YES

Problem:
 f(f(x)) -> f(g(f(x)))

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {1}
   transitions:
    f20() -> 2*
    f0(2) -> 3*
    f0(4) -> 1*
    g0(3) -> 4*
    1 -> 3*
  problem:
   
  Qed