NO af/ONE-SORTED/721.trs Input rules: [ b -> h(b,a), b -> h(f(b),f(h(b,a))) ] Sorts having no ground terms: Rules applicable to ground terms: [ b -> h(b,a), b -> h(f(b),f(h(b,a))) ] Constructor pattern: [h(?x_1,?x_2),a,f(?x_1)] Defined pattern: [b] 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: [] Constructor subsystem: [ b -> h(b,a), b -> h(f(b),f(h(b,a))) ] Modified Constructor subsystem: [ b -> h(b,a), b -> h(f(b),f(h(b,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}{b}Supplemented Rules: [ ] failed to supplement auxiliary rules 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 100 candidates for checking non-joinability check by TCAP-Approximation (success) Witness for Non-Confluence: h(b,a)> : Success(not GCR) (15 msec.) 0.03