NO af/ONE-SORTED/654.trs Input rules: [ a -> f(h(c,h(h(h(h(f(h(a,b)),a),h(h(h(f(f(a)),c),h(f(b),a)),a)),b),c))), h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(a),c)))),f(a)))) -> h(b,b), f(c) -> c, f(f(h(f(h(c,h(a,f(a)))),f(c)))) -> b ] Sorts having no ground terms: Rules applicable to ground terms: [ a -> f(h(c,h(h(h(h(f(h(a,b)),a),h(h(h(f(f(a)),c),h(f(b),a)),a)),b),c))), h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(a),c)))),f(a)))) -> h(b,b), f(c) -> c, f(f(h(f(h(c,h(a,f(a)))),f(c)))) -> b ] Constructor pattern: [f(?x_1),h(?x_1,?x_2),c,b] Defined pattern: [a] Constructor subsystem: [ f(c) -> c ] Modified Constructor subsystem: [ f(c) -> c ] No orientable rules for a. Add rules, and retry... failed to construct defining rules Retry with a different D/C-partition. Constructor pattern: [f(?x_1),h(?x_1,?x_2),c,b,a] Defined pattern: [] Constructor subsystem: [ a -> f(h(c,h(h(h(h(f(h(a,b)),a),h(h(h(f(f(a)),c),h(f(b),a)),a)),b),c))), h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(a),c)))),f(a)))) -> h(b,b), f(c) -> c, f(f(h(f(h(c,h(a,f(a)))),f(c)))) -> b ] Modified Constructor subsystem: [ a -> f(h(c,h(h(h(h(f(h(a,b)),a),h(h(h(f(f(a)),c),h(f(b),a)),a)),b),c))), h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(a),c)))),f(a)))) -> h(b,b), f(c) -> c, f(f(h(f(h(c,h(a,f(a)))),f(c)))) -> b ] Find a quasi-ordering ... order successfully found Precedence: f : Mul; a : Mul; c : Mul; b : Mul; h : Mul; Rules: [ h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(a),c)))),f(a)))) -> h(b,b), f(c) -> c, f(f(h(f(h(c,h(a,f(a)))),f(c)))) -> b ] Check confluence of constructor subsystem... Check Termination... Terminating, not WCR: not CR ...failed failed to find an ordering. Try to supplement auxiliary rules. {a}{h(b,b)}{}{}Supplemented Rules: [ ] failed to supplement auxiliary rules check Non-Ground-Confluence... ground constructor terms for instantiation: {c,b,f(c),f(b),h(c,c),h(c,b),h(b,c),h(b,b)} ground terms for instantiation: {c:o,b:o,f(c):o,f(b):o,h(c,c):o,h(c,b):o,h(b,c):o,h(b,b):o} obtain 13 rules by 3 steps unfolding obtain 48 candidates for checking non-joinability check by TCAP-Approximation (success) Witness for Non-Confluence: b> : Success(not GCR) (204 msec.) 0.21