NO af/ONE-SORTED/717.trs Input rules: [ a -> c, f(f(c)) -> h(a,h(h(c,c),b)), f(f(a)) -> b, b -> f(f(b)) ] Sorts having no ground terms: Rules applicable to ground terms: [ a -> c, f(f(c)) -> h(a,h(h(c,c),b)), f(f(a)) -> b, b -> f(f(b)) ] 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 -> f(f(b)) ] Modified Constructor subsystem: [ b -> f(f(b)) ] candidate for a: [ a -> c ] 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: [c,f(?x_1),h(?x_1,?x_2),b,a] Defined pattern: [] Constructor subsystem: [ a -> c, f(f(c)) -> h(a,h(h(c,c),b)), f(f(a)) -> b, b -> f(f(b)) ] Modified Constructor subsystem: [ a -> c, f(f(c)) -> h(a,h(h(c,c),b)), f(f(a)) -> b, b -> f(f(b)) ] Find a quasi-ordering ... order successfully found Precedence: f : Mul; b : Mul; h : Mul; c : Mul, a : Mul; Rules: [ f(f(c)) -> h(a,h(h(c,c),b)), f(f(a)) -> b, a -> c ] Check confluence of constructor subsystem... Check Termination... unknown Terminating, Linear, unknown Oostrom, unknown strongly closed: Can't judge ...failed failed to find an ordering. Try to supplement auxiliary rules. {}{}{}{b}Supplemented Rules: [ ] failed to supplement auxiliary rules 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 11 rules by 3 steps unfolding obtain 100 candidates for checking non-joinability check by TCAP-Approximation (failure) check by Ordering(rpo), check by Tree-Automata Approximation (success) Witness for Non-Confluence: b> : Success(not GCR) (69 msec.) 0.09