YES
O(n)
TRS:
 {   f(f(X)) -> f(a(b(f(X)))),
  f(a(g(X))) -> b(X),
        b(X) -> a(X)}
 DUP: We consider a non-duplicating system.
  Trs:
   {   f(f(X)) -> f(a(b(f(X)))),
    f(a(g(X))) -> b(X),
          b(X) -> a(X)}
  BOUND:
   Automaton:
    {
      g_0(5) -> 5,
      g_0(4) -> 5,
     b_2(55) -> 56,
     b_1(23) -> 24,
     b_1(18) -> 19,
     b_1(14) -> 15,
      b_0(5) -> 4,
      b_0(4) -> 4,
     a_3(59) -> 60,
     a_2(56) -> 57,
     a_2(48) -> 49,
     a_2(44) -> 45,
     a_2(37) -> 38,
     a_1(24) -> 25,
     a_1(10) -> 11,
      a_1(6) -> 7,
      a_0(5) -> 4,
      a_0(4) -> 4,
     f_2(57) -> 58,
     f_2(54) -> 55,
     f_1(29) -> 30,
     f_1(25) -> 26,
     f_1(22) -> 23,
      f_0(5) -> 4,
      f_0(4) -> 4,
          60 -> 56,
          58 -> 23,
          55 -> 59,
          49 -> 24,
          45 -> 19,
          38 -> 15,
          30 -> 23,
          26 -> 23 | 4,
          25 -> 54,
          23 -> 48,
          19 -> 23 | 4,
          18 -> 44,
          15 -> 23 | 4,
          14 -> 37,
          11 -> 4,
           7 -> 4,
           5 -> 29 | 18 | 10,
           4 -> 22 | 14 | 6
    }
   Strict:
    {}
   Qed