :
% [96]
% quotient(product(A,product(B,i(A))),i(A)) <->
% difference(i(A),product(eta(A),B))
% Current number of equations to process: 67
% Current number of ordered equations: 2
% Current number of rules: 89
% New rule produced :
% [97]
% difference(product(B,A),product(B,product(A,A))) ->
% quotient(t(A,product(B,A)),B)
% Current number of equations to process: 66
% Current number of ordered equations: 2
% Current number of rules: 90
% New rule produced :
% [98] quotient(t(eta(A),product(B,C)),t(eta(A),C)) -> t(eta(A),B)
% Current number of equations to process: 67
% Current number of ordered equations: 1
% Current number of rules: 91
% New rule produced :
% [99] difference(t(eta(A),B),t(eta(A),product(B,C))) -> t(eta(A),C)
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 92
% New rule produced :
% [100]
% difference(product(A,B),product(A,C)) <->
% quotient(difference(B,product(C,A)),A)
% Current number of equations to process: 78
% Current number of ordered equations: 1
% Current number of rules: 93
% New rule produced :
% [101]
% quotient(difference(B,product(C,A)),A) <->
% difference(product(A,B),product(A,C))
% Current number of equations to process: 78
% Current number of ordered equations: 0
% Current number of rules: 94
% New rule produced :
% [102] product(i(A),product(eta(A),j(quotient(j(A),A)))) -> j(j(A))
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [103]
% quotient(product(A,product(B,product(C,eta(B)))),eta(B)) ->
% product(A,product(B,C))
% Current number of equations to process: 91
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [104]
% difference(eta(B),product(i(B),product(B,A))) <->
% quotient(quotient(product(A,eta(B)),B),i(B))
% Current number of equations to process: 90
% Current number of ordered equations: 1
% Current number of rules: 97
% New rule produced :
% [105]
% quotient(quotient(product(A,eta(B)),B),i(B)) <->
% difference(eta(B),product(i(B),product(B,A)))
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [106]
% difference(B,product(C,product(difference(C,B),A))) <->
% quotient(quotient(product(A,B),difference(C,B)),C)
% Current number of equations to process: 89
% Current number of ordered equations: 1
% Current number of rules: 99
% New rule produced :
% [107]
% quotient(quotient(product(A,B),difference(C,B)),C) <->
% difference(B,product(C,product(difference(C,B),A)))
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [108]
% difference(B,product(quotient(B,C),product(C,A))) <->
% quotient(quotient(product(A,B),C),quotient(B,C))
% Current number of equations to process: 88
% Current number of ordered equations: 1
% Current number of rules: 101
% New rule produced :
% [109]
% quotient(quotient(product(A,B),C),quotient(B,C)) <->
% difference(B,product(quotient(B,C),product(C,A)))
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [110]
% difference(eta(B),product(B,product(j(B),A))) <->
% quotient(quotient(product(A,eta(B)),j(B)),B)
% Current number of equations to process: 87
% Current number of ordered equations: 1
% Current number of rules: 103
% New rule produced :
% [111]
% quotient(quotient(product(A,eta(B)),j(B)),B) <->
% difference(eta(B),product(B,product(j(B),A)))
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [112]
% product(A,product(eta(A),quotient(quotient(j(A),B),eta(B)))) -> j(i(i(B)))
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 105
% New rule produced :
% [113]
% product(A,product(eta(A),quotient(quotient(j(A),eta(B)),B))) -> j(j(j(B)))
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [114]
% quotient(product(eta(A),product(B,C)),product(eta(A),B)) ->
% t(product(eta(A),B),C)
% Current number of equations to process: 79
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [115] product(difference(product(A,B),i(eta(A))),i(i(i(i(A))))) -> i(B)
% Current number of equations to process: 78
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [116] product(difference(product(eta(A),B),i(A)),i(i(j(j(A))))) -> i(B)
% Current number of equations to process: 77
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [117]
% product(B,product(eta(B),product(quotient(j(B),A),eta(B)))) ->
% product(j(A),eta(B))
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced :
% [118]
% product(A,product(eta(A),quotient(quotient(j(A),C),eta(B)))) ->
% quotient(j(C),eta(B))
% Rule
% [112]
% product(A,product(eta(A),quotient(quotient(j(A),B),eta(B)))) -> j(i(i(B)))
% collapsed.
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 110
% New rule produced : [119] quotient(j(B),eta(B)) -> j(i(i(B)))
% Current number of equations to process: 79
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [120]
% product(difference(product(B,eta(A)),i(A)),i(difference(B,i(A)))) ->
% i(eta(A))
% Current number of equations to process: 78
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [121]
% difference(C,product(product(C,A),i(i(B)))) <->
% quotient(product(A,product(eta(B),product(B,C))),C)
% Current number of equations to process: 76
% Current number of ordered equations: 3
% Current number of rules: 113
% New rule produced :
% [122]
% difference(C,product(product(C,i(i(A))),B)) <->
% quotient(product(eta(A),product(A,product(B,C))),C)
% Current number of equations to process: 76
% Current number of ordered equations: 2
% Current number of rules: 114
% New rule produced :
% [123]
% quotient(product(A,product(eta(B),product(B,C))),C) <->
% difference(C,product(product(C,A),i(i(B))))
% Current number of equations to process: 76
% Current number of ordered equations: 1
% Current number of rules: 115
% New rule produced :
% [124]
% quotient(product(eta(A),product(A,product(B,C))),C) <->
% difference(C,product(product(C,i(i(A))),B))
% Current number of equations to process: 76
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [125]
% difference(C,product(product(C,A),j(j(B)))) <->
% quotient(product(A,product(B,product(eta(B),C))),C)
% Current number of equations to process: 74
% Current number of ordered equations: 3
% Current number of rules: 117
% New rule produced :
% [126]
% difference(C,product(product(C,j(j(A))),B)) <->
% quotient(product(A,product(eta(A),product(B,C))),C)
% Current number of equations to process: 74
% Current number of ordered equations: 2
% Current number of rules: 118
% New rule produced :
% [127]
% quotient(product(A,product(B,product(eta(B),C))),C) <->
% difference(C,product(product(C,A),j(j(B))))
% Current number of equations to process: 74
% Current number of ordered equations: 1
% Current number of rules: 119
% New rule produced :
% [128]
% quotient(product(A,product(eta(A),product(B,C))),C) <->
% difference(C,product(product(C,j(j(A))),B))
% Current number of equations to process: 74
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [129]
% difference(quotient(A,B),product(A,C)) <->
% quotient(product(B,product(C,quotient(A,B))),quotient(A,B))
% Current number of equations to process: 73
% Current number of ordered equations: 1
% Current number of rules: 121
% New rule produced :
% [130]
% quotient(product(B,product(C,quotient(A,B))),quotient(A,B)) <->
% difference(quotient(A,B),product(A,C))
% Current number of equations to process: 73
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [131]
% difference(j(A),product(quotient(j(A),A),B)) <->
% quotient(product(i(A),product(B,j(A))),j(A))
% Current number of equations to process: 72
% Current number of ordered equations: 1
% Current number of rules: 123
% New rule produced :
% [132]
% quotient(product(i(A),product(B,j(A))),j(A)) <->
% difference(j(A),product(quotient(j(A),A),B))
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [133] product(t(eta(A),B),i(t(eta(A),product(C,B)))) -> i(t(eta(A),C))
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [134] product(j(t(eta(A),product(B,C))),t(eta(A),B)) -> j(t(eta(A),C))
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [135]
% product(difference(product(A,B),product(A,product(B,C))),A) ->
% quotient(product(C,product(A,B)),B)
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [136]
% product(difference(B,i(A)),product(eta(difference(B,i(A))),j(i(A)))) -> j(B)
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [137]
% product(difference(product(B,C),i(eta(A))),i(difference(B,i(eta(A))))) ->
% i(C)
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [138]
% difference(V_3,product(product(V_3,A),product(eta(B),C))) <->
% quotient(product(A,product(eta(B),product(C,V_3))),V_3)
% Current number of equations to process: 66
% Current number of ordered equations: 3
% Current number of rules: 130
% New rule produced :
% [139]
% difference(V_3,product(product(V_3,product(eta(A),B)),C)) <->
% quotient(product(eta(A),product(B,product(C,V_3))),V_3)
% Current number of equations to process: 66
% Current number of ordered equations: 2
% Current number of rules: 131
% New rule produced :
% [140]
% quotient(product(A,product(eta(B),product(C,V_3))),V_3) <->
% difference(V_3,product(product(V_3,A),product(eta(B),C)))
% Current number of equations to process: 66
% Current number of ordered equations: 1
% Current number of rules: 132
% New rule produced :
% [141]
% quotient(product(eta(A),product(B,product(C,V_3))),V_3) <->
% difference(V_3,product(product(V_3,product(eta(A),B)),C))
% Current number of equations to process: 66
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [142]
% product(eta(A),product(A,product(eta(A),j(i(B))))) -> j(difference(B,i(A)))
% Current number of equations to process: 65
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [143]
% quotient(t(eta(A),product(B,C)),t(eta(A),B)) -> t(t(eta(A),B),t(eta(A),C))
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [144]
% difference(product(C,B),product(C,product(B,quotient(A,product(C,B))))) ->
% quotient(quotient(A,B),C)
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [145]
% quotient(quotient(product(B,product(A,i(B))),i(B)),A) ->
% difference(product(A,i(B)),product(A,eta(B)))
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 137
% New rule produced :
% [146]
% product(product(A,B),quotient(quotient(product(C,product(A,B)),B),A)) ->
% product(A,product(B,C))
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [147]
% product(quotient(j(A),B),product(B,eta(quotient(j(A),B)))) ->
% product(j(A),eta(quotient(j(A),B)))
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [148]
% product(eta(A),product(eta(eta(A)),quotient(quotient(j(eta(A)),B),A))) ->
% quotient(j(B),A)
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [149]
% product(eta(C),product(eta(eta(C)),product(quotient(j(eta(C)),A),B))) ->
% product(j(A),B)
% Current number of equations to process: 62
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [150]
% quotient(product(eta(A),product(quotient(j(A),B),product(C,A))),A) ->
% difference(A,product(j(B),C))
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [151]
% product(A,quotient(product(product(B,eta(A)),product(eta(product(A,B)),A)),A))
% -> product(product(A,B),product(eta(A),eta(product(A,B))))
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [152]
% product(A,quotient(product(eta(A),product(B,product(eta(j(j(A))),A))),A)) ->
% product(A,product(eta(A),product(B,eta(j(j(A))))))
% Current number of equations to process: 58
% Current number of ordered equations: 0
% Current number of rules: 144
% New rule produced :
% [153] product(i(t(eta(A),product(B,C))),i(i(t(eta(A),B)))) -> i(t(eta(A),C))
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [154]
% product(eta(A),product(A,product(eta(A),quotient(j(i(i(A))),B)))) -> j(B)
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [155]
% product(A,product(eta(A),product(eta(j(j(A))),quotient(j(j(j(A))),B)))) ->
% j(B)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [156]
% difference(i(i(A)),product(eta(A),product(product(A,B),C))) <->
% quotient(product(B,product(C,i(i(A)))),i(i(A)))
% Current number of equations to process: 53
% Current number of ordered equations: 1
% Current number of rules: 148
% New rule produced :
% [157]
% quotient(product(B,product(C,i(i(A)))),i(i(A))) <->
% difference(i(i(A)),product(eta(A),product(product(A,B),C)))
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [158]
% difference(j(j(A)),product(product(A,product(eta(A),B)),C)) <->
% quotient(product(B,product(C,j(j(A)))),j(j(A)))
% Current number of equations to process: 52
% Current number of ordered equations: 1
% Current number of rules: 150
% New rule produced :
% [159]
% quotient(product(B,product(C,j(j(A)))),j(j(A))) <->
% difference(j(j(A)),product(product(A,product(eta(A),B)),C))
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 151
% New rule produced :
% [160]
% difference(product(B,C),product(B,product(C,i(i(A))))) <->
% quotient(quotient(product(eta(A),product(A,product(B,C))),C),B)
% Current number of equations to process: 51
% Current number of ordered equations: 1
% Current number of rules: 152
% New rule produced :
% [161]
% quotient(quotient(product(eta(A),product(A,product(B,C))),C),B) <->
% difference(product(B,C),product(B,product(C,i(i(A)))))
% Current number of equations to process: 51
% Current number of ordered equations: 0
% Current number of rules: 153
% New rule produced :
% [162]
% difference(product(B,C),product(B,product(C,j(j(A))))) <->
% quotient(quotient(product(A,product(eta(A),product(B,C))),C),B)
% Current number of equations to process: 50
% Current number of ordered equations: 1
% Current number of rules: 154
% New rule produced :
% [163]
% quotient(quotient(product(A,product(eta(A),product(B,C))),C),B) <->
% difference(product(B,C),product(B,product(C,j(j(A)))))
% Current number of equations to process: 50
% Current number of ordered equations: 0
% Current number of rules: 155
% New rule produced :
% [164]
% quotient(quotient(product(C,product(A,quotient(B,C))),quotient(B,C)),A) ->
% difference(product(A,quotient(B,C)),product(A,B))
% Current number of equations to process: 49
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced :
% [165]
% difference(product(A,j(B)),product(A,quotient(j(B),B))) <->
% quotient(quotient(product(i(B),product(A,j(B))),j(B)),A)
% Current number of equations to process: 48
% Current number of ordered equations: 1
% Current number of rules: 157
% New rule produced :
% [166]
% quotient(quotient(product(i(B),product(A,j(B))),j(B)),A) <->
% difference(product(A,j(B)),product(A,quotient(j(B),B)))
% Current number of equations to process: 48
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced : [167] t(eta(A),product(B,eta(A))) <-> product(eta(A),B)
% Current number of equations to process: 50
% Current number of ordered equations: 1
% Current number of rules: 159
% New rule produced : [168] product(eta(A),B) <-> t(eta(A),product(B,eta(A)))
% Rule [45] product(eta(A),A) -> i(i(A)) collapsed.
% Rule
% [136]
% product(difference(B,i(A)),product(eta(difference(B,i(A))),j(i(A)))) -> j(B)
% collapsed.
% Rule
% [151]
% product(A,quotient(product(product(B,eta(A)),product(eta(product(A,B)),A)),A))
% -> product(product(A,B),product(eta(A),eta(product(A,B)))) collapsed.
% Rule
% [152]
% product(A,quotient(product(eta(A),product(B,product(eta(j(j(A))),A))),A)) ->
% product(A,product(eta(A),product(B,eta(j(j(A)))))) collapsed.
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced : [169] t(eta(A),j(j(A))) -> i(i(A))
% Current number of equations to process: 53
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced :
% [170] product(eta(A),t(eta(A),B)) -> t(eta(A),product(eta(A),B))
% Current number of equations to process: 52
% Current number of ordered equations: 0
% Current number of rules: 158
% Rule [119] quotient(j(B),eta(B)) -> j(i(i(B))) is composed into [119]
% quotient(
% j(B),
% eta(B)) ->
% i(B)
% New rule produced : [171] j(i(A)) -> A
% Rule [79] product(eta(A),product(A,j(i(i(A))))) -> eta(A) collapsed.
% Rule
% [142]
% product(eta(A),product(A,product(eta(A),j(i(B))))) -> j(difference(B,i(A)))
% collapsed.
% Rule
% [154]
% product(eta(A),product(A,product(eta(A),quotient(j(i(i(A))),B)))) -> j(B)
% collapsed.
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 156
% New rule produced : [172] t(A,i(A)) -> j(A)
% Current number of equations to process: 54
% Current number of ordered equations: 0
% Current number of rules: 157
% New rule produced : [173] product(eta(B),product(i(eta(B)),A)) -> A
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [174] product(B,product(i(B),A)) -> quotient(quotient(A,i(B)),B)
% Rule [173] product(eta(B),product(i(eta(B)),A)) -> A collapsed.
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced : [175] quotient(quotient(A,i(eta(B))),eta(B)) -> A
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 159
% New rule produced : [176] product(eta(A),product(A,i(i(i(A))))) -> one
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced : [177] product(A,product(eta(A),i(j(j(A))))) -> one
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [178] quotient(product(i(A),product(B,A)),A) -> difference(A,B)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced : [179] i(j(A)) -> A
% Rule [81] product(A,product(eta(A),i(j(A)))) -> quotient(j(j(A)),j(A))
% collapsed.
% Rule [116] product(difference(product(eta(A),B),i(A)),i(i(j(j(A))))) -> i(B)
% collapsed.
% Rule [177] product(A,product(eta(A),i(j(j(A))))) -> one collapsed.
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced : [180] t(j(A),A) -> j(j(A))
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced : [181] product(A,i(i(A))) -> quotient(j(j(A)),j(A))
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 162
% New rule produced :
% [182] product(j(B),product(B,A)) -> quotient(quotient(A,B),j(B))
% Current number of equations to process: 59
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [183] product(difference(product(eta(A),B),i(A)),A) -> i(B)
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 164
% New rule produced :
% [184] quotient(product(A,product(B,j(A))),j(A)) -> difference(j(A),B)
% Current number of equations to process: 56
% Current number of ordered equations: 0
% Current number of rules: 165
% New rule produced :
% [185] product(eta(A),product(A,product(eta(A),B))) -> j(difference(B,i(A)))
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 166
% New rule produced : [186] difference(t(A,B),product(A,B)) -> A
% Current number of equations to process: 57
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced : [187] difference(A,j(j(A))) -> eta(A)
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced : [188] quotient(j(j(A)),eta(A)) -> A
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced : [189] quotient(j(j(A)),A) -> t(A,eta(A))
% Current number of equations to process: 60
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced : [190] quotient(product(A,j(j(B))),eta(B)) -> product(A,B)
% Current number of equations to process: 64
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [191] difference(product(A,B),product(A,j(j(B)))) -> eta(B)
% Current number of equations to process: 63
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [192] product(A,product(eta(A),eta(j(j(A))))) -> j(j(j(j(A))))
% Current number of equations to process: 61
% Current number of ordered equations: 0
% Current number of rules: 173
% New rule produced : [193] difference(A,i(i(A))) -> i(eta(A))
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced : [194] difference(j(A),i(A)) -> i(eta(A))
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced : [195] difference(difference(B,A),i(B)) -> i(A)
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced : [196] difference(B,i(quotient(A,B))) -> i(A)
% Current number of equations to process: 68
% Current number of ordered equations: 0
% Current number of rules: 177
% New rule produced : [197] difference(i(A),A) -> i(quotient(j(A),A))
% Current number of equations to process: 67
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [198] difference(product(eta(A),B),i(A)) -> difference(B,j(A))
% Rule [183] product(difference(product(eta(A),B),i(A)),A) -> i(B) collapsed.
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced : [199] product(difference(B,j(A)),A) -> i(B)
% Current number of equations to process: 71
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [200] product(difference(A,i(B)),product(B,A)) -> eta(product(B,A))
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [201] difference(product(A,B),i(eta(A))) -> difference(B,i(i(i(A))))
% Rule [115] product(difference(product(A,B),i(eta(A))),i(i(i(i(A))))) -> i(B)
% collapsed.
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [202]
% difference(product(A,B),i(eta(C))) -> difference(B,difference(A,i(eta(C))))
% Rule
% [137]
% product(difference(product(B,C),i(eta(A))),i(difference(B,i(eta(A))))) ->
% i(C) collapsed.
% Rule [201] difference(product(A,B),i(eta(A))) -> difference(B,i(i(i(A))))
% collapsed.
% Current number of equations to process: 70
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced :
% [203] difference(B,difference(A,i(eta(A)))) -> difference(B,i(i(i(A))))
% Current number of equations to process: 69
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced : [204] difference(eta(A),i(A)) -> j(A)
% Current number of equations to process: 72
% Current number of ordered equations: 0
% Current number of rules: 181
% Rule [185]
% product(eta(A),product(A,product(eta(A),B))) -> j(difference(B,i(A))) is composed into 
% [185]
% product(eta(A),product(A,product(eta(A),B))) -> j(quotient(i(B),i(i(A))))
% Rule [48] i(product(B,A)) -> difference(A,i(B)) is composed into [48]
% i(product(B,A))
% ->
% quotient(
% i(A),
% i(i(B)))
% New rule produced : [205] difference(A,i(B)) -> quotient(i(A),i(i(B)))
% Rule [49] product(difference(B,i(A)),i(i(A))) -> i(B) collapsed.
% Rule
% [120]
% product(difference(product(B,eta(A)),i(A)),i(difference(B,i(A)))) ->
% i(eta(A)) collapsed.
% Rule [193] difference(A,i(i(A))) -> i(eta(A)) collapsed.
% Rule [194] difference(j(A),i(A)) -> i(eta(A)) collapsed.
% Rule [195] difference(difference(B,A),i(B)) -> i(A) collapsed.
% Rule [196] difference(B,i(quotient(A,B))) -> i(A) collapsed.
% Rule [198] difference(product(eta(A),B),i(A)) -> difference(B,j(A))
% collapsed.
% Rule [200] product(difference(A,i(B)),product(B,A)) -> eta(product(B,A))
% collapsed.
% Rule
% [202]
% difference(product(A,B),i(eta(C))) -> difference(B,difference(A,i(eta(C))))
% collapsed.
% Rule [203] difference(B,difference(A,i(eta(A)))) -> difference(B,i(i(i(A))))
% collapsed.
% Rule [204] difference(eta(A),i(A)) -> j(A) collapsed.
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced : [206] j(quotient(j(A),A)) -> quotient(A,j(A))
% Rule [102] product(i(A),product(eta(A),j(quotient(j(A),A)))) -> j(j(A))
% collapsed.
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 171
% Rule [189] quotient(j(j(A)),A) -> t(A,eta(A)) is composed into [189]
% quotient(
% j(j(A)),A) ->
% j(eta(A))
% New rule produced : [207] t(A,eta(A)) -> j(eta(A))
% Current number of equations to process: 90
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced : [208] quotient(j(A),i(A)) -> j(eta(A))
% Current number of equations to process: 89
% Current number of ordered equations: 0
% Current number of rules: 173
% New rule produced : [209] quotient(j(difference(B,A)),B) -> j(A)
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 174
% New rule produced : [210] quotient(j(B),quotient(A,B)) -> j(A)
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced : [211] quotient(i(eta(A)),i(i(A))) -> j(A)
% Current number of equations to process: 88
% Current number of ordered equations: 0
% Current number of rules: 176
% New rule produced : [212] product(A,quotient(eta(B),A)) -> eta(product(A,B))
% Current number of equations to process: 87
% Current number of ordered equations: 0
% Current number of rules: 177
% New rule produced : [213] quotient(i(A),i(i(i(A)))) -> i(eta(A))
% Current number of equations to process: 86
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced : [214] quotient(A,i(i(A))) -> i(eta(A))
% Rule [213] quotient(i(A),i(i(i(A)))) -> i(eta(A)) collapsed.
