NO af/ONE-SORTED/689.trs Input rules: [ b -> h(h(b,a),f(a)), h(h(a,c),b) -> b, c -> h(h(a,h(a,h(c,b))),f(f(h(h(a,h(h(f(a),c),f(c))),f(h(b,a)))))) ] Sorts having no ground terms: Rules applicable to ground terms: [ b -> h(h(b,a),f(a)), h(h(a,c),b) -> b, c -> h(h(a,h(a,h(c,b))),f(f(h(h(a,h(h(f(a),c),f(c))),f(h(b,a)))))) ] Constructor pattern: [h(?x_1,?x_2),a,f(?x_1)] Defined pattern: [c,b] Constructor subsystem: [ ] Modified Constructor subsystem: [ ] No orientable rules for c. 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),c] 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),c,b] Defined pattern: [] Constructor subsystem: [ b -> h(h(b,a),f(a)), h(h(a,c),b) -> b, c -> h(h(a,h(a,h(c,b))),f(f(h(h(a,h(h(f(a),c),f(c))),f(h(b,a)))))) ] Modified Constructor subsystem: [ b -> h(h(b,a),f(a)), h(h(a,c),b) -> b, c -> h(h(a,h(a,h(c,b))),f(f(h(h(a,h(h(f(a),c),f(c))),f(h(b,a)))))) ] Find a quasi-ordering ... order successfully found Precedence: c : Mul, b : Mul; f : Mul; a : Mul; h : Mul; Rules: [ h(h(a,c),b) -> b ] Check confluence of constructor subsystem... Check Termination... Terminating, WCR: CR Conjectures: [ b = h(h(b,a),f(a)), c = h(h(a,h(a,h(c,b))),f(f(h(h(a,h(h(f(a),c),f(c))),f(h(b,a)))))) ] STEP 0 ES: [ b = h(h(b,a),f(a)), c = h(h(a,h(a,h(c,b))),f(f(h(h(a,h(h(f(a),c),f(c))),f(h(b,a)))))) ] HS: [ ] ES0: [ b = h(h(b,a),f(a)), c = h(h(a,h(a,h(c,b))),f(f(h(h(a,h(h(f(a),c),f(c))),f(h(b,a)))))) ] HS0: [ ] ES1: [ b = h(h(b,a),f(a)), c = h(h(a,h(a,h(c,b))),f(f(h(h(a,h(h(f(a),c),f(c))),f(h(b,a)))))) ] 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 11 rules by 3 steps unfolding obtain 100 candidates for checking non-joinability check by TCAP-Approximation (success) Witness for Non-Confluence: h(h(b,a),f(a))> : Success(not GCR) (52 msec.) 0.06