YES (ignored inputs)COMMENT doi:10.23638/LMCS-13 ( 2:4 ) 2017 [131] Example 5.2 submitted by: Julian Nagele Rewrite Rules: [ a -> b, a -> d, b -> a, c -> a, c -> b ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ b = d, a = b ] 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: [ d = b, b = d, b = a, a = b ] 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),([],1)]> Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([],2)], []> joinable by a reduction of rules <[], [([],0)]> Satisfiable by 4>5,1>2>3; ; 4>5,1>2>3 Diagram Decreasing Direct Methods: CR Combined result: CR 761.trs: Success(CR) (7 msec.)