MAYBE af/ONE-SORTED/224.trs Input rules: [ -(+(x,-(x))) -> 0, +(x,-(x)) -> 0, 0 -> -(0) ] Sorts having no ground terms: Rules applicable to ground terms: [ -(+(x,-(x))) -> 0, +(x,-(x)) -> 0, 0 -> -(0) ] Constructor pattern: [-(?x_1),+(?x_1,?x_2),x] Defined pattern: [0] Constructor subsystem: [ ] Modified Constructor subsystem: [ ] No orientable rules for 0. Add rules, and retry... failed to construct defining rules Retry with a different D/C-partition. Constructor pattern: [-(?x_1),+(?x_1,?x_2),x,0] Defined pattern: [] Constructor subsystem: [ -(+(x,-(x))) -> 0, +(x,-(x)) -> 0, 0 -> -(0) ] Modified Constructor subsystem: [ -(+(x,-(x))) -> 0, +(x,-(x)) -> 0, 0 -> -(0) ] Find a quasi-ordering ... order successfully found Precedence: - : Mul; x : Mul; 0 : Mul; + : Mul; Rules: [ -(+(x,-(x))) -> 0, +(x,-(x)) -> 0 ] Check confluence of constructor subsystem... Check Termination... Terminating, not WCR: not CR ...failed failed to find an ordering. Try to supplement auxiliary rules. {}{}{0}Supplemented Rules: [ ] failed to supplement auxiliary rules check Non-Ground-Confluence... ground constructor terms for instantiation: {x,-(x),+(x,x)} ground terms for instantiation: {x:o,-(x):o,+(x,x):o} obtain 10 rules by 3 steps unfolding obtain 34 candidates for checking non-joinability check by TCAP-Approximation (failure) check by Ordering(rpo), check by Tree-Automata Approximation (failure) check by Interpretation(mod2) (failure) check by Descendants-Approximation, check by Ordering(poly) (failure) : Failure(unknown) (1119 msec.) 3.90