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)}
     UR:
      {b(y, z) -> y,
       b(y, z) -> z}
      BOUND:
       Bound: top(-raise)-DP-bounded by 4
       Automaton:
        { b_0(10, 10) -> 8*
           b_0(10, 9) -> 8*
           b_0(10, 8) -> 8*
           b_0(10, 7) -> 8*
           b_0(9, 10) -> 8*
            b_0(9, 9) -> 8*
            b_0(9, 8) -> 8*
            b_0(9, 7) -> 8*
           b_0(8, 10) -> 8*
            b_0(8, 9) -> 8*
            b_0(8, 8) -> 8*
            b_0(8, 7) -> 8*
           b_0(7, 10) -> 8*
            b_0(7, 9) -> 8*
            b_0(7, 8) -> 8*
            b_0(7, 7) -> 8*
                a_4() -> 17*
                a_3() -> 15*
                a_2() -> 13*
                a_1() -> 11*
                a_0() -> 9*
         f#_4(18, 16) -> 5*
         f#_3(16, 14) -> 5*
         f#_2(14, 12) -> 5*
         f#_1(12, 10) -> 5*
         f#_0(10, 10) -> 5*
          f#_0(10, 9) -> 5*
          f#_0(10, 8) -> 5*
          f#_0(10, 7) -> 5*
          f_4(16, 17) -> 18*
          f_3(14, 15) -> 16*
          f_2(12, 13) -> 14*
          f_1(10, 11) -> 12*
          f_0(10, 10) -> 7*
           f_0(10, 9) -> 10*
           f_0(10, 8) -> 7*
           f_0(10, 7) -> 7*
           f_0(9, 10) -> 7*
            f_0(9, 9) -> 10*
            f_0(9, 8) -> 7*
            f_0(9, 7) -> 7*
           f_0(8, 10) -> 7*
            f_0(8, 9) -> 10*
            f_0(8, 8) -> 7*
            f_0(8, 7) -> 7*
           f_0(7, 10) -> 7*
            f_0(7, 9) -> 10*
            f_0(7, 8) -> 7*
            f_0(7, 7) -> 7*
                   10 -> 8*
                    9 -> 8*
                    7 -> 8*}
       Strict:
        {}
       Qed