YES
Trs:
 {f(f(a())) -> f(g())}
 Comment:
  We consider a non-duplicating trs.
  BOUND:
   Automaton:
    {  a_0() -> q3,
       g_1() -> q4,
       g_0() -> q2,
     f_1(q4) -> q5,
     f_0(q3) -> q2,
     f_0(q2) -> q2,
          q5 -> q2}
   Strict:
   {}
   Qed