NO
(ignored inputs)COMMENT reduction failed
Rewrite Rules:
   [ b(a(a(?x))) -> a(?x),
     a(a(a(?x))) -> b(b(b(?x))),
     b(b(?x)) -> a(b(a(?x))) ]
Apply Direct Methods...
Inner CPs:
   [ b(b(b(b(?x_1)))) = a(a(?x_1)),
     b(a(b(b(b(?x_1))))) = a(a(a(?x_1))),
     b(a(?x)) = a(b(a(a(a(?x))))),
     a(b(b(b(?x)))) = b(b(b(a(?x)))),
     a(a(b(b(b(?x))))) = b(b(b(a(a(?x))))),
     b(a(b(a(?x)))) = a(b(a(b(?x)))) ]
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:
   [ b(b(b(b(?x_2)))) = a(a(?x_2)),
     b(a(b(b(b(?x_2))))) = a(a(a(?x_2))),
     a(b(a(b(b(b(?x_2)))))) = b(a(a(?x_2))),
     a(b(a(a(b(b(b(?x_2))))))) = b(a(a(a(?x_2)))),
     a(b(a(a(a(?x))))) = b(a(?x)),
     a(b(b(b(?x_1)))) = b(b(b(a(?x_1)))),
     a(a(b(b(b(?x_1))))) = b(b(b(a(a(?x_1))))),
     b(b(b(b(b(b(?x_1)))))) = a(b(b(b(a(a(?x_1)))))),
     b(b(b(b(b(b(?x_1)))))) = a(a(b(b(b(a(?x_1)))))),
     b(b(b(a(b(b(b(?x_1))))))) = a(a(b(b(b(a(a(?x_1))))))),
     a(b(b(b(?x_1)))) = b(b(b(b(a(a(?x_1)))))),
     a(b(b(b(?x_1)))) = b(a(b(b(b(a(?x_1)))))),
     a(a(b(b(b(?x_1))))) = b(a(b(b(b(a(a(?x_1))))))),
     b(b(b(a(?x)))) = a(b(b(b(?x)))),
     b(b(b(a(a(?x))))) = a(a(b(b(b(?x))))),
     a(a(?x)) = b(b(b(b(?x)))),
     a(a(a(?x))) = b(a(b(b(b(?x))))),
     b(a(b(a(?x_1)))) = a(b(a(b(?x_1)))),
     b(a(?x_2)) = a(b(a(a(a(?x_2))))),
     a(b(a(a(b(a(?x_1)))))) = b(a(b(a(b(?x_1))))),
     a(b(a(a(?x_2)))) = b(a(b(a(a(a(?x_2)))))),
     a(b(a(b(?x)))) = b(a(b(a(?x)))) ]
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 <b(b(b(b(?x_1)))), a(a(?x_1))> by Rules <1, 0> preceded by [(b,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 6 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
 (success)
 (success)
 (success)
 (success)
 (success)
 (success)
 (success)
 (success)
 (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <a(a(b(a(c_1)))) <- b(a(a(a(c_1)))) -> a(a(c_1))>
Direct Methods: not CR

Combined result: not CR
/tmp/filek38Ix2.trs: Success(not CR)
(124 msec.)