(ignored inputs)COMMENT doi:10.4230/LIPIcs.RTA.2012.165 [37] Section 4 ( R_65 )
Rewrite Rules:
   [ a -> b,
     a -> f(a),
     b -> f(f(b)),
     f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> b ]
Apply Direct Methods...
Inner CPs:
   [ f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = b ]
Outer CPs:
   [ b = f(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:
   [ f(a) = b,
     b = f(a),
     b = f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
     f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = 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(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), b> by Rules <2, 3> preceded by [(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1),(f,1)]
 joinable by a reduction of rules <[([(f,1),(f,1)],3)], [([],2)]>
Critical Pair <f(a), b> by Rules <1, 0> preceded by []
 joinable by a reduction of rules <[([(f,1)],1),([(f,1),(f,1)],0)], [([],2)]>
unknown Diagram Decreasing
check Non-Confluence...
obtain 11 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 (failure)
check by Interpretation(mod2)