TSTP Solution File: COL004-1 by CiME---2.01
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- Process Solution
%------------------------------------------------------------------------------
% File : CiME---2.01
% Problem : COL004-1 : TPTP v6.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_cime %s
% Computer : n093.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 00:19:36 EDT 2014
% Result : Timeout 300.07s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : COL004-1 : TPTP v6.0.0. Released v1.0.0.
% % Command : tptp2X_and_run_cime %s
% % Computer : n093.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 16:30:23 CDT 2014
% % CPUTime : 300.07
% Processing problem /tmp/CiME_57934_n093.star.cs.uiowa.edu
% #verbose 1;
% let F = signature " k,s : constant; g : 1; f : 1; 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;
% ";
%
% let s1 = status F "
% g lr_lex;
% f lr_lex;
% k lr_lex;
% apply lr_lex;
% s lr_lex;
% ";
%
% let p1 = precedence F "
% apply > f > g > s > k";
%
% let s2 = status F "
% g mul;
% f mul;
% k mul;
% apply mul;
% s mul;
% ";
%
% let p2 = precedence F "
% apply > f > g > s = k";
%
% let o_auto = AUTO Axioms;
%
% let o = LEX o_auto (LEX (ACRPO s1 p1) (ACRPO s2 p2));
%
% let Conjectures = equations F X " apply(apply(Z,f(Z)),g(Z)) = apply(g(Z),apply(apply(f(Z),f(Z)),g(Z)));"
% ;
% (*
% 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 } (2 equation(s))
% s1 : F status = <status>
% p1 : F precedence = <precedence>
% s2 : F status = <status>
% p2 : F precedence = <precedence>
%
% [k] = 1;
% [s] = 2;
% [g](x1) = 3 + x1;
% [f](x1) = 4 + x1;
% [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(apply(Z,f(Z)),g(Z)) =
% apply(g(Z),apply(apply(f(Z),f(Z)),g(Z))) }
% (1 equation(s))
% time is now on
%
% Initializing completion ...
% New rule produced : [1] (eq)(X,X) -> (true)
% Current number of equations to process: 0
% Current number of ordered equations: 4
% Current number of rules: 1
% New rule produced : [2] apply(apply(k,X),Y) -> X
% Current number of equations to process: 0
% Current number of ordered equations: 3
% Current number of rules: 2
% New rule produced :
% [3]
% (eq)(apply(apply(Z,f(Z)),g(Z)),apply(g(Z),apply(apply(f(Z),f(Z)),g(Z)))) ->
% (false)
% Current number of equations to process: 0
% Current number of ordered equations: 2
% Current number of rules: 3
% New rule produced :
% [4] apply(apply(X,Z),apply(Y,Z)) <-> apply(apply(apply(s,X),Y),Z)
% Current number of equations to process: 1
% Current number of ordered equations: 2
% Current number of rules: 4
% New rule produced :
% [5] apply(apply(apply(s,X),Y),Z) <-> apply(apply(X,Z),apply(Y,Z))
% Current number of equations to process: 1
% Current number of ordered equations: 1
% Current number of rules: 5
% New rule produced :
% [6] (eq)(f(k),apply(g(k),apply(apply(f(k),f(k)),g(k)))) -> (false)
% Current number of equations to process: 1
% Current number of ordered equations: 0
% Current number of rules: 6
% New rule produced : [7] apply(apply(apply(s,k),Y),X) -> X
% Current number of equations to process: 5
% Current number of ordered equations: 0
% Current number of rules: 7
% New rule produced : [8] apply(apply(apply(apply(s,s),X),k),Y) -> Y
% Current number of equations to process: 13
% Current number of ordered equations: 0
% Current number of rules: 8
% New rule produced :
% [9]
% (eq)(g(apply(s,k)),apply(g(apply(s,k)),apply(apply(f(apply(s,k)),f(apply(s,k))),
% g(apply(s,k))))) -> (false)
% Current number of equations to process: 17
% Current number of ordered equations: 0
% Current number of rules: 9
% New rule produced :
% [10]
% (eq)(apply(X,g(apply(k,X))),apply(g(apply(k,X)),apply(apply(f(apply(k,X)),
% f(apply(k,X))),
% g(apply(k,X))))) -> (false)
% Current number of equations to process: 16
% Current number of ordered equations: 0
% Current number of rules: 10
% New rule produced : [11] apply(apply(apply(s,apply(s,k)),X),Y) -> apply(X,Y)
% Current number of equations to process: 18
% Current number of ordered equations: 0
% Current number of rules: 11
% New rule produced :
% [12] apply(X,apply(Y,Z)) <-> apply(apply(apply(s,apply(k,X)),Y),Z)
% Rule
% [3]
% (eq)(apply(apply(Z,f(Z)),g(Z)),apply(g(Z),apply(apply(f(Z),f(Z)),g(Z)))) ->
% (false) collapsed.
% Rule [6] (eq)(f(k),apply(g(k),apply(apply(f(k),f(k)),g(k)))) -> (false)
% collapsed.
% Rule
% [9]
% (eq)(g(apply(s,k)),apply(g(apply(s,k)),apply(apply(f(apply(s,k)),f(apply(s,k))),
% g(apply(s,k))))) -> (false) collapsed.
% Rule
% [10]
% (eq)(apply(X,g(apply(k,X))),apply(g(apply(k,X)),apply(apply(f(apply(k,X)),
% f(apply(k,X))),
% g(apply(k,X))))) -> (false)
% collapsed.
% Current number of equations to process: 27
% Current number of ordered equations: 3
% Current number of rules: 8
% New rule produced :
% [13]
% (eq)(apply(apply(Z,f(Z)),g(Z)),apply(apply(apply(s,apply(k,g(Z))),apply(
% f(Z),
% f(Z))),
% g(Z))) -> (false)
% Current number of equations to process: 26
% Current number of ordered equations: 3
% Current number of rules: 9
% New rule produced :
% [14]
% (eq)(f(k),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(k)),apply(
% f(k),f(k))),
% g(k))) -> (false)
% Current number of equations to process: 25
% Current number of ordered equations: 3
% Current number of rules: 10
% New rule produced :
% [15] apply(apply(apply(s,apply(k,X)),Y),Z) <-> apply(X,apply(Y,Z))
% Current number of equations to process: 25
% Current number of ordered equations: 2
% Current number of rules: 11
% New rule produced :
% [16] apply(apply(apply(s,X),apply(k,Z)),Y) <-> apply(apply(X,Y),Z)
% Current number of equations to process: 25
% Current number of ordered equations: 1
% Current number of rules: 12
% New rule produced :
% [17] apply(apply(X,Y),Z) <-> apply(apply(apply(s,X),apply(k,Z)),Y)
% Current number of equations to process: 25
% Current number of ordered equations: 0
% Current number of rules: 13
% New rule produced :
% [18]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),k),
% g(X)),apply(f(X),f(X))),g(X))) ->
% (false)
% Current number of equations to process: 55
% Current number of ordered equations: 0
% Current number of rules: 14
% New rule produced :
% [19]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(s,
% apply(k,
% g(X))),apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 92
% Current number of ordered equations: 0
% Current number of rules: 15
% New rule produced :
% [20]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(s,s),apply(k,apply(
% f(X),
% f(X)))),
% apply(k,g(X))),g(X))) -> (false)
% Current number of equations to process: 94
% Current number of ordered equations: 0
% Current number of rules: 16
% New rule produced :
% [21]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) ->
% (false)
% Current number of equations to process: 123
% Current number of ordered equations: 0
% Current number of rules: 17
% New rule produced : [22] apply(apply(apply(apply(apply(s,s),X),s),k),Y) -> Y
% Current number of equations to process: 137
% Current number of ordered equations: 0
% Current number of rules: 18
% New rule produced :
% [23] apply(apply(X,Y),X) <-> apply(apply(apply(apply(s,s),k),X),Y)
% Current number of equations to process: 148
% Current number of ordered equations: 1
% Current number of rules: 19
% New rule produced :
% [24] apply(apply(apply(apply(s,s),k),X),Y) <-> apply(apply(X,Y),X)
% Current number of equations to process: 148
% Current number of ordered equations: 0
% Current number of rules: 20
% New rule produced :
% [25]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% g(X)),apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 183
% Current number of ordered equations: 0
% Current number of rules: 21
% New rule produced :
% [26]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(s,s),
% apply(k,
% apply(f(X),
% f(X)))),
% apply(k,g(X))),
% g(X))) -> (false)
% Current number of equations to process: 189
% Current number of ordered equations: 0
% Current number of rules: 22
% New rule produced :
% [27]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,s)),X),Y),k) ->
% apply(Y,k)
% Current number of equations to process: 198
% Current number of ordered equations: 0
% Current number of rules: 23
% New rule produced :
% [28] apply(apply(apply(s,apply(k,X)),apply(k,Y)),Z) -> apply(X,Y)
% Current number of equations to process: 212
% Current number of ordered equations: 1
% Current number of rules: 24
% New rule produced :
% [29] apply(apply(apply(apply(s,apply(k,k)),X),Y),Z) -> apply(X,Y)
% Current number of equations to process: 212
% Current number of ordered equations: 0
% Current number of rules: 25
% New rule produced :
% [30]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,g(X))),apply(k,g(X))),
% apply(f(X),f(X)))) -> (false)
% Current number of equations to process: 244
% Current number of ordered equations: 0
% Current number of rules: 26
% New rule produced :
% [31]
% (eq)(f(k),apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,g(k))),
% apply(k,g(k))),apply(f(k),f(k)))) -> (false)
% Current number of equations to process: 250
% Current number of ordered equations: 0
% Current number of rules: 27
% New rule produced :
% [32]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(s,apply(k,g(X))),apply(f(X),f(X))),
% g(X))) -> (false)
% Current number of equations to process: 269
% Current number of ordered equations: 0
% Current number of rules: 28
% New rule produced :
% [33]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(s,apply(s,s)),
% apply(k,apply(k,g(X)))),apply(k,
% apply(
% f(X),
% f(X)))),
% g(X))) -> (false)
% Current number of equations to process: 279
% Current number of ordered equations: 0
% Current number of rules: 29
% New rule produced :
% [34]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(X)),
% apply(
% f(X),
% f(X))),
% g(X))) ->
% (false)
% Current number of equations to process: 294
% Current number of ordered equations: 1
% Current number of rules: 30
% New rule produced :
% [35]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),X),apply(k,f(X))),
% apply(k,g(X))),apply(apply(apply(s,apply(k,g(X))),apply(f(X),f(X))),
% g(X))) -> (false)
% Current number of equations to process: 294
% Current number of ordered equations: 0
% Current number of rules: 31
% New rule produced :
% [36]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(
% apply(s,s),
% apply(k,
% apply(
% f(X),
% f(X)))),
% apply(k,
% g(X))),
% g(X))) ->
% (false)
% Current number of equations to process: 312
% Current number of ordered equations: 0
% Current number of rules: 32
% New rule produced :
% [37] apply(apply(apply(apply(s,apply(s,s)),s),k),X) -> apply(s,k)
% Current number of equations to process: 322
% Current number of ordered equations: 0
% Current number of rules: 33
% New rule produced :
% [38]
% (eq)(X,apply(apply(apply(apply(apply(s,apply(k,s)),k),g(apply(k,apply(k,X)))),
% apply(f(apply(k,apply(k,X))),f(apply(k,apply(k,X))))),g(
% apply(k,
% apply(k,X)))))
% -> (false)
% Current number of equations to process: 330
% Current number of ordered equations: 0
% Current number of rules: 34
% New rule produced :
% [39]
% 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: 340
% Current number of ordered equations: 3
% Current number of rules: 35
% New rule produced :
% [40] apply(apply(X,Y),Y) <-> apply(apply(apply(s,X),apply(apply(s,k),Z)),Y)
% Current number of equations to process: 340
% Current number of ordered equations: 2
% Current number of rules: 36
% New rule produced :
% [41] apply(apply(apply(s,X),apply(apply(s,k),Z)),Y) <-> apply(apply(X,Y),Y)
% Current number of equations to process: 340
% Current number of ordered equations: 1
% Current number of rules: 37
% New rule produced :
% [42]
% 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: 340
% Current number of ordered equations: 0
% Current number of rules: 38
% New rule produced :
% [43]
% 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: 483
% Current number of ordered equations: 1
% Current number of rules: 39
% New rule produced :
% [44]
% 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: 483
% Current number of ordered equations: 0
% Current number of rules: 40
% New rule produced :
% [45] apply(apply(apply(apply(s,apply(s,s)),apply(k,k)),X),Y) -> Y
% Current number of equations to process: 557
% Current number of ordered equations: 0
% Current number of rules: 41
% New rule produced :
% [46]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),apply(k,g(k))),k),apply(
% f(k),
% f(k))),
% g(k))) -> (false)
% Current number of equations to process: 576
% Current number of ordered equations: 1
% Current number of rules: 42
% New rule produced :
% [47]
% (eq)(f(k),apply(apply(apply(apply(apply(s,apply(k,s)),apply(apply(s,apply(k,s)),k)),
% g(k)),apply(k,g(k))),apply(f(k),f(k)))) -> (false)
% Current number of equations to process: 576
% Current number of ordered equations: 0
% Current number of rules: 43
% New rule produced :
% [48]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(s,s)),k),s),k),
% apply(k,apply(f(X),f(X)))),
% g(X)),g(X))) -> (false)
% Current number of equations to process: 592
% Current number of ordered equations: 0
% Current number of rules: 44
% New rule produced :
% [49]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(s,
% apply(k,s)),s),
% apply(k,
% g(X))),apply(k,
% g(X))),
% apply(f(X),f(X)))) ->
% (false)
% Current number of equations to process: 609
% Current number of ordered equations: 0
% Current number of rules: 45
% New rule produced :
% [50] apply(apply(apply(apply(apply(apply(s,s),X),s),s),k),Y) -> Y
% Current number of equations to process: 623
% Current number of ordered equations: 0
