YES
Time: 0.001823
TRS:
 {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(x, a()))}
 DP:
  DP:
   {f#(x, f(a(), a())) -> f#(x, a()),
    f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())),
    f#(x, f(a(), a())) -> f#(f(a(), a()), a())}
  TRS:
  {f(x, f(a(), a())) -> f(f(f(a(), a()), a()), f(x, a()))}
  UR:
   {}
   EDG:
    {(f#(x, f(a(), a())) -> f#(f(a(), a()), a()), f#(x, f(a(), a())) -> f#(f(a(), a()), a()))
     (f#(x, f(a(), a())) -> f#(f(a(), a()), a()), f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())))
     (f#(x, f(a(), a())) -> f#(f(a(), a()), a()), f#(x, f(a(), a())) -> f#(x, a()))
     (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())), f#(x, f(a(), a())) -> f#(x, a()))
     (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())), f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())))
     (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())), f#(x, f(a(), a())) -> f#(f(a(), a()), a()))
     (f#(x, f(a(), a())) -> f#(x, a()), f#(x, f(a(), a())) -> f#(x, a()))
     (f#(x, f(a(), a())) -> f#(x, a()), f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())))
     (f#(x, f(a(), a())) -> f#(x, a()), f#(x, f(a(), a())) -> f#(f(a(), a()), a()))}
    EDG:
     {(f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())), f#(x, f(a(), a())) -> f#(x, a()))
      (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())), f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())))
      (f#(x, f(a(), a())) -> f#(f(f(a(), a()), a()), f(x, a())), f#(x, f(a(), a())) -> f#(f(a(), a()), a()))}
     EDG:
      {}
      EDG:
       {}
       STATUS:
        arrows: 1.000000
        SCCS (0):