NO
(ignored inputs)COMMENT reduction failed
Rewrite Rules:
   [ a(a(?x)) -> b(c(?x)),
     b(b(?x)) -> c(d(?x)),
     c(c(?x)) -> d(d(d(?x))),
     d(d(d(?x))) -> a(c(?x)) ]
Apply Direct Methods...
Inner CPs:
   [ a(b(c(?x))) = b(c(a(?x))),
     b(c(d(?x))) = c(d(b(?x))),
     c(d(d(d(?x)))) = d(d(d(c(?x)))),
     d(a(c(?x))) = a(c(d(?x))),
     d(d(a(c(?x)))) = a(c(d(d(?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:
   [ a(b(c(?x_1))) = b(c(a(?x_1))),
     b(c(b(c(?x_1)))) = a(b(c(a(?x_1)))),
     b(c(a(?x))) = a(b(c(?x))),
     b(c(d(?x_1))) = c(d(b(?x_1))),
     c(d(c(d(?x_1)))) = b(c(d(b(?x_1)))),
     c(d(b(?x))) = b(c(d(?x))),
     c(d(d(d(?x_1)))) = d(d(d(c(?x_1)))),
     d(d(d(d(d(d(?x_1)))))) = c(d(d(d(c(?x_1))))),
     d(d(d(c(?x)))) = c(d(d(d(?x)))),
     d(a(c(?x_1))) = a(c(d(?x_1))),
     d(d(a(c(?x_1)))) = a(c(d(d(?x_1)))),
     a(c(a(c(?x_1)))) = d(a(c(d(d(?x_1))))),
     a(c(a(c(?x_1)))) = d(d(a(c(d(?x_1))))),
     a(c(d(a(c(?x_1))))) = d(d(a(c(d(d(?x_1)))))),
     a(c(d(?x))) = d(a(c(?x))),
     a(c(d(d(?x)))) = d(d(a(c(?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 <a(b(c(?x))), b(c(a(?x)))> by Rules <0, 0> preceded by [(a,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 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)
 (success)
 (success)
 (success)
 (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <a(c(d(c_1))) <- c(b(b(c_1))) -> d(a(c(c_1)))>
Direct Methods: not CR

Combined result: not CR
/tmp/filekEF8SJ.trs: Success(not CR)
(161 msec.)