(ignored inputs)COMMENT from p.811 of \cite{Hue80} 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 Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ G(G(F(?x))) = B, G(A) = B, F(H(?x)) = B, G(G(F(?x))) = F(H(?x)), G(A) = F(H(?x)), B = F(H(?x)), B = G(G(F(?x))), F(H(?x)) = G(G(F(?x))), A = G(F(?x)), B = G(A), F(H(?x)) = G(A), G(F(?x)) = A ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <0, 2> preceded by [(G,1)] joinable by a reduction of rules <[], [([],1),([(G,1)],0)]> Critical Pair by Rules <1, 2> preceded by [(G,1)] joinable by a reduction of rules <[([(G,1)],2)], [([],1)]> Critical Pair by Rules <0, 3> preceded by [(G,1)] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from G(F(?x_1)) Not Confluent Direct Methods: not CR Final result: not CR /local-scratch/hzankl/2012/cops2012/43.trs: Success(not CR) (2 msec.)