YES
Trs:
 {f(f(a())) -> c()}
 Comment:
  We consider a non-duplicating trs.
  BOUND:
   Automaton:
    {  a_0() -> q3,
     f_0(q3) -> q2,
     f_0(q2) -> q2,
       c_1() -> q4,
       c_0() -> q2,
          q4 -> q2}
   Strict:
   {}
   Qed