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced : [215] quotient(i(difference(B,A)),i(i(B))) -> i(A)
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 179
% New rule produced : [216] quotient(i(B),i(i(quotient(A,B)))) -> i(A)
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [217] quotient(quotient(j(A),eta(B)),B) -> quotient(j(A),j(j(B)))
% Rule
% [113]
% product(A,product(eta(A),quotient(quotient(j(A),eta(B)),B))) -> j(j(j(B)))
% collapsed.
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [218] quotient(quotient(j(A),B),eta(B)) -> quotient(j(A),i(i(B)))
% Current number of equations to process: 82
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [219] difference(quotient(i(A),i(i(B))),eta(product(B,A))) -> product(B,A)
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [220] quotient(j(A),product(eta(C),B)) <-> quotient(quotient(j(A),B),eta(C))
% Current number of equations to process: 80
% Current number of ordered equations: 1
% Current number of rules: 183
% New rule produced :
% [221] quotient(quotient(j(A),B),eta(C)) <-> quotient(j(A),product(eta(C),B))
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [222] difference(B,j(A)) -> quotient(quotient(i(B),i(i(eta(A)))),i(i(A)))
% Rule [187] difference(A,j(j(A))) -> eta(A) collapsed.
% Rule [199] product(difference(B,j(A)),A) -> i(B) collapsed.
% Current number of equations to process: 81
% Current number of ordered equations: 0
% Current number of rules: 183
% New rule produced :
% [223] product(i(A),product(eta(A),quotient(A,j(A)))) -> j(j(A))
% Current number of equations to process: 80
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced : [224] quotient(j(eta(A)),A) -> j(j(j(A)))
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced : [225] product(quotient(j(A),B),product(B,A)) -> one
% Rule
% [26]
% product(product(product(quotient(j(A),A),product(A,A)),B),C) ->
% product(product(quotient(j(A),A),product(A,A)),product(B,C)) collapsed.
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 185
% New rule produced :
% [226] quotient(eta(product(A,B)),quotient(j(B),A)) -> product(A,B)
% Current number of equations to process: 85
% Current number of ordered equations: 0
% Current number of rules: 186
% New rule produced :
% [227] t(product(A,B),quotient(j(B),A)) -> quotient(i(B),i(i(A)))
% Current number of equations to process: 84
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced :
% [228] t(B,product(eta(B),quotient(j(B),A))) -> quotient(j(A),B)
% Current number of equations to process: 83
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced : [229] quotient(product(A,B),t(A,B)) -> t(t(A,B),A)
% Current number of equations to process: 93
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced : [230] quotient(j(A),B) <-> quotient(j(B),t(B,A))
% Rule [188] quotient(j(j(A)),eta(A)) -> A collapsed.
% Rule [189] quotient(j(j(A)),A) -> j(eta(A)) collapsed.
% Rule [209] quotient(j(difference(B,A)),B) -> j(A) collapsed.
% Rule [224] quotient(j(eta(A)),A) -> j(j(j(A))) collapsed.
% Current number of equations to process: 101
% Current number of ordered equations: 1
% Current number of rules: 186
% New rule produced : [231] quotient(j(B),t(B,A)) <-> quotient(j(A),B)
% Current number of equations to process: 101
% Current number of ordered equations: 0
% Current number of rules: 187
% New rule produced : [232] quotient(j(A),j(eta(A))) -> j(j(j(A)))
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced : [233] quotient(j(eta(A)),t(eta(A),j(A))) -> A
% Current number of equations to process: 99
% Current number of ordered equations: 0
% Current number of rules: 189
% New rule produced : [234] difference(t(i(A),A),eta(A)) -> i(A)
% Current number of equations to process: 100
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced : [235] difference(t(quotient(A,B),B),A) -> quotient(A,B)
% Current number of equations to process: 102
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [236] quotient(j(j(j(B))),t(j(j(B)),quotient(j(B),A))) -> j(j(A))
% Current number of equations to process: 104
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced : [237] quotient(eta(A),t(i(A),A)) -> t(t(i(A),A),i(A))
% Current number of equations to process: 103
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced : [238] t(A,product(eta(A),j(A))) -> j(A)
% Current number of equations to process: 105
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced : [239] product(eta(A),j(A)) -> i(A)
% Rule [58] product(A,product(eta(A),j(A))) -> one collapsed.
% Rule [238] t(A,product(eta(A),j(A))) -> j(A) collapsed.
% Current number of equations to process: 106
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced : [240] quotient(eta(eta(A)),A) -> j(A)
% Current number of equations to process: 108
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [241] difference(B,eta(quotient(A,B))) -> quotient(eta(A),B)
% Current number of equations to process: 110
% Current number of ordered equations: 1
% Current number of rules: 195
% New rule produced :
% [242] product(difference(A,eta(B)),A) -> eta(product(B,A))
% Current number of equations to process: 110
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [243] difference(j(A),eta(A)) -> quotient(eta(eta(A)),j(A))
% Current number of equations to process: 111
% Current number of ordered equations: 0
% Current number of rules: 197
% New rule produced :
% [244] difference(difference(B,A),eta(B)) -> quotient(eta(A),difference(B,A))
% Current number of equations to process: 110
% Current number of ordered equations: 0
% Current number of rules: 198
% New rule produced : [245] difference(A,eta(j(A))) -> j(A)
% Current number of equations to process: 111
% Current number of ordered equations: 0
% Current number of rules: 199
% New rule produced : [246] quotient(eta(j(j(A))),eta(A)) -> one
% Current number of equations to process: 112
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced : [247] difference(A,eta(eta(A))) -> quotient(eta(j(A)),A)
% Current number of equations to process: 120
% Current number of ordered equations: 0
% Current number of rules: 201
% New rule produced : [248] difference(i(A),eta(eta(A))) -> t(i(A),A)
% Current number of equations to process: 119
% Current number of ordered equations: 0
% Current number of rules: 202
% Rule [59] quotient(eta(product(A,B)),B) -> difference(B,eta(A)) is composed into 
% [59] quotient(eta(product(A,B)),B) -> quotient(eta(difference(B,A)),B)
% New rule produced :
% [249] difference(A,eta(B)) -> quotient(eta(difference(A,B)),A)
% Rule [39] difference(A,eta(A)) -> j(A) collapsed.
% Rule [41] difference(i(A),eta(A)) -> A collapsed.
% Rule [60] difference(A,eta(product(A,B))) -> quotient(eta(B),A) collapsed.
% Rule
% [219] difference(quotient(i(A),i(i(B))),eta(product(B,A))) -> product(B,A)
% collapsed.
% Rule [234] difference(t(i(A),A),eta(A)) -> i(A) collapsed.
% Rule [241] difference(B,eta(quotient(A,B))) -> quotient(eta(A),B) collapsed.
% Rule [242] product(difference(A,eta(B)),A) -> eta(product(B,A)) collapsed.
% Rule [243] difference(j(A),eta(A)) -> quotient(eta(eta(A)),j(A)) collapsed.
% Rule
% [244] difference(difference(B,A),eta(B)) -> quotient(eta(A),difference(B,A))
% collapsed.
% Rule [245] difference(A,eta(j(A))) -> j(A) collapsed.
% Rule [247] difference(A,eta(eta(A))) -> quotient(eta(j(A)),A) collapsed.
% Rule [248] difference(i(A),eta(eta(A))) -> t(i(A),A) collapsed.
% Current number of equations to process: 127
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [250] quotient(eta(quotient(quotient(i(A),i(i(eta(A)))),i(i(A)))),A) -> j(A)
% Current number of equations to process: 126
% Current number of ordered equations: 0
% Current number of rules: 192
% New rule produced : [251] quotient(eta(quotient(j(A),A)),i(A)) -> A
% Current number of equations to process: 125
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced :
% [252] quotient(eta(product(A,B)),A) -> quotient(eta(difference(A,t(A,B))),A)
% Current number of equations to process: 123
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [253]
% quotient(eta(difference(quotient(eta(difference(A,B)),A),product(B,A))),
% quotient(eta(difference(A,B)),A)) -> A
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 195
% Rule [212] product(A,quotient(eta(B),A)) -> eta(product(A,B)) is composed into 
% [212] product(A,quotient(eta(B),A)) -> eta(difference(B,A))
% Rule [94]
% product(eta(A),product(B,quotient(j(B),eta(A)))) ->
% eta(product(eta(A),B)) is composed into [94]
% product(eta(A),product(B,
% quotient(
% j(B),eta(A)))) ->
% eta(difference(B,eta(A)))
% New rule produced : [254] eta(product(B,A)) -> eta(difference(A,B))
% Rule [59] quotient(eta(product(A,B)),B) -> quotient(eta(difference(B,A)),B)
% collapsed.
% Rule [226] quotient(eta(product(A,B)),quotient(j(B),A)) -> product(A,B)
% collapsed.
% Rule
% [252] quotient(eta(product(A,B)),A) -> quotient(eta(difference(A,t(A,B))),A)
% collapsed.
% Current number of equations to process: 121
% Current number of ordered equations: 0
% Current number of rules: 193
% Rule [221]
% quotient(quotient(j(A),B),eta(C)) <-> quotient(j(A),product(eta(C),B)) is composed into 
% [221]
% quotient(quotient(j(A),B),eta(C)) <->
% quotient(j(A),quotient(eta(difference(B,eta(C))),quotient(j(B),eta(C))))
% New rule produced :
% [255] product(A,B) -> quotient(eta(difference(B,A)),quotient(j(B),A))
% Rule [1] product(A,one) -> A collapsed.
% Rule [2] product(one,A) -> A collapsed.
% Rule [5] product(i(A),A) -> eta(A) collapsed.
% Rule [6] quotient(product(A,B),B) -> A collapsed.
% Rule [7] difference(A,product(A,B)) -> B collapsed.
% Rule [8] product(A,difference(A,B)) -> B collapsed.
% Rule [9] product(quotient(A,B),B) -> A collapsed.
% Rule [10] product(A,j(A)) -> eta(A) collapsed.
% Rule [11] quotient(product(A,B),A) -> t(A,B) collapsed.
% Rule [13] product(j(A),i(A)) -> quotient(j(A),A) collapsed.
% Rule [15] product(i(i(A)),B) -> product(eta(A),product(A,B)) collapsed.
% Rule [16] product(j(j(A)),B) -> product(A,product(eta(A),B)) collapsed.
% Rule [19] product(product(eta(A),B),C) -> product(eta(A),product(B,C))
% collapsed.
% Rule
% [21]
% quotient(product(B,product(C,A)),A) <-> difference(A,product(product(A,B),C))
% collapsed.
% Rule
% [22]
% difference(A,product(product(A,B),C)) <-> quotient(product(B,product(C,A)),A)
% collapsed.
% Rule [23] product(t(eta(A),B),t(eta(A),C)) -> t(eta(A),product(B,C))
% collapsed.
% Rule
% [24]
% quotient(quotient(product(C,product(A,B)),B),A) <->
% difference(product(A,B),product(A,product(B,C))) collapsed.
% Rule
% [25]
% difference(product(A,B),product(A,product(B,C))) <->
% quotient(quotient(product(C,product(A,B)),B),A) collapsed.
% Rule [34] product(A,i(A)) -> one collapsed.
% Rule [35] product(j(A),A) -> one collapsed.
% Rule [46] product(A,eta(A)) -> j(j(A)) collapsed.
% Rule [48] i(product(B,A)) -> quotient(i(A),i(i(B))) collapsed.
% Rule [50] j(product(B,A)) -> quotient(j(A),B) collapsed.
% Rule [51] product(A,product(eta(A),quotient(j(A),B))) -> j(B) collapsed.
% Rule [53] product(t(A,B),A) -> product(A,B) collapsed.
% Rule [64] quotient(product(A,product(eta(A),B)),B) -> j(j(A)) collapsed.
% Rule [65] product(A,product(j(A),eta(A))) -> product(eta(A),eta(A))
% collapsed.
% Rule [66] t(A,product(B,A)) <-> difference(A,product(product(A,A),B))
% collapsed.
% Rule [67] difference(A,product(product(A,A),B)) <-> t(A,product(B,A))
% collapsed.
% Rule [68] product(B,product(difference(B,A),eta(B))) -> product(A,eta(B))
% collapsed.
% Rule [69] quotient(product(eta(A),product(B,C)),C) -> product(eta(A),B)
% collapsed.
% Rule [70] quotient(product(A,i(i(B))),B) -> product(A,eta(B)) collapsed.
% Rule [71] difference(i(i(A)),product(eta(A),product(A,B))) -> B collapsed.
% Rule [72] product(eta(B),product(B,difference(i(i(B)),A))) -> A collapsed.
% Rule [73] difference(j(j(A)),product(A,product(eta(A),B))) -> B collapsed.
% Rule [74] product(B,product(eta(B),difference(j(j(B)),A))) -> A collapsed.
% Rule [76] product(eta(C),product(difference(eta(C),A),B)) -> product(A,B)
% collapsed.
% Rule [77] product(eta(A),product(j(eta(A)),B)) -> product(eta(eta(A)),B)
% collapsed.
% Rule [78] quotient(product(A,product(B,eta(C))),eta(C)) -> product(A,B)
% collapsed.
% Rule [80] product(A,product(eta(A),j(j(j(A))))) -> eta(j(j(A))) collapsed.
% Rule [82] product(i(A),j(j(A))) -> product(eta(A),eta(A)) collapsed.
% Rule [83] difference(product(A,B),product(A,product(B,eta(A)))) -> eta(A)
% collapsed.
% Rule
% [84]
% quotient(product(j(A),product(B,A)),A) -> difference(A,product(eta(A),B))
% collapsed.
% Rule [85] difference(product(eta(A),B),product(eta(A),product(B,C))) -> C
% collapsed.
% Rule [86] product(eta(B),product(C,difference(product(eta(B),C),A))) -> A
% collapsed.
% Rule
% [87]
% difference(C,product(product(C,A),quotient(B,C))) -> quotient(product(A,B),C)
% collapsed.
% Rule
% [88]
% product(difference(A,product(product(A,B),C)),A) -> product(B,product(C,A))
% collapsed.
% Rule
% [89]
% product(A,quotient(product(B,product(C,A)),A)) <-> product(product(A,B),C)
% collapsed.
% Rule
% [90]
% product(product(A,B),C) <-> product(A,quotient(product(B,product(C,A)),A))
% collapsed.
% Rule
% [91]
% quotient(product(difference(A,B),product(C,A)),A) ->
% difference(A,product(B,C)) collapsed.
% Rule [92] quotient(product(eta(A),product(A,B)),i(i(A))) -> t(i(i(A)),B)
% collapsed.
% Rule [93] quotient(product(A,product(eta(A),B)),j(j(A))) -> t(j(j(A)),B)
% collapsed.
% Rule
% [94]
% product(eta(A),product(B,quotient(j(B),eta(A)))) -> eta(difference(B,eta(A)))
% collapsed.
% Rule
% [95]
% difference(i(A),product(eta(A),B)) <->
% quotient(product(A,product(B,i(A))),i(A)) collapsed.
% Rule
% [96]
% quotient(product(A,product(B,i(A))),i(A)) <->
% difference(i(A),product(eta(A),B)) collapsed.
% Rule
% [97]
% difference(product(B,A),product(B,product(A,A))) ->
% quotient(t(A,product(B,A)),B) collapsed.
% Rule [98] quotient(t(eta(A),product(B,C)),t(eta(A),C)) -> t(eta(A),B)
% collapsed.
% Rule [99] difference(t(eta(A),B),t(eta(A),product(B,C))) -> t(eta(A),C)
% collapsed.
% Rule
% [100]
% difference(product(A,B),product(A,C)) <->
% quotient(difference(B,product(C,A)),A) collapsed.
% Rule
% [101]
% quotient(difference(B,product(C,A)),A) <->
% difference(product(A,B),product(A,C)) collapsed.
% Rule
% [103]
% quotient(product(A,product(B,product(C,eta(B)))),eta(B)) ->
% product(A,product(B,C)) collapsed.
% Rule
% [104]
% difference(eta(B),product(i(B),product(B,A))) <->
% quotient(quotient(product(A,eta(B)),B),i(B)) collapsed.
% Rule
% [105]
% quotient(quotient(product(A,eta(B)),B),i(B)) <->
% difference(eta(B),product(i(B),product(B,A))) collapsed.
% Rule
% [106]
% difference(B,product(C,product(difference(C,B),A))) <->
% quotient(quotient(product(A,B),difference(C,B)),C) collapsed.
% Rule
% [107]
% quotient(quotient(product(A,B),difference(C,B)),C) <->
% difference(B,product(C,product(difference(C,B),A))) collapsed.
% Rule
% [108]
% difference(B,product(quotient(B,C),product(C,A))) <->
% quotient(quotient(product(A,B),C),quotient(B,C)) collapsed.
% Rule
% [109]
% quotient(quotient(product(A,B),C),quotient(B,C)) <->
% difference(B,product(quotient(B,C),product(C,A))) collapsed.
% Rule
% [110]
% difference(eta(B),product(B,product(j(B),A))) <->
% quotient(quotient(product(A,eta(B)),j(B)),B) collapsed.
% Rule
% [111]
% quotient(quotient(product(A,eta(B)),j(B)),B) <->
% difference(eta(B),product(B,product(j(B),A))) collapsed.
% Rule
% [114]
% quotient(product(eta(A),product(B,C)),product(eta(A),B)) ->
% t(product(eta(A),B),C) collapsed.
% Rule
% [117]
% product(B,product(eta(B),product(quotient(j(B),A),eta(B)))) ->
% product(j(A),eta(B)) collapsed.
% Rule
% [118]
% product(A,product(eta(A),quotient(quotient(j(A),C),eta(B)))) ->
% quotient(j(C),eta(B)) collapsed.
% Rule
% [121]
% difference(C,product(product(C,A),i(i(B)))) <->
% quotient(product(A,product(eta(B),product(B,C))),C) collapsed.
% Rule
% [122]
% difference(C,product(product(C,i(i(A))),B)) <->
% quotient(product(eta(A),product(A,product(B,C))),C) collapsed.
% Rule
% [123]
% quotient(product(A,product(eta(B),product(B,C))),C) <->
% difference(C,product(product(C,A),i(i(B)))) collapsed.
% Rule
% [124]
% quotient(product(eta(A),product(A,product(B,C))),C) <->
% difference(C,product(product(C,i(i(A))),B)) collapsed.
% Rule
% [125]
% difference(C,product(product(C,A),j(j(B)))) <->
% quotient(product(A,product(B,product(eta(B),C))),C) collapsed.
% Rule
% [126]
% difference(C,product(product(C,j(j(A))),B)) <->
% quotient(product(A,product(eta(A),product(B,C))),C) collapsed.
% Rule
% [127]
% quotient(product(A,product(B,product(eta(B),C))),C) <->
% difference(C,product(product(C,A),j(j(B)))) collapsed.
% Rule
% [128]
% quotient(product(A,product(eta(A),product(B,C))),C) <->
% difference(C,product(product(C,j(j(A))),B)) collapsed.
% Rule
% [129]
% difference(quotient(A,B),product(A,C)) <->
% quotient(product(B,product(C,quotient(A,B))),quotient(A,B)) collapsed.
% Rule
% [130]
% quotient(product(B,product(C,quotient(A,B))),quotient(A,B)) <->
% difference(quotient(A,B),product(A,C)) collapsed.
% Rule
% [131]
% difference(j(A),product(quotient(j(A),A),B)) <->
% quotient(product(i(A),product(B,j(A))),j(A)) collapsed.
% Rule
% [132]
% quotient(product(i(A),product(B,j(A))),j(A)) <->
% difference(j(A),product(quotient(j(A),A),B)) collapsed.
% Rule [133] product(t(eta(A),B),i(t(eta(A),product(C,B)))) -> i(t(eta(A),C))
% collapsed.
% Rule [134] product(j(t(eta(A),product(B,C))),t(eta(A),B)) -> j(t(eta(A),C))
% collapsed.
% Rule
% [135]
% product(difference(product(A,B),product(A,product(B,C))),A) ->
% quotient(product(C,product(A,B)),B) collapsed.
% Rule
% [138]
% difference(V_3,product(product(V_3,A),product(eta(B),C))) <->
% quotient(product(A,product(eta(B),product(C,V_3))),V_3) collapsed.
% Rule
% [139]
% difference(V_3,product(product(V_3,product(eta(A),B)),C)) <->
% quotient(product(eta(A),product(B,product(C,V_3))),V_3) collapsed.
% Rule
% [140]
% quotient(product(A,product(eta(B),product(C,V_3))),V_3) <->
% difference(V_3,product(product(V_3,A),product(eta(B),C))) collapsed.
% Rule
% [141]
% quotient(product(eta(A),product(B,product(C,V_3))),V_3) <->
% difference(V_3,product(product(V_3,product(eta(A),B)),C)) collapsed.
% Rule
% [143]
% quotient(t(eta(A),product(B,C)),t(eta(A),B)) -> t(t(eta(A),B),t(eta(A),C))
% collapsed.
% Rule
% [144]
% difference(product(C,B),product(C,product(B,quotient(A,product(C,B))))) ->
% quotient(quotient(A,B),C) collapsed.
% Rule
% [145]
% quotient(quotient(product(B,product(A,i(B))),i(B)),A) ->
% difference(product(A,i(B)),product(A,eta(B))) collapsed.
% Rule
% [146]
% product(product(A,B),quotient(quotient(product(C,product(A,B)),B),A)) ->
% product(A,product(B,C)) collapsed.
% Rule
% [147]
% product(quotient(j(A),B),product(B,eta(quotient(j(A),B)))) ->
% product(j(A),eta(quotient(j(A),B))) collapsed.
% Rule
% [148]
% product(eta(A),product(eta(eta(A)),quotient(quotient(j(eta(A)),B),A))) ->
% quotient(j(B),A) collapsed.
% Rule
% [149]
% product(eta(C),product(eta(eta(C)),product(quotient(j(eta(C)),A),B))) ->
% product(j(A),B) collapsed.
% Rule
% [150]
% quotient(product(eta(A),product(quotient(j(A),B),product(C,A))),A) ->
% difference(A,product(j(B),C)) collapsed.
% Rule
% [153] product(i(t(eta(A),product(B,C))),i(i(t(eta(A),B)))) -> i(t(eta(A),C))
% collapsed.
