YES
TRS:
 {f(x, f(f(f(a(), a()), a()), a())) -> f(f(x, a()), x)}
 DP:
  Strict:
   {f#(x, f(f(f(a(), a()), a()), a())) -> f#(x, a()),
    f#(x, f(f(f(a(), a()), a()), a())) -> f#(f(x, a()), x)}
  Weak:
  {f(x, f(f(f(a(), a()), a()), a())) -> f(f(x, a()), x)}
  EDG:
   {(f#(x, f(f(f(a(), a()), a()), a())) -> f#(f(x, a()), x), f#(x, f(f(f(a(), a()), a()), a())) -> f#(x, a()))
    (f#(x, f(f(f(a(), a()), a()), a())) -> f#(f(x, a()), x), f#(x, f(f(f(a(), a()), a()), a())) -> f#(f(x, a()), x))}
   SCCS:
    Scc:
     {f#(x, f(f(f(a(), a()), a()), a())) -> f#(f(x, a()), x)}
    SCC:
     Strict:
      {f#(x, f(f(f(a(), a()), a()), a())) -> f#(f(x, a()), x)}
     Weak:
     {f(x, f(f(f(a(), a()), a()), a())) -> f(f(x, a()), x)}
     BOUND:
      Bound: roof(-raise)-bounded by 5
      Automaton:
       {      a_5() -> 10*
              a_4() -> 8*
              a_3() -> 6*
              a_2() -> 4*
              a_1() -> 2*
              a_0() -> 1*
        f#_5(11, 9) -> 1*
         f#_4(9, 7) -> 1*
         f#_3(7, 5) -> 1*
         f#_2(5, 3) -> 1*
         f#_1(3, 1) -> 1*
         f#_0(1, 1) -> 1*
         f_5(11, 9) -> 1*
         f_5(9, 10) -> 11*
          f_4(9, 7) -> 1*
          f_4(7, 8) -> 9*
          f_3(7, 5) -> 1*
          f_3(5, 6) -> 7*
          f_2(5, 3) -> 1*
          f_2(3, 4) -> 5*
          f_1(3, 1) -> 1*
          f_1(1, 2) -> 3*
          f_0(1, 1) -> 1*}
      Strict:
       {}
      Qed