NO
(ignored inputs)COMMENT generated by FORT "NFP & ~CR" submitted by: Franziska Rapp
Rewrite Rules:
   [ a -> a,
     a -> b,
     f(a,a) -> f(b,f(f(a,b),a)) ]
Apply Direct Methods...
Inner CPs:
   [ f(a,a) = f(b,f(f(a,b),a)),
     f(a,a) = f(b,f(f(a,b),a)),
     f(b,a) = f(b,f(f(a,b),a)),
     f(a,b) = f(b,f(f(a,b),a)) ]
Outer CPs:
   [ a = b ]
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 = a,
     f(b,f(f(a,b),a)) = f(a,a),
     a = b,
     f(b,f(f(a,b),a)) = f(b,a),
     f(b,f(f(a,b),a)) = f(a,b),
     f(a,a) = f(b,f(f(a,b),a)),
     f(a,b) = f(b,f(f(a,b),a)),
     f(b,a) = f(b,f(f(a,b),a)),
     f(b,b) = f(b,f(f(a,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(a,a), f(b,f(f(a,b),a))> by Rules <0, 2> preceded by [(f,1)]
 joinable by a reduction of rules <[([],2)], []>
Critical Pair <f(a,a), f(b,f(f(a,b),a))> by Rules <0, 2> preceded by [(f,2)]
 joinable by a reduction of rules <[([],2)], []>
Critical Pair <f(b,a), f(b,f(f(a,b),a))> by Rules <1, 2> preceded by [(f,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 6 rules by 3 steps unfolding
obtain 29 candidates for checking non-joinability
check by TCAP-Approximation (success)
 (success)
 (success)
 (success)
 (success)
 (success)
 (success)
 (success)
 (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <f(b,f(f(a,b),a)) <- f(a,a) -> f(a,b)>
Direct Methods: not CR

Combined result: not CR
735.trs: Success(not CR)
(26 msec.)