TSTP Solution File: COL006-6 by CiME---2.01
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- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL006-6 : TPTP v6.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n155.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 00:19:38 EDT 2014
% Result : Timeout 300.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL006-6 : TPTP v6.0.0. Released v2.1.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n155.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 : Thu Jun 5 16:54:28 CDT 2014
% % CPUTime : 300.02
% Processing problem /tmp/CiME_18051_n155.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " fixed_pt,strong_fixed_point,k,s : constant; apply : 2;";
% let X = vars "X Y Z";
% let Axioms = equations F X "
% apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z));
% apply(apply(k,X),Y) = X;
% strong_fixed_point = apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))));
% ";
%
% let s1 = status F "
% fixed_pt lr_lex;
% strong_fixed_point lr_lex;
% k lr_lex;
% apply lr_lex;
% s lr_lex;
% ";
%
% let p1 = precedence F "
% apply > s > k > strong_fixed_point > fixed_pt";
%
% let s2 = status F "
% fixed_pt mul;
% strong_fixed_point mul;
% k mul;
% apply mul;
% s mul;
% ";
%
% let p2 = precedence F "
% apply > s = k = strong_fixed_point = fixed_pt";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt));"
% ;
% (*
% 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 = { apply(apply(apply(s,X),Y),Z) =
% apply(apply(X,Z),apply(Y,Z)),
% apply(apply(k,X),Y) = X,
% strong_fixed_point =
% apply(apply(s,apply(k,apply(apply(s,apply(
% apply(s,k),k)),
% apply(apply(s,k),k)))),
% apply(apply(s,apply(apply(s,apply(k,s)),k)),
% apply(k,apply(apply(s,apply(apply(s,k),k)),
% apply(apply(s,k),k))))) }
% (3 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [fixed_pt] = 1;
% [strong_fixed_point] = 2;
% [k] = 3;
% [s] = 4;
% [apply](x1,x2) = 1 + x1 + x2;
% Chosen ordering : RPO
% o_auto : F term_ordering = <term ordering>
% o : F term_ordering = <term ordering>
% Conjectures : (F,X) equations = { apply(strong_fixed_point,fixed_pt) =
% apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] apply(apply(k,X),Y) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 1
% New rule produced :
% [2] apply(apply(X,Z),apply(Y,Z)) <-> apply(apply(apply(s,X),Y),Z)
% Current number of equations to process: 2
% Current number of ordered equations: 1
% Current number of rules: 2
% New rule produced :
% [3] apply(apply(apply(s,X),Y),Z) <-> apply(apply(X,Z),apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 3
% New rule produced :
% [4]
% strong_fixed_point <->
% apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,
% apply(apply(s,
% apply(
% apply(s,k),k)),
% apply(apply(s,k),k))))
% Current number of equations to process: 0
% Current number of ordered equations: 16
% Current number of rules: 4
% New rule produced :
% [5]
% apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,
% apply(apply(s,
% apply(
% apply(s,k),k)),
% apply(apply(s,k),k))))
% <-> strong_fixed_point
% Current number of equations to process: 0
% Current number of ordered equations: 15
% Current number of rules: 5
% New rule produced : [6] apply(apply(apply(s,k),Y),X) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 14
% Current number of rules: 6
% Rule [4]
% strong_fixed_point <->
% apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,
% apply(
% apply(s,
% apply(
% apply(s,k),k)),
% apply(
% apply(s,k),k)))) is composed into
% [4]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),apply(
% apply(s,
% apply(k,s)),
% apply(s,
% apply(k,s)))),k),
% apply(apply(apply(s,apply(k,k)),apply(apply(apply(s,apply(k,s)),apply(s,k)),k)),
% apply(apply(s,k),k)))
% New rule produced :
% [7] apply(X,apply(Y,Z)) <-> apply(apply(apply(s,apply(k,X)),Y),Z)
% Rule
% [5]
% apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,
% apply(apply(s,
% apply(
% apply(s,k),k)),
% apply(apply(s,k),k))))
% <-> strong_fixed_point collapsed.
% Current number of equations to process: 1
% Current number of ordered equations: 13
% Current number of rules: 6
% New rule produced :
% [8]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),apply(
% apply(
% apply(s,
% apply(s,s)),k),s)),k),
% apply(apply(apply(s,apply(k,k)),apply(apply(apply(s,apply(k,s)),apply(s,k)),k)),
% apply(apply(s,k),k)))
% Current number of equations to process: 0
% Current number of ordered equations: 42
% Current number of rules: 7
% New rule produced :
% [9]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),apply(
% apply(
% apply(s,
% apply(s,s)),k),s)),k),
% apply(apply(apply(s,apply(k,k)),apply(apply(apply(s,apply(k,s)),apply(s,k)),k)),
% apply(apply(s,k),k))) <-> strong_fixed_point
% Current number of equations to process: 0
% Current number of ordered equations: 41
% Current number of rules: 8
% New rule produced : [10] apply(apply(apply(apply(s,s),X),k),Y) -> Y
% Current number of equations to process: 0
% Current number of ordered equations: 40
% Current number of rules: 9
% New rule produced : [11] apply(apply(apply(s,apply(s,k)),X),Y) -> apply(X,Y)
% Current number of equations to process: 0
% Current number of ordered equations: 39
% Current number of rules: 10
% New rule produced :
% [12] apply(apply(apply(s,apply(k,X)),Y),Z) <-> apply(X,apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 38
% Current number of rules: 11
% New rule produced :
% [13] apply(apply(apply(s,X),apply(k,Z)),Y) <-> apply(apply(X,Y),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 37
% Current number of rules: 12
% New rule produced :
% [14] apply(apply(X,Y),Z) <-> apply(apply(apply(s,X),apply(k,Z)),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 36
% Current number of rules: 13
% New rule produced :
% [15] apply(apply(apply(s,apply(k,X)),apply(k,Y)),Z) -> apply(X,Y)
% Current number of equations to process: 0
% Current number of ordered equations: 35
% Current number of rules: 14
% New rule produced :
% [16] apply(apply(apply(apply(s,apply(k,k)),X),Y),Z) -> apply(X,Y)
% Current number of equations to process: 0
% Current number of ordered equations: 34
% Current number of rules: 15
% New rule produced :
% [17] apply(apply(X,Y),Y) <-> apply(apply(apply(s,X),apply(apply(s,k),Z)),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 33
% Current number of rules: 16
% New rule produced :
% [18] apply(apply(apply(s,X),apply(apply(s,k),Z)),Y) <-> apply(apply(X,Y),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 32
% Current number of rules: 17
% New rule produced :
% [19] apply(apply(apply(s,apply(k,X)),apply(apply(s,k),Z)),Y) -> apply(X,Y)
% Current number of equations to process: 0
% Current number of ordered equations: 31
% Current number of rules: 18
% Rule [4]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),
