YES
Time: 0.001807
TRS:
 {f(f(a(), x), a()) -> f(f(x, f(a(), a())), a())}
 DP:
  DP:
   {f#(f(a(), x), a()) -> f#(x, f(a(), a())),
    f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()),
    f#(f(a(), x), a()) -> f#(a(), a())}
  TRS:
  {f(f(a(), x), a()) -> f(f(x, f(a(), a())), a())}
  UR:
   {}
   EDG:
    {(f#(f(a(), x), a()) -> f#(a(), a()), f#(f(a(), x), a()) -> f#(a(), a()))
     (f#(f(a(), x), a()) -> f#(a(), a()), f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()))
     (f#(f(a(), x), a()) -> f#(a(), a()), f#(f(a(), x), a()) -> f#(x, f(a(), a())))
     (f#(f(a(), x), a()) -> f#(x, f(a(), a())), f#(f(a(), x), a()) -> f#(x, f(a(), a())))
     (f#(f(a(), x), a()) -> f#(x, f(a(), a())), f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()))
     (f#(f(a(), x), a()) -> f#(x, f(a(), a())), f#(f(a(), x), a()) -> f#(a(), a()))
     (f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()), f#(f(a(), x), a()) -> f#(x, f(a(), a())))
     (f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()), f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()))
     (f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()), f#(f(a(), x), a()) -> f#(a(), a()))}
    EDG:
     {(f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()), f#(f(a(), x), a()) -> f#(x, f(a(), a())))
      (f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()), f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()))
      (f#(f(a(), x), a()) -> f#(f(x, f(a(), a())), a()), f#(f(a(), x), a()) -> f#(a(), a()))}
     EDG:
      {}
      EDG:
       {}
       STATUS:
        arrows: 1.000000
        SCCS (0):