NO
(ignored inputs)COMMENT [111] Example 1
Rewrite Rules:
   [ a -> b,
     f(?x,a) -> f(b,b),
     f(b,?x) -> f(b,b),
     f(f(?x,?y),?z) -> f(b,b) ]
Apply Direct Methods...
Inner CPs:
   [ f(?x,b) = f(b,b),
     f(f(b,b),?z_2) = f(b,b),
     f(f(b,b),?z_2) = f(b,b),
     f(f(b,b),?z_1) = f(b,b) ]
Outer CPs:
   [ f(b,b) = f(b,b),
     f(b,b) = f(b,b) ]
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(b,b) = f(?x,b),
     f(b,b) = f(b,b),
     f(?x,b) = f(b,b),
     f(b,b) = f(f(b,b),?z_3),
     f(f(b,b),?z) = 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(?x,b), f(b,b)> by Rules <0, 1> preceded by [(f,2)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 5 rules by 3 steps unfolding
obtain 3 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <f(b,b) <- f(c_1,a) -> f(c_1,b)>
Direct Methods: not CR

Combined result: not CR
512.trs: Success(not CR)
(15 msec.)