% apply(apply(s,apply(k,s)),apply(s,apply(k,s)))),k),apply(
% apply(
% apply(s,
% apply(k,k)),
% apply(
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k)),k)),
% apply(
% apply(s,k),k))) is composed into
% [4]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),apply(
% apply(
% apply(s,
% apply(s,s)),k),s)),k),
% apply(apply(apply(s,apply(k,k)),apply(apply(apply(s,apply(k,s)),apply(s,k)),k)),
% apply(apply(s,k),k)))
% New rule produced :
% [20]
% apply(apply(X,apply(Y,Z)),apply(Z,apply(Y,Z))) <->
% apply(apply(apply(s,apply(s,X)),Y),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 30
% Current number of rules: 19
% New rule produced :
% [21]
% apply(apply(apply(s,apply(s,X)),Y),Z) <->
% apply(apply(X,apply(Y,Z)),apply(Z,apply(Y,Z)))
% Current number of equations to process: 0
% Current number of ordered equations: 29
% Current number of rules: 20
% New rule produced :
% [22] apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(k,X)),Y),Z) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 28
% Current number of rules: 21
% New rule produced :
% [23]
% apply(apply(X,Y),apply(apply(Z,Y),apply(V_3,Y))) <->
% apply(apply(apply(s,X),apply(apply(s,Z),V_3)),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 27
% Current number of rules: 22
% New rule produced :
% [24]
% apply(apply(apply(s,apply(apply(s,X),Z)),V_3),Y) <->
% apply(apply(apply(X,Y),apply(Z,Y)),apply(V_3,Y))
% Current number of equations to process: 0
% Current number of ordered equations: 26
% Current number of rules: 23
% New rule produced :
% [25]
% apply(apply(apply(X,Y),apply(Z,Y)),apply(V_3,Y)) <->
% apply(apply(apply(s,apply(apply(s,X),Z)),V_3),Y)
% Current number of equations to process: 0
% Current number of ordered equations: 25
% Current number of rules: 24
% New rule produced :
% [26]
% apply(apply(apply(s,X),apply(apply(s,Z),V_3)),Y) <->
% apply(apply(X,Y),apply(apply(Z,Y),apply(V_3,Y)))
% Current number of equations to process: 0
% Current number of ordered equations: 24
% Current number of rules: 25
% New rule produced :
% [27]
% apply(X,apply(apply(apply(s,apply(k,Y)),Z),V_3)) <->
% apply(apply(apply(s,apply(k,X)),Y),apply(Z,V_3))
% Current number of equations to process: 0
% Current number of ordered equations: 23
% Current number of rules: 26
% New rule produced :
% [28]
% apply(apply(apply(s,apply(k,X)),Y),apply(Z,V_3)) <->
% apply(X,apply(apply(apply(s,apply(k,Y)),Z),V_3))
% Current number of equations to process: 0
% Current number of ordered equations: 22
% Current number of rules: 27
% New rule produced :
% [29]
% apply(X,apply(Y,X)) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,k)),Z),Y),X)
% Current number of equations to process: 0
% Current number of ordered equations: 21
% Current number of rules: 28
% New rule produced :
% [30]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,k)),Z),Y),X) <->
% apply(X,apply(Y,X))
% Current number of equations to process: 0
% Current number of ordered equations: 20
% Current number of rules: 29
% New rule produced :
% [31]
% apply(X,apply(apply(apply(s,Y),Z),V_3)) <->
% apply(apply(apply(s,apply(k,X)),apply(Y,V_3)),apply(Z,V_3))
% Current number of equations to process: 0
% Current number of ordered equations: 19
% Current number of rules: 30
% New rule produced :
% [32]
% apply(apply(apply(s,apply(k,X)),apply(Y,V_3)),apply(Z,V_3)) <->
% apply(X,apply(apply(apply(s,Y),Z),V_3))
% Current number of equations to process: 0
% Current number of ordered equations: 18
% Current number of rules: 31
% New rule produced :
% [33]
% apply(X,apply(apply(Y,Z),apply(V_3,Z))) <->
% apply(apply(apply(s,apply(k,X)),apply(apply(s,Y),V_3)),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 17
% Current number of rules: 32
% New rule produced :
% [34]
% apply(apply(apply(s,apply(k,X)),apply(apply(s,Y),V_3)),Z) <->
% apply(X,apply(apply(Y,Z),apply(V_3,Z)))
% Current number of equations to process: 0
% Current number of ordered equations: 16
% Current number of rules: 33
% New rule produced :
% [35]
% apply(apply(apply(X,Y),V_3),apply(Z,V_3)) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),X),Y),Z),V_3)
% Current number of equations to process: 0
% Current number of ordered equations: 15
% Current number of rules: 34
% New rule produced :
% [36]
% apply(apply(apply(apply(apply(s,apply(k,s)),X),Y),Z),V_3) <->
% apply(apply(apply(X,Y),V_3),apply(Z,V_3))
% Current number of equations to process: 0
% Current number of ordered equations: 14
% Current number of rules: 35
% New rule produced :
% [37]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,k)),X),Y),Z) ->
% Z
% Current number of equations to process: 0
% Current number of ordered equations: 13
% Current number of rules: 36
% New rule produced :
% [38]
% apply(apply(apply(apply(s,X),Y),Z),apply(V_3,apply(Y,Z))) <->
% apply(apply(apply(s,apply(X,Z)),V_3),apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 12
% Current number of rules: 37
% New rule produced :
% [39]
% apply(apply(apply(s,apply(X,Z)),V_3),apply(Y,Z)) <->
% apply(apply(apply(apply(s,X),Y),Z),apply(V_3,apply(Y,Z)))
% Current number of equations to process: 0
% Current number of ordered equations: 11
% Current number of rules: 38
% New rule produced :
% [40]
% apply(apply(apply(s,X),apply(V_3,Z)),apply(Y,Z)) <->
% apply(apply(X,apply(Y,Z)),apply(apply(apply(s,V_3),Y),Z))
% Current number of equations to process: 0
% Current number of ordered equations: 10
% Current number of rules: 39
% New rule produced :
% [41]
% apply(apply(X,apply(Y,Z)),apply(apply(apply(s,V_3),Y),Z)) <->
% apply(apply(apply(s,X),apply(V_3,Z)),apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 9
% Current number of rules: 40
% New rule produced :
% [42]
% apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(X,Z)),Y),Z) ->
% apply(apply(apply(s,X),Y),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 8
% Current number of rules: 41
% New rule produced :
% [43]
% apply(apply(X,apply(Y,Z)),apply(apply(apply(s,apply(k,V_3)),Y),Z)) <->
% apply(apply(apply(s,X),V_3),apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 7
% Current number of rules: 42
% New rule produced :
% [44]
% apply(apply(apply(apply(s,apply(k,X)),Y),Z),apply(V_3,apply(Y,Z))) ->
% apply(apply(apply(s,X),V_3),apply(Y,Z))
% Current number of equations to process: 0
% Current number of ordered equations: 6
% Current number of rules: 43
% New rule produced :
% [45]
% apply(apply(apply(s,X),V_3),apply(Y,Z)) <->
% apply(apply(X,apply(Y,Z)),apply(apply(apply(s,apply(k,V_3)),Y),Z))
% Current number of equations to process: 0
% Current number of ordered equations: 5
% Current number of rules: 44
% New rule produced :
% [46]
% apply(apply(X,V_3),apply(apply(Y,Z),V_3)) <->
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),Y),Z),V_3)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 45
