YES
TRS:
 {f(a(), f(a(), x)) -> f(x, f(a(), f(f(a(), a()), a())))}
 DP:
  Strict:
   {f#(a(), f(a(), x)) -> f#(x, f(a(), f(f(a(), a()), a()))),
    f#(a(), f(a(), x)) -> f#(f(a(), a()), a()),
    f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), a())),
    f#(a(), f(a(), x)) -> f#(a(), a())}
  Weak:
  {f(a(), f(a(), x)) -> f(x, f(a(), f(f(a(), a()), a())))}
  EDG:
   {(f#(a(), f(a(), x)) -> f#(x, f(a(), f(f(a(), a()), a()))), f#(a(), f(a(), x)) -> f#(x, f(a(), f(f(a(), a()), a()))))
    (f#(a(), f(a(), x)) -> f#(x, f(a(), f(f(a(), a()), a()))), f#(a(), f(a(), x)) -> f#(f(a(), a()), a()))
    (f#(a(), f(a(), x)) -> f#(x, f(a(), f(f(a(), a()), a()))), f#(a(), f(a(), x)) -> f#(a(), f(f(a(), a()), a())))
    (f#(a(), f(a(), x)) -> f#(x, f(a(), f(f(a(), a()), a()))), f#(a(), f(a(), x)) -> f#(a(), a()))}
   SCCS:
    Scc:
     {f#(a(), f(a(), x)) -> f#(x, f(a(), f(f(a(), a()), a())))}
    SCC:
     Strict:
      {f#(a(), f(a(), x)) -> f#(x, f(a(), f(f(a(), a()), a())))}
     Weak:
     {f(a(), f(a(), x)) -> f(x, f(a(), f(f(a(), a()), a())))}
     UR:
      {}
      BOUND:
       Bound: match(-raise)-DP-bounded by 1
       Automaton:
        {       a_1() -> 13*
                a_0() -> 10*
         f#_1(11, 16) -> 4*
         f#_0(12, 12) -> 4*
         f#_0(11, 12) -> 4*
         f#_0(10, 12) -> 4*
          f#_0(9, 12) -> 4*
          f#_0(8, 12) -> 4*
          f_1(14, 13) -> 15*
          f_1(13, 15) -> 16*
          f_1(13, 13) -> 14*
          f_0(12, 12) -> 8*
          f_0(12, 11) -> 8*
          f_0(12, 10) -> 8*
           f_0(12, 9) -> 8*
           f_0(12, 8) -> 8*
          f_0(11, 12) -> 8*
          f_0(11, 11) -> 8*
          f_0(11, 10) -> 8*
           f_0(11, 9) -> 8*
           f_0(11, 8) -> 8*
          f_0(10, 12) -> 8*
          f_0(10, 11) -> 12*
          f_0(10, 10) -> 9*
           f_0(10, 9) -> 8*
           f_0(10, 8) -> 8*
           f_0(9, 12) -> 8*
           f_0(9, 11) -> 8*
           f_0(9, 10) -> 11*
            f_0(9, 9) -> 8*
            f_0(9, 8) -> 8*
           f_0(8, 12) -> 8*
           f_0(8, 11) -> 8*
           f_0(8, 10) -> 8*
            f_0(8, 9) -> 8*
            f_0(8, 8) -> 8*}
       Strict:
        {}
       Qed