% Current number of rules: 46
% New rule produced :
% [51] apply(X,apply(k,X)) <-> apply(apply(apply(apply(s,s),k),apply(k,X)),Y)
% Current number of equations to process: 645
% Current number of ordered equations: 1
% Current number of rules: 47
% New rule produced :
% [52] apply(apply(apply(apply(s,s),k),apply(k,X)),Y) <-> apply(X,apply(k,X))
% Current number of equations to process: 645
% Current number of ordered equations: 0
% Current number of rules: 48
% New rule produced :
% [53]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(X)),
% apply(f(X),f(X))),g(X))) -> (false)
% Current number of equations to process: 689
% Current number of ordered equations: 0
% Current number of rules: 49
% New rule produced :
% [54]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(s,s),apply(k,apply(f(X),f(X)))),
% apply(k,g(X))),g(X))) -> (false)
% Current number of equations to process: 702
% Current number of ordered equations: 0
% Current number of rules: 50
% New rule produced :
% [55]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(s,
% apply(s,s)),
% apply(k,
% apply(k,
% g(X)))),
% apply(k,apply(
% f(X),f(X)))),
% g(X))) -> (false)
% Current number of equations to process: 714
% Current number of ordered equations: 0
% Current number of rules: 51
% New rule produced :
% [56]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),X),apply(k,f(X))),
% apply(k,g(X))),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(X)),
% apply(f(X),f(X))),g(X))) -> (false)
% Current number of equations to process: 719
% Current number of ordered equations: 0
% Current number of rules: 52
% New rule produced :
% [57]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),X),apply(k,f(X))),
% apply(k,g(X))),apply(apply(apply(apply(s,s),apply(k,apply(f(X),f(X)))),
% apply(k,g(X))),g(X))) -> (false)
% Current number of equations to process: 731
% Current number of ordered equations: 0
% Current number of rules: 53
% New rule produced :
% [58] apply(apply(apply(apply(s,s),apply(s,k)),X),Y) <-> apply(apply(X,Y),Y)
% Current number of equations to process: 743
% Current number of ordered equations: 1
% Current number of rules: 54
% New rule produced :
% [59] apply(apply(X,Y),Y) <-> apply(apply(apply(apply(s,s),apply(s,k)),X),Y)
% Current number of equations to process: 743
% Current number of ordered equations: 0
% Current number of rules: 55
% New rule produced :
% [60] apply(apply(apply(apply(s,s),k),apply(k,apply(k,X))),Y) -> X
% Current number of equations to process: 823
% Current number of ordered equations: 0
% Current number of rules: 56
% New rule produced :
% [61] apply(apply(apply(apply(s,apply(s,s)),k),k),X) -> apply(k,apply(k,k))
% Current number of equations to process: 845
% Current number of ordered equations: 0
% Current number of rules: 57
% New rule produced :
% [62] apply(apply(apply(apply(s,s),apply(s,k)),apply(s,k)),X) -> X
% Current number of equations to process: 863
% Current number of ordered equations: 0
% Current number of rules: 58
% New rule produced :
% [63]
% (eq)(f(k),apply(apply(apply(apply(apply(s,s),apply(s,k)),apply(apply(s,
% apply(k,s)),s)),
% apply(k,g(k))),apply(f(k),f(k)))) -> (false)
% Current number of equations to process: 883
% Current number of ordered equations: 0
% Current number of rules: 59
% New rule produced :
% [64]
% (eq)(g(apply(s,k)),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(apply(s,k))),
% apply(f(apply(s,k)),f(apply(s,k)))),g(apply(s,k))))
% -> (false)
% Current number of equations to process: 890
% Current number of ordered equations: 0
% Current number of rules: 60
% New rule produced :
% [65]
% (eq)(apply(X,g(apply(k,X))),apply(apply(apply(apply(apply(s,apply(k,s)),k),
% g(apply(k,X))),apply(f(apply(k,X)),
% f(apply(k,X)))),
% g(apply(k,X)))) -> (false)
% Current number of equations to process: 893
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [66]
% apply(apply(apply(apply(s,s),X),apply(s,k)),Y) ->
% apply(apply(X,apply(s,k)),Y)
% Rule [62] apply(apply(apply(apply(s,s),apply(s,k)),apply(s,k)),X) -> X
% collapsed.
% Current number of equations to process: 912
% Current number of ordered equations: 0
% Current number of rules: 61
% New rule produced :
% [67] apply(apply(apply(s,apply(k,X)),apply(apply(s,k),Z)),Y) -> apply(X,Y)
% Current number of equations to process: 933
% Current number of ordered equations: 0
% Current number of rules: 62
% New rule produced :
% [68]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),
% apply(apply(s,
% apply(k,k)),s)),
% apply(k,g(X))),f(X)),
% f(X)),g(X))) -> (false)
% Current number of equations to process: 957
% Current number of ordered equations: 0
% Current number of rules: 63
% New rule produced :
% [69]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(s,apply(k,s)),apply(apply(s,
% apply(k,k)),s)),
% apply(k,g(k))),f(k)),f(k)),g(k))) -> (false)
% Current number of equations to process: 959
% Current number of ordered equations: 0
% Current number of rules: 64
% New rule produced :
% [70]
% apply(apply(Y,Z),apply(X,Z)) <->
% apply(apply(apply(apply(s,s),apply(k,X)),Y),Z)
% Current number of equations to process: 998
% Current number of ordered equations: 3
% Current number of rules: 65
% New rule produced :
% [71]
% apply(apply(X,Y),apply(Z,Y)) <->
% apply(apply(apply(s,apply(s,X)),apply(k,Y)),Z)
% Current number of equations to process: 998
% Current number of ordered equations: 2
% Current number of rules: 66
% New rule produced :
% [72]
% apply(apply(apply(s,apply(s,X)),apply(k,Y)),Z) <->
% apply(apply(X,Y),apply(Z,Y))
% Current number of equations to process: 998
% Current number of ordered equations: 1
% Current number of rules: 67
% New rule produced :
% [73]
% apply(apply(apply(apply(s,s),apply(k,X)),Y),Z) <->
% apply(apply(Y,Z),apply(X,Z))
% Current number of equations to process: 998
% Current number of ordered equations: 0
% Current number of rules: 68
% New rule produced :
% [74]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),k),
% apply(apply(apply(s,apply(k,k)),f(k)),f(k))),g(k)),
% g(k))) -> (false)
% Current number of equations to process: 1287
% Current number of ordered equations: 0
% Current number of rules: 69
% New rule produced :
% [75]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),s),
% apply(k,s)),apply(k,
% g(X))),k),
% apply(f(X),f(X))),g(X))) -> (false)
% Current number of equations to process: 1295
% Current number of ordered equations: 1
% Current number of rules: 70
% New rule produced :
% [76]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),
% apply(apply(s,apply(k,s)),k)),
% g(X)),apply(k,g(X))),apply(
% f(X),
% f(X)))) ->
% (false)
% Current number of equations to process: 1295
% Current number of ordered equations: 0
% Current number of rules: 71
% New rule produced :
% [77]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(s,s)),k),
% apply(f(X),f(X))),apply(k,g(X))),
% g(X))) -> (false)
% Current number of equations to process: 1353
% Current number of ordered equations: 0
% Current number of rules: 72
% New rule produced :
% [78]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(s,s)),k),apply(f(k),f(k))),apply(k,
% g(k))),
% g(k))) -> (false)
% Current number of equations to process: 1355
% Current number of ordered equations: 0
% Current number of rules: 73
% New rule produced :
% [79]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),
% apply(s,s)),apply(k,
% apply(f(X),
% f(X)))),
% apply(k,g(X))),apply(k,g(X)))) ->
% (false)
% Current number of equations to process: 1392
% Current number of ordered equations: 0
% Current number of rules: 74
% New rule produced :
% [80]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,
% g(X))),
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X)))) ->
% (false)
% Current number of equations to process: 1412
% Current number of ordered equations: 1
% Current number of rules: 75
% New rule produced :
% [81]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,X)),apply(k,
% apply(k,
% g(X)))),
% apply(k,f(X))),apply(apply(apply(s,apply(k,g(X))),apply(f(X),f(X))),
% g(X))) -> (false)
% Current number of equations to process: 1412
% Current number of ordered equations: 0
% Current number of rules: 76
% New rule produced :
% [82]
% apply(apply(X,Y),apply(s,Y)) <->
% apply(apply(apply(apply(apply(s,s),k),s),X),Y)
% Current number of equations to process: 1437
% Current number of ordered equations: 1
% Current number of rules: 77
% New rule produced :
% [83]
% apply(apply(apply(apply(apply(s,s),k),s),X),Y) <->
% apply(apply(X,Y),apply(s,Y))
% Current number of equations to process: 1437
% Current number of ordered equations: 0
% Current number of rules: 78
% New rule produced :
% [84]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),k),s),k),
% apply(k,
% apply(f(X),
% f(X)))),
% g(X)),g(X))) ->
% (false)
% Current number of equations to process: 1547
% Current number of ordered equations: 0
% Current number of rules: 79
% New rule produced :
% [85]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(s,apply(s,s)),
% apply(apply(apply(s,apply(k,k)),k),
% g(X))),apply(k,apply(f(X),f(X)))),
% g(X))) -> (false)
% Current number of equations to process: 1556
% Current number of ordered equations: 1
% Current number of rules: 80
% New rule produced :
% [86]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(s,apply(s,s)),
% apply(k,apply(k,g(X)))),apply(
% apply(
% apply(s,
% apply(k,k)),
% f(X)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 1556
% Current number of ordered equations: 0
% Current number of rules: 81
% New rule produced :
% [87]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),
% apply(k,
% apply(k,
% g(X)))),
% apply(k,
% apply(
% f(X),
% f(X)))),
% g(X))) ->
% (false)
% Current number of equations to process: 1588
% Current number of ordered equations: 0
% Current number of rules: 82
% New rule produced :
% [88]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),s),
% apply(apply(s,k),X)),apply(k,g(k))),apply(f(k),f(k))))
% -> (false)
% Current number of equations to process: 1599
% Current number of ordered equations: 0
% Current number of rules: 83
% New rule produced :
% [89]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),
% apply(apply(s,apply(k,s)),k)),k),g(k)),apply(
% f(k),
% f(k)))) ->
% (false)
% Current number of equations to process: 1613
% Current number of ordered equations: 0
% Current number of rules: 84
% New rule produced :
% [90] apply(apply(apply(apply(s,s),apply(s,k)),apply(k,X)),Y) -> apply(X,Y)
% Current number of equations to process: 1613
% Current number of ordered equations: 0
% Current number of rules: 85
% New rule produced :
% [91] apply(X,X) <-> apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),X)
% Current number of equations to process: 1648
% Current number of ordered equations: 1
% Current number of rules: 86
% New rule produced :
% [92] apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),X) <-> apply(X,X)
% Current number of equations to process: 1648
% Current number of ordered equations: 0
% Current number of rules: 87
% New rule produced :
% [93]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(s,apply(k,g(X))),apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),s),
% apply(s,k)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 1680
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [94]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,s),apply(s,k)),
% apply(apply(s,apply(k,s)),s)),
% apply(k,g(X))),apply(f(X),f(X)))) ->
% (false)
% Current number of equations to process: 1772
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [95]
% (eq)(f(k),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(k)),apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),s),
% apply(s,k)),
% f(k))),
% g(k))) -> (false)
% Current number of equations to process: 1807
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [96]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(s,
% apply(k,
% g(X))),apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),s),
% apply(s,k)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 1813
% Current number of ordered equations: 0
% Current number of rules: 91
% New rule produced :
% [97]
% 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: 1819
% Current number of ordered equations: 1
% Current number of rules: 92
% New rule produced :
% [98]
% 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: 1819
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [99]
% 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: 1982
% Current number of ordered equations: 3
% Current number of rules: 94
% New rule produced :
% [100]
% apply(apply(X,Y),Y) <->
% apply(apply(apply(s,X),apply(apply(apply(s,s),Z),k)),Y)
% Current number of equations to process: 1982
% Current number of ordered equations: 2
% Current number of rules: 95
% New rule produced :
% [101]
% apply(apply(apply(s,X),apply(apply(apply(s,s),Z),k)),Y) <->
% apply(apply(X,Y),Y)
% Current number of equations to process: 1982
% Current number of ordered equations: 1
% Current number of rules: 96
% New rule produced :
% [102]
% 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: 1982
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [103] apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(k,X)),Y),Z) -> X
% Current number of equations to process: 2296
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [104]
% apply(X,apply(Y,Z)) <->
% apply(apply(apply(apply(apply(s,apply(k,s)),k),X),Y),Z)
% Rule
% [20]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(s,s),apply(k,apply(
% f(X),
% f(X)))),
% apply(k,g(X))),g(X))) -> (false)
% collapsed.