% New rule produced :
% [47]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),Y),Z),V_3)
% <-> apply(apply(X,V_3),apply(apply(Y,Z),V_3))
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 46
% New rule produced :
% [48]
% apply(apply(X,apply(Y,Z)),apply(V_3,apply(Y,Z))) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,X),V_3)),Y),Z)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 47
% New rule produced :
% [49]
% apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,X),V_3)),Y),Z)
% <-> apply(apply(X,apply(Y,Z)),apply(V_3,apply(Y,Z)))
% Current number of equations to process: 0
% Current number of ordered equations: 1
% Current number of rules: 48
% New rule produced :
% [50]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(apply(s,apply(k,k)),
% apply(s,k))),Z),X),Y) ->
% apply(X,Y)
% Current number of equations to process: 0
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced : [51] apply(apply(apply(apply(apply(s,s),X),s),k),Y) -> Y
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [52]
% apply(apply(X,Y),Y) <->
% apply(apply(apply(s,X),apply(apply(apply(s,s),Z),k)),Y)
% Current number of equations to process: 12
% Current number of ordered equations: 1
% Current number of rules: 51
% New rule produced :
% [53]
% apply(apply(apply(s,X),apply(apply(apply(s,s),Z),k)),Y) <->
% apply(apply(X,Y),Y)
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [54]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,s)),X),Y),k) ->
% apply(Y,k)
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [55]
% apply(apply(apply(s,apply(k,X)),apply(apply(apply(s,s),Z),k)),Y) ->
% apply(X,Y)
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 54
% New rule produced :
% [56]
% apply(X,apply(Y,X)) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(apply(s,s),Z)),k),Y),X)
% Current number of equations to process: 9
% Current number of ordered equations: 1
% Current number of rules: 55
% New rule produced :
% [57]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(apply(s,s),Z)),k),Y),X) <->
% apply(X,apply(Y,X))
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [58]
% apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),X),Y),k),Z)
% -> Z
% Current number of equations to process: 8
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [59]
% apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,s)),
% apply(apply(s,s),X)),k),Y),Z) -> apply(Y,Z)
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [60]
% apply(apply(apply(apply(s,s),X),apply(s,k)),Y) ->
% apply(apply(X,apply(s,k)),Y)
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [61]
% apply(apply(X,Y),apply(Z,Y)) <->
% apply(apply(apply(s,X),apply(apply(s,apply(s,k)),Z)),Y)
% Current number of equations to process: 12
% Current number of ordered equations: 1
% Current number of rules: 60
% New rule produced :
% [62]
% apply(apply(apply(s,X),apply(apply(s,apply(s,k)),Z)),Y) <->
% apply(apply(X,Y),apply(Z,Y))
% Current number of equations to process: 12
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [63]
% apply(Y,apply(X,Y)) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,k)),X),Y)
% Current number of equations to process: 11
% Current number of ordered equations: 1
% Current number of rules: 62
% New rule produced :
% [64]
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,k)),X),Y) <->
% apply(Y,apply(X,Y))
% Current number of equations to process: 11
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [65]
% apply(X,apply(Y,Z)) <->
% apply(apply(apply(s,apply(k,X)),apply(apply(s,apply(s,k)),Y)),Z)
% Current number of equations to process: 10
% Current number of ordered equations: 1
% Current number of rules: 64
% New rule produced :
% [66]
% apply(apply(apply(s,apply(k,X)),apply(apply(s,apply(s,k)),Y)),Z) <->
% apply(X,apply(Y,Z))
% Current number of equations to process: 10
% Current number of ordered equations: 0
% Current number of rules: 65
% New rule produced :
% [67]
% apply(apply(X,Y),apply(Z,Y)) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,apply(s,k))),X),Z),Y)
% Current number of equations to process: 9
% Current number of ordered equations: 1
% Current number of rules: 66
% New rule produced :
% [68]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,apply(s,k))),X),Z),Y) <->
% apply(apply(X,Y),apply(Z,Y))
% Current number of equations to process: 9
% Current number of ordered equations: 0
% Current number of rules: 67
% New rule produced :
% [69]
% apply(X,apply(Y,Z)) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,apply(s,k)),X)),Y),Z)
% Current number of equations to process: 7
% Current number of ordered equations: 2
% Current number of rules: 68
% New rule produced :
% [70]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,apply(s,k))),X),Y),Z)
% -> apply(apply(X,Y),Z)
% Current number of equations to process: 7
% Current number of ordered equations: 1
% Current number of rules: 69
% New rule produced :
% [71]
% apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,apply(s,k)),X)),Y),Z)
% <-> apply(X,apply(Y,Z))
% Current number of equations to process: 7
% Current number of ordered equations: 0
% Current number of rules: 70
% Rule [8]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),
% apply(apply(apply(s,apply(s,s)),k),s)),k),apply(apply(
% apply(s,
% apply(k,k)),
% apply(
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k)),k)),
% apply(apply(s,k),k))) is composed into
% [8]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(apply(s,apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),apply(
% apply(s,
% apply(k,s)),k)),
% apply(apply(apply(s,apply(k,s)),k),apply(s,s))),
% apply(apply(apply(s,apply(s,s)),k),s)),k),apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k))
% Rule [4]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),
% apply(apply(apply(s,apply(s,s)),k),s)),k),apply(apply(
% apply(s,
% apply(k,k)),
% apply(
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k)),k)),
% apply(apply(s,k),k))) is composed into
% [4]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(apply(s,apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),apply(
% apply(s,
% apply(k,s)),k)),
% apply(apply(apply(s,apply(k,s)),k),apply(s,s))),
% apply(apply(apply(s,apply(s,s)),k),s)),k),apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k))
% New rule produced :
% [72]
% apply(X,apply(Y,Z)) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),k),X),Y),Z)
% Rule
% [9]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),apply(
% apply(
% apply(s,
% apply(s,s)),k),s)),k),
% apply(apply(apply(s,apply(k,k)),apply(apply(apply(s,apply(k,s)),apply(s,k)),k)),
% apply(apply(s,k),k))) <-> strong_fixed_point collapsed.
% Rule
% [50]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(apply(s,apply(k,k)),
% apply(s,k))),Z),X),Y) ->
% apply(X,Y) collapsed.
