YES
Time: 0.001468
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))}
  UR:
   {}
   EDG:
    {(f#(f(x, a()), y) -> f#(a(), x), f#(f(x, a()), y) -> f#(a(), x))
     (f#(f(x, a()), y) -> f#(a(), x), f#(f(x, a()), y) -> f#(a(), y))
     (f#(f(x, 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(), y), f#(f(x, a()), y) -> f#(a(), y))
     (f#(f(x, a()), y) -> f#(a(), y), f#(f(x, 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#(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))}
    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))}
     EDG:
      {}
      EDG:
       {}
       STATUS:
        arrows: 1.000000
        SCCS (0):