NO (ignored inputs)COMMENT [11] Example 3.3.1 submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama Rewrite Rules: [ b -> a, b -> c, c -> b, c -> d ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ a = c, 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 = b, 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),([],0)], []> Critical Pair by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], [([],1),([],3)]> unknown Diagram Decreasing check Non-Confluence... obtain 8 rules by 3 steps unfolding obtain 12 candidates for checking non-joinability check by TCAP-Approximation (success) (success) (failure) check by Ordering(rpo), check by Tree-Automata Approximation (success) Witness for Non-Confluence: d> Direct Methods: not CR Combined result: not CR 38.trs: Success(not CR) (17 msec.)