% Current number of equations to process: 16
% Current number of ordered equations: 1
% Current number of rules: 69
% New rule produced :
% [73]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(s,
% apply(s,s)),k),s),s),s),
% apply(k,s)),k),apply(
% apply(s,
% apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s))),
% apply(apply(apply(s,apply(s,s)),k),s)),k),apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k))
% Current number of equations to process: 62
% Current number of ordered equations: 11038
% Current number of rules: 70
% New rule produced :
% [74]
% apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(s,
% apply(s,s)),k),s),s),s),
% apply(k,s)),k),apply(
% apply(s,
% apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s))),
% apply(apply(apply(s,apply(s,s)),k),s)),k),apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k)) <-> strong_fixed_point
% Current number of equations to process: 62
% Current number of ordered equations: 11037
% Current number of rules: 71
% Rule [8]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(apply(s,apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s))),
% apply(apply(apply(s,apply(s,s)),k),s)),k),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k)) is composed into [8]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,s),k),
% apply(
% apply(s,
% apply(k,s)),k)),
% apply(
% apply(s,
% apply(k,s)),k)),
% apply(
% apply(s,
% apply(k,s)),k)),
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s))),
% apply(apply(
% apply(s,
% apply(s,s)),k),s)),k),
% apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k))
% Rule [4]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(apply(s,apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s))),
% apply(apply(apply(s,apply(s,s)),k),s)),k),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k)) is composed into [4]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,s),k),
% apply(
% apply(s,
% apply(k,s)),k)),
% apply(
% apply(s,
% apply(k,s)),k)),
% apply(
% apply(s,
% apply(k,s)),k)),
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s))),
% apply(apply(
% apply(s,
% apply(s,s)),k),s)),k),
% apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k))
% New rule produced :
% [75] apply(apply(X,Y),X) <-> apply(apply(apply(apply(s,s),k),X),Y)
% Current number of equations to process: 2319
% Current number of ordered equations: 8779
% Current number of rules: 72
% New rule produced :
% [76] apply(apply(apply(apply(s,s),k),X),Y) <-> apply(apply(X,Y),X)
% Current number of equations to process: 2319
% Current number of ordered equations: 8775
% Current number of rules: 73
% New rule produced :
% [77] apply(apply(apply(apply(s,apply(s,s)),s),k),X) -> apply(s,k)
% Current number of equations to process: 2319
% Current number of ordered equations: 8774
% Current number of rules: 74
% New rule produced :
% [78] apply(apply(apply(apply(s,apply(s,s)),apply(k,k)),X),Y) -> Y
% Current number of equations to process: 2319
% Current number of ordered equations: 8773
% Current number of rules: 75
% New rule produced :
% [79] apply(X,apply(k,X)) <-> apply(apply(apply(apply(s,s),k),apply(k,X)),Y)
% Current number of equations to process: 2319
% Current number of ordered equations: 8772
% Current number of rules: 76
% New rule produced :
% [80] apply(apply(apply(apply(s,s),k),apply(k,X)),Y) <-> apply(X,apply(k,X))
% Current number of equations to process: 2319
% Current number of ordered equations: 8771
% Current number of rules: 77
% Rule [8]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,s),k),
% apply(apply(s,apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s))),
% apply(apply(apply(s,apply(s,s)),k),s)),k),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k)) is composed into [8]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,s),
% apply(s,k)),
% apply(
% apply(s,s),k)),
% apply(
% apply(s,
% apply(k,s)),k)),
% apply(
% apply(s,
% apply(k,s)),k)),
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s))),
% apply(apply(
% apply(s,
% apply(s,s)),k),s)),k),
% apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k))
% Rule [4]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,s),k),
% apply(apply(s,apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),
% apply(apply(s,apply(k,s)),k)),apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s))),
% apply(apply(apply(s,apply(s,s)),k),s)),k),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k)) is composed into [4]
% strong_fixed_point <->
% apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,s),
% apply(s,k)),
% apply(
% apply(s,s),k)),
% apply(
% apply(s,
% apply(k,s)),k)),
% apply(
% apply(s,
% apply(k,s)),k)),
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s))),
% apply(apply(
% apply(s,
% apply(s,s)),k),s)),k),
% apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(apply(s,
% apply(k,s)),
% apply(s,k))),k)),
% apply(apply(s,k),k))
% New rule produced :
% [81] apply(apply(X,Y),Y) <-> apply(apply(apply(apply(s,s),apply(s,k)),X),Y)
% Current number of equations to process: 2319
% Current number of ordered equations: 8769
% Current number of rules: 78
% New rule produced :
% [82] apply(apply(apply(apply(s,s),apply(s,k)),X),Y) <-> apply(apply(X,Y),Y)
% Current number of equations to process: 2319
% Current number of ordered equations: 8767
% Current number of rules: 79
% New rule produced :
% [83] apply(apply(apply(apply(s,s),X),apply(k,apply(k,Y))),Z) -> Y
% Current number of equations to process: 2319
% Current number of ordered equations: 8766
% Current number of rules: 80
% New rule produced :
% [84] apply(apply(apply(apply(apply(apply(s,s),X),s),s),k),Y) -> Y
% Current number of equations to process: 2319
% Current number of ordered equations: 8764
% Current number of rules: 81
% New rule produced :
% [85]
% apply(apply(Y,Z),apply(X,Z)) <->
% apply(apply(apply(apply(s,s),apply(k,X)),Y),Z)
% Current number of equations to process: 2319
% Current number of ordered equations: 8763
% Current number of rules: 82
