/**
         
 * Warranty & Liability
         
 * To the extent permitted by applicable law and unless explicitly
         
 * otherwise agreed upon, XLOG Technologies AG makes no warranties
         
 * regarding the provided information. XLOG Technologies AG assumes
         
 * no liability that any problems might be solved with the information
         
 * provided by XLOG Technologies AG.
         
 *
         
 * Rights & License
         
 * All industrial property rights regarding the information - copyright
         
 * and patent rights in particular - are the sole property of XLOG
         
 * Technologies AG. If the company was not the originator of some
         
 * excerpts, XLOG Technologies AG has at least obtained the right to
         
 * reproduce, change and translate the information.
         
 *
         
 * Reproduction is restricted to the whole unaltered document. Reproduction
         
 * of the information is only allowed for non-commercial uses. Selling,
         
 * giving away or letting of the execution of the library is prohibited.
         
 * The library can be distributed as part of your applications and libraries
         
 * for execution provided this comment remains unchanged.
         
 *
         
 * Restrictions
         
 * Only to be distributed with programs that add significant and primary
         
 * functionality to the library. Not to be distributed with additional
         
 * software intended to replace any components of the library.
         
 *
         
 * Trademarks
         
 * Jekejeke is a registered trademark of XLOG Technologies AG.
         
 */
         

         
runner_file(extend, cyclic, 'XLOG 3.6 cyclic').
         

         
/****************************************************************/
         
/* term.p extras                                                */
         
/****************************************************************/
         

         
/* subsumes(X, Y) */
         

         
runner_pred(subsumes,2, extend, cyclic, 'XLOG 3.6.1').
         
runner_case(subsumes,2, extend, cyclic, 'XLOG 3.6.1, ISO 1') :-
         
   subsumes(a, a).
         
runner_case(subsumes,2, extend, cyclic, 'XLOG 3.6.1, ISO 2') :-
         
   subsumes(f(A,Z), f(B,Z)), A == B.
         
runner_case(subsumes,2, extend, cyclic, 'XLOG 3.6.1, ISO 3') :-
         
   subsumes(f(A,B), f(Z,Z)), A == Z, B == Z.
         
runner_case(subsumes,2, extend, cyclic, 'XLOG 3.6.1, ISO 4') :-
         
   \+ subsumes(f(_,A), f(A,_)).
         
runner_case(subsumes,2, extend, cyclic, 'XLOG 3.6.1, ISO 5') :-
         
   \+ subsumes(g(X), g(f(X))).
         
runner_case(subsumes,2, extend, cyclic, 'XLOG 3.6.1, ISO 6') :-
         
   subsumes(X, Y), \+ subsumes(Y, f(X)).
         

         
/* subsumes_term(X, Y) */
         

         
runner_pred(subsumes_term, 2, extend, cyclic, 'ISO 8.2.4.4').
         
runner_case(subsumes_term, 2, extend, cyclic, 'ISO 8.2.4.4, ISO 1') :-
         
   subsumes_term(a, a).
         
runner_case(subsumes_term, 2, extend, cyclic, 'ISO 8.2.4.4, ISO 2') :-
         
   subsumes_term(f(A,Z), f(B,Z)), A \== B.
         
runner_case(subsumes_term, 2, extend, cyclic, 'ISO 8.2.4.4, ISO 3') :-
         
   subsumes_term(f(A,B), f(Z,Z)), A \== Z, B \== Z.
         
runner_case(subsumes_term, 2, extend, cyclic, 'ISO 8.2.4.4, ISO 4') :-
         
   \+ subsumes_term(f(_,A), f(A,_)).
         
runner_case(subsumes_term, 2, extend, cyclic, 'ISO 8.2.4.4, ISO 5') :-
         
   \+ subsumes_term(g(X), g(f(X))).
         
runner_case(subsumes_term, 2, extend, cyclic, 'ISO 8.2.4.4, ISO 6') :-
         
   subsumes_term(X, Y), subsumes_term(Y, f(X)).
         

         
/* unify_with_occurs_check(X, Y) */
         

         
runner_pred(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4').
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, ISO 1') :-
         
   unify_with_occurs_check(1, 1).
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, ISO 2') :-
         
   unify_with_occurs_check(X, 1),
         
   X == 1.
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, ISO 3') :-
         
   unify_with_occurs_check(X, Y),
         
   X == Y.
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, ISO 4') :-
         
   unify_with_occurs_check(_, _).
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, ISO 6') :-
         
   unify_with_occurs_check(f(X,def), f(def,Y)),
         
   X == def, Y == def.
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, ISO 8') :-
         
   \+ unify_with_occurs_check(1, 1.0).
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, ISO 10') :-
         
   \+ unify_with_occurs_check(f(X, 1), f(a(X))).
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, ISO 11') :-
         
   \+ unify_with_occurs_check(f(X, Y, X), f(a(X), a(Y), Y, 2)).
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, ISO 13') :-
         
   \+ unify_with_occurs_check(f(X, 1), f(a(X), 1)).
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, ISO 16') :-
         
   \+ unify_with_occurs_check(f(X, Y, X, 1), f(a(X), a(Y), Y, 2)).
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, XLOG 1') :-
         
   X = f(X,_), unify_with_occurs_check(X, _).
         
runner_case(unify_with_occurs_check, 2, extend, cyclic, 'ISO 8.2.2.4, XLOG 2') :-
         
   X = f(X,A), \+ unify_with_occurs_check(X, A).
         

