YES
Time: 0.009007
TRS:
 {f(f(a(), x), a()) -> f(f(x, f(a(), f(a(), a()))), a())}
 DP:
  DP:
   {f#(f(a(), x), a()) -> f#(x, f(a(), f(a(), a()))),
    f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()),
    f#(f(a(), x), a()) -> f#(a(), f(a(), a())),
    f#(f(a(), x), a()) -> f#(a(), a())}
  TRS:
  {f(f(a(), x), a()) -> f(f(x, f(a(), f(a(), a()))), a())}
  EDG:
   {(f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()), f#(f(a(), x), a()) -> f#(x, f(a(), f(a(), a()))))
    (f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()), f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()))
    (f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()), f#(f(a(), x), a()) -> f#(a(), f(a(), a())))
    (f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a()), f#(f(a(), x), a()) -> f#(a(), a()))}
   SCCS (1):
    Scc:
     {f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a())}
    SCC (1):
     Strict:
      {f#(f(a(), x), a()) -> f#(f(x, f(a(), f(a(), a()))), a())}
     Weak:
     {f(f(a(), x), a()) -> f(f(x, f(a(), f(a(), a()))), a())}
     BOUND:
      Bound: match(-raise)-bounded by 1
      Automaton:
       {     a_1() -> 2*
             a_0() -> 1*
        f#_1(5, 2) -> 1*
        f#_0(1, 1) -> 1*
         f_1(5, 2) -> 1*
         f_1(4, 4) -> 5*
         f_1(2, 3) -> 4*
         f_1(2, 2) -> 3*
         f_1(1, 4) -> 5*
         f_0(1, 1) -> 1*}
      Strict:
       {}
      Qed