NO
(ignored inputs)COMMENT reduction failed
Rewrite Rules:
   [ b(?x) -> c(d(?x)),
     d(?x) -> c(b(?x)),
     c(?x) -> b(d(?x)),
     b(?x) -> c(d(?x)),
     a(?x) -> a(b(?x)),
     a(?x) -> b(c(?x)) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ c(d(?x)) = c(d(?x)),
     a(b(?x_4)) = b(c(?x_4)) ]
Overlay, check Innermost Termination...
unknown Innermost 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:
   [ c(d(?x)) = c(d(?x)),
     b(c(?x)) = a(b(?x)),
     a(b(?x)) = b(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 <c(d(?x_3)), c(d(?x_3))> by Rules <3, 0> preceded by []
 joinable by a reduction of rules <[], []>
Critical Pair <b(c(?x_5)), a(b(?x_5))> by Rules <5, 4> preceded by []
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 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) (success)
Polynomial Interpretation:
  b:= (1)+(1)*x1
  c:= (1)+(1)*x1
  d:= (1)*x1
  c_1:= 0
 [c(?x)]-[b(d(?x))] = 0 = 0 (mod 2)
 [b(?x)]-[c(d(?x))] = 0 = 0 (mod 2)
 [b(?x)]-[c(d(?x))] = 0 = 0 (mod 2)
 [d(?x)]-[c(b(?x))] = (~2) = 0 (mod 2)
 [b(d(?x))]-[c(?x)] = 0 = 0 (mod 2)
 [c(d(?x))]-[b(?x)] = 0 = 0 (mod 2)
 [c(d(?x))]-[b(?x)] = 0 = 0 (mod 2)
 [c(b(?x))]-[d(?x)] = (2) = 0 (mod 2)
 [b(c(b(c_1)))]-[b(c(c_1))] = (1) = 1 (mod 2)
 (success)
Witness for Non-Confluence: <b(c(b(c_1))) <- a(c_1) -> b(c(c_1))>
Direct Methods: not CR

Combined result: not CR
/tmp/filelTHcoL.trs: Success(not CR)
(1606 msec.)