(ignored inputs)COMMENT [130] Example 3.29 submitted by: Julian Nagele
Rewrite Rules:
   [ f(?x) -> f(f(?x)),
     g(?x) -> f(?x),
     f(?x) -> g(?x) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ f(f(?x)) = g(?x) ]
Overlay, check Innermost Termination...
unknown Innermost 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(?x) = f(f(?x)),
     f(f(?x)) = g(?x) ]
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(?x_2), f(f(?x_2))> by Rules <2, 0> preceded by []
 joinable by a reduction of rules <[([],1),([],0)], []>
Satisfiable by 3>2,1; f(0)g(0); 3>2,1
Diagram Decreasing
Direct Methods: CR

Combined result: CR
760.trs: Success(CR)
YES
(2 msec.)