YES
O(n)
TRS:
 {a(a(x)) -> a(b(a(x)))}
 DUP: We consider a non-duplicating system.
  Trs:
   {a(a(x)) -> a(b(a(x)))}
  BOUND:
   Automaton:
    {
     b_2(14) -> 15,
      b_1(4) -> 5,
      b_0(2) -> 2,
     a_2(15) -> 16,
     a_2(13) -> 14,
      a_1(5) -> 6,
      a_1(3) -> 4,
      a_0(2) -> 2,
          16 -> 4,
           6 -> 4 | 2,
           5 -> 13,
           2 -> 3
    }
   Strict:
    {}
   Qed