% Rule
% [26]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(s,s),
% apply(k,
% apply(f(X),
% f(X)))),
% apply(k,g(X))),
% g(X))) -> (false) collapsed.
% Rule
% [36]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(
% apply(s,s),
% apply(k,
% apply(
% f(X),
% f(X)))),
% apply(k,
% g(X))),
% g(X))) ->
% (false) collapsed.
% Rule
% [47]
% (eq)(f(k),apply(apply(apply(apply(apply(s,apply(k,s)),apply(apply(s,apply(k,s)),k)),
% g(k)),apply(k,g(k))),apply(f(k),f(k)))) -> (false)
% collapsed.
% Rule
% [54]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(s,s),apply(k,apply(f(X),f(X)))),
% apply(k,g(X))),g(X))) -> (false) collapsed.
% Rule
% [57]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),X),apply(k,f(X))),
% apply(k,g(X))),apply(apply(apply(apply(s,s),apply(k,apply(f(X),f(X)))),
% apply(k,g(X))),g(X))) -> (false) collapsed.
% Rule [60] apply(apply(apply(apply(s,s),k),apply(k,apply(k,X))),Y) -> X
% collapsed.
% Rule
% [68]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),
% apply(apply(s,
% apply(k,k)),s)),
% apply(k,g(X))),f(X)),
% f(X)),g(X))) -> (false) collapsed.
% Rule
% [69]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(s,apply(k,s)),apply(apply(s,
% apply(k,k)),s)),
% apply(k,g(k))),f(k)),f(k)),g(k))) -> (false)
% collapsed.
% Rule
% [74]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),k),
% apply(apply(apply(s,apply(k,k)),f(k)),f(k))),g(k)),
% g(k))) -> (false) collapsed.
% Rule
% [76]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),
% apply(apply(s,apply(k,s)),k)),
% g(X)),apply(k,g(X))),apply(
% f(X),
% f(X)))) ->
% (false) collapsed.
% Rule
% [85]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(s,apply(s,s)),
% apply(apply(apply(s,apply(k,k)),k),
% g(X))),apply(k,apply(f(X),f(X)))),
% g(X))) -> (false) collapsed.
% Current number of equations to process: 2368
% Current number of ordered equations: 1
% Current number of rules: 87
% New rule produced :
% [105]
% apply(apply(apply(apply(apply(s,apply(k,s)),k),X),Y),Z) <->
% apply(X,apply(Y,Z))
% Current number of equations to process: 2368
% Current number of ordered equations: 0
% Current number of rules: 88
% New rule produced :
% [106]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,
% g(X)))),
% f(X)),f(X)),
% g(X))) -> (false)
% Current number of equations to process: 2405
% Current number of ordered equations: 0
% Current number of rules: 89
% New rule produced :
% [107]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(s,apply(k,g(X)))),
% f(X)),f(X)),g(X))) -> (false)
% Current number of equations to process: 2422
% Current number of ordered equations: 0
% Current number of rules: 90
% New rule produced :
% [108]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,
% g(X)))),
% f(X)),
% f(X)),
% g(X))) ->
% (false)
% Current number of equations to process: 2526
% Current number of ordered equations: 2
% Current number of rules: 91
% New rule produced :
% [109]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,apply(s,X)),
% apply(k,f(X)))),k),
% g(X)),apply(apply(apply(s,apply(k,g(X))),apply(f(X),f(X))),g(X))) ->
% (false)
% Current number of equations to process: 2526
% Current number of ordered equations: 1
% Current number of rules: 92
% New rule produced :
% [110]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,apply(s,X))),k),
% f(X)),apply(k,g(X))),apply(apply(apply(s,apply(k,g(X))),apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 2526
% Current number of ordered equations: 0
% Current number of rules: 93
% New rule produced :
% [111]
% 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: 2784
% Current number of ordered equations: 1
% Current number of rules: 94
% New rule produced :
% [112]
% 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: 2784
% Current number of ordered equations: 0
% Current number of rules: 95
% New rule produced :
% [113]
% apply(Y,apply(X,Z)) <->
% apply(apply(apply(apply(s,s),apply(k,X)),apply(k,Y)),Z)
% Current number of equations to process: 2972
% Current number of ordered equations: 1
% Current number of rules: 96
% New rule produced :
% [114]
% apply(apply(apply(apply(s,s),apply(k,X)),apply(k,Y)),Z) <->
% apply(Y,apply(X,Z))
% Current number of equations to process: 2972
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [115]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,s),apply(k,
% f(X))),
% apply(apply(apply(s,apply(k,k)),s),
% apply(k,g(X)))),f(X)),g(X))) ->
% (false)
% Current number of equations to process: 3143
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [116] apply(apply(apply(apply(s,apply(s,s)),k),apply(k,X)),Y) -> X
% Current number of equations to process: 3320
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [117]
% apply(apply(Y,Z),X) <->
% apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),k),
% apply(k,X)),Y),Z)
% Current number of equations to process: 3436
% Current number of ordered equations: 2
% Current number of rules: 100
% New rule produced :
% [118]
% apply(apply(apply(s,apply(s,X)),apply(k,Y)),apply(k,Z)) ->
% apply(apply(X,Y),Z)
% Rule
% [21]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) ->
% (false) collapsed.
% Rule
% [33]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(s,apply(s,s)),
% apply(k,apply(k,g(X)))),apply(k,
% apply(
% f(X),
% f(X)))),
% g(X))) -> (false) collapsed.
% Rule
% [34]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(X)),
% apply(
% f(X),
% f(X))),
% g(X))) ->
% (false) collapsed.
% Rule
% [55]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(s,
% apply(s,s)),
% apply(k,
% apply(k,
% g(X)))),
% apply(k,apply(
% f(X),f(X)))),
% g(X))) -> (false) collapsed.
% Rule
% [80]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,
% g(X))),
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X)))) ->
% (false) collapsed.
% Rule
% [87]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),
% apply(k,
% apply(k,
% g(X)))),
% apply(k,
% apply(
% f(X),
% f(X)))),
% g(X))) ->
% (false) collapsed.
% Rule
% [108]
% (eq)(apply(apply(apply(s,apply(s,X)),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,
% g(X)))),
% f(X)),
% f(X)),
% g(X))) ->
% (false) collapsed.
% Current number of equations to process: 3436
% Current number of ordered equations: 1
% Current number of rules: 94
% New rule produced :
% [119]
% (eq)(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),k),
% apply(k,g(X))),X),f(X)),apply(apply(apply(s,apply(k,g(X))),
% apply(f(X),f(X))),g(X))) ->
% (false)
% Current number of equations to process: 3651
% Current number of ordered equations: 1
% Current number of rules: 95
% New rule produced :
% [120]
% apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),k),
% apply(k,X)),Y),Z) <-> apply(apply(Y,Z),X)
% Current number of equations to process: 3861
% Current number of ordered equations: 0
% Current number of rules: 96
% New rule produced :
% [121]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,
% apply(k,k))),s),
% apply(k,
% g(X))),
% f(X)),f(X)),
% g(X))) -> (false)
% Current number of equations to process: 4006
% Current number of ordered equations: 0
% Current number of rules: 97
% New rule produced :
% [122]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(s,s)),apply(apply(s,apply(k,k)),f(k))),
% f(k)),apply(k,g(k))),g(k))) -> (false)
% Current number of equations to process: 4053
% Current number of ordered equations: 0
% Current number of rules: 98
% New rule produced :
% [123]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s)),k),
% apply(f(X),
% f(X))),apply(k,
% g(X))),
% g(X))) -> (false)
% Current number of equations to process: 4068
% Current number of ordered equations: 0
% Current number of rules: 99
% New rule produced :
% [124] apply(apply(apply(apply(apply(s,apply(s,s)),apply(k,s)),X),k),Y) -> Y
% Current number of equations to process: 4091
% Current number of ordered equations: 0
% Current number of rules: 100
% New rule produced :
% [125]
% apply(apply(apply(apply(s,s),k),apply(apply(s,s),X)),k) ->
% apply(apply(s,s),X)
% Current number of equations to process: 4138
% Current number of ordered equations: 0
% Current number of rules: 101
% New rule produced :
% [126]
% apply(apply(apply(apply(s,s),k),apply(X,Y)),Y) ->
% apply(apply(apply(s,apply(X,Y)),X),Y)
% Current number of equations to process: 4167
% Current number of ordered equations: 0
% Current number of rules: 102
% New rule produced :
% [127]
% apply(apply(apply(X,k),Y),apply(X,k)) <->
% apply(apply(apply(apply(s,apply(s,s)),X),k),Y)
% Current number of equations to process: 4239
% Current number of ordered equations: 1
% Current number of rules: 103
% New rule produced :
% [128]
% apply(apply(apply(apply(s,apply(s,s)),X),k),Y) <->
% apply(apply(apply(X,k),Y),apply(X,k))
% Current number of equations to process: 4239
% Current number of ordered equations: 0
% Current number of rules: 104
% New rule produced :
% [129]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(k,
% g(X))),k),
% apply(f(X),f(X))),
% g(X))) -> (false)
% Current number of equations to process: 4412
% Current number of ordered equations: 1
% Current number of rules: 105
% New rule produced :
% [130]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,
% apply(k,s))),k),
% g(X)),apply(k,
% g(X))),
% apply(f(X),f(X)))) ->
% (false)
% Current number of equations to process: 4412
% Current number of ordered equations: 0
% Current number of rules: 106
% New rule produced :
% [131]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(s,
% apply(k,s)),
% apply(s,s)),
% apply(k,
% apply(f(X),
% f(X)))),
% apply(k,g(X))),
% apply(k,g(X)))) -> (false)
% Current number of equations to process: 4484
% Current number of ordered equations: 0
% Current number of rules: 107
% New rule produced :
% [132]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(s,s)),k),s),s),
% apply(k,apply(k,g(X)))),apply(k,
% g(X))),
% apply(f(X),f(X)))) -> (false)
% Current number of equations to process: 4511
% Current number of ordered equations: 0
% Current number of rules: 108
% New rule produced :
% [133]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),s),k),k),g(k)),f(k)),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(k)),
% apply(
% f(k),
% f(k))),
% g(k))) ->
% (false)
% Current number of equations to process: 4542
% Current number of ordered equations: 0
% Current number of rules: 109
% New rule produced :
% [134]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,g(X))),apply(k,g(X))),apply(
% f(X),
% f(X)))) ->
% (false)
% Current number of equations to process: 4563
% Current number of ordered equations: 1
% Current number of rules: 110
% New rule produced :
% [135]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),k),
% apply(k,k)),apply(s,X)),g(X)),f(X)),apply(apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 4563
% Current number of ordered equations: 0
% Current number of rules: 111
% New rule produced :
% [136]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(s,apply(s,s))),apply(apply(s,
% apply(k,k)),k)),
% g(k)),apply(apply(apply(s,apply(k,k)),f(k)),f(k))),
% g(k))) -> (false)
% Current number of equations to process: 4618
% Current number of ordered equations: 0
% Current number of rules: 112
% New rule produced :
% [137]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,X)),apply(k,
% apply(k,
% g(X)))),
% apply(k,f(X))),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(X)),
% apply(f(X),f(X))),g(X))) -> (false)
% Current number of equations to process: 4641
% Current number of ordered equations: 0
% Current number of rules: 113
% New rule produced :
% [138]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),X),apply(k,f(X))),
% apply(k,g(X))),apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,
% g(X))),
% apply(k,g(X))),apply(f(X),f(X)))) -> (false)
% Current number of equations to process: 4664
% Current number of ordered equations: 1
% Current number of rules: 114
% New rule produced :
% [139]
% (eq)(apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),s),
% apply(k,apply(k,f(X)))),X),apply(k,g(X))),apply(apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 4664
% Current number of ordered equations: 0
% Current number of rules: 115
% New rule produced :
% [140]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,X)),apply(k,
% apply(k,
% g(X)))),
% apply(k,f(X))),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(s,s)),k),apply(f(X),f(X))),
% apply(k,g(X))),g(X))) -> (false)
% Current number of equations to process: 4717
% Current number of ordered equations: 0
% Current number of rules: 116
% New rule produced :
% [141]
% apply(apply(apply(s,X),apply(apply(s,k),Y)),X) <->
% apply(apply(apply(apply(s,s),k),X),X)
% Current number of equations to process: 4746
% Current number of ordered equations: 1
% Current number of rules: 117
% New rule produced :
% [142]
% apply(apply(apply(apply(s,s),k),X),X) <->
% apply(apply(apply(s,X),apply(apply(s,k),Y)),X)
% Current number of equations to process: 4746
% Current number of ordered equations: 0
% Current number of rules: 118
% New rule produced :
% [143]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(s,s)),k),s),s),
% apply(apply(s,k),Y)),apply(k,g(X))),
% apply(f(X),f(X)))) -> (false)
% Current number of equations to process: 4822
% Current number of ordered equations: 0
% Current number of rules: 119
% New rule produced :
% [144]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),k),s),apply(k,g(k))),k),
% apply(f(k),f(k))),g(k))) -> (false)
% Current number of equations to process: 4891
% Current number of ordered equations: 0
% Current number of rules: 120
% New rule produced :
% [145]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(s,s)),k),s),k),
% apply(apply(apply(s,apply(k,k)),
% f(X)),f(X))),g(X)),g(X))) ->
% (false)
% Current number of equations to process: 4910
% Current number of ordered equations: 0
% Current number of rules: 121
% New rule produced :
% [146] apply(apply(apply(apply(apply(apply(apply(s,s),X),s),s),s),k),Y) -> Y
% Current number of equations to process: 4949
% Current number of ordered equations: 0
% Current number of rules: 122
% Rule [51]
% apply(X,apply(k,X)) <-> apply(apply(apply(apply(s,s),k),apply(k,X)),Y) is composed into
% [51] apply(X,apply(k,X)) <-> apply(apply(apply(s,apply(k,X)),k),X)
% New rule produced :
% [147]
% apply(apply(apply(apply(s,s),k),apply(k,X)),Y) ->
% apply(apply(apply(s,apply(k,X)),k),X)
% Rule
% [52] apply(apply(apply(apply(s,s),k),apply(k,X)),Y) <-> apply(X,apply(k,X))
% collapsed.
