YES
Time: 0.007938
TRS:
 {f(f(x, a()), y) -> f(f(a(), y), f(a(), x))}
 DP:
  DP:
   {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)}
  TRS:
  {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 (1):
    Scc:
     {f#(f(x, a()), y) -> f#(f(a(), y), f(a(), x))}
    SCC (1):
     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 1
      Automaton:
       {       a_1() -> 11*
               a_0() -> 9*
        f#_1(12, 13) -> 4*
        f#_0(10, 10) -> 4*
         f_1(11, 10) -> 12*
          f_1(11, 9) -> 13*
         f_0(10, 10) -> 8*
          f_0(10, 9) -> 8*
          f_0(10, 8) -> 8*
          f_0(9, 10) -> 10*
           f_0(9, 9) -> 10*
           f_0(9, 8) -> 10*
          f_0(8, 10) -> 8*
           f_0(8, 9) -> 8*
           f_0(8, 8) -> 8*}
      Strict:
       {}
      Qed