NO af/ONE-SORTED/704.trs Input rules: [ a -> f(a), h(c,a) -> b ] Sorts having no ground terms: Rules applicable to ground terms: [ a -> f(a), h(c,a) -> b ] 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(a), h(c,a) -> b ] Modified Constructor subsystem: [ a -> f(a), h(c,a) -> b ] Find a quasi-ordering ... order successfully found Precedence: c : Mul; h : Mul; f : Mul; b : Mul; a : Mul; Rules: [ h(c,a) -> b ] Check confluence of constructor subsystem... Check Termination... Terminating, WCR: CR Conjectures: [ a = f(a) ] STEP 0 ES: [ a = f(a) ] HS: [ ] ES0: [ a = f(a) ] HS0: [ ] ES1: [ a = f(a) ] 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 31 candidates for checking non-joinability check by TCAP-Approximation (success) Witness for Non-Confluence: b> : Success(not GCR) (3 msec.) 0.02