NO af/ONE-SORTED/703.trs Input rules: [ a -> f(f(h(a,c))), h(h(h(c,f(h(f(h(h(c,c),c)),b))),h(h(a,c),h(f(a),h(f(f(c)),h(c,b))))),h(f(a),c)) -> c ] Sorts having no ground terms: Rules applicable to ground terms: [ a -> f(f(h(a,c))), h(h(h(c,f(h(f(h(h(c,c),c)),b))),h(h(a,c),h(f(a),h(f(f(c)),h(c,b))))),h(f(a),c)) -> c ] Constructor pattern: [f(?x_1),h(?x_1,?x_2),c,b] Defined pattern: [a] Constructor subsystem: [ ] Modified Constructor subsystem: [ ] 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(f(h(a,c))), h(h(h(c,f(h(f(h(h(c,c),c)),b))),h(h(a,c),h(f(a),h(f(f(c)),h(c,b))))),h(f(a),c)) -> c ] Modified Constructor subsystem: [ a -> f(f(h(a,c))), h(h(h(c,f(h(f(h(h(c,c),c)),b))),h(h(a,c),h(f(a),h(f(f(c)),h(c,b))))),h(f(a),c)) -> c ] Find a quasi-ordering ... order successfully found Precedence: a : Mul; h : Mul; f : Mul; c : Mul, b : Mul; Rules: [ h(h(h(c,f(h(f(h(h(c,c),c)),b))),h(h(a,c),h(f(a),h(f(f(c)),h(c,b))))),h(f(a),c)) -> c ] Check confluence of constructor subsystem... Check Termination... Terminating, WCR: CR Conjectures: [ a = f(f(h(a,c))) ] STEP 0 ES: [ a = f(f(h(a,c))) ] HS: [ ] ES0: [ a = f(f(h(a,c))) ] HS0: [ ] ES1: [ a = f(f(h(a,c))) ] HS1: [ ] No equation to expand 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 10 rules by 3 steps unfolding obtain 100 candidates for checking non-joinability check by TCAP-Approximation (success) Witness for Non-Confluence: c> : Success(not GCR) (283 msec.) 0.28