/**
         
 * 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').
         

         
/* 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 3.6.1').
         
runner_case(acyclic_factorized,2, extend, cyclic, 'XLOG 3.6.1, 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 3.6.1, 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 3.6.1, 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 3.6.1, 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 3.6.1, 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 3.6.1, 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 3.6.1, 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 == [].