% Rule
% [155]
% product(A,product(eta(A),product(eta(j(j(A))),quotient(j(j(j(A))),B)))) ->
% j(B) collapsed.
% Rule
% [156]
% difference(i(i(A)),product(eta(A),product(product(A,B),C))) <->
% quotient(product(B,product(C,i(i(A)))),i(i(A))) collapsed.
% Rule
% [157]
% quotient(product(B,product(C,i(i(A)))),i(i(A))) <->
% difference(i(i(A)),product(eta(A),product(product(A,B),C))) collapsed.
% Rule
% [158]
% difference(j(j(A)),product(product(A,product(eta(A),B)),C)) <->
% quotient(product(B,product(C,j(j(A)))),j(j(A))) collapsed.
% Rule
% [159]
% quotient(product(B,product(C,j(j(A)))),j(j(A))) <->
% difference(j(j(A)),product(product(A,product(eta(A),B)),C)) collapsed.
% Rule
% [160]
% difference(product(B,C),product(B,product(C,i(i(A))))) <->
% quotient(quotient(product(eta(A),product(A,product(B,C))),C),B) collapsed.
% Rule
% [161]
% quotient(quotient(product(eta(A),product(A,product(B,C))),C),B) <->
% difference(product(B,C),product(B,product(C,i(i(A))))) collapsed.
% Rule
% [162]
% difference(product(B,C),product(B,product(C,j(j(A))))) <->
% quotient(quotient(product(A,product(eta(A),product(B,C))),C),B) collapsed.
% Rule
% [163]
% quotient(quotient(product(A,product(eta(A),product(B,C))),C),B) <->
% difference(product(B,C),product(B,product(C,j(j(A))))) collapsed.
% Rule
% [164]
% quotient(quotient(product(C,product(A,quotient(B,C))),quotient(B,C)),A) ->
% difference(product(A,quotient(B,C)),product(A,B)) collapsed.
% Rule
% [165]
% difference(product(A,j(B)),product(A,quotient(j(B),B))) <->
% quotient(quotient(product(i(B),product(A,j(B))),j(B)),A) collapsed.
% Rule
% [166]
% quotient(quotient(product(i(B),product(A,j(B))),j(B)),A) <->
% difference(product(A,j(B)),product(A,quotient(j(B),B))) collapsed.
% Rule [167] t(eta(A),product(B,eta(A))) <-> product(eta(A),B) collapsed.
% Rule [168] product(eta(A),B) <-> t(eta(A),product(B,eta(A))) collapsed.
% Rule [170] product(eta(A),t(eta(A),B)) -> t(eta(A),product(eta(A),B))
% collapsed.
% Rule [174] product(B,product(i(B),A)) -> quotient(quotient(A,i(B)),B)
% collapsed.
% Rule [176] product(eta(A),product(A,i(i(i(A))))) -> one collapsed.
% Rule [178] quotient(product(i(A),product(B,A)),A) -> difference(A,B)
% collapsed.
% Rule [181] product(A,i(i(A))) -> quotient(j(j(A)),j(A)) collapsed.
% Rule [182] product(j(B),product(B,A)) -> quotient(quotient(A,B),j(B))
% collapsed.
% Rule [184] quotient(product(A,product(B,j(A))),j(A)) -> difference(j(A),B)
% collapsed.
% Rule
% [185]
% product(eta(A),product(A,product(eta(A),B))) -> j(quotient(i(B),i(i(A))))
% collapsed.
% Rule [186] difference(t(A,B),product(A,B)) -> A collapsed.
% Rule [190] quotient(product(A,j(j(B))),eta(B)) -> product(A,B) collapsed.
% Rule [191] difference(product(A,B),product(A,j(j(B)))) -> eta(B) collapsed.
% Rule [192] product(A,product(eta(A),eta(j(j(A))))) -> j(j(j(j(A))))
% collapsed.
% Rule [212] product(A,quotient(eta(B),A)) -> eta(difference(B,A)) collapsed.
% Rule
% [220] quotient(j(A),product(eta(C),B)) <-> quotient(quotient(j(A),B),eta(C))
% collapsed.
% Rule [223] product(i(A),product(eta(A),quotient(A,j(A)))) -> j(j(A))
% collapsed.
% Rule [225] product(quotient(j(A),B),product(B,A)) -> one collapsed.
% Rule [227] t(product(A,B),quotient(j(B),A)) -> quotient(i(B),i(i(A)))
% collapsed.
% Rule [228] t(B,product(eta(B),quotient(j(B),A))) -> quotient(j(A),B)
% collapsed.
% Rule [229] quotient(product(A,B),t(A,B)) -> t(t(A,B),A) collapsed.
% Rule [239] product(eta(A),j(A)) -> i(A) collapsed.
% Rule
% [253]
% quotient(eta(difference(quotient(eta(difference(A,B)),A),product(B,A))),
% quotient(eta(difference(A,B)),A)) -> A collapsed.
% Rule [254] eta(product(B,A)) -> eta(difference(A,B)) collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% quotient(eta(difference(quotient(eta(difference(x2,x1)),quotient(j(x2),x1)),x0)),
% quotient(j(x0),t(x0,quotient(eta(difference(x2,x1)),quotient(j(x2),x1))))) = 
% quotient(eta(difference(quotient(eta(difference(x2,x0)),quotient(j(x2),x0)),
% t(x0,x1))),quotient(j(t(x0,x1)),t(t(x0,x1),quotient(eta(
% difference(x2,x0)),
% quotient(j(x2),x0)))))
% 
% Current number of equations to process: 230
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [256] difference(A,quotient(eta(difference(B,A)),quotient(j(B),A))) -> B
% Current number of equations to process: 215
% Current number of ordered equations: 15
% Current number of rules: 59
% New rule produced :
% [257] quotient(quotient(eta(difference(B,A)),quotient(j(B),A)),B) -> A
% Current number of equations to process: 215
% Current number of ordered equations: 14
% Current number of rules: 60
% New rule produced :
% [258] quotient(eta(difference(j(A),A)),j(eta(A))) -> eta(A)
% Current number of equations to process: 215
% Current number of ordered equations: 13
% Current number of rules: 61
% New rule produced :
% [259] quotient(eta(quotient(i(A),i(i(A)))),j(eta(A))) -> eta(A)
% Current number of equations to process: 215
% Current number of ordered equations: 12
% Current number of rules: 62
% New rule produced :
% [260] quotient(quotient(eta(difference(B,A)),quotient(j(B),A)),A) -> t(A,B)
% Current number of equations to process: 215
% Current number of ordered equations: 11
% Current number of rules: 63
% New rule produced :
% [261] quotient(eta(difference(B,quotient(A,B))),j(A)) -> A
% Current number of equations to process: 215
% Current number of ordered equations: 10
% Current number of rules: 64
% New rule produced :
% [262] quotient(eta(difference(difference(A,B),A)),j(B)) -> B
% Current number of equations to process: 215
% Current number of ordered equations: 9
% Current number of rules: 65
% New rule produced :
% [263]
% quotient(eta(quotient(quotient(i(i(A)),i(i(eta(A)))),i(i(A)))),quotient(A,
% j(A))) ->
% quotient(j(A),A)
% Current number of equations to process: 215
% Current number of ordered equations: 8
% Current number of rules: 66
% New rule produced :
% [264]
% quotient(eta(difference(t(eta(A),C),t(eta(A),B))),quotient(j(t(eta(A),C)),
% t(eta(A),B))) ->
% t(eta(A),quotient(eta(difference(C,B)),quotient(j(C),B)))
% Current number of equations to process: 215
% Current number of ordered equations: 7
% Current number of rules: 67
% New rule produced :
% [265]
% quotient(eta(quotient(eta(difference(quotient(eta(difference(B,A)),quotient(
% j(B),A)),A)),
% quotient(eta(difference(B,A)),quotient(j(B),A)))),quotient(
% j(eta(A)),
% t(eta(A),
% quotient(
% eta(difference(B,A)),
% quotient(
% j(B),A))))) ->
% quotient(eta(quotient(i(B),i(i(i(A))))),quotient(j(B),i(i(A))))
% Current number of equations to process: 215
% Current number of ordered equations: 6
% Current number of rules: 68
% New rule produced :
% [266]
% quotient(eta(difference(quotient(eta(quotient(eta(difference(B,A)),B)),
% quotient(j(B),eta(A))),A)),quotient(j(A),t(A,
% quotient(
% eta(
% quotient(
% eta(
% difference(B,A)),B)),
% quotient(
% j(B),
% eta(A))))))
% ->
% quotient(eta(quotient(quotient(i(B),i(i(eta(j(A))))),i(A))),quotient(
% j(B),j(j(A))))
% Current number of equations to process: 215
% Current number of ordered equations: 5
% Current number of rules: 69
% New rule produced :
% [267]
% difference(A,quotient(eta(difference(C,quotient(eta(difference(B,A)),
% quotient(j(B),A)))),quotient(j(C),
% quotient(eta(
% difference(B,A)),
% quotient(j(B),A)))))
% <->
% quotient(quotient(eta(difference(quotient(eta(difference(A,C)),quotient(
% j(A),C)),B)),
% quotient(j(quotient(eta(difference(A,C)),quotient(j(A),C))),B)),A)
% Current number of equations to process: 98
% Current number of ordered equations: 596
% Current number of rules: 70
% New rule produced :
% [268]
% quotient(quotient(eta(difference(quotient(eta(difference(A,C)),quotient(
% j(A),C)),B)),
% quotient(j(quotient(eta(difference(A,C)),quotient(j(A),C))),B)),A)
% <->
% difference(A,quotient(eta(difference(C,quotient(eta(difference(B,A)),
% quotient(j(B),A)))),quotient(j(C),
% quotient(eta(
% difference(B,A)),
% quotient(j(B),A)))))
% Current number of equations to process: 98
% Current number of ordered equations: 595
% Current number of rules: 71
% New rule produced :
% [269]
% quotient(eta(difference(quotient(eta(quotient(eta(difference(quotient(j(A),B),A)),
% quotient(j(A),B))),quotient(j(eta(A)),
% t(eta(A),quotient(
% j(A),B)))),A)),
% quotient(j(A),t(A,quotient(eta(quotient(eta(difference(quotient(j(A),B),A)),
% quotient(j(A),B))),quotient(j(eta(A)),
% t(eta(A),quotient(j(A),B)))))))
% -> j(B)
% Current number of equations to process: 98
% Current number of ordered equations: 594
% Current number of rules: 72
% New rule produced :
% [270]
% quotient(eta(quotient(eta(difference(quotient(eta(difference(C,B)),quotient(
% j(C),B)),A)),
% quotient(eta(difference(C,B)),quotient(j(C),B)))),quotient(
% j(quotient(
% eta(
% difference(C,B)),
% quotient(
% j(C),B))),
% eta(A))) ->
% quotient(eta(difference(C,quotient(eta(quotient(eta(difference(B,A)),B)),
% quotient(j(B),eta(A))))),quotient(j(C),quotient(
% eta(
% quotient(
% eta(
% difference(B,A)),B)),
% quotient(
% j(B),
% eta(A)))))
% Current number of equations to process: 104
% Current number of ordered equations: 583
% Current number of rules: 73
% New rule produced :
% [271]
% difference(quotient(eta(difference(B,A)),quotient(j(B),A)),quotient(eta(
% difference(
% quotient(
% eta(
% difference(C,B)),
% quotient(
% j(C),B)),A)),
% quotient(j(
% quotient(
% eta(
% difference(C,B)),
% quotient(
% j(C),B))),A)))
% ->
% quotient(quotient(quotient(eta(difference(quotient(eta(difference(B,A)),
% quotient(j(B),A)),C)),quotient(
% j(quotient(
% eta(
% difference(B,A)),
% quotient(
% j(B),A))),C)),B),A)
% Current number of equations to process: 107
% Current number of ordered equations: 577
% Current number of rules: 74
% Rule [266]
% quotient(eta(difference(quotient(eta(quotient(eta(difference(B,A)),B)),
% quotient(j(B),eta(A))),A)),quotient(j(A),
% t(A,quotient(
% eta(quotient(
% eta(difference(B,A)),B)),
% quotient(
% j(B),eta(A))))))
% ->
% quotient(eta(quotient(quotient(i(B),i(i(eta(j(A))))),i(A))),quotient(
% j(B),
% j(j(A)))) is composed into 
% [266]
% quotient(eta(difference(quotient(eta(quotient(eta(difference(B,A)),B)),
% quotient(j(B),eta(A))),A)),quotient(j(A),t(A,
% quotient(
% eta(
% quotient(
% eta(
% difference(B,A)),B)),
% quotient(
% j(B),
% eta(A))))))
% ->
% quotient(eta(quotient(quotient(i(B),i(i(eta(A)))),i(A))),quotient(j(B),
% j(j(A))))
% New rule produced : [272] eta(j(A)) -> eta(A)
% Rule [246] quotient(eta(j(j(A))),eta(A)) -> one collapsed.
% Current number of equations to process: 143
% Current number of ordered equations: 527
% Current number of rules: 74
% Rule [266]
% quotient(eta(difference(quotient(eta(quotient(eta(difference(B,A)),B)),
% quotient(j(B),eta(A))),A)),quotient(j(A),
% t(A,quotient(
% eta(quotient(
% eta(difference(B,A)),B)),
% quotient(
% j(B),eta(A))))))
% ->
% quotient(eta(quotient(quotient(i(B),i(i(eta(A)))),i(A))),quotient(
% j(B),j(j(A)))) is composed into 
% [266]
% quotient(eta(difference(quotient(eta(quotient(eta(difference(B,A)),B)),
% quotient(j(B),eta(A))),A)),quotient(j(A),t(A,
% quotient(
% eta(
% quotient(
% eta(
% difference(B,A)),B)),
% quotient(
% j(B),
% eta(A))))))
% ->
% quotient(eta(quotient(quotient(i(B),i(j(eta(A)))),i(A))),quotient(j(B),
% j(j(A))))
% Rule [222]
% difference(B,j(A)) -> quotient(quotient(i(B),i(i(eta(A)))),i(i(A))) is composed into 
% [222] difference(B,j(A)) -> quotient(quotient(i(B),i(j(eta(A)))),i(i(A)))
% Rule [214] quotient(A,i(i(A))) -> i(eta(A)) is composed into [214]
% quotient(A,
% i(i(A))) ->
% j(eta(A))
% New rule produced : [273] i(eta(A)) -> j(eta(A))
% Rule [175] quotient(quotient(A,i(eta(B))),eta(B)) -> A collapsed.
% Rule [211] quotient(i(eta(A)),i(i(A))) -> j(A) collapsed.
% Rule
% [250] quotient(eta(quotient(quotient(i(A),i(i(eta(A)))),i(i(A)))),A) -> j(A)
% collapsed.
% Rule
% [263]
% quotient(eta(quotient(quotient(i(i(A)),i(i(eta(A)))),i(i(A)))),quotient(A,
% j(A))) ->
% quotient(j(A),A) collapsed.
% Current number of equations to process: 226
% Current number of ordered equations: 411
% Current number of rules: 71
% New rule produced :
% [274]
% quotient(eta(quotient(quotient(i(i(A)),eta(A)),i(i(A)))),quotient(A,j(A))) ->
% quotient(j(A),A)
% Current number of equations to process: 225
% Current number of ordered equations: 411
% Current number of rules: 72
% New rule produced : [275] j(eta(eta(A))) -> one
% Current number of equations to process: 229
% Current number of ordered equations: 406
% Current number of rules: 73
% Rule [54] quotient(eta(A),i(A)) -> t(i(A),A) is composed into [54]
% quotient(
% eta(A),
% i(A)) ->
% i(i(A))
% New rule produced : [276] t(i(A),A) -> i(i(A))
% Rule [237] quotient(eta(A),t(i(A),A)) -> t(t(i(A),A),i(A)) collapsed.
% Current number of equations to process: 234
% Current number of ordered equations: 391
% Current number of rules: 73
% New rule produced : [277] quotient(A,eta(A)) -> i(i(A))
% Current number of equations to process: 234
% Current number of ordered equations: 390
% Current number of rules: 74
% New rule produced : [278] eta(quotient(j(A),A)) -> one
% Rule [251] quotient(eta(quotient(j(A),A)),i(A)) -> A collapsed.
% Current number of equations to process: 240
% Current number of ordered equations: 374
% Current number of rules: 74
% New rule produced : [279] t(i(A),eta(A)) -> j(eta(A))
% Current number of equations to process: 240
% Current number of ordered equations: 372
% Current number of rules: 75
% Rule [255] product(A,B) -> quotient(eta(difference(B,A)),quotient(j(B),A)) is composed into 
% [255] product(A,B) -> quotient(eta(quotient(i(B),i(A))),quotient(j(B),A))
% Rule [221]
% quotient(quotient(j(A),B),eta(C)) <->
% quotient(j(A),quotient(eta(difference(B,eta(C))),quotient(j(B),eta(C)))) is composed into 
% [221]
% quotient(quotient(j(A),B),eta(C)) <->
% quotient(j(A),quotient(eta(quotient(i(B),i(eta(C)))),quotient(j(B),eta(C))))
% New rule produced : [280] difference(A,B) -> quotient(i(A),i(B))
% Rule [4] difference(A,one) -> i(A) collapsed.
% Rule [31] difference(A,A) -> one collapsed.
% Rule [32] difference(one,A) -> A collapsed.
% Rule [42] quotient(A,difference(B,A)) -> B collapsed.
% Rule [43] difference(quotient(A,B),A) -> B collapsed.
% Rule [52] t(B,difference(B,A)) -> quotient(A,B) collapsed.
% Rule [57] difference(j(A),quotient(j(A),A)) -> i(A) collapsed.
% Rule [197] difference(i(A),A) -> i(quotient(j(A),A)) collapsed.
% Rule [205] difference(A,i(B)) -> quotient(i(A),i(i(B))) collapsed.
% Rule [215] quotient(i(difference(B,A)),i(i(B))) -> i(A) collapsed.
% Rule
% [222] difference(B,j(A)) -> quotient(quotient(i(B),i(j(eta(A)))),i(i(A)))
% collapsed.
% Rule [235] difference(t(quotient(A,B),B),A) -> quotient(A,B) collapsed.
% Rule [249] difference(A,eta(B)) -> quotient(eta(difference(A,B)),A)
% collapsed.
% Rule [256] difference(A,quotient(eta(difference(B,A)),quotient(j(B),A))) -> B
% collapsed.
% Rule [257] quotient(quotient(eta(difference(B,A)),quotient(j(B),A)),B) -> A
% collapsed.
% Rule [258] quotient(eta(difference(j(A),A)),j(eta(A))) -> eta(A) collapsed.
% Rule
% [260] quotient(quotient(eta(difference(B,A)),quotient(j(B),A)),A) -> t(A,B)
% collapsed.
% Rule [261] quotient(eta(difference(B,quotient(A,B))),j(A)) -> A collapsed.
% Rule [262] quotient(eta(difference(difference(A,B),A)),j(B)) -> B collapsed.
% Rule
% [264]
% quotient(eta(difference(t(eta(A),C),t(eta(A),B))),quotient(j(t(eta(A),C)),
% t(eta(A),B))) ->
% t(eta(A),quotient(eta(difference(C,B)),quotient(j(C),B))) collapsed.
% Rule
% [265]
% quotient(eta(quotient(eta(difference(quotient(eta(difference(B,A)),quotient(
% j(B),A)),A)),
% quotient(eta(difference(B,A)),quotient(j(B),A)))),quotient(
% j(eta(A)),
% t(eta(A),
% quotient(
% eta(difference(B,A)),
% quotient(
% j(B),A))))) ->
% quotient(eta(quotient(i(B),i(i(i(A))))),quotient(j(B),i(i(A)))) collapsed.
% Rule
% [266]
% quotient(eta(difference(quotient(eta(quotient(eta(difference(B,A)),B)),
% quotient(j(B),eta(A))),A)),quotient(j(A),t(A,
% quotient(
% eta(
% quotient(
% eta(
% difference(B,A)),B)),
% quotient(
% j(B),
% eta(A))))))
% ->
% quotient(eta(quotient(quotient(i(B),i(j(eta(A)))),i(A))),quotient(j(B),
% j(j(A)))) collapsed.
% Rule
% [267]
% difference(A,quotient(eta(difference(C,quotient(eta(difference(B,A)),
% quotient(j(B),A)))),quotient(j(C),
% quotient(eta(
% difference(B,A)),
% quotient(j(B),A)))))
% <->
% quotient(quotient(eta(difference(quotient(eta(difference(A,C)),quotient(
% j(A),C)),B)),
% quotient(j(quotient(eta(difference(A,C)),quotient(j(A),C))),B)),A)
% collapsed.
% Rule
% [268]
% quotient(quotient(eta(difference(quotient(eta(difference(A,C)),quotient(
% j(A),C)),B)),
% quotient(j(quotient(eta(difference(A,C)),quotient(j(A),C))),B)),A)
% <->
% difference(A,quotient(eta(difference(C,quotient(eta(difference(B,A)),
% quotient(j(B),A)))),quotient(j(C),
% quotient(eta(
% difference(B,A)),
% quotient(j(B),A)))))
% collapsed.
% Rule
% [269]
% quotient(eta(difference(quotient(eta(quotient(eta(difference(quotient(j(A),B),A)),
% quotient(j(A),B))),quotient(j(eta(A)),
% t(eta(A),quotient(
% j(A),B)))),A)),
% quotient(j(A),t(A,quotient(eta(quotient(eta(difference(quotient(j(A),B),A)),
% quotient(j(A),B))),quotient(j(eta(A)),
% t(eta(A),quotient(j(A),B)))))))
% -> j(B) collapsed.
% Rule
% [270]
% quotient(eta(quotient(eta(difference(quotient(eta(difference(C,B)),quotient(
% j(C),B)),A)),
% quotient(eta(difference(C,B)),quotient(j(C),B)))),quotient(
% j(quotient(
% eta(
% difference(C,B)),
% quotient(
% j(C),B))),
% eta(A))) ->
% quotient(eta(difference(C,quotient(eta(quotient(eta(difference(B,A)),B)),
% quotient(j(B),eta(A))))),quotient(j(C),quotient(
% eta(
% quotient(
% eta(
% difference(B,A)),B)),
% quotient(
% j(B),
% eta(A)))))
% collapsed.
