NO af/ONE-SORTED/696.trs Input rules: [ h(a,c) -> b, c -> a, b -> f(b) ] Sorts having no ground terms: Rules applicable to ground terms: [ h(a,c) -> b, c -> a, b -> f(b) ] Constructor pattern: [h(?x_1,?x_2),a,f(?x_1)] Defined pattern: [b,c] 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: [h(?x_1,?x_2),a,f(?x_1),b] Defined pattern: [c] Constructor subsystem: [ b -> f(b) ] Modified Constructor subsystem: [ b -> f(b) ] candidate for c: [ c -> a ] Find a quasi-ordering ... encodeSameNthStatus h/0, h/1 encodeSameNthStatus(sub) logArF:1, logArG:1 failed to find an ordering. Try to supplement auxiliary rules. {}{}{b}Supplemented Rules: [ ] failed to supplement auxiliary rules Retry with a different D/C-partition. Constructor pattern: [h(?x_1,?x_2),a,f(?x_1),b,c] Defined pattern: [] Constructor subsystem: [ h(a,c) -> b, c -> a, b -> f(b) ] Modified Constructor subsystem: [ h(a,c) -> b, c -> a, b -> f(b) ] Find a quasi-ordering ... order successfully found Precedence: f : Mul; b : Mul, a : Mul; h : Mul; c : Mul; Rules: [ h(a,c) -> b ] Check confluence of constructor subsystem... Check Termination... Terminating, WCR: CR Conjectures: [ c = a, b = f(b) ] STEP 0 ES: [ c = a, b = f(b) ] HS: [ ] ES0: [ c = a, b = f(b) ] HS0: [ ] ES1: [ c = a, b = f(b) ] HS1: [ ] No equation to expand check Non-Ground-Confluence... ground constructor terms for instantiation: {a,h(a,a),f(a)} ground terms for instantiation: {a:o,h(a,a):o,f(a):o} obtain 10 rules by 3 steps unfolding obtain 42 candidates for checking non-joinability check by TCAP-Approximation (success) Witness for Non-Confluence: f(b)> : Success(not GCR) (10 msec.) 0.03