NO
(ignored inputs)COMMENT [120] Example 1 submitted by: Aart Middeldorp
Rewrite Rules:
   [ f(c) -> g(c),
     g(c) -> f(c),
     c -> d ]
Apply Direct Methods...
Inner CPs:
   [ f(d) = g(c),
     g(d) = f(c) ]
Outer CPs:
   [  ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
inner CP cond (upside-parallel)
innter CP Cond (outside)
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ f(d) = g(c),
     g(d) = f(c),
     g(c) = f(d),
     f(c) = g(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 <f(d), g(c)> by Rules <2, 0> preceded by [(f,1)]
 joinable by a reduction of rules <[], [([],1),([(f,1)],2)]>
Critical Pair <g(d), f(c)> by Rules <2, 1> preceded by [(g,1)]
 joinable by a reduction of rules <[], [([],0),([(g,1)],2)]>
unknown Diagram Decreasing
check Non-Confluence...
obtain 9 rules by 3 steps unfolding
obtain 12 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <f(d) <- g(c) -> g(d)>
Direct Methods: not CR

Combined result: not CR
543.trs: Success(not CR)
(18 msec.)