% Current number of equations to process: 2579
% Current number of ordered equations: 0
% Current number of rules: 122
% New rule produced :
% [148]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(s,
% apply(s,s)),
% apply(k,
% apply(k,
% g(X)))),
% apply(apply(apply(s,
% apply(k,k)),
% f(X)),f(X))),
% g(X))) -> (false)
% Current number of equations to process: 2622
% Current number of ordered equations: 1
% Current number of rules: 123
% New rule produced :
% [149]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(s,s))),
% apply(
% apply(s,
% apply(k,k)),k)),
% g(X)),apply(k,
% apply(
% f(X),
% f(X)))),
% g(X))) -> (false)
% Current number of equations to process: 2622
% Current number of ordered equations: 0
% Current number of rules: 124
% New rule produced :
% [150]
% apply(apply(apply(apply(s,s),apply(s,k)),X),X) ->
% apply(apply(apply(apply(s,s),k),X),X)
% Current number of equations to process: 2672
% Current number of ordered equations: 0
% Current number of rules: 125
% New rule produced :
% [151]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(s,s),
% apply(s,k)),
% apply(apply(s,
% apply(k,s)),s)),
% apply(k,g(X))),
% apply(f(X),f(X)))) ->
% (false)
% Current number of equations to process: 2706
% Current number of ordered equations: 0
% Current number of rules: 126
% New rule produced :
% [152]
% apply(apply(apply(apply(apply(s,apply(s,s)),s),s),k),k) ->
% apply(k,apply(k,k))
% Current number of equations to process: 2733
% Current number of ordered equations: 0
% Current number of rules: 127
% New rule produced :
% [153]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(s,s)),k),s),
% apply(apply(s,apply(k,s)),k)),k),
% g(X)),apply(f(X),f(X)))) -> (false)
% Current number of equations to process: 2749
% Current number of ordered equations: 0
% Current number of rules: 128
% New rule produced :
% [154]
% (eq)(f(k),apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,s)),apply(
% apply(
% apply(s,
% apply(k,k)),
% f(k)),
% f(k))),
% apply(k,g(k))),apply(k,g(k)))) -> (false)
% Current number of equations to process: 2803
% Current number of ordered equations: 0
% Current number of rules: 129
% New rule produced :
% [155]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),s),
% apply(apply(apply(s,s),X),k)),apply(k,g(k))),apply(
% f(k),
% f(k)))) ->
% (false)
% Current number of equations to process: 2813
% Current number of ordered equations: 0
% Current number of rules: 130
% New rule produced :
% [156]
% apply(apply(apply(apply(s,apply(s,s)),k),apply(s,k)),X) ->
% apply(apply(s,k),X)
% Current number of equations to process: 2841
% Current number of ordered equations: 0
% Current number of rules: 131
% New rule produced :
% [157] apply(apply(apply(apply(s,apply(s,s)),s),apply(s,k)),apply(k,X)) -> X
% Current number of equations to process: 2888
% Current number of ordered equations: 0
% Current number of rules: 132
% New rule produced :
% [158]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),k),
% g(X)),apply(apply(apply(apply(s,
% apply(s,s)),s),
% apply(s,k)),f(X))),
% g(X))) -> (false)
% Current number of equations to process: 2924
% Current number of ordered equations: 0
% Current number of rules: 133
% New rule produced :
% [159]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),X),apply(k,f(X))),
% apply(k,g(X))),apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(s,apply(k,g(X)))),f(X)),f(X)),
% g(X))) -> (false)
% Current number of equations to process: 2979
% Current number of ordered equations: 0
% Current number of rules: 134
% New rule produced :
% [160]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(apply(s,apply(k,s)),s)),k),g(k)),
% apply(k,g(k))),apply(f(k),f(k)))) -> (false)
% Current number of equations to process: 3005
% Current number of ordered equations: 0
% Current number of rules: 135
% New rule produced :
% [161]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(s,apply(k,g(X)))),f(X)),
% f(X)),g(X))) -> (false)
% Current number of equations to process: 3025
% Current number of ordered equations: 0
% Current number of rules: 136
% New rule produced :
% [162]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,apply(s,X)),
% apply(k,f(X)))),k),
% g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(X)),apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3050
% Current number of ordered equations: 1
% Current number of rules: 137
% New rule produced :
% [163]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,apply(s,X))),k),
% f(X)),apply(k,g(X))),apply(apply(apply(apply(apply(s,apply(k,s)),k),
% g(X)),apply(f(X),f(X))),g(X))) ->
% (false)
% Current number of equations to process: 3050
% Current number of ordered equations: 0
% Current number of rules: 138
% New rule produced :
% [164]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(s,
% apply(s,s)),k),s),k),
% apply(k,f(X))),apply(s,
% apply(k,
% g(X)))),
% f(X)),g(X))) -> (false)
% Current number of equations to process: 3089
% Current number of ordered equations: 0
% Current number of rules: 139
% New rule produced :
% [165]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(s,s),
% apply(k,
% f(X))),
% apply(apply(
% apply(s,
% apply(k,k)),s),
% apply(k,
% g(X)))),
% f(X)),g(X))) ->
% (false)
% Current number of equations to process: 3113
% Current number of ordered equations: 0
% Current number of rules: 140
% New rule produced :
% [166] apply(apply(apply(apply(s,s),apply(k,Y)),apply(k,apply(k,X))),Z) -> X
% Current number of equations to process: 3136
% Current number of ordered equations: 0
% Current number of rules: 141
% New rule produced :
% [167]
% (eq)(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),k),
% apply(k,g(X))),X),f(X)),apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% g(X)),apply(f(X),f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3181
% Current number of ordered equations: 0
% Current number of rules: 142
% New rule produced :
% [168]
% apply(apply(apply(apply(s,apply(s,s)),apply(s,s)),k),k) ->
% apply(apply(s,s),k)
% Current number of equations to process: 3202
% Current number of ordered equations: 0
% Current number of rules: 143
% New rule produced :
% [169]
% apply(apply(apply(s,apply(X,k)),X),k) <->
% apply(apply(apply(apply(s,apply(s,s)),X),k),k)
% Current number of equations to process: 3231
% Current number of ordered equations: 1
% Current number of rules: 144
% New rule produced :
% [170]
% apply(apply(apply(apply(s,apply(s,s)),X),k),k) <->
% apply(apply(apply(s,apply(X,k)),X),k)
% Current number of equations to process: 3231
% Current number of ordered equations: 0
% Current number of rules: 145
% New rule produced :
% [171] apply(apply(apply(apply(s,apply(s,s)),apply(s,apply(s,k))),k),X) -> X
% Current number of equations to process: 3298
% Current number of ordered equations: 0
% Current number of rules: 146
% New rule produced :
% [172] apply(apply(apply(apply(apply(s,apply(s,s)),s),s),k),apply(k,X)) -> X
% Current number of equations to process: 3345
% Current number of ordered equations: 0
% Current number of rules: 147
% New rule produced :
% [173]
% (eq)(apply(f(apply(apply(s,k),X)),g(apply(apply(s,k),X))),apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(apply(
% apply(s,k),X))),
% apply(
% f(apply(
% apply(s,k),X)),
% f(apply(
% apply(s,k),X)))),
% g(apply(apply(s,k),X))))
% -> (false)
% Current number of equations to process: 3379
% Current number of ordered equations: 0
% Current number of rules: 148
% New rule produced :
% [174]
% (eq)(apply(f(apply(s,apply(s,k))),g(apply(s,apply(s,k)))),apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(apply(s,
% apply(s,k)))),
% apply(
% f(apply(s,
% apply(s,k))),
% f(apply(s,
% apply(s,k))))),
% g(apply(s,apply(s,k)))))
% -> (false)
% Current number of equations to process: 3425
% Current number of ordered equations: 0
% Current number of rules: 149
% New rule produced :
% [175]
% (eq)(g(apply(s,k)),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(apply(s,apply(k,s)),s)),k),
% g(apply(s,k))),apply(k,g(apply(s,k)))),
% apply(f(apply(s,k)),f(apply(s,k))))) -> (false)
% Current number of equations to process: 3433
% Current number of ordered equations: 0
% Current number of rules: 150
% New rule produced :
% [176]
% 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: 3452
% Current number of ordered equations: 3
% Current number of rules: 151
% New rule produced :
% [177]
% 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: 3452
% Current number of ordered equations: 2
% Current number of rules: 152
% New rule produced :
% [178]
% 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: 3452
% Current number of ordered equations: 1
% Current number of rules: 153
% New rule produced :
% [179]
% 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: 3452
% Current number of ordered equations: 0
% Current number of rules: 154
% New rule produced :
% [180]
% 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: 4300
% Current number of ordered equations: 3
% Current number of rules: 155
% New rule produced :
% [181]
% 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: 4300
% Current number of ordered equations: 2
% Current number of rules: 156
% New rule produced :
% [182]
% 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: 4300
% Current number of ordered equations: 1
% Current number of rules: 157
% New rule produced :
% [183]
% 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: 4300
% Current number of ordered equations: 0
% Current number of rules: 158
% New rule produced :
% [184]
% 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: 2295
% Current number of ordered equations: 1
% Current number of rules: 159
% New rule produced :
% [185]
% 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: 2295
% Current number of ordered equations: 0
% Current number of rules: 160
% New rule produced :
% [186]
% apply(apply(apply(s,apply(k,X)),apply(apply(apply(s,s),Z),k)),Y) ->
% apply(X,Y)
% Current number of equations to process: 2661
% Current number of ordered equations: 0
% Current number of rules: 161
% New rule produced :
% [187]
% 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: 2736
% Current number of ordered equations: 1
% Current number of rules: 162
% New rule produced :
% [188]
% 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: 2736
% Current number of ordered equations: 0
% Current number of rules: 163
% New rule produced :
% [189]
% 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: 2934
% Current number of ordered equations: 3
% Current number of rules: 164
% New rule produced :
% [190]
% 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: 2934
% Current number of ordered equations: 2
% Current number of rules: 165
% New rule produced :
% [191]
% 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: 2934
% Current number of ordered equations: 1
% Current number of rules: 166
% New rule produced :
% [192]
% 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: 2934
% Current number of ordered equations: 0
% Current number of rules: 167
% New rule produced :
% [193]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% g(X)),apply(
% apply(s,
% f(X)),
% apply(k,
% g(X)))),
% f(X))) -> (false)
% Current number of equations to process: 3447
% Current number of ordered equations: 0
% Current number of rules: 168
% New rule produced :
% [194]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),k),
% g(X)),apply(apply(s,f(X)),
% apply(k,g(X)))),f(X))) ->
% (false)
% Current number of equations to process: 3462
% Current number of ordered equations: 0
% Current number of rules: 169
% New rule produced :
% [195]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),X),apply(k,f(X))),
% apply(k,g(X))),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(X)),
% apply(apply(s,f(X)),apply(k,g(X)))),f(X))) ->
% (false)
% Current number of equations to process: 3517
% Current number of ordered equations: 0
% Current number of rules: 170
% New rule produced :
% [196]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(X)),
% apply(apply(s,f(X)),apply(k,g(X)))),f(X))) ->
% (false)
% Current number of equations to process: 3516
% Current number of ordered equations: 0
% Current number of rules: 171
% New rule produced :
% [197]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(s,apply(k,g(X)))),
% apply(s,f(X))),apply(k,g(X))),
% f(X))) -> (false)
% Current number of equations to process: 3702
% Current number of ordered equations: 0
% Current number of rules: 172
% New rule produced :
% [198]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,
% apply(k,
% g(X)))),
% apply(s,
% f(X))),apply(k,
% g(X))),
% f(X))) -> (false)
% Current number of equations to process: 3731
% Current number of ordered equations: 0
% Current number of rules: 173
% New rule produced :
% [199]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(s,s)),apply(
% apply(s,
% apply(k,k)),
% f(X))),
% f(X)),apply(k,g(X))),g(X))) ->
% (false)
% Current number of equations to process: 3815
% Current number of ordered equations: 1
% Current number of rules: 174
% New rule produced :
% [200]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(s,s)),apply(k,
% apply(
% f(X),
% f(X)))),k),
% g(X)),g(X))) -> (false)
% Current number of equations to process: 3815
% Current number of ordered equations: 0
% Current number of rules: 175
% New rule produced :
% [201]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(s,
% apply(k,k))),s),
% apply(s,X)),k),f(X)),apply(k,g(X))),apply(apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3927
% Current number of ordered equations: 2
% Current number of rules: 176
% New rule produced :
% [202]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(s,apply(k,k))),
% apply(s,apply(s,X))),apply(k,f(X))),k),g(X)),apply(
% apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) ->
% (false)
% Current number of equations to process: 3927
% Current number of ordered equations: 1
% Current number of rules: 177
% New rule produced :
% [203]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,
% apply(k,k))),s),
% apply(k,g(X))),f(X)),
% f(X)),g(X))) -> (false)
% Current number of equations to process: 3927
% Current number of ordered equations: 0
% Current number of rules: 178