% Rule
% [271]
% difference(quotient(eta(difference(B,A)),quotient(j(B),A)),quotient(eta(
% difference(
% quotient(
% eta(
% difference(C,B)),
% quotient(
% j(C),B)),A)),
% quotient(j(
% quotient(
% eta(
% difference(C,B)),
% quotient(
% j(C),B))),A)))
% ->
% quotient(quotient(quotient(eta(difference(quotient(eta(difference(B,A)),
% quotient(j(B),A)),C)),quotient(
% j(quotient(
% eta(
% difference(B,A)),
% quotient(
% j(B),A))),C)),B),A)
% collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% quotient(eta(quotient(i(quotient(eta(quotient(i(x2),i(x1))),quotient(
% j(x2),x1))),
% i(x0))),quotient(j(x0),t(x0,quotient(eta(quotient(i(x2),i(x1))),
% quotient(j(x2),x1))))) = quotient(
% eta(
% quotient(
% i(quotient(
% eta(
% quotient(
% i(x2),
% i(x0))),
% quotient(
% j(x2),x0))),
% i(t(x0,x1)))),
% quotient(
% j(t(x0,x1)),
% t(t(x0,x1),
% quotient(
% eta(
% quotient(
% i(x2),
% i(x0))),
% quotient(
% j(x2),x0)))))
% 
% Current number of equations to process: 396
% Current number of ordered equations: 92
% Current number of rules: 49
% New rule produced :
% [281] quotient(eta(quotient(i(B),i(quotient(A,B)))),j(A)) -> A
% Current number of equations to process: 383
% Current number of ordered equations: 107
% Current number of rules: 50
% New rule produced : [282] quotient(eta(quotient(A,i(A))),j(eta(A))) -> eta(A)
% Current number of equations to process: 383
% Current number of ordered equations: 106
% Current number of rules: 51
% New rule produced :
% [283] quotient(quotient(eta(quotient(i(B),i(A))),quotient(j(B),A)),B) -> A
% Current number of equations to process: 383
% Current number of ordered equations: 105
% Current number of rules: 52
% New rule produced :
% [284] quotient(eta(quotient(i(quotient(i(A),i(B))),i(A))),j(B)) -> B
% Current number of equations to process: 383
% Current number of ordered equations: 104
% Current number of rules: 53
% New rule produced :
% [285]
% quotient(quotient(eta(quotient(i(B),i(A))),quotient(j(B),A)),A) -> t(A,B)
% Current number of equations to process: 383
% Current number of ordered equations: 102
% Current number of rules: 54
% New rule produced :
% [286]
% quotient(i(A),i(quotient(eta(quotient(i(B),i(A))),quotient(j(B),A)))) -> B
% Current number of equations to process: 383
% Current number of ordered equations: 101
% Current number of rules: 55
% New rule produced :
% [287]
% quotient(eta(quotient(i(t(eta(A),C)),i(t(eta(A),B)))),quotient(j(t(eta(A),C)),
% t(eta(A),B))) ->
% t(eta(A),quotient(eta(quotient(i(C),i(B))),quotient(j(C),B)))
% Current number of equations to process: 383
% Current number of ordered equations: 100
% Current number of rules: 56
% New rule produced :
% [288]
% quotient(eta(quotient(i(quotient(eta(quotient(eta(quotient(i(B),i(A))),B)),
% quotient(j(B),eta(A)))),i(A))),quotient(j(A),
% t(A,quotient(eta(
% quotient(
% eta(
% quotient(
% i(B),
% i(A))),B)),
% quotient(j(B),
% eta(A)))))) ->
% quotient(eta(quotient(quotient(i(B),eta(A)),i(A))),quotient(j(B),j(j(A))))
% Current number of equations to process: 383
% Current number of ordered equations: 99
% Current number of rules: 57
% New rule produced :
% [289]
% quotient(i(A),i(quotient(eta(quotient(i(C),i(quotient(eta(quotient(i(B),i(A))),
% quotient(j(B),A))))),quotient(
% j(C),
% quotient(
% eta(
% quotient(
% i(B),
% i(A))),
% quotient(
% j(B),A))))))
% <->
% quotient(quotient(eta(quotient(i(quotient(eta(quotient(i(A),i(C))),quotient(
% j(A),C))),
% i(B))),quotient(j(quotient(eta(quotient(i(A),i(C))),
% quotient(j(A),C))),B)),A)
% Current number of equations to process: 71
% Current number of ordered equations: 614
% Current number of rules: 58
% New rule produced :
% [290]
% quotient(quotient(eta(quotient(i(quotient(eta(quotient(i(A),i(C))),quotient(
% j(A),C))),
% i(B))),quotient(j(quotient(eta(quotient(i(A),i(C))),
% quotient(j(A),C))),B)),A) <->
% quotient(i(A),i(quotient(eta(quotient(i(C),i(quotient(eta(quotient(i(B),i(A))),
% quotient(j(B),A))))),quotient(
% j(C),
% quotient(
% eta(
% quotient(
% i(B),
% i(A))),
% quotient(
% j(B),A))))))
% Current number of equations to process: 71
% Current number of ordered equations: 613
% Current number of rules: 59
% New rule produced :
% [291]
% quotient(eta(quotient(eta(quotient(i(quotient(eta(quotient(i(B),i(A))),
% quotient(j(B),A))),i(A))),quotient(
% eta(quotient(
% i(B),
% i(A))),
% quotient(
% j(B),A)))),
% quotient(j(eta(A)),t(eta(A),quotient(eta(quotient(i(B),i(A))),quotient(
% j(B),A))))) ->
% quotient(eta(quotient(i(B),i(i(i(A))))),quotient(j(B),i(i(A))))
% Current number of equations to process: 71
% Current number of ordered equations: 612
% Current number of rules: 60
% New rule produced :
% [292]
% quotient(i(quotient(eta(quotient(i(B),i(A))),quotient(j(B),A))),i(quotient(
% eta(
% quotient(
% i(quotient(
% eta(
% quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B))),
% i(A))),
% quotient(
% j(quotient(
% eta(
% quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B))),A))))
% <->
% quotient(quotient(quotient(eta(quotient(i(quotient(eta(quotient(i(B),i(A))),
% quotient(j(B),A))),i(C))),quotient(
% j(
% quotient(
% eta(
% quotient(
% i(B),
% i(A))),
% quotient(
% j(B),A))),C)),B),A)
% Current number of equations to process: 111
% Current number of ordered equations: 704
% Current number of rules: 61
% New rule produced :
% [293]
% quotient(quotient(quotient(eta(quotient(i(quotient(eta(quotient(i(B),i(A))),
% quotient(j(B),A))),i(C))),quotient(
% j(
% quotient(
% eta(
% quotient(
% i(B),
% i(A))),
% quotient(
% j(B),A))),C)),B),A)
% <->
% quotient(i(quotient(eta(quotient(i(B),i(A))),quotient(j(B),A))),i(quotient(
% eta(
% quotient(
% i(quotient(
% eta(
% quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B))),
% i(A))),
% quotient(
% j(quotient(
% eta(
% quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B))),A))))
% Current number of equations to process: 111
% Current number of ordered equations: 697
% Current number of rules: 62
% New rule produced :
% [294]
% quotient(eta(quotient(eta(quotient(i(quotient(eta(quotient(i(C),i(B))),
% quotient(j(C),B))),i(A))),quotient(
% eta(quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B)))),
% quotient(j(quotient(eta(quotient(i(C),i(B))),quotient(j(C),B))),eta(A))) <->
% quotient(eta(quotient(i(C),i(quotient(eta(quotient(eta(quotient(i(B),i(A))),B)),
% quotient(j(B),eta(A)))))),quotient(j(C),
% quotient(eta(quotient(
% eta(
% quotient(
% i(B),
% i(A))),B)),
% quotient(j(B),
% eta(A)))))
% Current number of equations to process: 190
% Current number of ordered equations: 747
% Current number of rules: 63
% New rule produced :
% [295]
% quotient(eta(quotient(i(C),i(quotient(eta(quotient(eta(quotient(i(B),i(A))),B)),
% quotient(j(B),eta(A)))))),quotient(j(C),
% quotient(eta(quotient(
% eta(
% quotient(
% i(B),
% i(A))),B)),
% quotient(j(B),
% eta(A))))) <->
% quotient(eta(quotient(eta(quotient(i(quotient(eta(quotient(i(C),i(B))),
% quotient(j(C),B))),i(A))),quotient(
% eta(quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B)))),
% quotient(j(quotient(eta(quotient(i(C),i(B))),quotient(j(C),B))),eta(A)))
% Current number of equations to process: 190
% Current number of ordered equations: 746
% Current number of rules: 64
% New rule produced :
% [296]
% quotient(eta(quotient(i(quotient(eta(quotient(eta(quotient(i(quotient(j(A),B)),
% i(A))),quotient(j(A),B))),
% quotient(j(eta(A)),t(eta(A),quotient(j(A),B))))),
% i(A))),quotient(j(A),t(A,quotient(eta(quotient(eta(quotient(
% i(quotient(
% j(A),B)),
% i(A))),
% quotient(j(A),B))),
% quotient(j(eta(A)),t(eta(A),quotient(
% j(A),B)))))))
% -> j(B)
% Current number of equations to process: 190
% Current number of ordered equations: 744
% Current number of rules: 65
% New rule produced : [297] eta(eta(A)) -> one
% Rule [240] quotient(eta(eta(A)),A) -> j(A) collapsed.
% Rule [275] j(eta(eta(A))) -> one collapsed.
% Current number of equations to process: 218
% Current number of ordered equations: 693
% Current number of rules: 64
% New rule produced : [298] j(j(eta(A))) -> eta(A)
% Current number of equations to process: 230
% Current number of ordered equations: 677
% Current number of rules: 65
% New rule produced : [299] eta(quotient(A,j(A))) -> one
% Current number of equations to process: 232
% Current number of ordered equations: 673
% Current number of rules: 66
% New rule produced : [300] eta(quotient(A,i(A))) -> one
% Rule [259] quotient(eta(quotient(i(A),i(i(A)))),j(eta(A))) -> eta(A)
% collapsed.
% Rule [282] quotient(eta(quotient(A,i(A))),j(eta(A))) -> eta(A) collapsed.
% Current number of equations to process: 233
% Current number of ordered equations: 656
% Current number of rules: 65
% New rule produced : [301] eta(quotient(i(A),A)) -> one
% Current number of equations to process: 241
% Current number of ordered equations: 641
% Current number of rules: 66
% New rule produced : [302] quotient(A,j(eta(A))) -> j(j(A))
% Current number of equations to process: 242
% Current number of ordered equations: 639
% Current number of rules: 67
% New rule produced : [303] t(j(A),eta(A)) -> j(eta(A))
% Current number of equations to process: 242
% Current number of ordered equations: 638
% Current number of rules: 68
% New rule produced : [304] quotient(quotient(A,j(A)),A) -> A
% Current number of equations to process: 242
% Current number of ordered equations: 636
% Current number of rules: 69
% New rule produced : [305] t(eta(A),j(A)) -> i(i(i(A)))
% Rule [233] quotient(j(eta(A)),t(eta(A),j(A))) -> A collapsed.
% Current number of equations to process: 243
% Current number of ordered equations: 626
% Current number of rules: 69
% New rule produced : [306] quotient(i(A),A) -> j(quotient(A,i(A)))
% Rule [301] eta(quotient(i(A),A)) -> one collapsed.
% Current number of equations to process: 250
% Current number of ordered equations: 618
% Current number of rules: 69
% Rule [274]
% quotient(eta(quotient(quotient(i(i(A)),eta(A)),i(i(A)))),quotient(A,
% j(A))) ->
% quotient(j(A),A) is composed into [274]
% quotient(eta(quotient(quotient(
% i(i(A)),
% eta(A)),
% i(i(A)))),quotient(A,
% j(A))) ->
% i(quotient(A,j(A)))
% New rule produced : [307] quotient(j(A),A) -> i(quotient(A,j(A)))
% Rule [56] quotient(quotient(j(A),A),i(A)) -> j(A) collapsed.
% Rule [62] quotient(quotient(j(A),A),j(A)) -> t(j(A),i(A)) collapsed.
% Rule [206] j(quotient(j(A),A)) -> quotient(A,j(A)) collapsed.
% Rule [278] eta(quotient(j(A),A)) -> one collapsed.
% Current number of equations to process: 278
% Current number of ordered equations: 523
% Current number of rules: 66
% New rule produced : [308] quotient(A,quotient(B,i(A))) -> j(B)
% Current number of equations to process: 278
% Current number of ordered equations: 521
% Current number of rules: 67
% New rule produced : [309] quotient(eta(A),j(j(A))) -> j(A)
% Current number of equations to process: 278
% Current number of ordered equations: 519
% Current number of rules: 68
% New rule produced : [310] quotient(i(A),eta(A)) -> i(i(i(A)))
% Current number of equations to process: 281
% Current number of ordered equations: 511
% Current number of rules: 69
% New rule produced : [311] quotient(i(quotient(A,B)),i(A)) -> B
% Current number of equations to process: 281
% Current number of ordered equations: 507
% Current number of rules: 70
% New rule produced : [312] t(i(quotient(A,j(A))),A) -> j(j(A))
% Current number of equations to process: 280
% Current number of ordered equations: 507
% Current number of rules: 71
% New rule produced : [313] quotient(j(eta(A)),i(A)) -> j(j(A))
% Current number of equations to process: 282
% Current number of ordered equations: 503
% Current number of rules: 72
% New rule produced : [314] quotient(i(i(A)),j(eta(A))) -> A
% Current number of equations to process: 282
% Current number of ordered equations: 501
% Current number of rules: 73
% New rule produced : [315] t(i(i(A)),eta(A)) -> j(eta(A))
% Current number of equations to process: 282
% Current number of ordered equations: 499
% Current number of rules: 74
% New rule produced : [316] quotient(j(eta(A)),i(i(A))) -> j(A)
% Current number of equations to process: 282
% Current number of ordered equations: 496
% Current number of rules: 75
% New rule produced : [317] quotient(eta(A),i(i(A))) -> i(i(i(A)))
% Current number of equations to process: 283
% Current number of ordered equations: 493
% Current number of rules: 76
% New rule produced : [318] t(j(eta(A)),i(A)) -> j(j(j(A)))
% Current number of equations to process: 284
% Current number of ordered equations: 491
% Current number of rules: 77
% New rule produced : [319] quotient(j(A),j(j(A))) -> j(quotient(A,i(A)))
% Current number of equations to process: 283
% Current number of ordered equations: 491
% Current number of rules: 78
% New rule produced : [320] t(eta(A),j(j(j(A)))) -> i(A)
% Current number of equations to process: 284
% Current number of ordered equations: 489
% Current number of rules: 79
% New rule produced : [321] t(B,quotient(i(B),i(A))) <-> quotient(A,B)
% Current number of equations to process: 284
% Current number of ordered equations: 488
% Current number of rules: 80
% Rule [255]
% product(A,B) -> quotient(eta(quotient(i(B),i(A))),quotient(j(B),A)) is composed into 
% [255]
% product(A,B) ->
% t(quotient(j(B),A),quotient(i(quotient(j(B),A)),i(eta(quotient(i(B),i(A))))))
% Rule [221]
% quotient(quotient(j(A),B),eta(C)) <->
% quotient(j(A),quotient(eta(quotient(i(B),i(eta(C)))),quotient(j(B),
% eta(C)))) is composed into 
% [221]
% quotient(quotient(j(A),B),eta(C)) <->
% quotient(j(A),t(quotient(j(B),eta(C)),quotient(i(quotient(j(B),eta(C))),
% i(eta(quotient(i(B),i(eta(C))))))))
% New rule produced : [322] quotient(A,B) <-> t(B,quotient(i(B),i(A)))
% Rule [217] quotient(quotient(j(A),eta(B)),B) -> quotient(j(A),j(j(B)))
% collapsed.
% Rule [218] quotient(quotient(j(A),B),eta(B)) -> quotient(j(A),i(i(B)))
% collapsed.
% Rule
% [274]
% quotient(eta(quotient(quotient(i(i(A)),eta(A)),i(i(A)))),quotient(A,j(A))) ->
% i(quotient(A,j(A))) collapsed.
% Rule [281] quotient(eta(quotient(i(B),i(quotient(A,B)))),j(A)) -> A
% collapsed.
% Rule
% [283] quotient(quotient(eta(quotient(i(B),i(A))),quotient(j(B),A)),B) -> A
% collapsed.
% Rule [284] quotient(eta(quotient(i(quotient(i(A),i(B))),i(A))),j(B)) -> B
% collapsed.
% Rule
% [285]
% quotient(quotient(eta(quotient(i(B),i(A))),quotient(j(B),A)),A) -> t(A,B)
% collapsed.
% Rule
% [286]
% quotient(i(A),i(quotient(eta(quotient(i(B),i(A))),quotient(j(B),A)))) -> B
% collapsed.
% Rule
% [287]
% quotient(eta(quotient(i(t(eta(A),C)),i(t(eta(A),B)))),quotient(j(t(eta(A),C)),
% t(eta(A),B))) ->
% t(eta(A),quotient(eta(quotient(i(C),i(B))),quotient(j(C),B))) collapsed.
% Rule
% [288]
% quotient(eta(quotient(i(quotient(eta(quotient(eta(quotient(i(B),i(A))),B)),
% quotient(j(B),eta(A)))),i(A))),quotient(j(A),
% t(A,quotient(eta(
% quotient(
% eta(
% quotient(
% i(B),
% i(A))),B)),
% quotient(j(B),
% eta(A)))))) ->
% quotient(eta(quotient(quotient(i(B),eta(A)),i(A))),quotient(j(B),j(j(A))))
% collapsed.
% Rule
% [289]
% quotient(i(A),i(quotient(eta(quotient(i(C),i(quotient(eta(quotient(i(B),i(A))),
% quotient(j(B),A))))),quotient(
% j(C),
% quotient(
% eta(
% quotient(
% i(B),
% i(A))),
% quotient(
% j(B),A))))))
% <->
% quotient(quotient(eta(quotient(i(quotient(eta(quotient(i(A),i(C))),quotient(
% j(A),C))),
% i(B))),quotient(j(quotient(eta(quotient(i(A),i(C))),
% quotient(j(A),C))),B)),A) collapsed.
% Rule
% [290]
% quotient(quotient(eta(quotient(i(quotient(eta(quotient(i(A),i(C))),quotient(
% j(A),C))),
% i(B))),quotient(j(quotient(eta(quotient(i(A),i(C))),
% quotient(j(A),C))),B)),A) <->
% quotient(i(A),i(quotient(eta(quotient(i(C),i(quotient(eta(quotient(i(B),i(A))),
% quotient(j(B),A))))),quotient(
% j(C),
% quotient(
% eta(
% quotient(
% i(B),
% i(A))),
% quotient(
% j(B),A))))))
% collapsed.
% Rule
% [291]
% quotient(eta(quotient(eta(quotient(i(quotient(eta(quotient(i(B),i(A))),
% quotient(j(B),A))),i(A))),quotient(
% eta(quotient(
% i(B),
% i(A))),
% quotient(
% j(B),A)))),
% quotient(j(eta(A)),t(eta(A),quotient(eta(quotient(i(B),i(A))),quotient(
% j(B),A))))) ->
% quotient(eta(quotient(i(B),i(i(i(A))))),quotient(j(B),i(i(A)))) collapsed.
% Rule
% [292]
% quotient(i(quotient(eta(quotient(i(B),i(A))),quotient(j(B),A))),i(quotient(
% eta(
% quotient(
% i(quotient(
% eta(
% quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B))),
% i(A))),
% quotient(
% j(quotient(
% eta(
% quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B))),A))))
% <->
% quotient(quotient(quotient(eta(quotient(i(quotient(eta(quotient(i(B),i(A))),
% quotient(j(B),A))),i(C))),quotient(
% j(
% quotient(
% eta(
% quotient(
% i(B),
% i(A))),
% quotient(
% j(B),A))),C)),B),A)
% collapsed.
% Rule
% [293]
% quotient(quotient(quotient(eta(quotient(i(quotient(eta(quotient(i(B),i(A))),
% quotient(j(B),A))),i(C))),quotient(
% j(
% quotient(
% eta(
% quotient(
% i(B),
% i(A))),
% quotient(
% j(B),A))),C)),B),A)
% <->
% quotient(i(quotient(eta(quotient(i(B),i(A))),quotient(j(B),A))),i(quotient(
% eta(
% quotient(
% i(quotient(
% eta(
% quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B))),
% i(A))),
% quotient(
% j(quotient(
% eta(
% quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B))),A))))
% collapsed.
% Rule
% [294]
% quotient(eta(quotient(eta(quotient(i(quotient(eta(quotient(i(C),i(B))),
% quotient(j(C),B))),i(A))),quotient(
% eta(quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B)))),
% quotient(j(quotient(eta(quotient(i(C),i(B))),quotient(j(C),B))),eta(A))) <->
% quotient(eta(quotient(i(C),i(quotient(eta(quotient(eta(quotient(i(B),i(A))),B)),
% quotient(j(B),eta(A)))))),quotient(j(C),
% quotient(eta(quotient(
% eta(
% quotient(
% i(B),
% i(A))),B)),
% quotient(j(B),
% eta(A))))) collapsed.
% Rule
% [295]
% quotient(eta(quotient(i(C),i(quotient(eta(quotient(eta(quotient(i(B),i(A))),B)),
% quotient(j(B),eta(A)))))),quotient(j(C),
% quotient(eta(quotient(
% eta(
% quotient(
% i(B),
% i(A))),B)),
% quotient(j(B),
% eta(A))))) <->
% quotient(eta(quotient(eta(quotient(i(quotient(eta(quotient(i(C),i(B))),
% quotient(j(C),B))),i(A))),quotient(
% eta(quotient(
% i(C),
% i(B))),
% quotient(
% j(C),B)))),
% quotient(j(quotient(eta(quotient(i(C),i(B))),quotient(j(C),B))),eta(A)))
% collapsed.
% Rule
% [296]
% quotient(eta(quotient(i(quotient(eta(quotient(eta(quotient(i(quotient(j(A),B)),
% i(A))),quotient(j(A),B))),
% quotient(j(eta(A)),t(eta(A),quotient(j(A),B))))),
% i(A))),quotient(j(A),t(A,quotient(eta(quotient(eta(quotient(
% i(quotient(
% j(A),B)),
% i(A))),
% quotient(j(A),B))),
% quotient(j(eta(A)),t(eta(A),quotient(
% j(A),B)))))))
% -> j(B) collapsed.
% Rule [304] quotient(quotient(A,j(A)),A) -> A collapsed.
% Rule [311] quotient(i(quotient(A,B)),i(A)) -> B collapsed.
