YES
O(n)
TRS:
 {f(f(a())) -> f(g())}
 DUP: We consider a non-duplicating system.
  Trs:
   {f(f(a())) -> f(g())}
  BOUND:
   Automaton:
    {
      a_0() -> 4,
      g_1() -> 5,
      g_0() -> 3,
     f_1(5) -> 6,
     f_0(4) -> 3,
     f_0(3) -> 3,
          6 -> 3
    }
   Strict:
    {}
   Qed