YES

Problem:
 f(g(X)) -> g(f(f(X)))
 f(h(X)) -> h(g(X))

Proof:
 String Reversal Processor:
  g(f(X)) -> f(f(g(X)))
  h(f(X)) -> g(h(X))
  Bounds Processor:
   bound: 0
   enrichment: match
   automaton:
    final states: {5,1}
    transitions:
     g0(2) -> 3*
     g0(6) -> 5*
     f30() -> 2*
     f0(3) -> 4*
     f0(4) -> 1*
     h0(2) -> 6*
     1 -> 3*
     5 -> 6*
   problem:
    
   Qed