NO af/ONE-SORTED/669.trs Input rules: [ a -> c, f(a) -> b, b -> b, b -> h(b,h(c,a)) ] Sorts having no ground terms: Rules applicable to ground terms: [ a -> c, f(a) -> b, b -> b, b -> h(b,h(c,a)) ] Constructor pattern: [c,f(?x_1),h(?x_1,?x_2)] Defined pattern: [b,a] Constructor subsystem: [ ] Modified Constructor subsystem: [ ] No orientable rules for b. Add rules, and retry... failed to construct defining rules Retry with a different D/C-partition. Constructor pattern: [c,f(?x_1),h(?x_1,?x_2),b] Defined pattern: [a] Constructor subsystem: [ b -> b ] b -> b {} [ ] Modified Constructor subsystem: [ ] candidate for a: [ a -> c ] Find a quasi-ordering ... order successfully found Precedence: f : Mul; a : Mul; b : Mul; h : Mul; c : Mul; Rules: [ a -> c ] Conjectures: [ f(a) = b, b = h(b,h(c,a)) ] STEP 0 ES: [ f(a) = b, b = h(b,h(c,a)) ] HS: [ ] ES0: [ f(c) = b, b = h(b,h(c,c)) ] HS0: [ ] ES1: [ f(c) = b, b = h(b,h(c,c)) ] HS1: [ ] No equation to expand check Non-Ground-Confluence... ground constructor terms for instantiation: {c,f(c),h(c,c)} ground terms for instantiation: {c:o,f(c):o,h(c,c):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(c)> : Success(not GCR) (7 msec.) 0.02