NO
(ignored inputs)COMMENT generated by FORT "UN & ~UNC" submitted by: Franziska Rapp
Rewrite Rules:
   [ a -> a,
     g(g(a)) -> b,
     g(g(?x)) -> g(g(g(b))) ]
Apply Direct Methods...
Inner CPs:
   [ g(g(a)) = b,
     g(b) = g(g(g(b))),
     g(g(g(g(b)))) = g(g(g(b))) ]
Outer CPs:
   [ b = g(g(g(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
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ b = g(g(a)),
     g(g(g(b))) = b,
     g(g(a)) = b,
     g(g(g(b))) = g(b),
     b = g(g(g(b))),
     g(g(g(g(b)))) = g(g(g(b))),
     g(b) = g(g(g(b))),
     g(g(g(b))) = g(g(g(g(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 <g(g(a)), b> by Rules <0, 1> preceded by [(g,1),(g,1)]
 joinable by a reduction of rules <[([],1)], []>
Critical Pair <g(b), g(g(g(b)))> by Rules <1, 2> preceded by [(g,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 3 rules by 3 steps unfolding
obtain 19 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
<F,Q,Q_f,Delta> where
   F = {(a,0),(b,0),(g,1)}
   Q = {q_0,q_1,q_{g(g(b))},q_{b},q_{g(b)}}
   Qf = {q_0,q_1}
   Delta = 
   [ b -> q_1,
     b -> q_{b},
     g(q_{g(g(b))}) -> q_0,
     g(q_{g(g(b))}) -> q_{g(g(b))},
     g(q_{b}) -> q_{g(b)},
     g(q_{g(b)}) -> q_{g(g(b))} ]
Witness for Non-Confluence: <g(g(g(b))), b>
Direct Methods: not CR

Combined result: not CR
739.trs: Success(not CR)
(11 msec.)