% New rule produced :
% [86]
% apply(apply(X,Y),apply(Z,Y)) <->
% apply(apply(apply(s,apply(s,X)),apply(k,Y)),Z)
% Current number of equations to process: 2319
% Current number of ordered equations: 8761
% Current number of rules: 83
% New rule produced :
% [87]
% apply(apply(apply(s,apply(s,X)),apply(k,Y)),Z) <->
% apply(apply(X,Y),apply(Z,Y))
% Current number of equations to process: 2319
% Current number of ordered equations: 8759
% Current number of rules: 84
% New rule produced :
% [88]
% apply(apply(apply(apply(s,s),apply(k,X)),Y),Z) <->
% apply(apply(Y,Z),apply(X,Z))
% Current number of equations to process: 2319
% Current number of ordered equations: 8758
% Current number of rules: 85
% New rule produced :
% [89] apply(apply(apply(apply(s,s),apply(s,k)),apply(k,X)),Y) -> apply(X,Y)
% Current number of equations to process: 2319
% Current number of ordered equations: 8756
% Current number of rules: 86
% New rule produced :
% [90]
% apply(apply(apply(apply(apply(s,apply(k,s)),k),X),Y),Z) <->
% apply(X,apply(Y,Z))
% Current number of equations to process: 2319
% Current number of ordered equations: 8755
% Current number of rules: 87
% New rule produced :
% [91]
% apply(apply(apply(s,apply(s,X)),Y),apply(k,Z)) <->
% apply(apply(X,apply(Y,apply(k,Z))),Z)
% Current number of equations to process: 2319
% Current number of ordered equations: 8753
% Current number of rules: 88
% New rule produced :
% [92]
% apply(apply(X,apply(Y,apply(k,Z))),Z) <->
% apply(apply(apply(s,apply(s,X)),Y),apply(k,Z))
% Current number of equations to process: 2319
% Current number of ordered equations: 8751
% Current number of rules: 89
% New rule produced :
% [93]
% apply(Y,apply(X,Z)) <->
% apply(apply(apply(apply(s,s),apply(k,X)),apply(k,Y)),Z)
% Current number of equations to process: 2319
% Current number of ordered equations: 8750
% Current number of rules: 90
% New rule produced :
% [94]
% apply(apply(apply(apply(s,s),apply(k,X)),apply(k,Y)),Z) <->
% apply(Y,apply(X,Z))
% Current number of equations to process: 2319
% Current number of ordered equations: 8749
% Current number of rules: 91
% New rule produced :
% [95]
% apply(apply(apply(s,apply(s,X)),apply(k,Y)),apply(k,Z)) ->
% apply(apply(X,Y),Z)
% Current number of equations to process: 2319
% Current number of ordered equations: 8748
% Current number of rules: 92
% New rule produced :
% [96] apply(apply(apply(apply(apply(s,s),X),apply(k,apply(s,k))),Y),Z) -> Z
% Current number of equations to process: 2319
% Current number of ordered equations: 8747
% Current number of rules: 93
% New rule produced :
% [97] apply(apply(apply(apply(apply(s,apply(s,s)),apply(k,s)),X),k),Y) -> Y
% Current number of equations to process: 2319
% Current number of ordered equations: 8746
% Current number of rules: 94
% New rule produced :
% [98]
% apply(X,apply(apply(apply(s,Y),apply(k,Z)),V_3)) <->
% apply(apply(apply(s,apply(k,X)),apply(Y,V_3)),Z)
% Current number of equations to process: 2319
% Current number of ordered equations: 8744
% Current number of rules: 95
% New rule produced :
% [99]
% apply(apply(apply(apply(s,apply(k,X)),Y),Z),V_3) <->
% apply(apply(apply(s,X),apply(k,V_3)),apply(Y,Z))
% Current number of equations to process: 2319
% Current number of ordered equations: 8742
% Current number of rules: 96
% New rule produced :
% [100]
% apply(apply(apply(s,apply(k,X)),apply(Y,V_3)),Z) <->
% apply(X,apply(apply(apply(s,Y),apply(k,Z)),V_3))
% Current number of equations to process: 2319
% Current number of ordered equations: 8740
% Current number of rules: 97
% New rule produced :
% [101]
% apply(apply(apply(s,X),apply(k,V_3)),apply(Y,Z)) <->
% apply(apply(apply(apply(s,apply(k,X)),Y),Z),V_3)
% Current number of equations to process: 2319
% Current number of ordered equations: 8738
% Current number of rules: 98
% New rule produced :
% [102]
% apply(apply(apply(apply(s,X),apply(k,Y)),Z),V_3) <->
% apply(apply(apply(s,apply(X,Z)),apply(k,V_3)),Y)
% Current number of equations to process: 2319
% Current number of ordered equations: 8737
% Current number of rules: 99
% New rule produced :
% [103]
% apply(apply(apply(s,apply(X,Z)),apply(k,V_3)),Y) <->
% apply(apply(apply(apply(s,X),apply(k,Y)),Z),V_3)
% Current number of equations to process: 2319
% Current number of ordered equations: 8736
% Current number of rules: 100
% New rule produced :
% [104]
% apply(apply(apply(apply(apply(s,apply(k,s)),k),X),apply(k,Y)),Z) ->
% apply(X,Y)
% Current number of equations to process: 2319
% Current number of ordered equations: 8729
% Current number of rules: 101
% New rule produced :
% [105]
% apply(apply(apply(apply(apply(s,s),X),apply(k,k)),Y),Z) ->
% apply(apply(X,apply(k,k)),Y)
% Current number of equations to process: 2319
% Current number of ordered equations: 8724
% Current number of rules: 102
% New rule produced :
% [106]
% apply(apply(X,Y),apply(Y,Y)) <->
% apply(apply(apply(s,apply(s,X)),apply(apply(s,k),Z)),Y)
% Current number of equations to process: 2319
% Current number of ordered equations: 8722
% Current number of rules: 103
% New rule produced :
% [107]
% apply(apply(apply(s,apply(s,X)),apply(apply(s,k),Z)),Y) <->
% apply(apply(X,Y),apply(Y,Y))
% Current number of equations to process: 2319
% Current number of ordered equations: 8720
% Current number of rules: 104
% Rule [65]
% apply(X,apply(Y,Z)) <->
% apply(apply(apply(s,apply(k,X)),apply(apply(s,apply(s,k)),Y)),Z) is composed into
% [65] apply(X,apply(Y,Z)) <-> apply(apply(apply(s,apply(k,X)),Y),Z)
% Rule [61]
% apply(apply(X,Y),apply(Z,Y)) <->
% apply(apply(apply(s,X),apply(apply(s,apply(s,k)),Z)),Y) is composed into
% [61] apply(apply(X,Y),apply(Z,Y)) <-> apply(apply(apply(s,X),Z),Y)
% New rule produced :
% [108]
% apply(apply(apply(s,X),apply(apply(s,apply(s,k)),Y)),Z) ->
% apply(apply(apply(s,X),Y),Z)
% Rule
% [62]
% apply(apply(apply(s,X),apply(apply(s,apply(s,k)),Z)),Y) <->
% apply(apply(X,Y),apply(Z,Y)) collapsed.
% Rule
% [66]
% apply(apply(apply(s,apply(k,X)),apply(apply(s,apply(s,k)),Y)),Z) <->
% apply(X,apply(Y,Z)) collapsed.
