(ignored inputs)COMMENT doi:10.1016/0890-5401 ( 90 ) 90015-A [24] Example 1 submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama
Rewrite Rules:
   [ a -> f(a,b),
     f(a,b) -> f(b,a) ]
Apply Direct Methods...
Inner CPs:
   [ f(f(a,b),b) = f(b,a) ]
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(b,a) = f(f(a,b),b),
     f(f(a,b),b) = f(b,a) ]
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(f(a,b),b), f(b,a)> by Rules <0, 1> preceded by [(f,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <f(f(b,a),b) <- a -> f(b,a)>
Direct Methods: not CR

Combined result: not CR
80.trs: Success(not CR)
NO
(9 msec.)