YES(?,O(n^1))

Problem:
 f(h(x)) -> f(i(x))
 g(i(x)) -> g(h(x))
 h(a()) -> b()
 i(a()) -> b()

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5,4,3}
   transitions:
    b1() -> 8*
    f0(2) -> 3*
    f0(1) -> 3*
    h0(2) -> 5*
    h0(1) -> 5*
    i0(2) -> 6*
    i0(1) -> 6*
    g0(2) -> 4*
    g0(1) -> 4*
    a0() -> 1*
    b0() -> 2*
    8 -> 6,5
  problem:
   
  Qed