% Rule [314] quotient(i(i(A)),j(eta(A))) -> A collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% t(quotient(j(x0),t(x0,t(quotient(j(x2),x1),quotient(i(quotient(j(x2),x1)),
% j(eta(quotient(i(x2),i(x1)))))))),
% quotient(i(quotient(j(x0),t(x0,t(quotient(j(x2),x1),quotient(i(quotient(
% j(x2),x1)),
% j(eta(quotient(i(x2),
% i(x1))))))))),
% j(eta(t(i(x0),quotient(i(i(x0)),i(i(t(quotient(j(x2),x1),quotient(i(quotient(
% j(x2),x1)),
% j(eta(quotient(
% i(x2),
% i(x1)))))))))))))) = 
% t(quotient(j(t(x0,x1)),t(t(x0,x1),t(quotient(j(x2),x0),quotient(i(quotient(
% j(x2),x0)),
% j(eta(quotient(
% i(x2),i(x0)))))))),
% quotient(i(quotient(j(t(x0,x1)),t(t(x0,x1),t(quotient(j(x2),x0),quotient(
% i(quotient(
% j(x2),x0)),
% j(eta(
% quotient(
% i(x2),
% i(x0))))))))),
% j(eta(t(i(t(x0,x1)),quotient(i(i(t(x0,x1))),i(i(t(quotient(j(x2),x0),
% quotient(i(quotient(j(x2),x0)),
% j(eta(quotient(i(x2),i(x0))))))))))))))
% 
% Current number of equations to process: 530
% Current number of ordered equations: 37
% Current number of rules: 60
% New rule produced :
% [323] t(j(A),quotient(A,j(eta(quotient(i(B),i(quotient(A,B))))))) -> A
% Current number of equations to process: 517
% Current number of ordered equations: 52
% Current number of rules: 61
% New rule produced :
% [324]
% quotient(i(A),i(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(eta(
% quotient(
% i(B),
% i(A))))))))
% -> B
% Current number of equations to process: 517
% Current number of ordered equations: 50
% Current number of rules: 62
% New rule produced :
% [325]
% t(j(B),quotient(B,j(eta(t(i(A),quotient(i(i(A)),i(i(quotient(i(A),i(B))))))))))
% -> B
% Current number of equations to process: 517
% Current number of ordered equations: 49
% Current number of rules: 63
% New rule produced :
% [326]
% t(B,quotient(i(B),i(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(
% eta(
% quotient(
% i(B),
% i(A)))))))))
% -> A
% Current number of equations to process: 517
% Current number of ordered equations: 48
% Current number of rules: 64
% New rule produced :
% [327]
% t(quotient(A,j(A)),quotient(i(quotient(A,j(A))),j(eta(t(i(i(A)),quotient(
% i(i(i(A))),
% i(t(eta(A),
% quotient(
% j(eta(A)),
% i(i(i(A))))))))))))
% -> i(quotient(A,j(A)))
% Current number of equations to process: 517
% Current number of ordered equations: 47
% Current number of rules: 65
% New rule produced :
% [328]
% t(quotient(j(t(eta(A),C)),t(eta(A),B)),quotient(i(quotient(j(t(eta(A),C)),
% t(eta(A),B))),j(eta(
% quotient(
% i(t(
% eta(A),C)),
% i(t(
% eta(A),B)))))))
% ->
% t(eta(A),t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(eta(quotient(
% i(C),i(B)))))))
% Current number of equations to process: 517
% Current number of ordered equations: 46
% Current number of rules: 66
% New rule produced :
% [329]
% t(A,quotient(i(A),i(t(quotient(j(t(quotient(j(A),C),quotient(i(quotient(
% j(A),C)),
% j(eta(quotient(i(A),i(C))))))),B),
% quotient(i(quotient(j(t(quotient(j(A),C),quotient(
% i(quotient(
% j(A),C)),
% j(eta(quotient(
% i(A),
% i(C))))))),B)),
% j(eta(quotient(i(t(quotient(j(A),C),quotient(i(quotient(
% j(A),C)),
% j(eta(quotient(
% i(A),i(C))))))),
% i(B))))))))) <->
% quotient(i(A),i(t(quotient(j(C),t(quotient(j(B),A),quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(i(B),i(A))))))),
% quotient(i(quotient(j(C),t(quotient(j(B),A),quotient(
% i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A)))))))),
% j(eta(quotient(i(C),i(t(quotient(j(B),A),quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),i(A))))))))))))))
% Current number of equations to process: 61
% Current number of ordered equations: 817
% Current number of rules: 67
% New rule produced :
% [330]
% quotient(i(A),i(t(quotient(j(C),t(quotient(j(B),A),quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(i(B),i(A))))))),
% quotient(i(quotient(j(C),t(quotient(j(B),A),quotient(
% i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A)))))))),
% j(eta(quotient(i(C),i(t(quotient(j(B),A),quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),i(A))))))))))))))
% <->
% t(A,quotient(i(A),i(t(quotient(j(t(quotient(j(A),C),quotient(i(quotient(
% j(A),C)),
% j(eta(quotient(i(A),i(C))))))),B),
% quotient(i(quotient(j(t(quotient(j(A),C),quotient(
% i(quotient(
% j(A),C)),
% j(eta(quotient(
% i(A),
% i(C))))))),B)),
% j(eta(quotient(i(t(quotient(j(A),C),quotient(i(quotient(
% j(A),C)),
% j(eta(quotient(
% i(A),i(C))))))),
% i(B)))))))))
% Current number of equations to process: 61
% Current number of ordered equations: 816
% Current number of rules: 68
% New rule produced :
% [331]
% t(quotient(j(A),t(A,t(quotient(j(B),eta(A)),quotient(i(quotient(j(B),eta(A))),
% j(eta(t(B,quotient(i(B),j(
% eta(
% quotient(
% i(B),
% i(A)))))))))))),
% quotient(i(quotient(j(A),t(A,t(quotient(j(B),eta(A)),quotient(i(quotient(
% j(B),
% eta(A))),
% j(eta(t(B,quotient(
% i(B),j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))),
% j(eta(t(i(A),quotient(i(i(A)),i(i(t(quotient(j(B),eta(A)),quotient(i(
% quotient(
% j(B),
% eta(A))),
% j(eta(t(B,quotient(
% i(B),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))))))
% ->
% t(quotient(j(B),j(j(A))),quotient(i(quotient(j(B),j(j(A)))),j(eta(t(i(A),
% quotient(
% i(i(A)),
% i(quotient(
% i(B),
% eta(A)))))))))
% Current number of equations to process: 70
% Current number of ordered equations: 806
% Current number of rules: 69
% New rule produced :
% [332]
% t(A,quotient(i(A),i(t(B,quotient(i(B),i(t(quotient(j(t(quotient(j(B),A),
% quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(i(B),
% i(A))))))),C),
% quotient(i(quotient(j(t(quotient(
% j(B),A),
% quotient(
% i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A))))))),C)),
% j(eta(quotient(i(t(quotient(j(B),A),
% quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),i(A))))))),
% i(C)))))))))))) <->
% quotient(i(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(eta(quotient(
% i(B),
% i(A))))))),
% i(t(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(eta(
% quotient(
% i(C),
% i(B))))))),A),
% quotient(i(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),
% j(eta(quotient(i(C),i(B))))))),A)),
% j(eta(quotient(i(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(
% eta(
% quotient(
% i(C),
% i(B))))))),
% i(A))))))))
% Current number of equations to process: 120
% Current number of ordered equations: 982
% Current number of rules: 70
% New rule produced :
% [333]
% quotient(i(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(eta(quotient(
% i(B),
% i(A))))))),
% i(t(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(eta(
% quotient(
% i(C),
% i(B))))))),A),
% quotient(i(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),
% j(eta(quotient(i(C),i(B))))))),A)),
% j(eta(quotient(i(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(
% eta(
% quotient(
% i(C),
% i(B))))))),
% i(A)))))))) <->
% t(A,quotient(i(A),i(t(B,quotient(i(B),i(t(quotient(j(t(quotient(j(B),A),
% quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(i(B),
% i(A))))))),C),
% quotient(i(quotient(j(t(quotient(
% j(B),A),
% quotient(
% i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A))))))),C)),
% j(eta(quotient(i(t(quotient(j(B),A),
% quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),i(A))))))),
% i(C))))))))))))
% Current number of equations to process: 120
% Current number of ordered equations: 981
% Current number of rules: 71
% New rule produced :
% [334]
% t(quotient(j(eta(A)),t(eta(A),t(quotient(j(B),A),quotient(i(quotient(j(B),A)),
% j(eta(quotient(i(B),i(A)))))))),
% quotient(i(quotient(j(eta(A)),t(eta(A),t(quotient(j(B),A),quotient(i(
% quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A))))))))),
% j(eta(t(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(eta(quotient(
% i(B),i(A)))))),
% quotient(i(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(eta(
% quotient(
% i(B),
% i(A))))))),
% j(eta(t(i(A),quotient(i(i(A)),i(i(t(quotient(j(B),A),quotient(i(
% quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A))))))))))))))))))
% ->
% t(quotient(j(B),i(i(A))),quotient(i(quotient(j(B),i(i(A)))),j(eta(quotient(
% i(B),
% i(i(i(A))))))))
% Current number of equations to process: 126
% Current number of ordered equations: 974
% Current number of rules: 72
% New rule produced :
% [335]
% t(quotient(j(C),t(quotient(j(B),eta(A)),quotient(i(quotient(j(B),eta(A))),
% j(eta(t(B,quotient(i(B),j(eta(
% quotient(
% i(B),
% i(A))))))))))),
% quotient(i(quotient(j(C),t(quotient(j(B),eta(A)),quotient(i(quotient(
% j(B),eta(A))),
% j(eta(t(B,quotient(i(B),
% j(eta(quotient(
% i(B),
% i(A)))))))))))),
% j(eta(quotient(i(C),i(t(quotient(j(B),eta(A)),quotient(i(quotient(j(B),
% eta(A))),j(eta(
% t(B,
% quotient(
% i(B),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))))
% <->
% t(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(eta(quotient(
% i(C),
% i(B))))))),
% eta(A)),quotient(i(quotient(j(t(quotient(j(C),B),quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(i(C),i(B))))))),
% eta(A))),j(eta(t(t(quotient(j(C),B),quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(
% i(C),i(B)))))),
% quotient(i(t(quotient(j(C),B),quotient(
% i(quotient(
% j(C),B)),
% j(eta(
% quotient(
% i(C),
% i(B))))))),
% j(eta(quotient(i(t(quotient(j(C),B),
% quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(i(C),
% i(B))))))),
% i(A))))))))))
% Current number of equations to process: 198
% Current number of ordered equations: 1262
% Current number of rules: 73
% New rule produced :
% [336]
% t(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(eta(quotient(
% i(C),
% i(B))))))),
% eta(A)),quotient(i(quotient(j(t(quotient(j(C),B),quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(i(C),i(B))))))),
% eta(A))),j(eta(t(t(quotient(j(C),B),quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(
% i(C),i(B)))))),
% quotient(i(t(quotient(j(C),B),quotient(
% i(quotient(
% j(C),B)),
% j(eta(
% quotient(
% i(C),
% i(B))))))),
% j(eta(quotient(i(t(quotient(j(C),B),
% quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(i(C),
% i(B))))))),
% i(A)))))))))) <->
% t(quotient(j(C),t(quotient(j(B),eta(A)),quotient(i(quotient(j(B),eta(A))),
% j(eta(t(B,quotient(i(B),j(eta(
% quotient(
% i(B),
% i(A))))))))))),
% quotient(i(quotient(j(C),t(quotient(j(B),eta(A)),quotient(i(quotient(
% j(B),eta(A))),
% j(eta(t(B,quotient(i(B),
% j(eta(quotient(
% i(B),
% i(A)))))))))))),
% j(eta(quotient(i(C),i(t(quotient(j(B),eta(A)),quotient(i(quotient(j(B),
% eta(A))),j(eta(
% t(B,
% quotient(
% i(B),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))))
% Current number of equations to process: 198
% Current number of ordered equations: 1261
% Current number of rules: 74
% New rule produced :
% [337]
% t(quotient(j(A),t(A,t(quotient(j(eta(A)),t(eta(A),quotient(j(A),B))),
% quotient(i(quotient(j(eta(A)),t(eta(A),quotient(j(A),B)))),
% j(eta(t(quotient(j(A),B),quotient(i(quotient(j(A),B)),
% j(eta(t(i(A),quotient(i(i(A)),
% i(i(quotient(
% j(A),B))))))))))))))),
% quotient(i(quotient(j(A),t(A,t(quotient(j(eta(A)),t(eta(A),quotient(j(A),B))),
% quotient(i(quotient(j(eta(A)),t(eta(A),quotient(
% j(A),B)))),
% j(eta(t(quotient(j(A),B),quotient(i(quotient(
% j(A),B)),
% j(eta(t(i(A),quotient(
% i(
% i(A)),
% i(
% i(
% quotient(
% j(A),B)))))))))))))))),
% j(eta(t(i(A),quotient(i(i(A)),i(i(t(quotient(j(eta(A)),t(eta(A),quotient(
% j(A),B))),
% quotient(i(quotient(j(eta(A)),t(eta(A),
% quotient(
% j(A),B)))),
% j(eta(t(quotient(j(A),B),quotient(i(
% quotient(
% j(A),B)),
% j(eta(t(i(A),
% quotient(
% i(i(A)),
% i(i(
% quotient(
% j(A),B)))))))))))))))))))))
% -> j(B)
% Current number of equations to process: 198
% Current number of ordered equations: 1260
% Current number of rules: 75
% New rule produced : [338] t(A,j(eta(A))) -> eta(A)
% Current number of equations to process: 199
% Current number of ordered equations: 1255
% Current number of rules: 76
% New rule produced : [339] quotient(A,j(j(A))) -> eta(A)
% Current number of equations to process: 202
% Current number of ordered equations: 1251
% Current number of rules: 77
% New rule produced : [340] quotient(i(A),j(A)) -> eta(A)
% Current number of equations to process: 202
% Current number of ordered equations: 1250
% Current number of rules: 78
% New rule produced : [341] t(A,j(j(A))) -> i(i(A))
% Current number of equations to process: 202
% Current number of ordered equations: 1249
% Current number of rules: 79
% New rule produced : [342] quotient(i(A),j(eta(A))) -> j(A)
% Current number of equations to process: 211
% Current number of ordered equations: 1233
% Current number of rules: 80
% New rule produced : [343] t(eta(A),A) -> i(i(i(i(A))))
% Current number of equations to process: 212
% Current number of ordered equations: 1231
% Current number of rules: 81
% New rule produced : [344] t(i(A),j(eta(A))) -> eta(A)
% Current number of equations to process: 222
% Current number of ordered equations: 1216
% Current number of rules: 82
% Rule [307] quotient(j(A),A) -> i(quotient(A,j(A))) is composed into [307]
% quotient(
% j(A),A)
% ->
% j(
% quotient(A,
% j(A)))
% New rule produced : [345] i(quotient(A,j(A))) -> j(quotient(A,j(A)))
% Rule [312] t(i(quotient(A,j(A))),A) -> j(j(A)) collapsed.
% Rule
% [327]
% t(quotient(A,j(A)),quotient(i(quotient(A,j(A))),j(eta(t(i(i(A)),quotient(
% i(i(i(A))),
% i(t(eta(A),
% quotient(
% j(eta(A)),
% i(i(i(A))))))))))))
% -> i(quotient(A,j(A))) collapsed.
% Current number of equations to process: 293
% Current number of ordered equations: 1117
% Current number of rules: 81
% New rule produced :
% [346]
% t(quotient(A,j(A)),quotient(j(quotient(A,j(A))),j(eta(t(i(i(A)),quotient(
% i(i(i(A))),
% i(t(eta(A),
% quotient(
% j(eta(A)),
% i(i(i(A))))))))))))
% -> j(quotient(A,j(A)))
% Current number of equations to process: 292
% Current number of ordered equations: 1117
% Current number of rules: 82
% New rule produced : [347] i(quotient(A,i(A))) -> j(quotient(A,i(A)))
% Current number of equations to process: 299
% Current number of ordered equations: 1103
% Current number of rules: 83
% New rule produced : [348] t(j(j(A)),eta(A)) -> j(eta(A))
% Current number of equations to process: 299
% Current number of ordered equations: 1102
% Current number of rules: 84
% New rule produced : [349] t(j(eta(A)),A) -> j(j(j(j(A))))
% Current number of equations to process: 299
% Current number of ordered equations: 1101
% Current number of rules: 85
% New rule produced : [350] j(j(quotient(A,j(A)))) -> quotient(A,j(A))
% Current number of equations to process: 299
% Current number of ordered equations: 1096
% Current number of rules: 86
% New rule produced : [351] j(j(quotient(A,i(A)))) -> quotient(A,i(A))
% Current number of equations to process: 299
% Current number of ordered equations: 1091
% Current number of rules: 87
% New rule produced : [352] t(quotient(A,i(A)),i(A)) -> j(A)
% Current number of equations to process: 299
% Current number of ordered equations: 1090
% Current number of rules: 88
% New rule produced : [353] t(A,quotient(i(A),B)) <-> quotient(j(B),A)
% Current number of equations to process: 299
% Current number of ordered equations: 1089
% Current number of rules: 89
% New rule produced : [354] quotient(j(B),A) <-> t(A,quotient(i(A),B))
% Current number of equations to process: 299
% Current number of ordered equations: 1088
% Current number of rules: 90
% New rule produced :
% [355] t(eta(B),quotient(j(eta(B)),i(quotient(A,j(eta(B)))))) -> A
% Current number of equations to process: 299
% Current number of ordered equations: 1087
% Current number of rules: 91
% New rule produced : [356] quotient(j(eta(A)),i(i(i(A)))) -> A
% Rule
% [346]
% t(quotient(A,j(A)),quotient(j(quotient(A,j(A))),j(eta(t(i(i(A)),quotient(
% i(i(i(A))),
% i(t(eta(A),
% quotient(
% j(eta(A)),
% i(i(i(A))))))))))))
% -> j(quotient(A,j(A))) collapsed.
% Current number of equations to process: 305
% Current number of ordered equations: 1071
% Current number of rules: 91
% New rule produced :
% [357]
% t(quotient(A,j(A)),t(j(eta(t(i(i(A)),j(eta(A))))),quotient(eta(t(i(i(A)),
% j(eta(A)))),
% quotient(A,j(A))))) ->
% j(quotient(A,j(A)))
% Current number of equations to process: 304
% Current number of ordered equations: 1071
% Current number of rules: 92
% New rule produced : [358] j(quotient(i(A),i(i(A)))) -> quotient(A,j(A))
% Current number of equations to process: 306
% Current number of ordered equations: 1066
% Current number of rules: 93
% New rule produced : [359] t(j(B),quotient(B,A)) <-> quotient(j(A),j(B))
% Current number of equations to process: 305
% Current number of ordered equations: 1065
% Current number of rules: 94
% New rule produced : [360] quotient(j(A),j(B)) <-> t(j(B),quotient(B,A))
% Rule [232] quotient(j(A),j(eta(A))) -> j(j(j(A))) collapsed.
% Rule [319] quotient(j(A),j(j(A))) -> j(quotient(A,i(A))) collapsed.
% Current number of equations to process: 307
% Current number of ordered equations: 1040
% Current number of rules: 93
% New rule produced : [361] t(j(quotient(A,j(A))),A) -> j(j(A))
% Current number of equations to process: 307
% Current number of ordered equations: 1039
% Current number of rules: 94
% New rule produced : [362] quotient(A,B) <-> quotient(j(B),t(B,i(A)))
% Rule [306] quotient(i(A),A) -> j(quotient(A,i(A))) collapsed.
% Rule [310] quotient(i(A),eta(A)) -> i(i(i(A))) collapsed.
% Rule [340] quotient(i(A),j(A)) -> eta(A) collapsed.
% Rule [342] quotient(i(A),j(eta(A))) -> j(A) collapsed.
% Current number of equations to process: 310
% Current number of ordered equations: 1034
% Current number of rules: 91
% New rule produced : [363] quotient(j(B),t(B,i(A))) <-> quotient(A,B)
% Current number of equations to process: 310
% Current number of ordered equations: 1032
% Current number of rules: 92
% New rule produced : [364] quotient(A,t(i(A),B)) <-> quotient(j(B),i(A))
% Current number of equations to process: 310
% Current number of ordered equations: 1031
% Current number of rules: 93
% New rule produced : [365] quotient(j(B),i(A)) <-> quotient(A,t(i(A),B))
% Rule [208] quotient(j(A),i(A)) -> j(eta(A)) collapsed.
% Rule [313] quotient(j(eta(A)),i(A)) -> j(j(A)) collapsed.
% Current number of equations to process: 312
% Current number of ordered equations: 1015
% Current number of rules: 92
% New rule produced : [366] quotient(eta(A),j(j(j(A)))) -> j(j(A))
% Current number of equations to process: 313
% Current number of ordered equations: 1011
% Current number of rules: 93
% New rule produced : [367] t(i(i(i(A))),eta(A)) -> j(eta(A))
% Current number of equations to process: 313
% Current number of ordered equations: 1010
% Current number of rules: 94
% New rule produced : [368] t(j(eta(A)),i(i(A))) -> j(j(A))
% Current number of equations to process: 313
% Current number of ordered equations: 1006
% Current number of rules: 95
% New rule produced : [369] t(eta(A),j(j(j(j(A))))) -> A
% Current number of equations to process: 313
% Current number of ordered equations: 1005
% Current number of rules: 96
% New rule produced : [370] eta(t(j(A),quotient(A,i(A)))) -> one
% Current number of equations to process: 313
% Current number of ordered equations: 1004
% Current number of rules: 97
% New rule produced : [371] quotient(i(A),j(quotient(A,j(A)))) -> A
% Current number of equations to process: 312
% Current number of ordered equations: 1004
% Current number of rules: 98
% New rule produced : [372] t(i(A),quotient(i(i(A)),quotient(A,j(A)))) -> j(A)
% Current number of equations to process: 311
% Current number of ordered equations: 1004
% Current number of rules: 99
% New rule produced : [373] quotient(A,i(i(quotient(B,j(A))))) -> i(B)
% Current number of equations to process: 311
% Current number of ordered equations: 1003
% Current number of rules: 100
% New rule produced : [374] quotient(eta(A),quotient(B,j(eta(A)))) -> j(B)
% Current number of equations to process: 311
% Current number of ordered equations: 1001
% Current number of rules: 101
% New rule produced : [375] t(j(B),quotient(B,i(A))) <-> quotient(A,j(B))
% Rule [370] eta(t(j(A),quotient(A,i(A)))) -> one collapsed.
