NO
(ignored inputs)COMMENT generated by FORT -f "a:0 b:0 f:2" -r 5 "UN & ~UNC & ~SN" submitted by: Franziska Rapp
Rewrite Rules:
   [ a -> a,
     a -> b,
     a -> f(a,a),
     f(b,b) -> f(a,a),
     f(?x0,a) -> f(a,b) ]
Apply Direct Methods...
Inner CPs:
   [ f(?x0,a) = f(a,b),
     f(?x0,b) = f(a,b),
     f(?x0,f(a,a)) = f(a,b) ]
Outer CPs:
   [ a = b,
     a = f(a,a),
     b = f(a,a) ]
not Overlay, check Termination...
unknown/not 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:
   [ b = a,
     f(a,a) = a,
     f(a,b) = f(?x0,a),
     a = b,
     f(a,a) = b,
     f(a,b) = f(?x0,b),
     a = f(a,a),
     b = f(a,a),
     f(a,b) = f(?x0,f(a,a)),
     f(?x0,a) = f(a,b),
     f(?x0,b) = f(a,b),
     f(?x0,f(a,a)) = f(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 <f(?x0,a), f(a,b)> by Rules <0, 4> preceded by [(f,2)]
 joinable by a reduction of rules <[([],4)], []>
Critical Pair <f(?x0,b), f(a,b)> by Rules <1, 4> preceded by [(f,2)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 12 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <f(a,a) <- a -> b>
Direct Methods: not CR

Combined result: not CR
732.trs: Success(not CR)
(17 msec.)