YES
(ignored inputs)COMMENT Example 3.2 of cite{Toy88}
Rewrite Rules:
   [ f(?x) -> g(f(?x)),
     h(?x) -> p(h(?x)),
     f(?x) -> h(f(?x)),
     g(?x) -> p(p(h(?x))) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ g(f(?x)) = h(f(?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:
   [ h(f(?x)) = g(f(?x)),
     g(f(?x)) = h(f(?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 <h(f(?x_2)), g(f(?x_2))> by Rules <2, 0> preceded by []
 joinable by a reduction of rules <[([],1),([(p,1)],1)], [([],3)]>
Satisfiable by 1,2>3,4; f(0)g(0)h(0)p(0); 1>3,4>2
Diagram Decreasing
Direct Methods: CR

Final result: CR
87.trs: Success(CR)
(2 msec.)