NO
(ignored inputs)COMMENT Example 3.3.1 of \cite{Gra96thesis}
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 <c, a> by Rules <1, 0> preceded by []
 joinable by a reduction of rules <[([],2),([],0)], []>
Critical Pair <d, b> by Rules <3, 2> preceded by []
 joinable by a reduction of rules <[], [([],1),([],3)]>
unknown Diagram Decreasing
check Non-Confluence...
obtain 12 rules by 3 steps unfolding
strenghten a and b
strenghten a and c
strenghten a and d
strenghten b and a
strenghten b and c
strenghten b and d
strenghten c and a
strenghten c and b
strenghten c and d
strenghten d and a
strenghten d and b
strenghten d and c
obtain 12 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <a, d>
Direct Methods: not CR

Final result: not CR
38.trs: Success(not CR)
(12 msec.)