         
/* occurs_check(X, Y) */
         

         
runner_pred(occurs_check, 2, extend, cyclic, 'ISO 7.3.3').
         
runner_case(occurs_check, 2, extend, cyclic, 'ISO 7.3.3, ISO 1') :-
         
   occurs_check(X, f(_,X,_)).
         
runner_case(occurs_check, 2, extend, cyclic, 'ISO 7.3.3, ISO 2') :-
         
   \+ occurs_check(_, f(_,_,_)).
         

         
/* acyclic_term(X) */
         

         
runner_pred(acyclic_term, 1, extend, cyclic, 'Corr.2 8.3.11.4').
         
runner_case(acyclic_term, 1, extend, cyclic, 'Corr.2 8.3.11.4, ISO 1') :-
         
   acyclic_term(a(_,1)).
         
runner_case(acyclic_term, 1, extend, cyclic, 'Corr.2 8.3.11.4, ISO 2') :-
         
   X = f(X), \+ acyclic_term(X).
         
runner_case(acyclic_term, 1, extend, cyclic, 'Corr.2 8.3.11.4, XLOG 1') :-
         
   X = f(X), Y = g(X), \+ acyclic_term(Y).
         
runner_case(acyclic_term, 1, extend, cyclic, 'Corr.2 8.3.11.4, XLOG 2') :-
         
   X = f(Y), Y = g(X), Z = h(X), \+ acyclic_term(Z).
         
runner_case(acyclic_term, 1, extend, cyclic, 'Corr.2 8.3.11.4, XLOG 3') :-
         
   X = [a,b,Y|c], Y = [d,e,Z|f], Z = [g,h,i], acyclic_term(X).
         
runner_case(acyclic_term, 1, extend, cyclic, 'Corr.2 8.3.11.4, XLOG 4') :-
         
   X = [a,b,Y|c], Y = [d,e,Z|f], Z = [g,h,X|i], \+ acyclic_term(X).
         

         
/* acyclic_factorized(L, R) */
         

         
runner_pred(acyclic_factorized,2, extend, cyclic, 'XLOG 3.6.2').
         
runner_case(acyclic_factorized,2, extend, cyclic, 'XLOG 3.6.2, XLOG 1') :-
         
   Y = f(Y), acyclic_factorized([Y-Y],[[T|L]]),
         
   L = [A=_], T == A-A, L == [A = f(A)].
         
runner_case(acyclic_factorized,2, extend, cyclic, 'XLOG 3.6.2, XLOG 2') :-
         
   Y = f(Y), X = g(X,Y), Z = h(Z), acyclic_factorized([X-Z],[[T|L]]),
         
   L = [C=_, B=_, A=_], T == B-C, L == [C = h(C), B = g(B, A), A = f(A)].
         
runner_case(acyclic_factorized,2, extend, cyclic, 'XLOG 3.6.2, XLOG 3') :-
         
   X = f(f(f(X))), Y = f(f(Y)), acyclic_factorized([X-Y],[[T|L]]),
         
   L = [A=_], T == A-A, L == [A = f(A)].
         
runner_case(acyclic_factorized,2, extend, cyclic, 'XLOG 3.6.2, XLOG 4') :-
         
   X = a(f(X,Y)), Y = a(f(Y,X)), acyclic_factorized([X-Y],[[T|L]]),
         
   L = [A=_], T == A-A, L == [A = a(f(A, A))].
         
runner_case(acyclic_factorized,2, extend, cyclic, 'XLOG 3.6.2, XLOG 5') :-
         
   X = s(s(X,Y),A), Y = s(Y,X), acyclic_factorized([X-Y],[[T|L]]),
         
   L = [C=_, B=_], T == C-B, L == [C = s(s(C, B), A), B = s(B, C)].
         
runner_case(acyclic_factorized,2, extend, cyclic, 'XLOG 3.6.2, XLOG 6') :-
         
   Y = s(s(Y,B),B), X = s(s(X,Y),A), acyclic_factorized([Y,X],[[S|R],[T|L]]),
         
   R == [S = s(S, B)], L == [T = s(s(T, S), A)].
         
runner_case(acyclic_factorized,2, extend, cyclic, 'XLOG 3.6.2, XLOG 7') :-
         
   X = s(s(X,Y),A), Y = s(s(Y,B),B), acyclic_factorized([X,Y],[[T|L],[S|R]]),
         
   L == [T = s(s(T, S), A), S = s(S, B)], R == [].