(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.)