MAYBE
(ignored inputs)COMMENT The first rule is redundant; it can be simulated by the second rule. Confluent by feeble orthogonality ( van Oostrom ) or Okui's simultaneous critical pair criterion.
Rewrite Rules:
   [ g(f(f(h(?x))),?y) -> g(g(f(h(?x)),f(f(h(?x)))),?y),
     f(?x) -> g(?x,f(?x)),
     h(?x) -> g(f(?x),?x),
     g(?x,?y) -> h(g(f(?x),f(?y))) ]
Apply Direct Methods...
Inner CPs:
   [ g(g(f(h(?x)),f(f(h(?x)))),?y) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     g(f(g(h(?x),f(h(?x)))),?y) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     g(f(f(g(f(?x_2),?x_2))),?y) = g(g(f(h(?x_2)),f(f(h(?x_2)))),?y) ]
Outer CPs:
   [ g(g(f(h(?x)),f(f(h(?x)))),?y) = h(g(f(f(f(h(?x)))),f(?y))) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Left-Linear, not Right-Linear
unknown Development Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs:
   [ g(f(f(g(f(?x_3),?x_3))),?y) = g(g(f(h(?x_3)),f(f(h(?x_3)))),?y) {?x_3},
     g(f(g(?x_5,f(?x_5))),?y) = g(g(f(h(?x)),f(f(h(?x)))),?y) {?x},
     g(g(f(h(?x)),f(f(h(?x)))),?y) = g(g(f(h(?x)),f(f(h(?x)))),?y) {?x} ]
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ h(g(f(g(g(g(f(?x),?x),f(g(f(?x),?x))),f(g(g(f(?x),?x),f(g(f(?x),?x)))))),f(?y))) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     h(g(f(g(g(h(?x),f(h(?x))),f(g(h(?x),f(h(?x)))))),f(?y))) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     h(g(f(g(f(g(f(?x),?x)),f(f(g(f(?x),?x))))),f(?y))) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     h(g(f(f(g(g(f(?x),?x),f(g(f(?x),?x))))),f(?y))) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     g(g(g(g(f(?x),?x),f(g(f(?x),?x))),f(g(g(f(?x),?x),f(g(f(?x),?x))))),?y) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     h(g(f(g(f(h(?x)),f(f(h(?x))))),f(?y))) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     h(g(f(f(g(h(?x),f(h(?x))))),f(?y))) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     h(g(f(f(f(g(f(?x),?x)))),f(?y))) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     g(g(g(h(?x),f(h(?x))),f(g(h(?x),f(h(?x))))),?y) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     g(g(f(g(f(?x),?x)),f(f(g(f(?x),?x)))),?y) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     g(f(g(g(f(?x),?x),f(g(f(?x),?x)))),?y) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     h(g(f(f(f(h(?x)))),f(?y))) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     g(g(f(h(?x)),f(f(h(?x)))),?y) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     g(f(g(h(?x),f(h(?x)))),?y) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     g(f(f(g(f(?x),?x))),?y) = g(g(f(h(?x)),f(f(h(?x)))),?y),
     g(g(f(h(?x_2)),f(f(h(?x_2)))),?y_2) = g(f(g(h(?x_2),f(h(?x_2)))),?y_2),
     g(g(f(h(?x)),f(f(h(?x)))),?y_2) = g(f(f(g(f(?x),?x))),?y_2),
     g(g(f(h(?x_1)),f(f(h(?x_1)))),?y) = h(g(f(f(f(h(?x_1)))),f(?y))) ]
423.trs: Failure(timeout)
(107406 msec.)