NO af/ONE-SORTED/511.trs Input rules: [ b -> a, b -> c, c -> c, d -> c, d -> e, f(?x:o,a) -> A, f(?x:o,e) -> A, f(?x:o,A) -> A, f(c,?x:o) -> A ] Sorts having no ground terms: Rules applicable to ground terms: [ b -> a, b -> c, c -> c, d -> c, d -> e, f(?x:o,a) -> A, f(?x:o,e) -> A, f(?x:o,A) -> A, f(c,?x:o) -> A ] Constructor pattern: [a,e,A] Defined pattern: [f(?x_2,?x_3),d,c,b] Constructor subsystem: [ ] Modified Constructor subsystem: [ ] candidate for f(?x_2,?x_3): [ f(?x,a) -> A, f(?x,e) -> A, f(?x,A) -> A ] candidate for d: [ d -> c ] [ d -> e ] No orientable rules for c. Add rules, and retry... failed to construct defining rules Retry with a different D/C-partition. Constructor pattern: [a,e,A,c] Defined pattern: [f(?x_2,?x_3),d,b] Constructor subsystem: [ c -> c ] c -> c {} [ ] Modified Constructor subsystem: [ ] candidate for f(?x_2,?x_3): No canditates. Supplement rules, and retry... patlist: {?x,a} {?x,e} {?x,A} {c,?x} Required Patterns: {f(e,c),f(A,c),f(a,c)} failed to construct defining rules Retry with a different D/C-partition. Constructor pattern: [a,e,A,c,f(?x_2,?x_3)] Defined pattern: [d,b] Constructor subsystem: [ c -> c, f(?x,a) -> A, f(?x,e) -> A, f(?x,A) -> A, f(c,?x) -> A ] c -> c {} [ ] Modified Constructor subsystem: [ f(?x,a) -> A, f(?x,e) -> A, f(?x,A) -> A, f(c,?x) -> A ] candidate for d: [ d -> c ] [ d -> e ] candidate for b: [ b -> a ] [ b -> c ] Find a quasi-ordering ... order successfully found Precedence: e : Mul; d : Mul, b : Mul, a : Mul; A : Mul; c : Mul; f : Mul; Rules: [ d -> c, b -> c, f(?x,a) -> A, f(?x,e) -> A, f(?x,A) -> A ] Check confluence of constructor subsystem... Check Termination... Terminating, WCR: CR Conjectures: [ b = a, d = e, f(c,?x) = A ] STEP 0 ES: [ b = a, d = e, f(c,?x) = A ] HS: [ ] ES0: [ c = a, c = e, f(c,?x) = A ] HS0: [ ] ES1: [ c = a, c = e, f(c,?x) = A ] HS1: [ ] : Success(not GCR) (4 msec.) 0.02