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)}
     UR:
      {}
      BOUND:
       Bound: match(-raise)-bounded by 1
       Automaton:
        {     a_1() -> 2*
              a_0() -> 1*
         f#_1(5, 5) -> 1*
         f#_1(5, 1) -> 1*
         f#_0(1, 1) -> 1*
          f_1(4, 4) -> 5*
          f_1(3, 2) -> 4*
          f_1(2, 2) -> 3*
          f_1(1, 4) -> 5*
          f_0(1, 1) -> 1*}
       Strict:
        {}
       Qed