% New rule produced :
% [204]
% apply(X,apply(apply(s,k),Y)) <->
% apply(apply(apply(apply(s,s),k),apply(apply(s,k),Y)),X)
% Current number of equations to process: 4130
% Current number of ordered equations: 1
% Current number of rules: 179
% New rule produced :
% [205]
% apply(apply(apply(apply(s,s),k),apply(apply(s,k),Y)),X) <->
% apply(X,apply(apply(s,k),Y))
% Current number of equations to process: 4130
% Current number of ordered equations: 0
% Current number of rules: 180
% New rule produced :
% [206] apply(apply(apply(apply(s,s),k),apply(apply(s,k),Y)),apply(k,X)) -> X
% Current number of equations to process: 4196
% Current number of ordered equations: 0
% Current number of rules: 181
% New rule produced :
% [207] apply(apply(apply(apply(s,apply(s,s)),apply(s,k)),k),apply(k,X)) -> X
% Current number of equations to process: 4387
% Current number of ordered equations: 0
% Current number of rules: 182
% New rule produced :
% [208]
% apply(X,apply(s,apply(s,k))) <->
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,s),k)),s),
% apply(s,k)),X)
% Current number of equations to process: 4451
% Current number of ordered equations: 1
% Current number of rules: 183
% New rule produced :
% [209]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,s),k)),s),
% apply(s,k)),X) <-> apply(X,apply(s,apply(s,k)))
% Current number of equations to process: 4451
% Current number of ordered equations: 0
% Current number of rules: 184
% New rule produced :
% [210]
% apply(X,apply(apply(apply(apply(s,s),k),Y),Z)) <->
% apply(apply(apply(s,apply(k,X)),apply(Y,Z)),Y)
% Current number of equations to process: 4637
% Current number of ordered equations: 3
% Current number of rules: 185
% New rule produced :
% [211]
% apply(apply(apply(apply(s,apply(k,X)),Y),Z),X) <->
% apply(apply(apply(apply(s,s),k),X),apply(Y,Z))
% Current number of equations to process: 4637
% Current number of ordered equations: 2
% Current number of rules: 186
% New rule produced :
% [212]
% apply(apply(apply(s,apply(k,X)),apply(Y,Z)),Y) <->
% apply(X,apply(apply(apply(apply(s,s),k),Y),Z))
% Current number of equations to process: 4637
% Current number of ordered equations: 1
% Current number of rules: 187
% New rule produced :
% [213]
% apply(apply(apply(apply(s,s),k),X),apply(Y,Z)) <->
% apply(apply(apply(apply(s,apply(k,X)),Y),Z),X)
% Current number of equations to process: 4637
% Current number of ordered equations: 0
% Current number of rules: 188
% New rule produced :
% [214]
% apply(apply(apply(apply(s,s),k),apply(s,X)),apply(k,Y)) <->
% apply(apply(X,apply(s,X)),Y)
% Current number of equations to process: 1538
% Current number of ordered equations: 1
% Current number of rules: 189
% New rule produced :
% [215]
% apply(apply(X,apply(s,X)),Y) <->
% apply(apply(apply(apply(s,s),k),apply(s,X)),apply(k,Y))
% Current number of equations to process: 1538
% Current number of ordered equations: 0
% Current number of rules: 190
% New rule produced :
% [216]
% apply(apply(apply(apply(apply(s,apply(k,s)),k),X),apply(k,Y)),Z) ->
% apply(X,Y)
% Current number of equations to process: 1693
% Current number of ordered equations: 0
% Current number of rules: 191
% New rule produced :
% [217]
% apply(Y,X) <->
% apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),k),
% apply(k,X)),apply(k,Y)),Z)
% Current number of equations to process: 1801
% Current number of ordered equations: 1
% Current number of rules: 192
% New rule produced :
% [218]
% apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),k),
% apply(k,X)),apply(k,Y)),Z) <-> apply(Y,X)
% Current number of equations to process: 1801
% Current number of ordered equations: 0
% Current number of rules: 193
% New rule produced :
% [219]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,s),k)),s),
% apply(k,X)),apply(k,Y)) -> apply(X,Y)
% Current number of equations to process: 2789
% Current number of ordered equations: 0
% Current number of rules: 194
% New rule produced :
% [220]
% 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: 2876
% Current number of ordered equations: 0
% Current number of rules: 195
% New rule produced :
% [221]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,s),k)),
% apply(s,apply(k,k))),X),Y) -> apply(X,Y)
% Current number of equations to process: 2988
% Current number of ordered equations: 0
% Current number of rules: 196
% New rule produced :
% [222]
% (eq)(apply(X,g(apply(k,X))),apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,g(apply(k,X)))),apply(k,
% g(apply(k,X)))),
% apply(f(apply(k,X)),f(apply(k,X))))) -> (false)
% Current number of equations to process: 3097
% Current number of ordered equations: 0
% Current number of rules: 197
% New rule produced :
% [223]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),s),
% apply(k,s)),apply(k,
% apply(k,
% g(X)))),s),
% apply(k,g(X))),apply(f(X),f(X)))) ->
% (false)
% Current number of equations to process: 3120
% Current number of ordered equations: 1
% Current number of rules: 198
% New rule produced :
% [224]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,apply(k,s))),s),
% apply(k,g(X))),apply(k,apply(
% f(X),
% f(X)))),
% apply(k,g(X)))) -> (false)
% Current number of equations to process: 3120
% Current number of ordered equations: 0
% Current number of rules: 199
% New rule produced :
% [225]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,apply(k,s))),k),
% apply(apply(apply(s,apply(s,s)),k),s)),s),
% apply(apply(s,apply(k,k)),k)),g(k)),apply(k,g(k))),
% apply(f(k),f(k)))) -> (false)
% Current number of equations to process: 3237
% Current number of ordered equations: 0
% Current number of rules: 200
% New rule produced :
% [226]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(s,
% apply(k,s))),k),
% apply(s,X)),apply(k,g(X))),k),f(X)),apply(apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3295
% Current number of ordered equations: 2
% Current number of rules: 201
% New rule produced :
% [227]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(apply(s,
% apply(k,s)),k)),
% apply(s,X)),k),apply(k,f(X))),g(X)),apply(apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3295
% Current number of ordered equations: 1
% Current number of rules: 202
% New rule produced :
% [228]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),apply(k,apply(s,X))),k),k),
% g(X)),f(X)),apply(apply(apply(s,apply(k,g(X))),apply(f(X),f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3295
% Current number of ordered equations: 0
% Current number of rules: 203
% New rule produced :
% [229]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),
% apply(s,apply(s,s))),
% apply(k,apply(k,g(X)))),apply(k,
% g(X))),
% apply(k,apply(f(X),f(X))))) -> (false)
% Current number of equations to process: 3481
% Current number of ordered equations: 0
% Current number of rules: 204
% New rule produced :
% [230]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,apply(k,s))),k),
% g(X)),apply(k,g(X))),apply(
% f(X),
% f(X)))) ->
% (false)
% Current number of equations to process: 3524
% Current number of ordered equations: 0
% Current number of rules: 205
% New rule produced :
% [231]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(s,apply(k,s))),s),X),
% apply(k,apply(k,g(X)))),apply(k,f(X))),apply(apply(apply(s,
% apply(k,
% g(X))),
% apply(f(X),f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3608
% Current number of ordered equations: 1
% Current number of rules: 206
% New rule produced :
% [232]
% (eq)(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,s)),
% apply(k,X)),s),apply(k,f(X))),apply(k,g(X))),apply(
% apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) ->
% (false)
% Current number of equations to process: 3608
% Current number of ordered equations: 0
% Current number of rules: 207
% New rule produced :
% [233]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,s),k)),
% apply(s,apply(s,s))),s),k) -> apply(s,k)
% Current number of equations to process: 3718
% Current number of ordered equations: 0
% Current number of rules: 208
% New rule produced :
% [234]
% 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: 3778
% Current number of ordered equations: 1
% Current number of rules: 209
% New rule produced :
% [235]
% 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: 3778
% Current number of ordered equations: 0
% Current number of rules: 210
% New rule produced :
% [236]
% apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),
% apply(s,k)),X),apply(k,Y)),Z) -> apply(Y,Y)
% Current number of equations to process: 4053
% Current number of ordered equations: 0
% Current number of rules: 211
% New rule produced :
% [237]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),k),s),s),
% apply(k,
% apply(k,
% g(X)))),
% apply(k,g(X))),
% apply(f(X),f(X)))) ->
% (false)
% Current number of equations to process: 4177
% Current number of ordered equations: 0
% Current number of rules: 212
% New rule produced :
% [238]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),k),s),s),
% apply(apply(s,k),Y)),
% apply(k,g(X))),
% apply(f(X),f(X)))) ->
% (false)
% Current number of equations to process: 4205
% Current number of ordered equations: 0
% Current number of rules: 213
% New rule produced :
% [239]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),k),
% apply(k,apply(f(X),f(X)))),g(X)),g(X))) ->
% (false)
% Current number of equations to process: 4252
% Current number of ordered equations: 1
% Current number of rules: 214
% New rule produced :
% [240]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),k),
% apply(k,k)),apply(s,X)),g(X)),f(X)),apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(X)),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 4252
% Current number of ordered equations: 0
% Current number of rules: 215
% New rule produced :
% [241]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),k),
% apply(k,k)),apply(s,X)),g(X)),f(X)),apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s)),k),
% apply(
% f(X),
% f(X))),
% apply(k,
% g(X))),
% g(X))) -> (false)
% Current number of equations to process: 4338
% Current number of ordered equations: 0
% Current number of rules: 216
% New rule produced :
% [242]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),X),apply(k,f(X))),
% apply(k,g(X))),apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),k),
% apply(k,apply(f(X),f(X)))),g(X)),g(X))) ->
% (false)
% Current number of equations to process: 4392
% Current number of ordered equations: 1
% Current number of rules: 217
% New rule produced :
% [243]
% (eq)(apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),s),
% apply(k,apply(k,f(X)))),X),apply(k,g(X))),apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(X)),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 4392
% Current number of ordered equations: 0
% Current number of rules: 218
% New rule produced :
% [244]
% (eq)(apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),s),
% apply(k,apply(k,f(X)))),X),apply(k,g(X))),apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s)),k),
% apply(
% f(X),
% f(X))),
% apply(k,
% g(X))),
% g(X))) -> (false)
% Current number of equations to process: 4462
% Current number of ordered equations: 0
% Current number of rules: 219
% New rule produced :
% [245]
% apply(apply(X,Y),apply(Y,Y)) <->
% apply(apply(apply(apply(s,s),apply(s,k)),apply(s,X)),Y)
% Current number of equations to process: 4502
% Current number of ordered equations: 1
% Current number of rules: 220
% New rule produced :
% [246]
% apply(apply(apply(apply(s,s),apply(s,k)),apply(s,X)),Y) <->
% apply(apply(X,Y),apply(Y,Y))
% Current number of equations to process: 4502
% Current number of ordered equations: 0
% Current number of rules: 221
% New rule produced :
% [247]
% apply(X,X) <->
% apply(apply(apply(apply(s,s),apply(s,k)),apply(apply(s,k),Y)),X)
% Current number of equations to process: 4782
% Current number of ordered equations: 1
% Current number of rules: 222
% New rule produced :
% [248]
% apply(apply(apply(apply(s,s),apply(s,k)),apply(apply(s,k),Y)),X) <->
% apply(X,X)
% Current number of equations to process: 4782
% Current number of ordered equations: 0
% Current number of rules: 223
% New rule produced :
% [249]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(s,apply(k,g(X))),apply(
% apply(
% apply(
% apply(s,s),
% apply(s,k)),
% apply(
% apply(s,k),Y)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 4818
% Current number of ordered equations: 0
% Current number of rules: 224
% New rule produced :
% [250]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(s,
% apply(k,
% g(X))),apply(
% apply(
% apply(
% apply(s,s),
% apply(s,k)),
% apply(
% apply(s,k),Y)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 4849
% Current number of ordered equations: 0
% Current number of rules: 225
% New rule produced :
% [251]
% (eq)(f(k),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(k)),apply(
% apply(
% apply(
% apply(s,s),
% apply(s,k)),
% apply(
% apply(s,k),X)),
% f(k))),
% g(k))) -> (false)
% Current number of equations to process: 4848
% Current number of ordered equations: 0
% Current number of rules: 226
% New rule produced :
% [252]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(s,apply(k,g(X))),apply(
% apply(
% apply(
% apply(s,s),
% apply(s,k)),
% apply(
% apply(
% apply(s,s),Y),k)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 2308
% Current number of ordered equations: 0
% Current number of rules: 227
% New rule produced :
% [253]
% apply(apply(apply(apply(apply(s,s),apply(s,k)),s),apply(k,X)),Y) ->
% apply(X,X)
% Current number of equations to process: 2395
% Current number of ordered equations: 0
% Current number of rules: 228
% New rule produced :
% [254]
% apply(apply(apply(s,X),apply(apply(s,k),Y)),Z) <->
% apply(apply(apply(apply(s,s),apply(s,k)),X),Z)
% Current number of equations to process: 2482
% Current number of ordered equations: 1
% Current number of rules: 229
% New rule produced :
% [255]
% apply(apply(apply(apply(s,s),apply(s,k)),X),Z) <->
% apply(apply(apply(s,X),apply(apply(s,k),Y)),Z)
% Rule
% [63]
% (eq)(f(k),apply(apply(apply(apply(apply(s,s),apply(s,k)),apply(apply(s,
% apply(k,s)),s)),
% apply(k,g(k))),apply(f(k),f(k)))) -> (false) collapsed.
