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