(ignored inputs)COMMENT doi:10.1007/11805618_6 [7] Example 3 submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama Rewrite Rules: [ b -> a, b -> c, c -> h(b), c -> d, a -> h(a), d -> h(d) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ a = c, h(b) = d ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth & Bendix Linear unknown Development Closed unknown Strongly Closed unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ c = a, a = c, d = h(b), h(b) = d ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <1, 0> preceded by [] joinable by a reduction of rules <[([],2),([(h,1)],0)], [([],4)]> Critical Pair by Rules <3, 2> preceded by [] joinable by a reduction of rules <[([],5)], [([(h,1)],1),([(h,1)],3)]> unknown Diagram Decreasing check Non-Confluence... obtain 12 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: d> Direct Methods: not CR Combined result: not CR 21.trs: Success(not CR) NO (30 msec.)