% Rule
% [94]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,s),apply(s,k)),
% apply(apply(s,apply(k,s)),s)),
% apply(k,g(X))),apply(f(X),f(X)))) ->
% (false) collapsed.
% Rule
% [151]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(s,s),
% apply(s,k)),
% apply(apply(s,
% apply(k,s)),s)),
% apply(k,g(X))),
% apply(f(X),f(X)))) ->
% (false) collapsed.
% Rule
% [252]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(s,apply(k,g(X))),apply(
% apply(
% apply(
% apply(s,s),
% apply(s,k)),
% apply(
% apply(
% apply(s,s),Y),k)),
% f(X))),
% g(X))) -> (false) collapsed.
% Current number of equations to process: 2483
% Current number of ordered equations: 0
% Current number of rules: 226
% New rule produced :
% [256]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(s,apply(k,g(X))),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),
% apply(
% apply(s,s),Y)),k),
% apply(
% apply(s,k),Y)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 2518
% Current number of ordered equations: 0
% Current number of rules: 227
% New rule produced :
% [257]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,
% apply(k,s))),k),
% apply(s,s)),apply(s,k)),
% apply(apply(apply(apply(s,
% apply(s,s)),k),s),k)),
% apply(k,apply(f(X),f(X)))),g(X))) ->
% (false)
% Current number of equations to process: 2741
% Current number of ordered equations: 0
% Current number of rules: 228
% New rule produced :
% [258]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s))),
% apply(s,
% apply(k,s))),k),k),
% apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,apply(k,s))),k)),
% apply(s,s)),apply(s,k)),
% apply(apply(apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(s,
% apply(k,k)))),s),
% apply(k,g(k))),f(k)),g(k))) -> (false)
% Current number of equations to process: 2812
% Current number of ordered equations: 0
% Current number of rules: 229
% New rule produced :
% [259]
% apply(apply(apply(apply(s,s),apply(k,X)),apply(apply(s,s),Y)),k) ->
% apply(X,k)
% Current number of equations to process: 2961
% Current number of ordered equations: 0
% Current number of rules: 230
% New rule produced :
% [260]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),k),s),
% apply(k,g(X))),k),apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3023
% Current number of ordered equations: 0
% Current number of rules: 231
% New rule produced :
% [261]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),k),
% apply(k,k)),apply(s,s)),apply(f(k),f(k))),
% apply(k,g(k))),g(k))) -> (false)
% Current number of equations to process: 3091
% Current number of ordered equations: 0
% Current number of rules: 232
% New rule produced :
% [262]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),
% apply(s,s)),apply(apply(
% apply(s,
% apply(k,k)),
% f(X)),
% f(X))),apply(k,
% g(X))),
% apply(k,g(X)))) -> (false)
% Current number of equations to process: 3124
% Current number of ordered equations: 0
% Current number of rules: 233
% New rule produced :
% [263]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,
% apply(k,s))),k),
% apply(s,s)),apply(s,k)),
% apply(apply(s,apply(k,s)),
% apply(s,s))),apply(k,apply(
% f(X),
% f(X)))),
% apply(k,g(X)))) -> (false)
% Current number of equations to process: 3181
% Current number of ordered equations: 0
% Current number of rules: 234
% New rule produced :
% [264]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,X)),apply(k,
% apply(k,
% g(X)))),
% apply(k,f(X))),apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,
% g(X))),
% apply(k,g(X))),apply(f(X),f(X)))) -> (false)
% Current number of equations to process: 3257
% Current number of ordered equations: 0
% Current number of rules: 235
% New rule produced :
% [265]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,X)),apply(
% apply(
% apply(s,
% apply(k,k)),k),
% g(X))),
% apply(k,f(X))),apply(apply(apply(s,apply(k,g(X))),apply(f(X),f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3299
% Current number of ordered equations: 0
% Current number of rules: 236
% New rule produced :
% [266]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(s,apply(s,s))),
% apply(apply(s,apply(k,k)),k)),
% g(X)),apply(apply(apply(s,
% apply(k,k)),
% f(X)),f(X))),g(X))) ->
% (false)
% Current number of equations to process: 3332
% Current number of ordered equations: 1
% Current number of rules: 237
% New rule produced :
% [267]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(s,apply(s,s)),
% apply(k,apply(k,g(X)))),apply(
% apply(
% apply(
% apply(s,s),
% apply(k,
% f(X))),
% apply(k,k)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3395
% Current number of ordered equations: 1
% Current number of rules: 238
% New rule produced :
% [268]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(s,apply(s,s))),
% apply(apply(s,apply(k,k)),k)),
% g(X)),apply(k,apply(f(X),f(X)))),
% g(X))) -> (false)
% Current number of equations to process: 3436
% Current number of ordered equations: 1
% Current number of rules: 239
% New rule produced :
% [269]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,apply(s,s))),k),s),
% apply(s,k)),s),apply(k,g(k))),apply(f(k),f(k))))
% -> (false)
% Current number of equations to process: 3474
% Current number of ordered equations: 1
% Current number of rules: 240
% New rule produced :
% [270]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% g(X)),apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),s),
% apply(s,k)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3537
% Current number of ordered equations: 1
% Current number of rules: 241
% New rule produced :
% [271]
% (eq)(f(k),apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,g(k))),
% apply(k,g(k))),apply(apply(apply(apply(s,apply(s,s)),s),
% apply(s,k)),f(k)))) -> (false)
% Current number of equations to process: 3568
% Current number of ordered equations: 1
% Current number of rules: 242
% New rule produced :
% [272]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),X),apply(k,f(X))),
% apply(k,g(X))),apply(apply(apply(s,apply(k,g(X))),apply(apply(apply(
% apply(s,
% apply(s,s)),s),
% apply(s,k)),
% f(X))),g(X))) ->
% (false)
% Current number of equations to process: 3596
% Current number of ordered equations: 2
% Current number of rules: 243
% New rule produced :
% [273]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(s,apply(k,g(X))),apply(apply(
% apply(
% apply(s,
% apply(s,s)),s),
% apply(s,k)),
% f(X))),g(X))) ->
% (false)
% Current number of equations to process: 3630
% Current number of ordered equations: 1
% Current number of rules: 244
% New rule produced :
% [274]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(s,s)),k),s),s),
% apply(apply(apply(s,s),Y),k)),
% apply(k,g(X))),apply(f(X),f(X)))) ->
% (false)
% Current number of equations to process: 3663
% Current number of ordered equations: 1
% Current number of rules: 245
% New rule produced :
% [275]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),k),s),k),
% apply(apply(
% apply(s,
% apply(k,k)),
% f(X)),
% f(X))),g(X)),
% g(X))) -> (false)
% Current number of equations to process: 3756
% Current number of ordered equations: 0
% Current number of rules: 246
% New rule produced :
% [276]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(apply(s,
% apply(k,s)),s)),k),
% g(X)),apply(k,g(X))),apply(
% f(X),
% f(X)))) ->
% (false)
% Current number of equations to process: 3792
% Current number of ordered equations: 0
% Current number of rules: 247
% New rule produced :
% [277]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(s,apply(s,s))),k),
% apply(k,g(X))),apply(k,apply(
% f(X),
% f(X)))),
% g(X))) -> (false)
% Current number of equations to process: 3858
% Current number of ordered equations: 0
% Current number of rules: 248
% New rule produced :
% [278]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,apply(s,X)),
% apply(k,f(X)))),k),
% g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(k,g(X))),
% apply(k,g(X))),apply(f(X),f(X)))) -> (false)
% Current number of equations to process: 3898
% Current number of ordered equations: 1
% Current number of rules: 249
% New rule produced :
% [279]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,apply(s,X))),k),
% f(X)),apply(k,g(X))),apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,g(X))),apply(k,g(X))),
% apply(f(X),f(X)))) -> (false)
% Current number of equations to process: 3898
% Current number of ordered equations: 0
% Current number of rules: 250
% New rule produced :
% [280]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,X)),apply(k,
% apply(k,
% g(X)))),
% apply(k,f(X))),apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(s,apply(k,g(X)))),f(X)),f(X)),
% g(X))) -> (false)
% Current number of equations to process: 3986
% Current number of ordered equations: 0
% Current number of rules: 251
% New rule produced :
% [281]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),k),s),k),
% apply(k,
% f(X))),
% apply(s,
% apply(k,
% g(X)))),
% f(X)),g(X))) ->
% (false)
% Current number of equations to process: 4025
% Current number of ordered equations: 1
% Current number of rules: 252
% New rule produced :
% [282]
% (eq)(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),k),
% apply(k,g(X))),X),f(X)),apply(apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(s,apply(k,
% g(X)))),
% f(X)),f(X)),g(X))) ->
% (false)
% Current number of equations to process: 4025
% Current number of ordered equations: 0
% Current number of rules: 253
% New rule produced :
% [283]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,apply(s,X)),
% apply(k,f(X)))),k),
% g(X)),apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,
% apply(k,
% g(X)))),
% f(X)),f(X)),g(X))) -> (false)
% Current number of equations to process: 4091
% Current number of ordered equations: 1
% Current number of rules: 254
% New rule produced :
% [284]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,apply(s,X))),k),
% f(X)),apply(k,g(X))),apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(s,apply(k,g(X)))),
% f(X)),f(X)),g(X))) -> (false)
% Current number of equations to process: 4091
% Current number of ordered equations: 0
% Current number of rules: 255
% New rule produced :
% [285]
% (eq)(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),k),
% apply(k,f(X))),apply(s,X)),apply(k,g(X))),apply(apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 4168
% Current number of ordered equations: 0
% Current number of rules: 256
% New rule produced :
% [286]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(s,s)),k),
% apply(k,g(X))),apply(s,apply(k,
% g(X)))),
% apply(f(X),f(X)))) -> (false)
% Current number of equations to process: 4203
% Current number of ordered equations: 1
% Current number of rules: 257
% New rule produced :
% [287]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s)),k),
% apply(k,apply(f(X),f(X)))),s),
% apply(k,g(X))),g(X))) -> (false)
% Current number of equations to process: 4203
% Current number of ordered equations: 0
% Current number of rules: 258
% New rule produced :
% [288]
% (eq)(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),k),
% apply(k,g(X))),X),f(X)),apply(apply(apply(apply(apply(s,
% apply(k,s)),s),
% apply(k,g(X))),apply(k,
% g(X))),
% apply(f(X),f(X)))) -> (false)
% Current number of equations to process: 4289
% Current number of ordered equations: 0
% Current number of rules: 259
% New rule produced :
% [289]
% apply(X,apply(apply(s,k),k)) <->
% apply(apply(apply(apply(s,apply(s,s)),apply(s,k)),k),X)
% Current number of equations to process: 4325
% Current number of ordered equations: 1
% Current number of rules: 260
% New rule produced :
% [290]
% apply(apply(apply(apply(s,apply(s,s)),apply(s,k)),k),X) <->
% apply(X,apply(apply(s,k),k))
% Current number of equations to process: 4325
% Current number of ordered equations: 0
% Current number of rules: 261
% New rule produced :
% [291]
% apply(apply(apply(apply(s,apply(s,s)),apply(s,apply(k,k))),k),X) ->
% apply(k,X)
% Current number of equations to process: 4487
% Current number of ordered equations: 0
% Current number of rules: 262
% New rule produced :
% [292]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),s),k),k),g(k)),f(k)),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,
% g(k))),
% apply(k,
% g(k))),
% apply(
% f(k),
% f(k))))
% -> (false)
% Current number of equations to process: 4568
% Current number of ordered equations: 0
% Current number of rules: 263
% New rule produced :
% [293]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(s,s)),k),s),
% apply(
% apply(s,
% apply(k,s)),k)),k),
% g(X)),apply(f(X),f(X))))
% -> (false)
% Current number of equations to process: 4612
% Current number of ordered equations: 0
% Current number of rules: 264
% New rule produced :
% [294]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),s),
% apply(apply(apply(apply(s,s),X),s),k)),apply(k,g(k))),
% apply(f(k),f(k)))) -> (false)
% Current number of equations to process: 4645
% Current number of ordered equations: 0
% Current number of rules: 265
% New rule produced :
% [295]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),k),
% apply(k,f(k))),apply(apply(apply(s,apply(k,s)),k),
% g(k))),f(k)),g(k))) -> (false)
% Current number of equations to process: 4682
% Current number of ordered equations: 0
% Current number of rules: 266
% Rule [180]
% apply(apply(X,Y),apply(Z,Y)) <->
% apply(apply(apply(s,X),apply(apply(s,apply(s,k)),Z)),Y) is composed into
% [180] apply(apply(X,Y),apply(Z,Y)) <-> apply(apply(apply(s,X),Z),Y)
% New rule produced :
% [296]
% apply(apply(apply(s,X),apply(apply(s,apply(s,k)),Y)),Z) ->
% apply(apply(apply(s,X),Y),Z)
% Rule
% [182]
% apply(apply(apply(s,X),apply(apply(s,apply(s,k)),Z)),Y) <->
% apply(apply(X,Y),apply(Z,Y)) collapsed.
