YES
TRS:
 {f(f(x, a()), y) -> f(f(a(), y), f(a(), x))}
 DP:
  Strict:
   {f#(f(x, a()), y) -> f#(f(a(), y), f(a(), x)),
    f#(f(x, a()), y) -> f#(a(), y),
    f#(f(x, a()), y) -> f#(a(), x)}
  Weak:
  {f(f(x, a()), y) -> f(f(a(), y), f(a(), x))}
  EDG:
   {(f#(f(x, a()), y) -> f#(f(a(), y), f(a(), x)), f#(f(x, a()), y) -> f#(f(a(), y), f(a(), x)))
    (f#(f(x, a()), y) -> f#(f(a(), y), f(a(), x)), f#(f(x, a()), y) -> f#(a(), y))
    (f#(f(x, a()), y) -> f#(f(a(), y), f(a(), x)), f#(f(x, a()), y) -> f#(a(), x))}
   SCCS:
    Scc:
     {f#(f(x, a()), y) -> f#(f(a(), y), f(a(), x))}
    SCC:
     Strict:
      {f#(f(x, a()), y) -> f#(f(a(), y), f(a(), x))}
     Weak:
     {f(f(x, a()), y) -> f(f(a(), y), f(a(), x))}
     BOUND:
      Bound: match(-raise)-DP-bounded by 0
      Automaton:
       {     b_0() -> 3*
             a_0() -> 2*
        f#_0(4, 5) -> 1*
         f_0(2, 5) -> 4*
         f_0(2, 3) -> 5 | 4
         f_0(2, 2) -> 5*}
      Strict:
       {}
      Qed