% Current number of equations to process: 309
% Current number of ordered equations: 999
% Current number of rules: 101
% New rule produced : [376] quotient(A,j(B)) <-> t(j(B),quotient(B,i(A)))
% Rule [44] quotient(eta(A),j(A)) -> A collapsed.
% Current number of equations to process: 309
% Current number of ordered equations: 997
% Current number of rules: 101
% New rule produced : [377] t(quotient(A,B),t(B,i(A))) -> j(A)
% Current number of equations to process: 309
% Current number of ordered equations: 995
% Current number of rules: 102
% Rule [354] quotient(j(B),A) <-> t(A,quotient(i(A),B)) is composed into 
% [354] quotient(j(B),A) <-> quotient(j(A),t(A,B))
% Rule [322] quotient(A,B) <-> t(B,quotient(i(B),i(A))) is composed into 
% [322] quotient(A,B) <-> quotient(j(B),t(B,i(A)))
% Rule [255]
% product(A,B) ->
% t(quotient(j(B),A),quotient(i(quotient(j(B),A)),i(eta(quotient(i(B),
% i(A)))))) is composed into 
% [255]
% product(A,B) ->
% quotient(j(quotient(j(B),A)),t(quotient(j(B),A),i(eta(quotient(i(B),i(A))))))
% Rule [221]
% quotient(quotient(j(A),B),eta(C)) <->
% quotient(j(A),t(quotient(j(B),eta(C)),quotient(i(quotient(j(B),eta(C))),
% i(eta(quotient(i(B),i(eta(C)))))))) is composed into 
% [221]
% quotient(quotient(j(A),B),eta(C)) <->
% quotient(j(A),quotient(j(quotient(j(B),eta(C))),t(quotient(j(B),eta(C)),
% i(eta(quotient(i(B),i(eta(C))))))))
% New rule produced : [378] t(A,quotient(i(A),B)) -> quotient(j(A),t(A,B))
% Rule [321] t(B,quotient(i(B),i(A))) <-> quotient(A,B) collapsed.
% Rule
% [324]
% quotient(i(A),i(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(eta(
% quotient(
% i(B),
% i(A))))))))
% -> B collapsed.
% Rule
% [325]
% t(j(B),quotient(B,j(eta(t(i(A),quotient(i(i(A)),i(i(quotient(i(A),i(B))))))))))
% -> B collapsed.
% Rule
% [326]
% t(B,quotient(i(B),i(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(
% eta(
% quotient(
% i(B),
% i(A)))))))))
% -> A collapsed.
% Rule
% [328]
% t(quotient(j(t(eta(A),C)),t(eta(A),B)),quotient(i(quotient(j(t(eta(A),C)),
% t(eta(A),B))),j(eta(
% quotient(
% i(t(
% eta(A),C)),
% i(t(
% eta(A),B)))))))
% ->
% t(eta(A),t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(eta(quotient(
% i(C),i(B)))))))
% collapsed.
% Rule
% [329]
% t(A,quotient(i(A),i(t(quotient(j(t(quotient(j(A),C),quotient(i(quotient(
% j(A),C)),
% j(eta(quotient(i(A),i(C))))))),B),
% quotient(i(quotient(j(t(quotient(j(A),C),quotient(
% i(quotient(
% j(A),C)),
% j(eta(quotient(
% i(A),
% i(C))))))),B)),
% j(eta(quotient(i(t(quotient(j(A),C),quotient(i(quotient(
% j(A),C)),
% j(eta(quotient(
% i(A),i(C))))))),
% i(B))))))))) <->
% quotient(i(A),i(t(quotient(j(C),t(quotient(j(B),A),quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(i(B),i(A))))))),
% quotient(i(quotient(j(C),t(quotient(j(B),A),quotient(
% i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A)))))))),
% j(eta(quotient(i(C),i(t(quotient(j(B),A),quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),i(A))))))))))))))
% collapsed.
% Rule
% [330]
% quotient(i(A),i(t(quotient(j(C),t(quotient(j(B),A),quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(i(B),i(A))))))),
% quotient(i(quotient(j(C),t(quotient(j(B),A),quotient(
% i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A)))))))),
% j(eta(quotient(i(C),i(t(quotient(j(B),A),quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),i(A))))))))))))))
% <->
% t(A,quotient(i(A),i(t(quotient(j(t(quotient(j(A),C),quotient(i(quotient(
% j(A),C)),
% j(eta(quotient(i(A),i(C))))))),B),
% quotient(i(quotient(j(t(quotient(j(A),C),quotient(
% i(quotient(
% j(A),C)),
% j(eta(quotient(
% i(A),
% i(C))))))),B)),
% j(eta(quotient(i(t(quotient(j(A),C),quotient(i(quotient(
% j(A),C)),
% j(eta(quotient(
% i(A),i(C))))))),
% i(B))))))))) collapsed.
% Rule
% [331]
% t(quotient(j(A),t(A,t(quotient(j(B),eta(A)),quotient(i(quotient(j(B),eta(A))),
% j(eta(t(B,quotient(i(B),j(
% eta(
% quotient(
% i(B),
% i(A)))))))))))),
% quotient(i(quotient(j(A),t(A,t(quotient(j(B),eta(A)),quotient(i(quotient(
% j(B),
% eta(A))),
% j(eta(t(B,quotient(
% i(B),j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))),
% j(eta(t(i(A),quotient(i(i(A)),i(i(t(quotient(j(B),eta(A)),quotient(i(
% quotient(
% j(B),
% eta(A))),
% j(eta(t(B,quotient(
% i(B),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))))))
% ->
% t(quotient(j(B),j(j(A))),quotient(i(quotient(j(B),j(j(A)))),j(eta(t(i(A),
% quotient(
% i(i(A)),
% i(quotient(
% i(B),
% eta(A)))))))))
% collapsed.
% Rule
% [332]
% t(A,quotient(i(A),i(t(B,quotient(i(B),i(t(quotient(j(t(quotient(j(B),A),
% quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(i(B),
% i(A))))))),C),
% quotient(i(quotient(j(t(quotient(
% j(B),A),
% quotient(
% i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A))))))),C)),
% j(eta(quotient(i(t(quotient(j(B),A),
% quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),i(A))))))),
% i(C)))))))))))) <->
% quotient(i(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(eta(quotient(
% i(B),
% i(A))))))),
% i(t(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(eta(
% quotient(
% i(C),
% i(B))))))),A),
% quotient(i(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),
% j(eta(quotient(i(C),i(B))))))),A)),
% j(eta(quotient(i(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(
% eta(
% quotient(
% i(C),
% i(B))))))),
% i(A)))))))) collapsed.
% Rule
% [333]
% quotient(i(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(eta(quotient(
% i(B),
% i(A))))))),
% i(t(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(eta(
% quotient(
% i(C),
% i(B))))))),A),
% quotient(i(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),
% j(eta(quotient(i(C),i(B))))))),A)),
% j(eta(quotient(i(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(
% eta(
% quotient(
% i(C),
% i(B))))))),
% i(A)))))))) <->
% t(A,quotient(i(A),i(t(B,quotient(i(B),i(t(quotient(j(t(quotient(j(B),A),
% quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(i(B),
% i(A))))))),C),
% quotient(i(quotient(j(t(quotient(
% j(B),A),
% quotient(
% i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A))))))),C)),
% j(eta(quotient(i(t(quotient(j(B),A),
% quotient(i(quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),i(A))))))),
% i(C)))))))))))) collapsed.
% Rule
% [334]
% t(quotient(j(eta(A)),t(eta(A),t(quotient(j(B),A),quotient(i(quotient(j(B),A)),
% j(eta(quotient(i(B),i(A)))))))),
% quotient(i(quotient(j(eta(A)),t(eta(A),t(quotient(j(B),A),quotient(i(
% quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A))))))))),
% j(eta(t(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(eta(quotient(
% i(B),i(A)))))),
% quotient(i(t(quotient(j(B),A),quotient(i(quotient(j(B),A)),j(eta(
% quotient(
% i(B),
% i(A))))))),
% j(eta(t(i(A),quotient(i(i(A)),i(i(t(quotient(j(B),A),quotient(i(
% quotient(
% j(B),A)),
% j(eta(quotient(
% i(B),
% i(A))))))))))))))))))
% ->
% t(quotient(j(B),i(i(A))),quotient(i(quotient(j(B),i(i(A)))),j(eta(quotient(
% i(B),
% i(i(i(A))))))))
% collapsed.
% Rule
% [335]
% t(quotient(j(C),t(quotient(j(B),eta(A)),quotient(i(quotient(j(B),eta(A))),
% j(eta(t(B,quotient(i(B),j(eta(
% quotient(
% i(B),
% i(A))))))))))),
% quotient(i(quotient(j(C),t(quotient(j(B),eta(A)),quotient(i(quotient(
% j(B),eta(A))),
% j(eta(t(B,quotient(i(B),
% j(eta(quotient(
% i(B),
% i(A)))))))))))),
% j(eta(quotient(i(C),i(t(quotient(j(B),eta(A)),quotient(i(quotient(j(B),
% eta(A))),j(eta(
% t(B,
% quotient(
% i(B),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))))
% <->
% t(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(eta(quotient(
% i(C),
% i(B))))))),
% eta(A)),quotient(i(quotient(j(t(quotient(j(C),B),quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(i(C),i(B))))))),
% eta(A))),j(eta(t(t(quotient(j(C),B),quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(
% i(C),i(B)))))),
% quotient(i(t(quotient(j(C),B),quotient(
% i(quotient(
% j(C),B)),
% j(eta(
% quotient(
% i(C),
% i(B))))))),
% j(eta(quotient(i(t(quotient(j(C),B),
% quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(i(C),
% i(B))))))),
% i(A)))))))))) collapsed.
% Rule
% [336]
% t(quotient(j(t(quotient(j(C),B),quotient(i(quotient(j(C),B)),j(eta(quotient(
% i(C),
% i(B))))))),
% eta(A)),quotient(i(quotient(j(t(quotient(j(C),B),quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(i(C),i(B))))))),
% eta(A))),j(eta(t(t(quotient(j(C),B),quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(
% i(C),i(B)))))),
% quotient(i(t(quotient(j(C),B),quotient(
% i(quotient(
% j(C),B)),
% j(eta(
% quotient(
% i(C),
% i(B))))))),
% j(eta(quotient(i(t(quotient(j(C),B),
% quotient(i(quotient(
% j(C),B)),
% j(eta(quotient(i(C),
% i(B))))))),
% i(A)))))))))) <->
% t(quotient(j(C),t(quotient(j(B),eta(A)),quotient(i(quotient(j(B),eta(A))),
% j(eta(t(B,quotient(i(B),j(eta(
% quotient(
% i(B),
% i(A))))))))))),
% quotient(i(quotient(j(C),t(quotient(j(B),eta(A)),quotient(i(quotient(
% j(B),eta(A))),
% j(eta(t(B,quotient(i(B),
% j(eta(quotient(
% i(B),
% i(A)))))))))))),
% j(eta(quotient(i(C),i(t(quotient(j(B),eta(A)),quotient(i(quotient(j(B),
% eta(A))),j(eta(
% t(B,
% quotient(
% i(B),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))))
% collapsed.
% Rule
% [337]
% t(quotient(j(A),t(A,t(quotient(j(eta(A)),t(eta(A),quotient(j(A),B))),
% quotient(i(quotient(j(eta(A)),t(eta(A),quotient(j(A),B)))),
% j(eta(t(quotient(j(A),B),quotient(i(quotient(j(A),B)),
% j(eta(t(i(A),quotient(i(i(A)),
% i(i(quotient(
% j(A),B))))))))))))))),
% quotient(i(quotient(j(A),t(A,t(quotient(j(eta(A)),t(eta(A),quotient(j(A),B))),
% quotient(i(quotient(j(eta(A)),t(eta(A),quotient(
% j(A),B)))),
% j(eta(t(quotient(j(A),B),quotient(i(quotient(
% j(A),B)),
% j(eta(t(i(A),quotient(
% i(
% i(A)),
% i(
% i(
% quotient(
% j(A),B)))))))))))))))),
% j(eta(t(i(A),quotient(i(i(A)),i(i(t(quotient(j(eta(A)),t(eta(A),quotient(
% j(A),B))),
% quotient(i(quotient(j(eta(A)),t(eta(A),
% quotient(
% j(A),B)))),
% j(eta(t(quotient(j(A),B),quotient(i(
% quotient(
% j(A),B)),
% j(eta(t(i(A),
% quotient(
% i(i(A)),
% i(i(
% quotient(
% j(A),B)))))))))))))))))))))
% -> j(B) collapsed.
% Rule [353] t(A,quotient(i(A),B)) <-> quotient(j(B),A) collapsed.
% Rule [372] t(i(A),quotient(i(i(A)),quotient(A,j(A)))) -> j(A) collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% quotient(eta(quotient(x0,t(i(x0),i(i(quotient(j(quotient(j(x2),x1)),t(
% quotient(
% j(x2),x1),
% j(
% eta(
% quotient(
% i(x2),
% i(x1))))))))))),
% quotient(j(x0),t(x0,quotient(j(quotient(j(x2),x1)),t(quotient(j(x2),x1),
% j(eta(quotient(i(x2),
% i(x1))))))))) = 
% quotient(eta(quotient(t(x0,x1),t(i(t(x0,x1)),i(i(quotient(j(quotient(
% j(x2),x0)),
% t(quotient(j(x2),x0),
% j(eta(quotient(i(x2),i(x0))))))))))),
% quotient(j(t(x0,x1)),t(t(x0,x1),quotient(j(quotient(j(x2),x0)),t(quotient(
% j(x2),x0),
% j(eta(
% quotient(
% i(x2),
% i(x0)))))))))
% 
% Current number of equations to process: 776
% Current number of ordered equations: 59
% Current number of rules: 87
% New rule produced :
% [379]
% t(j(B),quotient(B,j(eta(quotient(A,t(i(A),i(i(quotient(i(A),i(B)))))))))) ->
% B
% Current number of equations to process: 766
% Current number of ordered equations: 71
% Current number of rules: 88
% New rule produced :
% [380]
% quotient(i(A),i(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(eta(
% quotient(
% i(B),
% i(A))))))))
% -> B
% Current number of equations to process: 766
% Current number of ordered equations: 70
% Current number of rules: 89
% New rule produced :
% [381]
% quotient(j(B),t(B,i(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(
% eta(
% quotient(
% i(B),
% i(A)))))))))
% -> A
% Current number of equations to process: 766
% Current number of ordered equations: 69
% Current number of rules: 90
% New rule produced :
% [382]
% quotient(j(quotient(j(t(eta(A),C)),t(eta(A),B))),t(quotient(j(t(eta(A),C)),
% t(eta(A),B)),j(eta(
% quotient(
% i(t(
% eta(A),C)),
% i(t(
% eta(A),B)))))))
% ->
% t(eta(A),quotient(j(quotient(j(C),B)),t(quotient(j(C),B),j(eta(quotient(
% i(C),i(B)))))))
% Current number of equations to process: 766
% Current number of ordered equations: 68
% Current number of rules: 91
% New rule produced :
% [383]
% quotient(i(A),i(quotient(j(quotient(j(C),quotient(j(quotient(j(B),A)),
% t(quotient(j(B),A),j(eta(quotient(
% i(B),
% i(A)))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),A)),t(quotient(
% j(B),A),
% j(eta(quotient(
% i(B),
% i(A))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),A)),t(
% quotient(
% j(B),A),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))
% <->
% quotient(j(A),t(A,i(quotient(j(quotient(j(quotient(j(quotient(j(A),C)),
% t(quotient(j(A),C),j(eta(quotient(
% i(A),
% i(C))))))),B)),
% t(quotient(j(quotient(j(quotient(j(A),C)),t(quotient(
% j(A),C),
% j(eta(quotient(
% i(A),
% i(C))))))),B),
% j(eta(quotient(i(quotient(j(quotient(j(A),C)),t(quotient(
% j(A),C),
% j(eta(
% quotient(
% i(A),
% i(C))))))),
% i(B)))))))))
% Current number of equations to process: 229
% Current number of ordered equations: 1071
% Current number of rules: 92
% New rule produced :
% [384]
% quotient(j(A),t(A,i(quotient(j(quotient(j(quotient(j(quotient(j(A),C)),
% t(quotient(j(A),C),j(eta(quotient(
% i(A),
% i(C))))))),B)),
% t(quotient(j(quotient(j(quotient(j(A),C)),t(quotient(
% j(A),C),
% j(eta(quotient(
% i(A),
% i(C))))))),B),
% j(eta(quotient(i(quotient(j(quotient(j(A),C)),t(quotient(
% j(A),C),
% j(eta(
% quotient(
% i(A),
% i(C))))))),
% i(B))))))))) <->
% quotient(i(A),i(quotient(j(quotient(j(C),quotient(j(quotient(j(B),A)),
% t(quotient(j(B),A),j(eta(quotient(
% i(B),
% i(A)))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),A)),t(quotient(
% j(B),A),
% j(eta(quotient(
% i(B),
% i(A))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),A)),t(
% quotient(
% j(B),A),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))
% Current number of equations to process: 229
% Current number of ordered equations: 1070
% Current number of rules: 93
% New rule produced :
% [385]
% quotient(eta(quotient(A,t(i(A),i(i(quotient(j(quotient(j(B),eta(A))),
% t(quotient(j(B),eta(A)),j(eta(quotient(
% j(B),
% t(B,
% j(eta(
% quotient(
% i(B),
% i(A))))))))))))))),
% quotient(j(A),t(A,quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),eta(A)),
% j(eta(quotient(j(B),
% t(B,j(eta(quotient(
% i(B),
% i(A)))))))))))))
% ->
% quotient(j(quotient(j(B),j(j(A)))),t(quotient(j(B),j(j(A))),j(eta(quotient(A,
% t(i(A),
% i(quotient(
% i(B),
% eta(A)))))))))
% Current number of equations to process: 229
% Current number of ordered equations: 1069
% Current number of rules: 94
% New rule produced :
% [386]
% quotient(i(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(eta(quotient(
% i(B),
% i(A))))))),
% i(quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(i(C),
% i(B))))))),A)),
% t(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),j(eta(
% quotient(
% i(C),
% i(B))))))),A),
% j(eta(quotient(i(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),j(
% eta(
% quotient(
% i(C),
% i(B))))))),
% i(A)))))))) <->
% quotient(j(A),t(A,i(quotient(j(B),t(B,i(quotient(j(quotient(j(quotient(
% j(quotient(
% j(B),A)),
% t(quotient(
% j(B),A),
% j(eta(quotient(
% i(B),
% i(A))))))),C)),
% t(quotient(j(quotient(j(quotient(
% j(B),A)),
% t(quotient(j(B),A),
% j(eta(quotient(i(B),
% i(A))))))),C),
% j(eta(quotient(i(quotient(j(quotient(
% j(B),A)),
% t(quotient(j(B),A),
% j(eta(quotient(
% i(B),i(A))))))),
% i(C))))))))))))
% Current number of equations to process: 305
% Current number of ordered equations: 1361
% Current number of rules: 95
% New rule produced :
% [387]
% quotient(j(A),t(A,i(quotient(j(B),t(B,i(quotient(j(quotient(j(quotient(
% j(quotient(
% j(B),A)),
% t(quotient(
% j(B),A),
% j(eta(quotient(
% i(B),
% i(A))))))),C)),
% t(quotient(j(quotient(j(quotient(
% j(B),A)),
% t(quotient(j(B),A),
% j(eta(quotient(i(B),
% i(A))))))),C),
% j(eta(quotient(i(quotient(j(quotient(
% j(B),A)),
% t(quotient(j(B),A),
% j(eta(quotient(
% i(B),i(A))))))),
% i(C)))))))))))) <->
% quotient(i(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(eta(quotient(
% i(B),
% i(A))))))),
% i(quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(i(C),
% i(B))))))),A)),
% t(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),j(eta(
% quotient(
% i(C),
% i(B))))))),A),
% j(eta(quotient(i(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),j(
% eta(
% quotient(
% i(C),
% i(B))))))),
% i(A))))))))
% Current number of equations to process: 305
% Current number of ordered equations: 1360
% Current number of rules: 96
% New rule produced :
% [388]
% quotient(j(quotient(j(eta(A)),t(eta(A),quotient(j(quotient(j(B),A)),t(
% quotient(
% j(B),A),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))),
% t(quotient(j(eta(A)),t(eta(A),quotient(j(quotient(j(B),A)),t(quotient(j(B),A),
% j(eta(quotient(
% i(B),
% i(A)))))))),
% j(eta(quotient(j(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(eta(
% quotient(
% i(B),
% i(A))))))),
% t(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(eta(quotient(
% i(B),i(A)))))),
% j(eta(quotient(A,t(i(A),i(i(quotient(j(quotient(j(B),A)),t(quotient(
% j(B),A),
% j(eta(
% quotient(
% i(B),
% i(A))))))))))))))))))
% ->
% quotient(j(quotient(j(B),i(i(A)))),t(quotient(j(B),i(i(A))),j(eta(quotient(
% i(B),
% i(i(i(A))))))))
% Current number of equations to process: 305
% Current number of ordered equations: 1359
% Current number of rules: 97
% New rule produced :
% [389]
% quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(i(C),i(B))))))),
% eta(A))),t(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(
% j(C),B),
% j(eta(quotient(
% i(C),
% i(B))))))),
% eta(A)),j(eta(quotient(j(quotient(j(quotient(j(C),B)),
% t(quotient(j(C),B),j(eta(
% quotient(
% i(C),
% i(B))))))),
% t(quotient(j(quotient(j(C),B)),t(
% quotient(
% j(C),B),
% j(
% eta(
% quotient(
% i(C),
% i(B)))))),
% j(eta(quotient(i(quotient(j(quotient(
% j(C),B)),
% t(quotient(j(C),B),
% j(eta(quotient(i(C),
% i(B))))))),
% i(A)))))))))) <->
% quotient(j(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(
% j(B),eta(A)),
% j(eta(quotient(
% j(B),
% t(B,
% j(eta(
% quotient(
% i(B),
% i(A)))))))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),eta(A)),
% j(eta(quotient(j(B),
% t(B,j(eta(quotient(
% i(B),
% i(A))))))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),
% eta(A)),j(eta(
% quotient(
% j(B),
% t(B,
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))))
% Current number of equations to process: 488
% Current number of ordered equations: 1780
% Current number of rules: 98
% New rule produced :
% [390]
% quotient(j(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(
% j(B),eta(A)),
% j(eta(quotient(
% j(B),
% t(B,
% j(eta(
% quotient(
% i(B),
% i(A)))))))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),eta(A)),
% j(eta(quotient(j(B),
% t(B,j(eta(quotient(
% i(B),
% i(A))))))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),
% eta(A)),j(eta(
% quotient(
% j(B),
% t(B,
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))))
% <->
% quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(i(C),i(B))))))),
% eta(A))),t(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(
% j(C),B),
% j(eta(quotient(
% i(C),
% i(B))))))),
% eta(A)),j(eta(quotient(j(quotient(j(quotient(j(C),B)),
% t(quotient(j(C),B),j(eta(
% quotient(
% i(C),
% i(B))))))),
% t(quotient(j(quotient(j(C),B)),t(
% quotient(
% j(C),B),
% j(
% eta(
% quotient(
% i(C),
% i(B)))))),
% j(eta(quotient(i(quotient(j(quotient(
% j(C),B)),
% t(quotient(j(C),B),
% j(eta(quotient(i(C),
% i(B))))))),
% i(A))))))))))
% Current number of equations to process: 488
% Current number of ordered equations: 1779
% Current number of rules: 99
% New rule produced :
% [391]
% quotient(eta(quotient(A,t(i(A),i(i(quotient(j(quotient(j(eta(A)),t(eta(A),
% quotient(
% j(A),B)))),
% t(quotient(j(eta(A)),t(eta(A),quotient(
% j(A),B))),
% j(eta(quotient(j(quotient(j(A),B)),
% t(quotient(j(A),B),j(eta(quotient(A,
% t(i(A),
% i(i(
% quotient(
% j(A),B)))))))))))))))))),
% quotient(j(A),t(A,quotient(j(quotient(j(eta(A)),t(eta(A),quotient(j(A),B)))),
% t(quotient(j(eta(A)),t(eta(A),quotient(j(A),B))),j(
% eta(
% quotient(
% j(
% quotient(
% j(A),B)),
% t(
% quotient(
% j(A),B),
% j(
% eta(
% quotient(A,
% t(
% i(A),
% i(
% i(
% quotient(
% j(A),B))))))))))))))))
% -> j(B)
% Current number of equations to process: 488
% Current number of ordered equations: 1778
% Current number of rules: 100
% New rule produced : [392] t(j(A),j(eta(A))) -> eta(A)
% Current number of equations to process: 489
% Current number of ordered equations: 1749
% Current number of rules: 101
% New rule produced : [393] t(i(A),j(A)) -> i(i(i(A)))
% Current number of equations to process: 490
% Current number of ordered equations: 1747
% Current number of rules: 102
% New rule produced : [394] t(i(i(A)),j(eta(A))) -> eta(A)
% Rule
% [357]
% t(quotient(A,j(A)),t(j(eta(t(i(i(A)),j(eta(A))))),quotient(eta(t(i(i(A)),
% j(eta(A)))),
% quotient(A,j(A))))) ->
% j(quotient(A,j(A))) collapsed.