% Current number of equations to process: 4705
% Current number of ordered equations: 0
% Current number of rules: 266
% New rule produced :
% [297]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,X)),apply(k,
% apply(k,
% g(X)))),
% apply(k,f(X))),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(X)),
% apply(apply(s,f(X)),apply(k,g(X)))),f(X))) ->
% (false)
% Current number of equations to process: 4793
% Current number of ordered equations: 0
% Current number of rules: 267
% New rule produced :
% [298]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,apply(s,X)),
% apply(k,f(X)))),k),
% g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(X)),apply(
% apply(s,
% f(X)),
% apply(k,
% g(X)))),
% f(X))) -> (false)
% Current number of equations to process: 4834
% Current number of ordered equations: 0
% Current number of rules: 268
% New rule produced :
% [299]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,apply(s,X))),k),
% f(X)),apply(k,g(X))),apply(apply(apply(apply(apply(s,apply(k,s)),k),
% g(X)),apply(apply(s,f(X)),
% apply(k,g(X)))),f(X))) ->
% (false)
% Current number of equations to process: 4872
% Current number of ordered equations: 0
% Current number of rules: 269
% New rule produced :
% [300]
% (eq)(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),k),
% apply(k,g(X))),X),f(X)),apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% g(X)),apply(apply(s,
% f(X)),
% apply(k,g(X)))),
% f(X))) -> (false)
% Current number of equations to process: 4911
% Current number of ordered equations: 0
% Current number of rules: 270
% New rule produced :
% [301]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),s),
% apply(k,s)),apply(k,
% g(X))),k),
% apply(apply(s,f(X)),apply(k,g(X)))),
% f(X))) -> (false)
% Current number of equations to process: 4946
% Current number of ordered equations: 0
% Current number of rules: 271
% New rule produced :
% [302]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),apply(k,g(k))),k),apply(
% apply(s,
% f(k)),
% apply(k,
% g(k)))),
% f(k))) -> (false)
% Current number of equations to process: 4989
% Current number of ordered equations: 0
% Current number of rules: 272
% New rule produced :
% [303]
% (eq)(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,s)),k),
% apply(k,g(X))),apply(k,apply(X,f(X)))),Y),apply(apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 1671
% Current number of ordered equations: 0
% Current number of rules: 273
% New rule produced :
% [304]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(s,apply(k,s)),k),
% g(X)),apply(apply(apply(apply(s,s),
% apply(s,k)),
% apply(apply(s,k),Y)),
% f(X))),g(X))) -> (false)
% Current number of equations to process: 1731
% Current number of ordered equations: 0
% Current number of rules: 274
% New rule produced :
% [305]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(s,
% apply(k,
% g(X))),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),
% apply(
% apply(s,s),Y)),k),
% apply(
% apply(s,k),Y)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 1840
% Current number of ordered equations: 0
% Current number of rules: 275
% New rule produced :
% [306]
% (eq)(f(k),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(k)),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),
% apply(
% apply(s,s),X)),k),
% apply(
% apply(s,k),k)),
% f(k))),
% g(k))) -> (false)
% Current number of equations to process: 1899
% Current number of ordered equations: 0
% Current number of rules: 276
% New rule produced :
% [307]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(s,apply(k,g(X))),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),
% apply(
% apply(
% apply(s,s),Y),s)),k),
% apply(
% apply(s,k),Y)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 1944
% Current number of ordered equations: 0
% Current number of rules: 277
% New rule produced :
% [308]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(s,apply(k,g(X))),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),
% apply(s,k)),Y),
% apply(
% apply(s,k),Z)),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 2014
% Current number of ordered equations: 0
% Current number of rules: 278
% New rule produced :
% [309]
% apply(apply(apply(apply(s,apply(s,s)),apply(s,s)),apply(k,X)),k) ->
% apply(X,k)
% Current number of equations to process: 2092
% Current number of ordered equations: 0
% Current number of rules: 279
% New rule produced :
% [310]
% (eq)(g(apply(s,k)),apply(apply(apply(apply(apply(apply(apply(s,apply(s,s)),k),s),s),
% apply(apply(s,k),k)),apply(k,g(apply(s,k)))),
% apply(f(apply(s,k)),f(apply(s,k))))) -> (false)
% Current number of equations to process: 2145
% Current number of ordered equations: 0
% Current number of rules: 280
% New rule produced :
% [311]
% 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: 2173
% Current number of ordered equations: 3
% Current number of rules: 281
% New rule produced :
% [312]
% 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: 2173
% Current number of ordered equations: 2
% Current number of rules: 282
% Rule [208]
% apply(X,apply(s,apply(s,k))) <->
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,s),k)),s),
% apply(s,k)),X) is composed into [208]
% apply(X,apply(s,apply(s,k))) <->
% apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(s,k)),X)
% New rule produced :
% [313]
% 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)
% Rule
% [121]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,
% apply(k,k))),s),
% apply(k,
% g(X))),
% f(X)),f(X)),
% g(X))) -> (false) collapsed.
% Rule
% [130]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,
% apply(k,s))),k),
% g(X)),apply(k,
% g(X))),
% apply(f(X),f(X)))) ->
% (false) collapsed.
% Rule
% [200]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(s,s)),apply(k,
% apply(
% f(X),
% f(X)))),k),
% g(X)),g(X))) -> (false) collapsed.
% Rule
% [201]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(s,
% apply(k,k))),s),
% apply(s,X)),k),f(X)),apply(k,g(X))),apply(apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% collapsed.
% Rule
% [202]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(s,apply(k,k))),
% apply(s,apply(s,X))),apply(k,f(X))),k),g(X)),apply(
% apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) ->
% (false) collapsed.
% Rule
% [203]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,
% apply(k,k))),s),
% apply(k,g(X))),f(X)),
% f(X)),g(X))) -> (false) collapsed.
% Rule
% [209]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,s),k)),s),
% apply(s,k)),X) <-> apply(X,apply(s,apply(s,k))) collapsed.
% Rule
% [219]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,s),k)),s),
% apply(k,X)),apply(k,Y)) -> apply(X,Y) collapsed.
% Rule
% [221]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,s),k)),
% apply(s,apply(k,k))),X),Y) -> apply(X,Y) collapsed.
% Rule
% [224]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,apply(k,s))),s),
% apply(k,g(X))),apply(k,apply(
% f(X),
% f(X)))),
% apply(k,g(X)))) -> (false) collapsed.
% Rule
% [225]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,apply(k,s))),k),
% apply(apply(apply(s,apply(s,s)),k),s)),s),
% apply(apply(s,apply(k,k)),k)),g(k)),apply(k,g(k))),
% apply(f(k),f(k)))) -> (false) collapsed.
% Rule
% [226]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(s,
% apply(k,s))),k),
% apply(s,X)),apply(k,g(X))),k),f(X)),apply(apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% collapsed.
% Rule
% [227]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(apply(s,
% apply(k,s)),k)),
% apply(s,X)),k),apply(k,f(X))),g(X)),apply(apply(
% apply(s,
% apply(k,
% g(X))),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% collapsed.
% Rule
% [230]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,apply(k,s))),k),
% g(X)),apply(k,g(X))),apply(
% f(X),
% f(X)))) ->
% (false) collapsed.
% Rule
% [231]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(s,apply(k,s))),s),X),
% apply(k,apply(k,g(X)))),apply(k,f(X))),apply(apply(apply(s,
% apply(k,
% g(X))),
% apply(f(X),f(X))),
% g(X))) -> (false)
% collapsed.
% Rule
% [233]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(apply(s,s),k)),
% apply(s,apply(s,s))),s),k) -> apply(s,k) collapsed.
% Rule
% [257]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,
% apply(k,s))),k),
% apply(s,s)),apply(s,k)),
% apply(apply(apply(apply(s,
% apply(s,s)),k),s),k)),
% apply(k,apply(f(X),f(X)))),g(X))) ->
% (false) collapsed.
% Rule
% [258]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s))),
% apply(s,
% apply(k,s))),k),k),
% apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,apply(k,s))),k)),
% apply(s,s)),apply(s,k)),
% apply(apply(apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% apply(apply(s,s),k)),s),
% apply(k,s)),k),apply(s,
% apply(k,k)))),s),
% apply(k,g(k))),f(k)),g(k))) -> (false) collapsed.
% Rule
% [263]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,
% apply(k,s))),k),
% apply(s,s)),apply(s,k)),
% apply(apply(s,apply(k,s)),
% apply(s,s))),apply(k,apply(
% f(X),
% f(X)))),
% apply(k,g(X)))) -> (false) collapsed.
% Rule
% [269]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(
% apply(s,s),k)),s),
% apply(k,s)),k),
% apply(s,apply(s,s))),k),s),
% apply(s,k)),s),apply(k,g(k))),apply(f(k),f(k))))
% -> (false) collapsed.
% Current number of equations to process: 2193
% Current number of ordered equations: 1
% Current number of rules: 263
% New rule produced :
% [314]
% 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))
% Rule
% [133]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),s),k),k),g(k)),f(k)),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(k)),
% apply(
% f(k),
% f(k))),
% g(k))) ->
% (false) collapsed.
% Rule
% [144]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),k),s),apply(k,g(k))),k),
% apply(f(k),f(k))),g(k))) -> (false) collapsed.
% Rule
% [260]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),k),s),
% apply(k,g(X))),k),apply(
% f(X),
% f(X))),
% g(X))) -> (false) collapsed.
% Rule
% [292]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),s),k),k),g(k)),f(k)),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,
% g(k))),
% apply(k,
% g(k))),
% apply(
% f(k),
% f(k))))
% -> (false) collapsed.
