NO
(ignored inputs)COMMENT For an infeasibility problem. submitted by: Akihisa Yamada
Rewrite Rules:
   [ f(f(?x)) -> f(g(f(f(?x)))),
     f(?x) -> ?x ]
Apply Direct Methods...
Inner CPs:
   [ f(?x_1) = f(g(f(f(?x_1)))),
     f(f(g(f(f(?x))))) = f(g(f(f(f(?x))))) ]
Outer CPs:
   [ f(g(f(f(?x)))) = f(?x) ]
not Overlay, check Termination...
unknown/not 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:
   [ f(g(f(f(?x_1)))) = f(g(f(f(f(?x_1))))),
     ?x = f(g(f(f(?x)))),
     f(?x) = f(g(f(f(?x)))),
     f(f(g(f(f(?x_1))))) = f(g(f(f(f(?x_1))))),
     f(g(f(f(f(g(f(f(?x_1)))))))) = f(f(g(f(f(f(?x_1)))))),
     f(g(f(f(?x)))) = f(f(g(f(f(?x))))),
     f(g(f(f(f(?x))))) = f(f(g(f(f(?x))))),
     f(g(f(f(?x_1)))) = f(?x_1) ]
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_1), f(g(f(f(?x_1))))> by Rules <1, 0> preceded by [(f,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 5 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)
 (success)
 (success)
 (success)
 (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <g(c_1) <- f(f(c_1)) -> c_1>
Direct Methods: not CR

Combined result: not CR
1280.trs: Success(not CR)
(22 msec.)