% Current number of equations to process: 490
% Current number of ordered equations: 1739
% Current number of rules: 102
% New rule produced : [395] t(A,i(i(i(A)))) -> j(j(j(A)))
% Current number of equations to process: 493
% Current number of ordered equations: 1729
% Current number of rules: 103
% New rule produced : [396] t(quotient(A,j(A)),j(A)) -> i(A)
% Current number of equations to process: 495
% Current number of ordered equations: 1716
% Current number of rules: 104
% New rule produced : [397] t(j(j(A)),j(eta(A))) -> eta(A)
% Current number of equations to process: 495
% Current number of ordered equations: 1714
% Current number of rules: 105
% New rule produced : [398] t(eta(A),i(A)) -> i(i(i(i(i(A)))))
% Current number of equations to process: 495
% Current number of ordered equations: 1712
% Current number of rules: 106
% New rule produced : [399] t(j(j(j(A))),eta(A)) -> j(eta(A))
% Current number of equations to process: 495
% Current number of ordered equations: 1711
% Current number of rules: 107
% New rule produced : [400] quotient(i(A),i(i(A))) -> j(quotient(A,j(A)))
% Rule [358] j(quotient(i(A),i(i(A)))) -> quotient(A,j(A)) collapsed.
% Current number of equations to process: 497
% Current number of ordered equations: 1679
% Current number of rules: 107
% New rule produced : [401] t(j(eta(A)),j(A)) -> j(j(j(j(j(A)))))
% Current number of equations to process: 498
% Current number of ordered equations: 1676
% Current number of rules: 108
% New rule produced : [402] quotient(i(i(A)),quotient(A,i(A))) -> i(A)
% Current number of equations to process: 498
% Current number of ordered equations: 1675
% Current number of rules: 109
% New rule produced : [403] t(j(j(A)),i(A)) -> j(j(j(j(j(A)))))
% Current number of equations to process: 498
% Current number of ordered equations: 1674
% Current number of rules: 110
% New rule produced : [404] t(j(eta(A)),i(i(i(A)))) -> j(A)
% Current number of equations to process: 500
% Current number of ordered equations: 1666
% Current number of rules: 111
% New rule produced : [405] t(j(j(j(A))),j(eta(A))) -> eta(A)
% Current number of equations to process: 500
% Current number of ordered equations: 1664
% Current number of rules: 112
% New rule produced : [406] quotient(A,t(i(A),i(B))) <-> quotient(B,i(A))
% Current number of equations to process: 500
% Current number of ordered equations: 1662
% Current number of rules: 113
% New rule produced : [407] quotient(B,i(A)) <-> quotient(A,t(i(A),i(B)))
% Rule [54] quotient(eta(A),i(A)) -> i(i(A)) collapsed.
% The conjecture has been reduced. 
% Conjecture is now:
% quotient(eta(quotient(x0,t(i(x0),i(i(quotient(eta(quotient(x1,t(i(x1),
% i(i(x2))))),
% quotient(j(x2),x1))))))),quotient(
% j(x0),t(x0,
% quotient(
% eta(
% quotient(x1,
% t(
% i(x1),
% i(
% i(x2))))),
% quotient(
% j(x2),x1))))) = 
% quotient(eta(quotient(t(x0,x1),t(i(t(x0,x1)),i(i(quotient(eta(quotient(x0,
% t(i(x0),
% i(i(x2))))),
% quotient(j(x2),x0))))))),
% quotient(j(t(x0,x1)),t(t(x0,x1),quotient(eta(quotient(x0,t(i(x0),i(i(x2))))),
% quotient(j(x2),x0)))))
% 
% Current number of equations to process: 500
% Current number of ordered equations: 1657
% Current number of rules: 113
% New rule produced : [408] quotient(i(A),j(quotient(A,i(A)))) -> i(i(A))
% Current number of equations to process: 500
% Current number of ordered equations: 1656
% Current number of rules: 114
% New rule produced : [409] quotient(j(A),j(quotient(A,j(A)))) -> j(j(A))
% Current number of equations to process: 500
% Current number of ordered equations: 1651
% Current number of rules: 115
% New rule produced : [410] quotient(eta(A),i(i(i(A)))) -> i(i(i(i(A))))
% Current number of equations to process: 516
% Current number of ordered equations: 1634
% Current number of rules: 116
% New rule produced : [411] t(A,j(quotient(A,i(A)))) -> j(quotient(A,j(A)))
% Current number of equations to process: 516
% Current number of ordered equations: 1633
% Current number of rules: 117
% New rule produced : [412] t(eta(A),t(j(A),i(i(A)))) -> A
% Current number of equations to process: 516
% Current number of ordered equations: 1632
% Current number of rules: 118
% New rule produced : [413] t(j(B),t(quotient(B,A),A)) -> j(j(A))
% Current number of equations to process: 520
% Current number of ordered equations: 1622
% Current number of rules: 119
% New rule produced : [414] t(i(i(i(i(A)))),eta(A)) -> j(eta(A))
% Current number of equations to process: 520
% Current number of ordered equations: 1621
% Current number of rules: 120
% New rule produced : [415] t(quotient(j(A),B),t(B,A)) -> j(j(A))
% Current number of equations to process: 521
% Current number of ordered equations: 1619
% Current number of rules: 121
% New rule produced :
% [416] quotient(eta(A),B) <-> quotient(j(B),t(B,j(eta(A))))
% Current number of equations to process: 521
% Current number of ordered equations: 1616
% Current number of rules: 122
% New rule produced :
% [417] quotient(j(B),t(B,j(eta(A)))) <-> quotient(eta(A),B)
% Current number of equations to process: 521
% Current number of ordered equations: 1613
% Current number of rules: 123
% New rule produced : [418] t(j(A),i(i(A))) -> j(j(j(j(A))))
% Rule [412] t(eta(A),t(j(A),i(i(A)))) -> A collapsed.
% Current number of equations to process: 522
% Current number of ordered equations: 1610
% Current number of rules: 123
% New rule produced : [419] quotient(j(eta(A)),i(i(i(i(A))))) -> i(A)
% Current number of equations to process: 533
% Current number of ordered equations: 1591
% Current number of rules: 124
% New rule produced : [420] quotient(eta(A),j(j(j(j(A))))) -> j(j(j(A)))
% Current number of equations to process: 533
% Current number of ordered equations: 1590
% Current number of rules: 125
% New rule produced : [421] t(eta(A),j(j(j(j(j(A)))))) -> j(A)
% Current number of equations to process: 533
% Current number of ordered equations: 1589
% Current number of rules: 126
% New rule produced :
% [422] quotient(A,t(i(A),i(i(t(quotient(A,B),B))))) -> quotient(A,B)
% Current number of equations to process: 532
% Current number of ordered equations: 1588
% Current number of rules: 127
% New rule produced : [423] quotient(j(A),t(A,i(i(A)))) -> j(quotient(A,i(A)))
% Current number of equations to process: 543
% Current number of ordered equations: 1566
% Current number of rules: 128
% New rule produced : [424] t(i(B),i(i(quotient(B,A)))) <-> quotient(i(A),i(B))
% Current number of equations to process: 543
% Current number of ordered equations: 1565
% Current number of rules: 129
% New rule produced : [425] quotient(i(A),i(B)) <-> t(i(B),i(i(quotient(B,A))))
% Rule [400] quotient(i(A),i(i(A))) -> j(quotient(A,j(A))) collapsed.
% Current number of equations to process: 544
% Current number of ordered equations: 1564
% Current number of rules: 129
% Rule [423] quotient(j(A),t(A,i(i(A)))) -> j(quotient(A,i(A))) is composed into 
% [423] quotient(j(A),t(A,i(i(A)))) -> t(j(j(A)),j(quotient(A,j(A))))
% Rule [347] i(quotient(A,i(A))) -> j(quotient(A,i(A))) is composed into 
% [347] i(quotient(A,i(A))) -> t(j(j(A)),j(quotient(A,j(A))))
% New rule produced :
% [426] j(quotient(A,i(A))) -> t(j(j(A)),j(quotient(A,j(A))))
% Rule [351] j(j(quotient(A,i(A)))) -> quotient(A,i(A)) collapsed.
% Rule [408] quotient(i(A),j(quotient(A,i(A)))) -> i(i(A)) collapsed.
% Rule [411] t(A,j(quotient(A,i(A)))) -> j(quotient(A,j(A))) collapsed.
% Current number of equations to process: 583
% Current number of ordered equations: 1499
% Current number of rules: 127
% New rule produced : [427] quotient(j(t(A,B)),quotient(j(B),A)) -> j(j(A))
% Current number of equations to process: 583
% Current number of ordered equations: 1497
% Current number of rules: 128
% New rule produced : [428] eta(t(j(j(A)),j(quotient(A,j(A))))) -> one
% Current number of equations to process: 583
% Current number of ordered equations: 1495
% Current number of rules: 129
% New rule produced :
% [429] t(eta(A),quotient(j(eta(A)),B)) <-> quotient(j(B),eta(A))
% Current number of equations to process: 583
% Current number of ordered equations: 1493
% Current number of rules: 130
% New rule produced :
% [430] quotient(j(B),eta(A)) <-> t(eta(A),quotient(j(eta(A)),B))
% Current number of equations to process: 583
% Current number of ordered equations: 1491
% Current number of rules: 131
% New rule produced :
% [431] t(j(B),quotient(B,j(eta(A)))) <-> quotient(eta(A),j(B))
% Current number of equations to process: 583
% Current number of ordered equations: 1488
% Current number of rules: 132
% New rule produced :
% [432] quotient(eta(A),j(B)) <-> t(j(B),quotient(B,j(eta(A))))
% Current number of equations to process: 583
% Current number of ordered equations: 1485
% Current number of rules: 133
% New rule produced : [433] quotient(j(t(A,i(B))),quotient(B,A)) -> j(j(A))
% Current number of equations to process: 583
% Current number of ordered equations: 1484
% Current number of rules: 134
% New rule produced :
% [434] quotient(B,t(i(B),j(eta(A)))) <-> quotient(eta(A),i(B))
% Current number of equations to process: 583
% Current number of ordered equations: 1483
% Current number of rules: 135
% New rule produced :
% [435] quotient(eta(A),i(B)) <-> quotient(B,t(i(B),j(eta(A))))
% Current number of equations to process: 583
% Current number of ordered equations: 1482
% Current number of rules: 136
% New rule produced : [436] quotient(A,i(i(t(j(A),quotient(A,B))))) -> B
% Current number of equations to process: 584
% Current number of ordered equations: 1479
% Current number of rules: 137
% New rule produced : [437] quotient(j(A),t(A,j(quotient(A,j(A))))) -> A
% Current number of equations to process: 584
% Current number of ordered equations: 1477
% Current number of rules: 138
% New rule produced :
% [438] quotient(i(A),i(i(B))) <-> quotient(i(B),i(i(t(B,A))))
% Current number of equations to process: 584
% Current number of ordered equations: 1476
% Current number of rules: 139
% New rule produced :
% [439] quotient(i(B),i(i(t(B,A)))) <-> quotient(i(A),i(i(B)))
% Current number of equations to process: 584
% Current number of ordered equations: 1474
% Current number of rules: 140
% New rule produced :
% [440]
% quotient(j(B),t(B,j(eta(quotient(j(quotient(j(B),i(i(A)))),t(quotient(
% j(B),i(i(A))),
% j(eta(quotient(
% i(B),
% i(i(i(A))))))))))))
% -> quotient(j(B),t(B,j(eta(quotient(i(B),i(A))))))
% Current number of equations to process: 584
% Current number of ordered equations: 1473
% Current number of rules: 141
% New rule produced :
% [441]
% quotient(j(A),t(A,j(eta(quotient(i(A),i(t(A,B))))))) <->
% quotient(j(A),t(A,j(eta(quotient(i(B),i(A))))))
% Current number of equations to process: 584
% Current number of ordered equations: 1472
% Current number of rules: 142
% New rule produced :
% [442]
% quotient(j(A),t(A,j(eta(quotient(i(B),i(A)))))) <->
% quotient(j(A),t(A,j(eta(quotient(i(A),i(t(A,B)))))))
% Current number of equations to process: 584
% Current number of ordered equations: 1471
% Current number of rules: 143
% Rule [442]
% quotient(j(A),t(A,j(eta(quotient(i(B),i(A)))))) <->
% quotient(j(A),t(A,j(eta(quotient(i(A),i(t(A,B))))))) is composed into 
% [442]
% quotient(j(A),t(A,j(eta(quotient(i(B),i(A)))))) <->
% quotient(i(A),j(eta(t(A,B))))
% Rule [440]
% quotient(j(B),t(B,j(eta(quotient(j(quotient(j(B),i(i(A)))),t(quotient(
% j(B),
% i(i(A))),
% j(eta(
% quotient(
% i(B),
% i(i(i(A))))))))))))
% -> quotient(j(B),t(B,j(eta(quotient(i(B),i(A)))))) is composed into 
% [440]
% quotient(j(B),t(B,j(eta(quotient(j(quotient(j(B),i(i(A)))),t(quotient(
% j(B),i(i(A))),
% j(eta(quotient(
% i(B),
% i(i(i(A))))))))))))
% -> quotient(i(B),j(eta(A)))
% New rule produced :
% [443]
% quotient(j(A),t(A,j(eta(quotient(i(A),i(B)))))) -> quotient(i(A),j(eta(B)))
% Rule
% [385]
% quotient(eta(quotient(A,t(i(A),i(i(quotient(j(quotient(j(B),eta(A))),
% t(quotient(j(B),eta(A)),j(eta(quotient(
% j(B),
% t(B,
% j(eta(
% quotient(
% i(B),
% i(A))))))))))))))),
% quotient(j(A),t(A,quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),eta(A)),
% j(eta(quotient(j(B),
% t(B,j(eta(quotient(
% i(B),
% i(A)))))))))))))
% ->
% quotient(j(quotient(j(B),j(j(A)))),t(quotient(j(B),j(j(A))),j(eta(quotient(A,
% t(i(A),
% i(quotient(
% i(B),
% eta(A)))))))))
% collapsed.
% Rule
% [389]
% quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(i(C),i(B))))))),
% eta(A))),t(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(
% j(C),B),
% j(eta(quotient(
% i(C),
% i(B))))))),
% eta(A)),j(eta(quotient(j(quotient(j(quotient(j(C),B)),
% t(quotient(j(C),B),j(eta(
% quotient(
% i(C),
% i(B))))))),
% t(quotient(j(quotient(j(C),B)),t(
% quotient(
% j(C),B),
% j(
% eta(
% quotient(
% i(C),
% i(B)))))),
% j(eta(quotient(i(quotient(j(quotient(
% j(C),B)),
% t(quotient(j(C),B),
% j(eta(quotient(i(C),
% i(B))))))),
% i(A)))))))))) <->
% quotient(j(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(
% j(B),eta(A)),
% j(eta(quotient(
% j(B),
% t(B,
% j(eta(
% quotient(
% i(B),
% i(A)))))))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),eta(A)),
% j(eta(quotient(j(B),
% t(B,j(eta(quotient(
% i(B),
% i(A))))))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),
% eta(A)),j(eta(
% quotient(
% j(B),
% t(B,
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))))
% collapsed.
% Rule
% [390]
% quotient(j(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(
% j(B),eta(A)),
% j(eta(quotient(
% j(B),
% t(B,
% j(eta(
% quotient(
% i(B),
% i(A)))))))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),eta(A)),
% j(eta(quotient(j(B),
% t(B,j(eta(quotient(
% i(B),
% i(A))))))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),
% eta(A)),j(eta(
% quotient(
% j(B),
% t(B,
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))))
% <->
% quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(i(C),i(B))))))),
% eta(A))),t(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(
% j(C),B),
% j(eta(quotient(
% i(C),
% i(B))))))),
% eta(A)),j(eta(quotient(j(quotient(j(quotient(j(C),B)),
% t(quotient(j(C),B),j(eta(
% quotient(
% i(C),
% i(B))))))),
% t(quotient(j(quotient(j(C),B)),t(
% quotient(
% j(C),B),
% j(
% eta(
% quotient(
% i(C),
% i(B)))))),
% j(eta(quotient(i(quotient(j(quotient(
% j(C),B)),
% t(quotient(j(C),B),
% j(eta(quotient(i(C),
% i(B))))))),
% i(A)))))))))) collapsed.
% Rule
% [441]
% quotient(j(A),t(A,j(eta(quotient(i(A),i(t(A,B))))))) <->
% quotient(j(A),t(A,j(eta(quotient(i(B),i(A)))))) collapsed.
% Current number of equations to process: 649
% Current number of ordered equations: 1377
% Current number of rules: 140
% New rule produced :
% [444]
% quotient(eta(quotient(A,t(i(A),i(i(quotient(j(quotient(j(B),eta(A))),
% t(quotient(j(B),eta(A)),j(eta(quotient(
% i(B),
% j(eta(A)))))))))))),
% quotient(j(A),t(A,quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),eta(A)),
% j(eta(quotient(i(B),
% j(eta(A))))))))))
% ->
% quotient(j(quotient(j(B),j(j(A)))),t(quotient(j(B),j(j(A))),j(eta(quotient(A,
% t(i(A),
% i(quotient(
% i(B),
% eta(A)))))))))
% Current number of equations to process: 647
% Current number of ordered equations: 1379
% Current number of rules: 141
% New rule produced :
% [445]
% quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(i(C),i(B))))))),
% eta(A))),t(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(
% j(C),B),
% j(eta(quotient(
% i(C),
% i(B))))))),
% eta(A)),j(eta(quotient(i(quotient(j(quotient(j(C),B)),
% t(quotient(j(C),B),j(eta(
% quotient(
% i(C),
% i(B))))))),
% j(eta(A))))))) <->
% quotient(j(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(
% j(B),eta(A)),
% j(eta(quotient(
% i(B),
% j(eta(A))))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),eta(A)),
% j(eta(quotient(i(B),
% j(eta(A)))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),
% eta(A)),j(eta(
% quotient(
% i(B),
% j(
% eta(A)))))))))))))
% Current number of equations to process: 596
% Current number of ordered equations: 1518
% Current number of rules: 142
% New rule produced :
% [446]
% quotient(j(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(
% j(B),eta(A)),
% j(eta(quotient(
% i(B),
% j(eta(A))))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),eta(A)),
% j(eta(quotient(i(B),
% j(eta(A)))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),
% eta(A)),j(eta(
% quotient(
% i(B),
% j(
% eta(A)))))))))))))
% <->
% quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(i(C),i(B))))))),
% eta(A))),t(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(
% j(C),B),
% j(eta(quotient(
% i(C),
% i(B))))))),
% eta(A)),j(eta(quotient(i(quotient(j(quotient(j(C),B)),
% t(quotient(j(C),B),j(eta(
% quotient(
% i(C),
% i(B))))))),
% j(eta(A)))))))
% Current number of equations to process: 596
% Current number of ordered equations: 1517
% Current number of rules: 143
% New rule produced : [447] eta(quotient(A,t(i(A),i(i(i(A)))))) -> one
% Current number of equations to process: 597
% Current number of ordered equations: 1515
% Current number of rules: 144
% New rule produced : [448] t(j(eta(A)),quotient(eta(A),i(i(i(i(A)))))) -> i(A)
% Current number of equations to process: 598
% Current number of ordered equations: 1512
% Current number of rules: 145
% New rule produced :
% [449] quotient(j(eta(A)),i(i(quotient(B,eta(A))))) -> i(B)
% Current number of equations to process: 598
% Current number of ordered equations: 1510
% Current number of rules: 146
% New rule produced :
% [450] quotient(eta(A),t(j(eta(A)),B)) <-> quotient(j(B),j(eta(A)))
% Current number of equations to process: 598
% Current number of ordered equations: 1503
% Current number of rules: 147
% New rule produced :
% [451] quotient(j(B),j(eta(A))) <-> quotient(eta(A),t(j(eta(A)),B))
% Current number of equations to process: 598
% Current number of ordered equations: 1500
% Current number of rules: 148
% New rule produced : [452] t(quotient(j(A),t(A,i(B))),t(A,i(B))) -> j(B)
% Current number of equations to process: 599
% Current number of ordered equations: 1494
% Current number of rules: 149
% New rule produced :
% [453] quotient(j(j(A)),t(j(A),B)) -> t(j(A),quotient(A,B))
% Rule [236] quotient(j(j(j(B))),t(j(j(B)),quotient(j(B),A))) -> j(j(A))
% collapsed.