% Current number of equations to process: 2682
% Current number of ordered equations: 0
% Current number of rules: 260
% New rule produced :
% [315]
% 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: 3531
% Current number of ordered equations: 1
% Current number of rules: 261
% New rule produced :
% [316]
% 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: 3531
% Current number of ordered equations: 0
% Current number of rules: 262
% New rule produced :
% [317]
% apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,k)),X),Y),Z) ->
% Z
% Current number of equations to process: 4252
% Current number of ordered equations: 0
% Current number of rules: 263
% New rule produced :
% [318]
% 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: 4402
% Current number of ordered equations: 1
% Current number of rules: 264
% New rule produced :
% [319]
% 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: 4402
% Current number of ordered equations: 0
% Current number of rules: 265
% New rule produced :
% [320]
% 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: 2661
% Current number of ordered equations: 1
% Current number of rules: 266
% New rule produced :
% [321]
% 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: 2661
% Current number of ordered equations: 0
% Current number of rules: 267
% New rule produced :
% [322]
% 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: 3411
% Current number of ordered equations: 1
% Current number of rules: 268
% New rule produced :
% [323]
% 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: 3411
% Current number of ordered equations: 0
% Current number of rules: 269
% New rule produced :
% [324]
% 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: 4038
% Current number of ordered equations: 5
% Current number of rules: 270
% New rule produced :
% [325]
% 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: 4038
% Current number of ordered equations: 4
% Current number of rules: 271
% New rule produced :
% [326]
% 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: 4038
% Current number of ordered equations: 3
% Current number of rules: 272
% New rule produced :
% [327]
% 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: 4038
% Current number of ordered equations: 2
% Current number of rules: 273
% New rule produced :
% [328]
% 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: 4038
% Current number of ordered equations: 1
% Current number of rules: 274
% New rule produced :
% [329]
% 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: 4038
% Current number of ordered equations: 0
% Current number of rules: 275
% New rule produced :
% [330]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(s,
% apply(k,s))),k),
% g(k)),apply(k,g(k))),apply(f(k),f(k)))) -> (false)
% Current number of equations to process: 3264
% Current number of ordered equations: 0
% Current number of rules: 276
% New rule produced :
% [331]
% 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: 3323
% Current number of ordered equations: 1
% Current number of rules: 277
% New rule produced :
% [332]
% 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: 3323
% Current number of ordered equations: 0
% Current number of rules: 278
% New rule produced :
% [333]
% apply(apply(X,Y),apply(apply(apply(apply(s,s),k),Y),Z)) <->
% apply(apply(apply(s,X),apply(Y,Z)),Y)
% Current number of equations to process: 3912
% Current number of ordered equations: 3
% Current number of rules: 279
% New rule produced :
% [334]
% apply(apply(apply(s,apply(X,Y)),Z),X) <->
% apply(apply(apply(apply(apply(s,s),k),X),Y),apply(Z,X))
% Current number of equations to process: 3912
% Current number of ordered equations: 2
% Current number of rules: 280
% New rule produced :
% [335]
% apply(apply(apply(s,X),apply(Y,Z)),Y) <->
% apply(apply(X,Y),apply(apply(apply(apply(s,s),k),Y),Z))
% Current number of equations to process: 3912
% Current number of ordered equations: 1
% Current number of rules: 281
% New rule produced :
% [336]
% apply(apply(apply(apply(apply(s,s),k),X),Y),apply(Z,X)) <->
% apply(apply(apply(s,apply(X,Y)),Z),X)
% Current number of equations to process: 3912
% Current number of ordered equations: 0
% Current number of rules: 282
% New rule produced :
% [337]
% apply(apply(X,Y),apply(apply(Z,Y),Z)) <->
% apply(apply(apply(s,X),apply(apply(apply(s,s),k),Z)),Y)
% Current number of equations to process: 4862
% Current number of ordered equations: 1
% Current number of rules: 283
% New rule produced :
% [338]
% apply(apply(apply(s,X),apply(apply(apply(s,s),k),Z)),Y) <->
% apply(apply(X,Y),apply(apply(Z,Y),Z))
% Current number of equations to process: 4862
% Current number of ordered equations: 0
% Current number of rules: 284
% New rule produced :
% [339]
% apply(apply(X,apply(apply(s,s),k)),X) ->
% apply(apply(apply(apply(s,apply(s,s)),apply(s,s)),k),X)
% Current number of equations to process: 3410
% Current number of ordered equations: 0
% Current number of rules: 285
% New rule produced :
% [340]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s)),
% apply(
% apply(s,
% apply(k,k)),
% f(X))),
% f(X)),apply(k,
% g(X))),
% g(X))) -> (false)
% Current number of equations to process: 3612
% Current number of ordered equations: 2
% Current number of rules: 286
% New rule produced :
% [341]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),
% apply(s,
% apply(k,k))),
% apply(s,s)),
% apply(k,
% apply(
% f(X),
% f(X)))),k),
% g(X)),g(X))) ->
% (false)
% Current number of equations to process: 3612
% Current number of ordered equations: 1
% Current number of rules: 287
% New rule produced :
% [342]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(s,s)),k),apply(f(X),
% f(X))),
% apply(k,g(X))),g(X))) -> (false)
% Current number of equations to process: 3612
% Current number of ordered equations: 0
% Current number of rules: 288
% New rule produced :
% [343]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),apply(apply(apply(s,apply(k,k)),k),
% g(k))),s),apply(k,g(k))),
% apply(f(k),f(k)))) -> (false)
% Current number of equations to process: 3768
% Current number of ordered equations: 1
% Current number of rules: 289
% New rule produced :
% [344]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(s,
% apply(k,s))),s),
% apply(k,g(k))),apply(apply(apply(s,apply(k,k)),f(k)),
% f(k))),apply(k,g(k)))) -> (false)
% Current number of equations to process: 3768
% Current number of ordered equations: 0
% Current number of rules: 290
% New rule produced :
% [345]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),
% apply(s,apply(k,k))),s),
% apply(k,g(X))),f(X)),f(X)),g(X))) ->
% (false)
% Current number of equations to process: 3871
% Current number of ordered equations: 0
% Current number of rules: 291
% New rule produced :
% [346]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(s,
% apply(k,k))),s),
% apply(s,X)),k),f(X)),apply(k,g(X))),apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(X)),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 3957
% Current number of ordered equations: 1
% Current number of rules: 292
% New rule produced :
% [347]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(s,apply(k,k))),
% apply(s,apply(s,X))),apply(k,f(X))),k),g(X)),apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(X)),
% apply(
% f(X),
% f(X))),
% g(X))) ->
% (false)
% Current number of equations to process: 3957
% Current number of ordered equations: 0
% Current number of rules: 293
% New rule produced :
% [348]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),X),apply(k,f(X))),
% apply(k,g(X))),apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),
% apply(s,apply(k,k))),s),
% apply(k,g(X))),f(X)),f(X)),g(X))) ->
% (false)
% Current number of equations to process: 4127
% Current number of ordered equations: 0
% Current number of rules: 294
% New rule produced :
% [349]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(s,
% apply(k,k))),s),
% apply(s,X)),k),f(X)),apply(k,g(X))),apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s)),k),
% apply(
% f(X),
% f(X))),
% apply(k,
% g(X))),
% g(X))) -> (false)
% Current number of equations to process: 4215
% Current number of ordered equations: 2
% Current number of rules: 295
% New rule produced :
% [350]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(s,apply(k,k))),
% apply(s,apply(s,X))),apply(k,f(X))),k),g(X)),apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s)),k),
% apply(
% f(X),
% f(X))),
% apply(k,
% g(X))),
% g(X))) ->
% (false)
% Current number of equations to process: 4215
% Current number of ordered equations: 1
% Current number of rules: 296
% New rule produced :
% [351]
% (eq)(apply(apply(apply(apply(apply(s,apply(k,s)),s),X),apply(k,f(X))),
% apply(k,g(X))),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(s,s)),k),apply(f(X),f(X))),
% apply(k,g(X))),g(X))) -> (false)
% Current number of equations to process: 4215
% Current number of ordered equations: 0
% Current number of rules: 297
% New rule produced :
% [352]
% apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,k)),Y),Z),apply(k,X)) ->
% X
% Current number of equations to process: 4448
% Current number of ordered equations: 0
% Current number of rules: 298
% New rule produced :
% [353]
% 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: 4601
% Current number of ordered equations: 0
% Current number of rules: 299
% New rule produced :
% [354]
% apply(apply(apply(apply(apply(s,apply(k,s)),s),apply(s,k)),Y),apply(k,X)) ->
% X
% Current number of equations to process: 4711
% Current number of ordered equations: 0
% Current number of rules: 300
% New rule produced :
% [355]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(s,
% apply(s,s)),k),s),s),k),
% apply(k,s)),s),apply(k,g(k))),k),
% apply(f(k),f(k))),g(k))) -> (false)
% Current number of equations to process: 4830
% Current number of ordered equations: 2
% Current number of rules: 301
% New rule produced :
% [356]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),
% apply(s,apply(k,s))),s),
% apply(k,s)),apply(k,k)),apply(k,g(k))),
% apply(f(k),f(k))),g(k))) -> (false)
% Current number of equations to process: 4830
% Current number of ordered equations: 1
% Current number of rules: 302
% New rule produced :
% [357]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s))),
% apply(k,g(k))),k),apply(k,g(k))),apply(f(k),f(k))))
% -> (false)
% Current number of equations to process: 4830
% Current number of ordered equations: 0
% Current number of rules: 303
% New rule produced :
% [358]
% (eq)(f(k),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),apply(k,g(k))),apply(apply(s,
% apply(k,s)),k)),
% apply(k,g(k))),apply(f(k),f(k)))) -> (false)
% Current number of equations to process: 1344
% Current number of ordered equations: 0
% Current number of rules: 304
% New rule produced :
% [359]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(s,s)),
% apply(k,s)),k),k),
% apply(k,apply(f(X),f(X)))),
% g(X)),g(X))) -> (false)
% Current number of equations to process: 1376
% Current number of ordered equations: 2
% Current number of rules: 305
% New rule produced :
% [360]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),
% apply(apply(s,
% apply(s,s)),k)),s),k),
% apply(k,g(X))),apply(k,apply(
% f(X),
% f(X)))),
% g(X))) -> (false)
% Current number of equations to process: 1376
% Current number of ordered equations: 1
% Current number of rules: 306
% New rule produced :
% [361]
% (eq)(apply(apply(X,f(X)),g(X)),apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),
% apply(apply(apply(s,
% apply(s,s)),k),s)),k),
% apply(k,apply(f(X),f(X)))),
% apply(k,g(X))),g(X))) -> (false)
% Current number of equations to process: 1376
% Current number of ordered equations: 0
% Current number of rules: 307
% New rule produced :
% [362]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(k,
% apply(k,
% g(X)))),s),
% apply(k,g(X))),
% apply(f(X),f(X)))) ->
% (false)
% Current number of equations to process: 1611
% Current number of ordered equations: 1
% Current number of rules: 308
% New rule produced :
% [363]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),
% apply(s,
% apply(k,s))),s),
% apply(k,
% g(X))),apply(k,
% apply(
% f(X),
% f(X)))),
% apply(k,g(X)))) -> (false)
% Current number of equations to process: 1611
% Current number of ordered equations: 0
% Current number of rules: 309
% New rule produced :
% [364]
% apply(apply(apply(apply(apply(apply(s,apply(s,s)),apply(k,s)),X),s),k),Y) ->
% Y
% Current number of equations to process: 1719
% Current number of ordered equations: 0
% Current number of rules: 310
% New rule produced :
% [365]
% apply(X,apply(k,X)) <->
% apply(apply(apply(apply(s,apply(s,s)),apply(s,s)),k),apply(k,X))
% Current number of equations to process: 1843
% Current number of ordered equations: 1
% Current number of rules: 311
% New rule produced :
% [366]
% apply(apply(apply(apply(s,apply(s,s)),apply(s,s)),k),apply(k,X)) <->
% apply(X,apply(k,X))
% Current number of equations to process: 1843
% Current number of ordered equations: 0
% Current number of rules: 312
% New rule produced :
% [367]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(apply(s,
% apply(k,s)),k)),
% apply(s,X)),k),apply(k,f(X))),g(X)),apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(X)),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 2009
% Current number of ordered equations: 4
% Current number of rules: 313
% New rule produced :
% [368]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),apply(k,g(X))),k),
% apply(f(X),f(X))),g(X))) -> (false)
% Current number of equations to process: 2009
% Current number of ordered equations: 3
% Current number of rules: 314
% New rule produced :
% [369]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),
% apply(s,apply(k,s))),k),
% g(X)),apply(k,g(X))),apply(f(X),f(X)))) ->
% (false)
% Current number of equations to process: 2009
% Current number of ordered equations: 2
% Current number of rules: 315
% New rule produced :
% [370]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),apply(k,apply(s,X))),k),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(s,apply(k,s)),k),g(X)),
% apply(f(X),f(X))),g(X))) -> (false)
% Current number of equations to process: 2009
% Current number of ordered equations: 1
% Current number of rules: 316
% New rule produced :
% [371]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(s,
% apply(k,s))),k),
% apply(s,X)),apply(k,g(X))),k),f(X)),apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% g(X)),
% apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 2009
% Current number of ordered equations: 0
% Current number of rules: 317
% New rule produced :
% [372]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(apply(s,
% apply(k,s)),k)),
% apply(s,X)),k),apply(k,f(X))),g(X)),apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s)),k),
% apply(
% f(X),
% f(X))),
% apply(k,
% g(X))),
% g(X))) -> (false)
% Current number of equations to process: 2370
% Current number of ordered equations: 3
% Current number of rules: 318
% New rule produced :
% [373]
% (eq)(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),apply(s,X)),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(s,apply(k,s)),apply(s,s)),
% apply(k,apply(f(X),f(X)))),apply(k,g(X))),
% apply(k,g(X)))) -> (false)
% Current number of equations to process: 2370
% Current number of ordered equations: 2
% Current number of rules: 319
% New rule produced :
% [374]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),s),
% apply(k,s)),apply(k,apply(s,X))),k),k),
% g(X)),f(X)),apply(apply(apply(apply(apply(apply(apply(s,apply(k,s)),k),
% apply(s,s)),k),apply(f(X),
% f(X))),
% apply(k,g(X))),g(X))) -> (false)
% Current number of equations to process: 2370
% Current number of ordered equations: 1
% Current number of rules: 320
% New rule produced :
% [375]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(s,
% apply(k,s))),k),
% apply(s,X)),apply(k,g(X))),k),f(X)),apply(apply(
% apply(
% apply(
% apply(
% apply(
% apply(s,
% apply(k,s)),k),
% apply(s,s)),k),
% apply(
% f(X),
% f(X))),
% apply(k,
% g(X))),
% g(X))) -> (false)
% Current number of equations to process: 2370
% Current number of ordered equations: 0
% Current number of rules: 321
% New rule produced :
% [376]
% (eq)(apply(apply(apply(s,X),apply(k,g(X))),f(X)),apply(apply(apply(apply(
% apply(s,
% apply(k,s)),
% apply(s,
% apply(s,s))),
% apply(k,
% apply(k,
% g(X)))),
% apply(k,g(X))),
% apply(k,apply(f(X),f(X)))))
% -> (false)
% Current number of equations to process: 2665
% Current number of ordered equations: 0
% Current number of rules: 322
% New rule produced :
% [377]
% (eq)(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(apply(
% apply(
% apply(s,
% apply(k,s)),s),
% apply(k,s)),
% apply(s,s)),k),s),
% apply(k,s)),k),apply(s,apply(k,s))),s),X),
% apply(k,apply(k,g(X)))),apply(k,f(X))),apply(apply(apply(apply(
% apply(s,
% apply(k,s)),k),
% g(X)),apply(
% f(X),
% f(X))),
% g(X))) -> (false)
% Current number of equations to process: 2698
% Current number of ordered equations: 3
% Current number of rules: 323
% New rule produced :
% [378]
% (eq)(apply(apply(apply(Cputime limit exceeded (core dumped)
%
% EOF
%------------------------------------------------------------------------------