(ignored inputs)COMMENT doi:10.1145/322217.322230 [12] p. 811 submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama
Rewrite Rules:
   [ F(?x) -> A,
     F(?x) -> G(F(?x)),
     G(F(?x)) -> F(H(?x)),
     G(F(?x)) -> B ]
Apply Direct Methods...
Inner CPs:
   [ G(A) = F(H(?x)),
     G(G(F(?x_1))) = F(H(?x_1)),
     G(A) = B,
     G(G(F(?x_1))) = B ]
Outer CPs:
   [ A = G(F(?x)),
     F(H(?x_2)) = 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
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ G(F(?x)) = A,
     F(H(?x)) = G(A),
     B = G(A),
     A = G(F(?x)),
     F(H(?x)) = G(G(F(?x))),
     B = G(G(F(?x))),
     B = F(H(?x)),
     G(A) = F(H(?x)),
     G(G(F(?x))) = F(H(?x)),
     F(H(?x)) = B,
     G(A) = B,
     G(G(F(?x))) = 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 <G(A), F(H(?x))> by Rules <0, 2> preceded by [(G,1)]
 joinable by a reduction of rules <[], [([],1),([(G,1)],0)]>
Critical Pair <G(G(F(?x_1))), F(H(?x_1))> by Rules <1, 2> preceded by [(G,1)]
 joinable by a reduction of rules <[([(G,1)],2)], [([],1)]>
Critical Pair <G(A), B> by Rules <0, 3> preceded by [(G,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 8 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <A <- G(F(c_1)) -> B>
Direct Methods: not CR

Combined result: not CR
43.trs: Success(not CR)
NO
(12 msec.)