YES
Time: 0.001274
TRS:
 {f(f(x, a()), a()) -> f(f(f(x, a()), f(a(), a())), a())}
 DP:
  DP:
   {f#(f(x, a()), a()) -> f#(f(x, a()), f(a(), a())),
    f#(f(x, a()), a()) -> f#(f(f(x, a()), f(a(), a())), a()),
    f#(f(x, a()), a()) -> f#(a(), a())}
  TRS:
  {f(f(x, a()), a()) -> f(f(f(x, a()), f(a(), a())), a())}
  UR:
   {f(f(x, a()), a()) -> f(f(f(x, a()), f(a(), a())), a())}
   EDG:
    {}
    STATUS:
     arrows: 1.000000
     SCCS (0):