YES
O(n)
TRS:
 {
  f(a(), f(a(), f(b(), f(a(), f(a(), f(b(), f(a(), x))))))) ->
  f(a(), f(b(), f(a(), f(a(), f(b(), f(a(), f(a(), f(a(), f(b(), x)))))))))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
    f(a(), f(a(), f(b(), f(a(), f(a(), f(b(), f(a(), x))))))) ->
    f(a(), f(b(), f(a(), f(a(), f(b(), f(a(), f(a(), f(a(), f(b(), x)))))))))
   }
  BOUND:
   Automaton:
    {
           b_3() -> 77,
           b_2() -> 25,
           b_1() -> 5,
           b_0() -> 3,
           a_3() -> 76,
           a_2() -> 24,
           a_1() -> 4,
           a_0() -> 3,
     f_3(77, 92) -> 93,
     f_3(77, 89) -> 90,
     f_3(77, 84) -> 85,
     f_3(77, 81) -> 82,
     f_3(77, 31) -> 86,
     f_3(77, 28) -> 78,
     f_3(76, 93) -> 84 | 40,
     f_3(76, 91) -> 92,
     f_3(76, 90) -> 91,
     f_3(76, 88) -> 89,
     f_3(76, 87) -> 88,
     f_3(76, 86) -> 87,
     f_3(76, 85) -> 81 | 37,
     f_3(76, 83) -> 84,
     f_3(76, 82) -> 83,
     f_3(76, 80) -> 81,
     f_3(76, 79) -> 80,
     f_3(76, 78) -> 79,
     f_2(25, 59) -> 52,
     f_2(25, 58) -> 59,
     f_2(25, 55) -> 56,
     f_2(25, 41) -> 34,
     f_2(25, 40) -> 41,
     f_2(25, 37) -> 38,
     f_2(25, 33) -> 26,
     f_2(25, 32) -> 33,
     f_2(25, 31) -> 52,
     f_2(25, 29) -> 30,
     f_2(25, 28) -> 34,
     f_2(25, 13) -> 26,
     f_2(25, 11) -> 52,
     f_2(25, 10) -> 26,
      f_2(25, 8) -> 34,
      f_2(25, 7) -> 26,
      f_2(25, 6) -> 26,
     f_2(24, 59) -> 40 | 12,
     f_2(24, 57) -> 58,
     f_2(24, 56) -> 57,
     f_2(24, 54) -> 55,
     f_2(24, 53) -> 54,
     f_2(24, 52) -> 53,
     f_2(24, 41) -> 37 | 9,
     f_2(24, 39) -> 40,
     f_2(24, 38) -> 39,
     f_2(24, 36) -> 37,
     f_2(24, 35) -> 36,
     f_2(24, 34) -> 35,
     f_2(24, 33) -> 80 | 36 | 8,
     f_2(24, 31) -> 32,
     f_2(24, 30) -> 31,
     f_2(24, 28) -> 29,
     f_2(24, 27) -> 28,
     f_2(24, 26) -> 27,
      f_1(5, 59) -> 6,
      f_1(5, 41) -> 6,
      f_1(5, 13) -> 6,
      f_1(5, 12) -> 13,
      f_1(5, 11) -> 6,
       f_1(5, 9) -> 10,
       f_1(5, 8) -> 6,
       f_1(5, 3) -> 6,
      f_1(4, 13) -> 36 | 8 | 3,
      f_1(4, 11) -> 12,
      f_1(4, 10) -> 11,
       f_1(4, 8) -> 9,
       f_1(4, 7) -> 8,
       f_1(4, 6) -> 7,
       f_0(3, 3) -> 3
    }
   Strict:
    {}
   Qed