(ignored inputs)COMMENT Example 2 of \cite{Tiw02} Rewrite Rules: [ g(f(a)) -> f(g(f(a))), g(f(a)) -> f(f(a)), f(f(a)) -> f(a) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ f(g(f(a))) = f(f(a)) ] Overlay, check Innermost Termination... unknown Innermost 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: [ f(g(f(a))) = f(f(a)), f(f(a)) = f(g(f(a))) ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], [([(f,1)],1),([(f,1)],2)]> Satisfiable by 1>2,3; f(0)g(0); 1>2,3 Diagram Decreasing Direct Methods: CR Final result: CR /local-scratch/hzankl/2012/cops2012/81.trs: Success(CR) (3 msec.)