NO
(ignored inputs)COMMENT reduction failed
Rewrite Rules:
   [ a -> a,
     f(f(?x,a),a) -> b ]
Apply Direct Methods...
Inner CPs:
   [ f(f(?x,a),a) = b,
     f(f(?x,a),a) = b,
     f(b,a) = b ]
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:
   [ b = f(f(?x,a),a),
     f(b,a) = b,
     f(f(?x,a),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(?x,a),a), b> by Rules <0, 1> preceded by [(f,1),(f,2)]
 joinable by a reduction of rules <[([],1)], []>
Critical Pair <f(f(?x,a),a), b> by Rules <0, 1> preceded by [(f,2)]
 joinable by a reduction of rules <[([],1)], []>
Critical Pair <f(b,a), b> by Rules <1, 1> preceded by [(f,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 2 rules by 3 steps unfolding
obtain 2 candidates for checking non-joinability
check by TCAP-Approximation (success)
 (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <f(b,a) <- f(f(f(c_1,a),a),a) -> b>
Direct Methods: not CR

Combined result: not CR
/tmp/fileni9B9a.trs: Success(not CR)
(8 msec.)