% Current number of equations to process: 2652
% Current number of ordered equations: 7931
% Current number of rules: 103
% New rule produced :
% [109]
% apply(apply(X,Y),apply(Z,apply(V_3,Y))) <->
% apply(apply(apply(s,X),apply(apply(s,apply(k,Z)),V_3)),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7929
% Current number of rules: 104
% New rule produced :
% [110]
% apply(apply(apply(s,X),apply(apply(s,apply(k,Z)),V_3)),Y) <->
% apply(apply(X,Y),apply(Z,apply(V_3,Y)))
% Current number of equations to process: 2652
% Current number of ordered equations: 7927
% Current number of rules: 105
% New rule produced :
% [111]
% apply(apply(X,Y),apply(apply(Z,Y),V_3)) <->
% apply(apply(apply(s,X),apply(apply(s,Z),apply(k,V_3))),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7925
% Current number of rules: 106
% New rule produced :
% [112]
% apply(apply(apply(s,X),apply(apply(s,Z),apply(k,V_3))),Y) <->
% apply(apply(X,Y),apply(apply(Z,Y),V_3))
% Current number of equations to process: 2652
% Current number of ordered equations: 7923
% Current number of rules: 107
% New rule produced :
% [113]
% apply(apply(apply(apply(s,X),Y),Z),V_3) <->
% apply(apply(apply(s,apply(X,Z)),apply(k,V_3)),apply(Y,Z))
% Current number of equations to process: 2652
% Current number of ordered equations: 7921
% Current number of rules: 108
% New rule produced :
% [114]
% apply(apply(apply(s,apply(X,Z)),V_3),Y) <->
% apply(apply(apply(apply(s,X),apply(k,Y)),Z),apply(V_3,Y))
% Current number of equations to process: 2652
% Current number of ordered equations: 7918
% Current number of rules: 109
% New rule produced :
% [115]
% apply(apply(X,Y),apply(apply(apply(s,Z),apply(k,Y)),V_3)) <->
% apply(apply(apply(s,X),apply(Z,V_3)),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7915
% Current number of rules: 110
% New rule produced :
% [116]
% apply(apply(apply(apply(s,X),apply(k,Y)),Z),apply(V_3,Y)) <->
% apply(apply(apply(s,apply(X,Z)),V_3),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7912
% Current number of rules: 111
% New rule produced :
% [117]
% apply(apply(apply(s,apply(X,Z)),apply(k,V_3)),apply(Y,Z)) <->
% apply(apply(apply(apply(s,X),Y),Z),V_3)
% Current number of equations to process: 2652
% Current number of ordered equations: 7910
% Current number of rules: 112
% New rule produced :
% [118]
% apply(apply(apply(s,X),apply(Z,V_3)),Y) <->
% apply(apply(X,Y),apply(apply(apply(s,Z),apply(k,Y)),V_3))
% Current number of equations to process: 2652
% Current number of ordered equations: 7907
% Current number of rules: 113
% New rule produced :
% [119]
% apply(apply(apply(X,Y),apply(Z,Y)),V_3) <->
% apply(apply(apply(s,apply(apply(s,X),Z)),apply(k,V_3)),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7905
% Current number of rules: 114
% New rule produced :
% [120]
% apply(apply(apply(s,apply(apply(s,X),Z)),apply(k,V_3)),Y) <->
% apply(apply(apply(X,Y),apply(Z,Y)),V_3)
% Current number of equations to process: 2652
% Current number of ordered equations: 7903
% Current number of rules: 115
% New rule produced :
% [121]
% apply(apply(apply(s,apply(s,X)),apply(k,Y)),apply(apply(s,k),Z)) ->
% apply(apply(X,Y),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7902
% Current number of rules: 116
% New rule produced :
% [122]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,k)),Y),Z),apply(k,X)) ->
% X
% Current number of equations to process: 2652
% Current number of ordered equations: 7901
% Current number of rules: 117
% New rule produced :
% [123]
% apply(apply(X,Y),Y) <->
% apply(apply(apply(s,X),apply(apply(apply(apply(s,s),Z),s),k)),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7898
% Current number of rules: 118
% New rule produced :
% [124]
% apply(apply(apply(s,X),apply(apply(apply(apply(s,s),Z),s),k)),Y) <->
% apply(apply(X,Y),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7895
% Current number of rules: 119
% New rule produced :
% [125]
% apply(apply(apply(apply(s,s),X),apply(apply(s,s),Y)),k) ->
% apply(apply(X,apply(apply(s,s),Y)),k)
% Current number of equations to process: 2652
% Current number of ordered equations: 7894
% Current number of rules: 120
% New rule produced :
% [126]
% apply(apply(apply(apply(apply(apply(s,s),X),apply(k,apply(s,s))),Y),k),Z) ->
% Z
% Current number of equations to process: 2652
% Current number of ordered equations: 7893
% Current number of rules: 121
% New rule produced :
% [127]
% apply(apply(apply(apply(apply(s,s),X),s),apply(s,k)),Y) ->
% apply(apply(apply(X,s),apply(s,k)),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7890
% Current number of rules: 122
% New rule produced :
% [128]
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,k)),Y),apply(k,X)) ->
% X
% Current number of equations to process: 2652
% Current number of ordered equations: 7889
% Current number of rules: 123
% New rule produced :
% [129]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,apply(s,k))),k),Y),X) ->
% X
% Current number of equations to process: 2652
% Current number of ordered equations: 7888
% Current number of rules: 124
% New rule produced :
% [130]
% apply(X,apply(Z,apply(Y,Z))) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,X)),Y),Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7885
% Current number of rules: 125
% New rule produced :
% [131]
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,X)),Y),Z) <->
% apply(X,apply(Z,apply(Y,Z)))
% Current number of equations to process: 2652
% Current number of ordered equations: 7882
% Current number of rules: 126
% New rule produced :
% [132]
% apply(X,apply(Y,apply(Z,V_3))) <->
% apply(apply(apply(s,apply(k,X)),apply(apply(s,apply(k,Y)),Z)),V_3)
% Current number of equations to process: 2652
% Current number of ordered equations: 7880
% Current number of rules: 127
% New rule produced :
% [133]
% apply(apply(apply(s,apply(k,X)),apply(apply(s,apply(k,Y)),Z)),V_3) <->
% apply(X,apply(Y,apply(Z,V_3)))
% Current number of equations to process: 2652
% Current number of ordered equations: 7878
% Current number of rules: 128
% New rule produced :
% [134]
% apply(X,apply(apply(Y,Z),V_3)) <->
% apply(apply(apply(s,apply(k,X)),apply(apply(s,Y),apply(k,V_3))),Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7876
% Current number of rules: 129
% New rule produced :
% [135]
% apply(apply(X,V_3),apply(Y,Z)) <->
% apply(apply(apply(s,X),apply(apply(apply(s,apply(k,k)),Y),Z)),V_3)
% Current number of equations to process: 2652
% Current number of ordered equations: 7873
% Current number of rules: 130
% New rule produced :
% [136]
% apply(apply(apply(X,Y),V_3),Z) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),X),Y),apply(k,Z)),V_3)
% Current number of equations to process: 2652
% Current number of ordered equations: 7870
% Current number of rules: 131
% New rule produced :
% [137]
% apply(apply(apply(apply(apply(s,apply(k,s)),X),Y),apply(k,Z)),V_3) <->
% apply(apply(apply(X,Y),V_3),Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7850
% Current number of rules: 132
% New rule produced :
% [138]
% apply(apply(apply(s,X),apply(apply(apply(s,apply(k,k)),Y),Z)),V_3) <->
% apply(apply(X,V_3),apply(Y,Z))
% Current number of equations to process: 2652
% Current number of ordered equations: 7839
% Current number of rules: 133
