NO af/ONE-SORTED/685.trs Input rules: [ c -> c, a -> f(h(h(f(a),f(f(c))),b)), c -> a, h(c,f(b)) -> c ] Sorts having no ground terms: Rules applicable to ground terms: [ c -> c, a -> f(h(h(f(a),f(f(c))),b)), c -> a, h(c,f(b)) -> c ] Constructor pattern: [f(?x_1),h(?x_1,?x_2),b] Defined pattern: [a,c] 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),b,a] Defined pattern: [c] Constructor subsystem: [ ] Modified Constructor subsystem: [ ] candidate for c: [ c -> a ] Find a quasi-ordering ... order successfully found Precedence: f : Mul; c : Mul, b : Mul; a : Mul; h : Mul; Rules: [ c -> a ] Conjectures: [ h(c,f(b)) = c, c = c, a = f(h(h(f(a),f(f(c))),b)) ] STEP 0 ES: [ h(c,f(b)) = c, c = c, a = f(h(h(f(a),f(f(c))),b)) ] HS: [ ] ES0: [ h(a,f(b)) = a, a = a, a = f(h(h(f(a),f(f(a))),b)) ] HS0: [ ] ES1: [ h(a,f(b)) = a, a = f(h(h(f(a),f(f(a))),b)) ] HS1: [ ] No equation to expand check Non-Ground-Confluence... ground constructor terms for instantiation: {b,f(b),h(b,b)} ground terms for instantiation: {b:o,f(b):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: f(h(h(f(a),f(f(a))),b))> : Success(not GCR) (9 msec.) 0.02