(ignored inputs)COMMENT submitted by: Johannes Waldmann
Rewrite Rules:
   [ f(f(?x,a),a) -> f(f(f(f(a,f(a,?x)),a),a),a) ]
Apply Direct Methods...
Inner CPs:
   [ f(f(f(f(f(a,f(a,?x)),a),a),a),a) = f(f(f(f(a,f(a,f(?x,a))),a),a),a) ]
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:
   [ f(f(f(f(f(a,f(a,?x_1)),a),a),a),a) = f(f(f(f(a,f(a,f(?x_1,a))),a),a),a),
     f(f(f(f(a,f(a,f(f(f(f(a,f(a,?x_1)),a),a),a))),a),a),a) = f(f(f(f(f(a,f(a,f(?x_1,a))),a),a),a),a),
     f(f(f(f(a,f(a,f(?x,a))),a),a),a) = f(f(f(f(f(a,f(a,?x)),a),a),a),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(f(f(f(a,f(a,?x)),a),a),a),a), f(f(f(f(a,f(a,f(?x,a))),a),a),a)> by Rules <0, 0> preceded by [(f,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 3 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)