% New rule produced :
% [139]
% apply(apply(apply(s,apply(k,X)),apply(apply(s,Y),apply(k,V_3))),Z) <->
% apply(X,apply(apply(Y,Z),V_3))
% Current number of equations to process: 2652
% Current number of ordered equations: 7837
% Current number of rules: 134
% New rule produced :
% [140]
% apply(X,Y) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,k)),Z),apply(k,Y)),X)
% Current number of equations to process: 2652
% Current number of ordered equations: 7835
% Current number of rules: 135
% New rule produced :
% [141]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,k)),Z),apply(k,Y)),X) <->
% apply(X,Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7833
% Current number of rules: 136
% New rule produced :
% [142]
% apply(X,Y) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,k)),apply(k,Y)),X)
% Current number of equations to process: 2652
% Current number of ordered equations: 7831
% Current number of rules: 137
% New rule produced :
% [143]
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,k)),apply(k,Y)),X) <->
% apply(X,Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7829
% Current number of rules: 138
% New rule produced :
% [144]
% apply(apply(X,Y),apply(Z,V_3)) <->
% apply(apply(apply(s,X),apply(apply(s,apply(k,Z)),apply(k,V_3))),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7828
% Current number of rules: 139
% New rule produced :
% [145]
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,X)),Y),apply(k,Z)) ->
% apply(X,Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7819
% Current number of rules: 140
% New rule produced :
% [146]
% apply(apply(apply(s,X),apply(apply(s,apply(k,Z)),apply(k,V_3))),Y) <->
% apply(apply(X,Y),apply(Z,V_3))
% Current number of equations to process: 2652
% Current number of ordered equations: 7818
% Current number of rules: 141
% New rule produced :
% [147]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,apply(k,k))),X),Y),Z) ->
% apply(X,Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7809
% Current number of rules: 142
% New rule produced :
% [148]
% apply(X,apply(apply(apply(s,Y),apply(apply(s,k),Z)),V_3)) <->
% apply(apply(apply(s,apply(k,X)),apply(Y,V_3)),V_3)
% Current number of equations to process: 2652
% Current number of ordered equations: 7807
% Current number of rules: 143
% New rule produced :
% [149]
% apply(apply(apply(s,apply(k,X)),apply(Y,V_3)),V_3) <->
% apply(X,apply(apply(apply(s,Y),apply(apply(s,k),Z)),V_3))
% Current number of equations to process: 2652
% Current number of ordered equations: 7805
% Current number of rules: 144
% New rule produced :
% [150]
% apply(apply(apply(s,apply(s,X)),apply(apply(s,k),Z)),apply(k,Y)) ->
% apply(apply(X,apply(k,Y)),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7804
% Current number of rules: 145
% New rule produced :
% [151]
% apply(apply(apply(apply(s,X),apply(k,Y)),Z),Y) <->
% apply(apply(apply(s,apply(X,Z)),apply(apply(s,k),V_3)),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7803
% Current number of rules: 146
% New rule produced :
% [152]
% apply(apply(apply(s,apply(X,Z)),apply(apply(s,k),V_3)),Y) <->
% apply(apply(apply(apply(s,X),apply(k,Y)),Z),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7802
% Current number of rules: 147
% New rule produced :
% [153]
% apply(apply(apply(apply(apply(s,apply(k,s)),k),X),apply(apply(s,k),Y)),Z) ->
% apply(X,Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7794
% Current number of rules: 148
% New rule produced :
% [154]
% apply(apply(X,apply(Y,Z)),apply(Z,apply(Y,Z))) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),s),X),Y),Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7791
% Current number of rules: 149
% New rule produced :
% [155]
% apply(apply(apply(apply(apply(s,apply(k,s)),s),X),Y),Z) <->
% apply(apply(X,apply(Y,Z)),apply(Z,apply(Y,Z)))
% Current number of equations to process: 2652
% Current number of ordered equations: 7788
% Current number of rules: 150
% New rule produced :
% [156]
% apply(apply(apply(apply(s,s),apply(k,X)),apply(s,Y)),Z) <->
% apply(apply(Y,apply(X,Z)),apply(Z,apply(X,Z)))
% Current number of equations to process: 2652
% Current number of ordered equations: 7787
% Current number of rules: 151
% New rule produced :
% [157]
% apply(apply(Y,apply(X,Z)),apply(Z,apply(X,Z))) <->
% apply(apply(apply(apply(s,s),apply(k,X)),apply(s,Y)),Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7786
% Current number of rules: 152
% New rule produced :
% [158]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,k)),X),Y),k),Z) ->
% apply(Y,k)
% Current number of equations to process: 2652
% Current number of ordered equations: 7785
% Current number of rules: 153
% New rule produced :
% [159]
% apply(apply(apply(s,apply(k,Y)),apply(X,Z)),Y) <->
% apply(apply(apply(apply(s,s),apply(s,X)),apply(k,Y)),Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7784
% Current number of rules: 154
% New rule produced :
% [160]
% apply(apply(apply(apply(s,s),apply(s,X)),apply(k,Y)),Z) <->
% apply(apply(apply(s,apply(k,Y)),apply(X,Z)),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7783
% Current number of rules: 155
% New rule produced :
% [161]
% apply(apply(X,apply(apply(apply(s,Y),k),Z)),Z) <->
% apply(apply(apply(s,apply(s,X)),apply(Y,Z)),apply(k,Z))
% Current number of equations to process: 2652
% Current number of ordered equations: 7782
% Current number of rules: 156
% New rule produced :
% [162]
% apply(apply(apply(s,apply(s,X)),apply(Y,Z)),apply(k,Z)) <->
% apply(apply(X,apply(apply(apply(s,Y),k),Z)),Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7781
% Current number of rules: 157
% New rule produced :
% [163]
% apply(apply(apply(s,apply(s,X)),Y),apply(k,Z)) <->
% apply(apply(X,apply(apply(apply(s,apply(k,Y)),k),Z)),Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7780
% Current number of rules: 158
% New rule produced :
% [164]
% apply(apply(X,apply(apply(apply(s,apply(k,Y)),k),Z)),Z) <->
% apply(apply(apply(s,apply(s,X)),Y),apply(k,Z))
% Current number of equations to process: 2652
% Current number of ordered equations: 7779
% Current number of rules: 159
% New rule produced :
% [165]
% apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,k),Z)),X),Y) ->
% apply(X,Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7777
% Current number of rules: 160
% New rule produced :
% [166]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(apply(s,s),X)),s),Y),k) ->
% apply(Y,k)
% Current number of equations to process: 2652
% Current number of ordered equations: 7769
% Current number of rules: 161
% New rule produced :
% [167]
% apply(apply(apply(s,apply(k,X)),apply(apply(apply(apply(s,s),Z),s),k)),Y) ->
% apply(X,Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7757
% Current number of rules: 162
% New rule produced :
% [168]
% apply(apply(apply(s,apply(s,X)),apply(apply(apply(s,s),Z),k)),Y) <->
% apply(apply(X,Y),apply(Y,Y))
% Current number of equations to process: 2652
% Current number of ordered equations: 7756
% Current number of rules: 163
% New rule produced :
% [169]
% apply(apply(X,Y),apply(Y,Y)) <->
% apply(apply(apply(s,apply(s,X)),apply(apply(apply(s,s),Z),k)),Y)
% Current number of equations to process: 2652
% Current number of ordered equations: 7755