% Current number of equations to process: 653
% Current number of ordered equations: 1375
% Current number of rules: 149
% New rule produced : [454] t(i(B),i(i(quotient(B,j(A))))) <-> quotient(A,i(B))
% Current number of equations to process: 653
% Current number of ordered equations: 1374
% Current number of rules: 150
% New rule produced : [455] quotient(A,i(B)) <-> t(i(B),i(i(quotient(B,j(A)))))
% Rule [300] eta(quotient(A,i(A))) -> one collapsed.
% Rule [347] i(quotient(A,i(A))) -> t(j(j(A)),j(quotient(A,j(A)))) collapsed.
% Rule [352] t(quotient(A,i(A)),i(A)) -> j(A) collapsed.
% Rule [402] quotient(i(i(A)),quotient(A,i(A))) -> i(A) collapsed.
% Rule [426] j(quotient(A,i(A))) -> t(j(j(A)),j(quotient(A,j(A)))) collapsed.
% Current number of equations to process: 661
% Current number of ordered equations: 1338
% Current number of rules: 146
% New rule produced : [456] eta(t(i(A),quotient(A,j(A)))) -> one
% Current number of equations to process: 660
% Current number of ordered equations: 1338
% Current number of rules: 147
% New rule produced :
% [457] t(eta(A),quotient(j(eta(A)),i(B))) <-> quotient(B,eta(A))
% Current number of equations to process: 660
% Current number of ordered equations: 1336
% Current number of rules: 148
% New rule produced :
% [458] quotient(B,eta(A)) <-> t(eta(A),quotient(j(eta(A)),i(B)))
% Current number of equations to process: 660
% Current number of ordered equations: 1334
% Current number of rules: 149
% New rule produced :
% [459] quotient(i(B),t(i(i(B)),i(quotient(A,eta(B))))) -> quotient(A,B)
% Current number of equations to process: 678
% Current number of ordered equations: 1312
% Current number of rules: 150
% New rule produced : [460] t(quotient(j(A),t(A,B)),t(A,B)) -> j(j(B))
% Rule [452] t(quotient(j(A),t(A,i(B))),t(A,i(B))) -> j(B) collapsed.
% Current number of equations to process: 679
% Current number of ordered equations: 1308
% Current number of rules: 150
% New rule produced : [461] quotient(i(A),i(i(quotient(j(A),t(A,B))))) -> B
% Current number of equations to process: 679
% Current number of ordered equations: 1304
% Current number of rules: 151
% New rule produced : [462] quotient(i(t(A,B)),i(i(quotient(j(B),A)))) -> A
% Current number of equations to process: 679
% Current number of ordered equations: 1302
% Current number of rules: 152
% New rule produced :
% [463] quotient(A,quotient(j(B),t(B,i(A)))) -> t(quotient(A,B),B)
% Current number of equations to process: 679
% Current number of ordered equations: 1300
% Current number of rules: 153
% New rule produced : [464] t(j(eta(A)),i(i(i(i(A))))) -> A
% Current number of equations to process: 683
% Current number of ordered equations: 1290
% Current number of rules: 154
% New rule produced : [465] quotient(i(t(A,i(B))),i(i(quotient(B,A)))) -> A
% Current number of equations to process: 683
% Current number of ordered equations: 1289
% Current number of rules: 155
% New rule produced :
% [466] quotient(B,j(eta(A))) <-> quotient(eta(A),t(j(eta(A)),i(B)))
% Current number of equations to process: 683
% Current number of ordered equations: 1288
% Current number of rules: 156
% New rule produced :
% [467] quotient(eta(A),t(j(eta(A)),i(B))) <-> quotient(B,j(eta(A)))
% Current number of equations to process: 683
% Current number of ordered equations: 1287
% Current number of rules: 157
% Rule [423] quotient(j(A),t(A,i(i(A)))) -> t(j(j(A)),j(quotient(A,j(A)))) is composed into 
% [423] quotient(j(A),t(A,i(i(A)))) -> t(A,j(quotient(A,j(A))))
% New rule produced :
% [468] t(j(j(A)),j(quotient(A,j(A)))) -> t(A,j(quotient(A,j(A))))
% Rule [428] eta(t(j(j(A)),j(quotient(A,j(A))))) -> one collapsed.
% Current number of equations to process: 700
% Current number of ordered equations: 1270
% Current number of rules: 157
% New rule produced : [469] eta(t(A,j(quotient(A,j(A))))) -> one
% Current number of equations to process: 699
% Current number of ordered equations: 1270
% Current number of rules: 158
% New rule produced : [470] t(quotient(eta(A),B),t(B,j(eta(A)))) -> j(eta(A))
% Current number of equations to process: 699
% Current number of ordered equations: 1269
% Current number of rules: 159
% New rule produced : [471] t(quotient(j(A),B),t(t(B,A),B)) -> j(j(B))
% Current number of equations to process: 699
% Current number of ordered equations: 1267
% Current number of rules: 160
% New rule produced : [472] t(A,t(j(quotient(A,j(A))),i(i(A)))) -> A
% Current number of equations to process: 699
% Current number of ordered equations: 1266
% Current number of rules: 161
% New rule produced : [473] quotient(i(i(i(A))),quotient(j(A),i(i(A)))) -> A
% Current number of equations to process: 699
% Current number of ordered equations: 1264
% Current number of rules: 162
% New rule produced : [474] quotient(A,t(i(A),quotient(A,j(A)))) -> j(A)
% Current number of equations to process: 702
% Current number of ordered equations: 1260
% Current number of rules: 163
% Rule [446]
% quotient(j(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(
% j(B),
% eta(A)),
% j(eta(
% quotient(
% i(B),
% j(eta(A))))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),
% eta(A)),j(eta(
% quotient(
% i(B),
% j(
% eta(A)))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),eta(A))),t(quotient(
% j(B),eta(A)),
% j(eta(quotient(
% i(B),
% j(
% eta(A)))))))))))))
% <->
% quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(
% i(C),i(B))))))),
% eta(A))),t(quotient(j(quotient(j(quotient(j(C),B)),t(
% quotient(
% j(C),B),
% j(
% eta(
% quotient(
% i(C),
% i(B))))))),
% eta(A)),j(eta(quotient(i(quotient(j(quotient(
% j(C),B)),
% t(quotient(j(C),B),
% j(eta(quotient(i(C),i(B))))))),
% j(eta(A))))))) is composed into 
% [446]
% quotient(j(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(
% j(B),eta(A)),
% j(eta(quotient(
% i(B),
% j(eta(A))))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),eta(A)),
% j(eta(quotient(i(B),
% j(eta(A)))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),
% eta(A)),j(eta(
% quotient(
% i(B),
% j(
% eta(A)))))))))))))
% <->
% quotient(j(quotient(quotient(j(C),B),eta(A))),t(quotient(quotient(j(C),B),
% eta(A)),j(eta(quotient(
% i(quotient(
% j(quotient(
% j(C),B)),
% t(quotient(
% j(C),B),
% j(eta(
% quotient(
% i(C),
% i(B))))))),
% j(eta(A)))))))
% Rule [383]
% quotient(i(A),i(quotient(j(quotient(j(C),quotient(j(quotient(j(B),A)),
% t(quotient(j(B),A),j(eta(
% quotient(
% i(B),
% i(A)))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),A)),t(quotient(
% j(B),A),
% j(eta(
% quotient(
% i(B),
% i(A))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),A)),
% t(quotient(j(B),A),j(eta(quotient(
% i(B),
% i(A))))))))))))))
% <->
% quotient(j(A),t(A,i(quotient(j(quotient(j(quotient(j(quotient(j(A),C)),
% t(quotient(j(A),C),j(eta(
% quotient(
% i(A),
% i(C))))))),B)),
% t(quotient(j(quotient(j(quotient(j(A),C)),t(
% quotient(
% j(A),C),
% j(
% eta(
% quotient(
% i(A),
% i(C))))))),B),
% j(eta(quotient(i(quotient(j(quotient(j(A),C)),
% t(quotient(j(A),C),j(eta(quotient(
% i(A),
% i(C))))))),
% i(B))))))))) is composed into [383]
% quotient(
% i(A),i(quotient(
% j(
% quotient(
% j(C),
% quotient(
% j(
% quotient(
% j(B),A)),
% t(
% quotient(
% j(B),A),
% j(
% eta(
% quotient(
% i(B),
% i(A)))))))),
% t(
% quotient(
% j(C),
% quotient(
% j(
% quotient(
% j(B),A)),
% t(
% quotient(
% j(B),A),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))),
% j(
% eta(
% quotient(
% i(C),
% i(
% quotient(
% j(
% quotient(
% j(B),A)),
% t(
% quotient(
% j(B),A),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))
% <->
% quotient(
% j(A),t(A,
% i(quotient(
% j(
% quotient(
% quotient(
% j(A),C),B)),
% t(
% quotient(
% quotient(
% j(A),C),B),
% j(
% eta(
% quotient(
% i(
% quotient(
% j(
% quotient(
% j(A),C)),
% t(
% quotient(
% j(A),C),
% j(
% eta(
% quotient(
% i(A),
% i(C))))))),
% i(B)))))))))
% New rule produced :
% [475]
% j(quotient(j(quotient(j(A),B)),t(quotient(j(A),B),j(eta(quotient(i(A),i(B)))))))
% -> quotient(j(A),B)
% Rule
% [384]
% quotient(j(A),t(A,i(quotient(j(quotient(j(quotient(j(quotient(j(A),C)),
% t(quotient(j(A),C),j(eta(quotient(
% i(A),
% i(C))))))),B)),
% t(quotient(j(quotient(j(quotient(j(A),C)),t(quotient(
% j(A),C),
% j(eta(quotient(
% i(A),
% i(C))))))),B),
% j(eta(quotient(i(quotient(j(quotient(j(A),C)),t(quotient(
% j(A),C),
% j(eta(
% quotient(
% i(A),
% i(C))))))),
% i(B))))))))) <->
% quotient(i(A),i(quotient(j(quotient(j(C),quotient(j(quotient(j(B),A)),
% t(quotient(j(B),A),j(eta(quotient(
% i(B),
% i(A)))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),A)),t(quotient(
% j(B),A),
% j(eta(quotient(
% i(B),
% i(A))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),A)),t(
% quotient(
% j(B),A),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))))))))
% collapsed.
% Rule
% [386]
% quotient(i(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(eta(quotient(
% i(B),
% i(A))))))),
% i(quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(i(C),
% i(B))))))),A)),
% t(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),j(eta(
% quotient(
% i(C),
% i(B))))))),A),
% j(eta(quotient(i(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),j(
% eta(
% quotient(
% i(C),
% i(B))))))),
% i(A)))))))) <->
% quotient(j(A),t(A,i(quotient(j(B),t(B,i(quotient(j(quotient(j(quotient(
% j(quotient(
% j(B),A)),
% t(quotient(
% j(B),A),
% j(eta(quotient(
% i(B),
% i(A))))))),C)),
% t(quotient(j(quotient(j(quotient(
% j(B),A)),
% t(quotient(j(B),A),
% j(eta(quotient(i(B),
% i(A))))))),C),
% j(eta(quotient(i(quotient(j(quotient(
% j(B),A)),
% t(quotient(j(B),A),
% j(eta(quotient(
% i(B),i(A))))))),
% i(C)))))))))))) collapsed.
% Rule
% [387]
% quotient(j(A),t(A,i(quotient(j(B),t(B,i(quotient(j(quotient(j(quotient(
% j(quotient(
% j(B),A)),
% t(quotient(
% j(B),A),
% j(eta(quotient(
% i(B),
% i(A))))))),C)),
% t(quotient(j(quotient(j(quotient(
% j(B),A)),
% t(quotient(j(B),A),
% j(eta(quotient(i(B),
% i(A))))))),C),
% j(eta(quotient(i(quotient(j(quotient(
% j(B),A)),
% t(quotient(j(B),A),
% j(eta(quotient(
% i(B),i(A))))))),
% i(C)))))))))))) <->
% quotient(i(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(eta(quotient(
% i(B),
% i(A))))))),
% i(quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(i(C),
% i(B))))))),A)),
% t(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),j(eta(
% quotient(
% i(C),
% i(B))))))),A),
% j(eta(quotient(i(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),j(
% eta(
% quotient(
% i(C),
% i(B))))))),
% i(A)))))))) collapsed.
% Rule
% [388]
% quotient(j(quotient(j(eta(A)),t(eta(A),quotient(j(quotient(j(B),A)),t(
% quotient(
% j(B),A),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))),
% t(quotient(j(eta(A)),t(eta(A),quotient(j(quotient(j(B),A)),t(quotient(j(B),A),
% j(eta(quotient(
% i(B),
% i(A)))))))),
% j(eta(quotient(j(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(eta(
% quotient(
% i(B),
% i(A))))))),
% t(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(eta(quotient(
% i(B),i(A)))))),
% j(eta(quotient(A,t(i(A),i(i(quotient(j(quotient(j(B),A)),t(quotient(
% j(B),A),
% j(eta(
% quotient(
% i(B),
% i(A))))))))))))))))))
% ->
% quotient(j(quotient(j(B),i(i(A)))),t(quotient(j(B),i(i(A))),j(eta(quotient(
% i(B),
% i(i(i(A))))))))
% collapsed.
% Rule
% [445]
% quotient(j(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(j(C),B),
% j(eta(quotient(i(C),i(B))))))),
% eta(A))),t(quotient(j(quotient(j(quotient(j(C),B)),t(quotient(
% j(C),B),
% j(eta(quotient(
% i(C),
% i(B))))))),
% eta(A)),j(eta(quotient(i(quotient(j(quotient(j(C),B)),
% t(quotient(j(C),B),j(eta(
% quotient(
% i(C),
% i(B))))))),
% j(eta(A))))))) <->
% quotient(j(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(
% j(B),eta(A)),
% j(eta(quotient(
% i(B),
% j(eta(A))))))))),
% t(quotient(j(C),quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),eta(A)),
% j(eta(quotient(i(B),
% j(eta(A)))))))),
% j(eta(quotient(i(C),i(quotient(j(quotient(j(B),eta(A))),t(quotient(j(B),
% eta(A)),j(eta(
% quotient(
% i(B),
% j(
% eta(A)))))))))))))
% collapsed.
% Current number of equations to process: 951
% Current number of ordered equations: 569
% Current number of rules: 159
% New rule produced :
% [476]
% quotient(i(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(eta(quotient(
% i(B),
% i(A))))))),
% i(quotient(j(quotient(quotient(j(C),B),A)),t(quotient(quotient(j(C),B),A),
% j(eta(quotient(i(quotient(
% j(quotient(
% j(C),B)),
% t(quotient(
% j(C),B),
% j(eta(quotient(
% i(C),
% i(B))))))),
% i(A)))))))) <->
% quotient(j(A),t(A,i(quotient(j(B),t(B,i(quotient(j(quotient(quotient(j(B),A),C)),
% t(quotient(quotient(j(B),A),C),
% j(eta(quotient(i(quotient(j(quotient(
% j(B),A)),
% t(quotient(j(B),A),
% j(eta(quotient(
% i(B),i(A))))))),
% i(C))))))))))))
% Current number of equations to process: 764
% Current number of ordered equations: 751
% Current number of rules: 160
% New rule produced :
% [477]
% quotient(j(A),t(A,i(quotient(j(B),t(B,i(quotient(j(quotient(quotient(j(B),A),C)),
% t(quotient(quotient(j(B),A),C),
% j(eta(quotient(i(quotient(j(quotient(
% j(B),A)),
% t(quotient(j(B),A),
% j(eta(quotient(
% i(B),i(A))))))),
% i(C)))))))))))) <->
% quotient(i(quotient(j(quotient(j(B),A)),t(quotient(j(B),A),j(eta(quotient(
% i(B),
% i(A))))))),
% i(quotient(j(quotient(quotient(j(C),B),A)),t(quotient(quotient(j(C),B),A),
% j(eta(quotient(i(quotient(
% j(quotient(
% j(C),B)),
% t(quotient(
% j(C),B),
% j(eta(quotient(
% i(C),
% i(B))))))),
% i(A))))))))
% Current number of equations to process: 764
% Current number of ordered equations: 750
% Current number of rules: 161
% New rule produced :
% [478]
% quotient(j(quotient(j(eta(A)),t(eta(A),quotient(j(quotient(j(B),A)),t(
% quotient(
% j(B),A),
% j(
% eta(
% quotient(
% i(B),
% i(A))))))))),
% t(quotient(j(eta(A)),t(eta(A),quotient(j(quotient(j(B),A)),t(quotient(j(B),A),
% j(eta(quotient(
% i(B),
% i(A)))))))),
% j(eta(quotient(quotient(j(B),A),t(quotient(j(quotient(j(B),A)),t(quotient(
% j(B),A),
% j(eta(
% quotient(
% i(B),
% i(A)))))),
% j(eta(quotient(A,t(i(A),i(i(quotient(
% j(quotient(
% j(B),A)),
% t(quotient(
% j(B),A),
% j(eta(quotient(
% i(B),
% i(A))))))))))))))))))
% ->
% quotient(j(quotient(j(B),i(i(A)))),t(quotient(j(B),i(i(A))),j(eta(quotient(
% i(B),
% i(i(i(A))))))))
% Current number of equations to process: 764
% Current number of ordered equations: 749
% Current number of rules: 162
% New rule produced :
% [479]
% t(eta(A),quotient(j(quotient(j(B),j(eta(A)))),t(quotient(j(B),j(eta(A))),
% j(eta(quotient(i(B),eta(A)))))))
% <->
% quotient(j(quotient(eta(A),t(j(eta(A)),t(eta(A),B)))),t(quotient(eta(A),
% t(j(eta(A)),t(
% eta(A),B))),
% j(eta(t(eta(A),
% quotient(
% j(eta(A)),
% i(i(t(eta(A),B)))))))))
% Current number of equations to process: 764
% Current number of ordered equations: 745
% Current number of rules: 163
% New rule produced :
% [480]
% quotient(j(quotient(eta(A),t(j(eta(A)),t(eta(A),B)))),t(quotient(eta(A),
% t(j(eta(A)),t(
% eta(A),B))),
% j(eta(t(eta(A),
% quotient(
% j(eta(A)),
% i(i(t(eta(A),B)))))))))
% <->
% t(eta(A),quotient(j(quotient(j(B),j(eta(A)))),t(quotient(j(B),j(eta(A))),
% j(eta(quotient(i(B),eta(A)))))))
% Current number of equations to process: 764
% Current number of ordered equations: 741
% Current number of rules: 164
% New rule produced :
% [481]
% quotient(j(quotient(eta(A),t(eta(A),B))),t(quotient(eta(A),t(eta(A),B)),
% j(eta(quotient(eta(A),i(t(eta(A),B)))))))
% ->
% t(eta(A),quotient(j(quotient(eta(A),B)),t(quotient(eta(A),B),j(eta(quotient(
% eta(A),
% i(B)))))))
% Current number of equations to process: 764
% Current number of ordered equations: 736
% Current number of rules: 165
% New rule produced :
% [482]
% quotient(eta(quotient(quotient(i(A),i(i(B))),t(i(quotient(i(A),i(i(B)))),
% i(i(quotient(j(quotient(j(A),B)),
% t(quotient(j(A),B),j(
% eta(
% quotient(
% i(A),
% i(B))))))))))),
% quotient(j(quotient(i(A),i(i(B)))),t(quotient(i(A),i(i(B))),quotient(
% j(quotient(
% j(A),B)),
% t(quotient(
% j(A),B),
% j(eta(quotient(
% i(A),
% i(B)))))))))
% ->
% eta(quotient(j(quotient(j(A),B)),t(quotient(j(A),B),j(eta(quotient(i(A),i(B)))))))
% Current number of equations to process: 764
% Current number of ordered equations: 735
% Current number of rules: 166
% New rule produced :
% [483]
% quotient(j(B),t(B,j(eta(quotient(j(quotient(j(B),j(j(A)))),t(quotient(
% j(B),j(j(A))),
% j(eta(quotient(A,
% t(i(A),
% i(quotient(
% i(B),
% eta(A)))))))))))))
% -> quotient(j(B),t(B,j(eta(quotient(A,t(i(A),i(quotient(i(B),eta(A)))))))))
% Current number of equations to process: 764
% Current number of ordered equations: 734
% Current number of rules: 167
% Rule [482]
% quotient(eta(quotient(quotient(i(A),i(i(B))),t(i(quotient(i(A),i(i(B)))),
% i(i(quotient(j(quotient(
% j(A),B)),
% t(quotient(j(A),B),
% j(eta(quotient(
% i(A),i(B))))))))))),
% quotient(j(quotient(i(A),i(i(B)))),t(quotient(i(A),i(i(B))),quotient(
% j(quotient(
% j(A),B)),
% t(quotient(
% j(A),B),
% j(eta(
% quotient(
% i(A),
% i(B)))))))))
% ->
% eta(quotient(j(quotient(j(A),B)),t(quotient(j(A),B),j(eta(quotient(
% i(A),i(B))))))) is composed into 
% [482]
% quotient(eta(quotient(quotient(i(A),i(i(B))),t(i(quotient(i(A),i(i(B)))),
% i(i(quotient(j(quotient(j(A),B)),
% t(quotient(j(A),B),j(
% eta(
% quotient(
% i(A),
% i(B))))))))))),
% quotient(j(quotient(i(A),i(i(B)))),t(quotient(i(A),i(i(B))),quotient(
% j(quotient(
% j(A),B)),
% t(quotient(
% j(A),B),
% j(eta(quotient(
% i(A),
% i(B)))))))))
% -> eta(quotient(i(A),i(B)))
% New rule produced :
% [484]
% eta(quotient(j(quotient(j(A),B)),t(quotient(j(A),B),j(eta(quotient(i(A),i(B)))))))
% -> eta(quotient(i(A),i(B)))
% Rule
% [440]
% quotient(j(B),t(B,j(eta(quotient(j(quotient(j(B),i(i(A)))),t(quotient(
% j(B),i(i(A))),
% j(eta(quotient(
% i(B),
% i(i(i(A))Cputime limit exceeded (core dumped)
% 
% EOF
%------------------------------------------------------------------------------