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: {7,8}
   transitions:
    b1() -> 30*
    g1(22) -> 23*
    h1(24) -> 25*
    h1(21) -> 22*
    f1(13) -> 14*
    i1(15) -> 16*
    i1(12) -> 13*
    f0(7) -> 7*
    f0(8) -> 7*
    h0(7) -> 7*
    h0(8) -> 7*
    i0(7) -> 7*
    i0(8) -> 7*
    g0(7) -> 7*
    g0(8) -> 7*
    a0() -> 8*
    b0() -> 7*
    7 -> 21,12
    8 -> 24,15
    14 -> 7*
    16 -> 13*
    23 -> 7*
    25 -> 22*
    30 -> 16,13,25,22,7
  problem:
   
  Qed