% Current number of rules: 164
% New rule produced :
% [170]
% apply(apply(apply(s,X),apply(apply(s,k),Y)),Z) <->
% apply(apply(apply(s,X),apply(apply(apply(s,s),V_3),k)),Z)
% Current number of equations to process: 2652
% Current number of ordered equations: 7754
% Current number of rules: 165
% New rule produced :
% [171]
% apply(apply(apply(s,X),apply(apply(apply(s,s),V_3),k)),Z) <->
% apply(apply(apply(s,X),apply(apply(s,k),Y)),Z)
% Current number of equations to process: 2680
% Current number of ordered equations: 7725
% Current number of rules: 166
% New rule produced :
% [172]
% apply(apply(X,apply(s,k)),Y) <->
% apply(apply(apply(apply(s,apply(s,s)),apply(k,apply(s,k))),X),Y)
% Current number of equations to process: 2680
% Current number of ordered equations: 7724
% Current number of rules: 167
% New rule produced :
% [173]
% apply(apply(apply(apply(s,apply(s,s)),apply(k,apply(s,k))),X),Y) <->
% apply(apply(X,apply(s,k)),Y)
% Current number of equations to process: 2680
% Current number of ordered equations: 7723
% Current number of rules: 168
% New rule produced :
% [174]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,k)),X),k),Y) ->
% apply(X,k)
% Current number of equations to process: 2680
% Current number of ordered equations: 7722
% Current number of rules: 169
% New rule produced :
% [175]
% apply(apply(X,Z),Y) <->
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),Y),Z)
% Current number of equations to process: 2680
% Current number of ordered equations: 7719
% Current number of rules: 170
% New rule produced :
% [176]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),Y),Z) <->
% apply(apply(X,Z),Y)
% Current number of equations to process: 2680
% Current number of ordered equations: 7713
% Current number of rules: 171
% New rule produced :
% [177]
% apply(X,apply(Y,Z)) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,X)),apply(k,Z)),Y)
% Current number of equations to process: 2680
% Current number of ordered equations: 7712
% Current number of rules: 172
% New rule produced :
% [178]
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,X)),apply(k,Z)),Y) <->
% apply(X,apply(Y,Z))
% Current number of equations to process: 2680
% Current number of ordered equations: 7711
% Current number of rules: 173
% New rule produced :
% [179]
% apply(apply(apply(s,apply(k,X)),apply(apply(s,apply(k,Y)),apply(k,Z))),V_3)
% -> apply(X,apply(Y,Z))
% Current number of equations to process: 2680
% Current number of ordered equations: 7701
% Current number of rules: 174
% New rule produced :
% [180]
% apply(apply(apply(s,apply(k,X)),apply(apply(apply(s,apply(k,k)),Y),Z)),V_3)
% -> apply(X,apply(Y,Z))
% Current number of equations to process: 2680
% Current number of ordered equations: 7690
% Current number of rules: 175
% New rule produced :
% [181]
% apply(Y,apply(X,Y)) <->
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,k)),X),Y),Z)
% Current number of equations to process: 2680
% Current number of ordered equations: 7688
% Current number of rules: 176
% New rule produced :
% [182]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,k)),X),Y),Z) <->
% apply(Y,apply(X,Y))
% Current number of equations to process: 2680
% Current number of ordered equations: 7686
% Current number of rules: 177
% New rule produced :
% [183]
% apply(apply(apply(s,apply(X,Z)),V_3),Z) <->
% apply(apply(apply(apply(s,X),apply(apply(s,k),Y)),Z),apply(V_3,Z))
% Current number of equations to process: 2680
% Current number of ordered equations: 7683
% Current number of rules: 178
% New rule produced :
% [184]
% apply(apply(X,Y),apply(apply(apply(s,Z),apply(apply(s,k),V_3)),Y)) <->
% apply(apply(apply(s,X),apply(Z,Y)),Y)
% Current number of equations to process: 2680
% Current number of ordered equations: 7680
% Current number of rules: 179
% New rule produced :
% [185]
% apply(apply(apply(apply(s,X),apply(apply(s,k),Y)),Z),apply(V_3,Z)) <->
% apply(apply(apply(s,apply(X,Z)),V_3),Z)
% Current number of equations to process: 2680
% Current number of ordered equations: 7677
% Current number of rules: 180
% New rule produced :
% [186]
% apply(apply(apply(s,X),apply(Z,Y)),Y) <->
% apply(apply(X,Y),apply(apply(apply(s,Z),apply(apply(s,k),V_3)),Y))
% Current number of equations to process: 2680
% Current number of ordered equations: 7674
% Current number of rules: 181
% New rule produced :
% [187]
% apply(apply(apply(X,Y),apply(Z,Y)),Y) <->
% apply(apply(apply(s,apply(apply(s,X),Z)),apply(apply(s,k),V_3)),Y)
% Current number of equations to process: 2680
% Current number of ordered equations: 7672
% Current number of rules: 182
% New rule produced :
% [188]
% apply(apply(apply(s,apply(apply(s,X),Z)),apply(apply(s,k),V_3)),Y) <->
% apply(apply(apply(X,Y),apply(Z,Y)),Y)
% Current number of equations to process: 2680
% Current number of ordered equations: 7670
% Current number of rules: 183
% New rule produced :
% [189]
% apply(apply(apply(apply(s,apply(k,X)),Y),Z),apply(Y,Z)) <->
% apply(apply(apply(s,X),apply(apply(s,k),V_3)),apply(Y,Z))
% Current number of equations to process: 2680
% Current number of ordered equations: 7668
% Current number of rules: 184
% New rule produced :
% [190]
% apply(apply(apply(s,X),apply(apply(s,k),V_3)),apply(Y,Z)) <->
% apply(apply(apply(apply(s,apply(k,X)),Y),Z),apply(Y,Z))
% Current number of equations to process: 2680
% Current number of ordered equations: 7666
% Current number of rules: 185
% New rule produced :
% [191]
% apply(apply(X,Y),apply(apply(Z,Y),Y)) <->
% apply(apply(apply(s,X),apply(apply(s,Z),apply(apply(s,k),V_3))),Y)
% Current number of equations to process: 2680
% Current number of ordered equations: 7664
% Current number of rules: 186
% New rule produced :
% [192]
% apply(apply(apply(s,X),apply(apply(s,Z),apply(apply(s,k),V_3))),Y) <->
% apply(apply(X,Y),apply(apply(Z,Y),Y))
% Current number of equations to process: 2680
% Current number of ordered equations: 7662
% Current number of rules: 187
% New rule produced :
% [193]
% apply(apply(X,apply(Y,Z)),apply(apply(apply(s,apply(k,Z)),Y),Z)) <->
% apply(apply(apply(s,apply(s,X)),Y),Z)
% Current number of equations to process: 2680
% Current number of ordered equations: 7660
% Current number of rules: 188
% New rule produced :
% [194]
% apply(apply(apply(s,apply(s,X)),Y),Z) <->
% apply(apply(X,apply(Y,Z)),apply(apply(apply(s,apply(k,Z)),Y),Z))
% Current number of equations to process: 2680
% Current number of ordered equations: 7658
% Current number of rules: 189
% New rule produced :
% [195]
% apply(apply(X,apply(Y,apply(k,Y))),Y) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,X)),k),Y)
% Current number of equations to process: 2680
% Current number of ordered equations: 7657
% Current number of rules: 190
% New rule produced :
% [196]
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,X)),k),Y) <->
% apply(apply(X,apply(Y,apply(k,Y))),Y)
% Current number of equations to process: 2680
% Current number of ordered equations: 7656
% Current number of rules: 191
% New rule produced :
% [197]
% apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),k),X),apply(k,Y)),Z)
% -> Y
% Current number of equations to Cputime limit exceeded (core dumped)
%
% EOF
%------------------------------------------------------------------------------