YES
O(n)
TRS:
 {f(h(x)) -> f(i(x)),
   i(a()) -> b(),
   h(a()) -> b(),
  g(i(x)) -> g(h(x))}
 DUP: We consider a non-duplicating system.
  Trs:
   {f(h(x)) -> f(i(x)),
     i(a()) -> b(),
     h(a()) -> b(),
    g(i(x)) -> g(h(x))}
  BOUND:
   Automaton:
    {
       a_0() -> 7,
       b_1() -> 8,
       b_0() -> 6,
     g_1(21) -> 22,
      g_0(7) -> 6,
      g_0(6) -> 6,
     h_1(25) -> 26,
     h_1(20) -> 21,
      h_0(7) -> 6,
      h_0(6) -> 6,
     i_1(16) -> 17,
     i_1(10) -> 11,
      i_0(7) -> 6,
      i_0(6) -> 6,
     f_1(11) -> 12,
      f_0(7) -> 6,
      f_0(6) -> 6,
          26 -> 21,
          22 -> 6,
          17 -> 11,
          12 -> 6,
           8 -> 26 | 17 | 6,
           7 -> 25 | 16,
           6 -> 20 | 10
    }
   Strict:
    {}
   Qed