MAYBE
Time: 0.519946
TRS:
 {        f(x, f(x, y)) -> f(f(f(x, a()), a()), a()),
  f(y, f(x, f(a(), x))) -> f(f(a(), f(x, a())), f(a(), y))}
 DP:
  DP:
   {        f#(x, f(x, y)) -> f#(x, a()),
            f#(x, f(x, y)) -> f#(f(x, a()), a()),
            f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()),
    f#(y, f(x, f(a(), x))) -> f#(x, a()),
    f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)),
    f#(y, f(x, f(a(), x))) -> f#(a(), y),
    f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a()))}
  TRS:
  {        f(x, f(x, y)) -> f(f(f(x, a()), a()), a()),
   f(y, f(x, f(a(), x))) -> f(f(a(), f(x, a())), f(a(), y))}
  EDG:
   {(f#(x, f(x, y)) -> f#(f(x, a()), a()), f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())))
    (f#(x, f(x, y)) -> f#(f(x, a()), a()), f#(y, f(x, f(a(), x))) -> f#(a(), y))
    (f#(x, f(x, y)) -> f#(f(x, a()), a()), f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)))
    (f#(x, f(x, y)) -> f#(f(x, a()), a()), f#(y, f(x, f(a(), x))) -> f#(x, a()))
    (f#(x, f(x, y)) -> f#(f(x, a()), a()), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
    (f#(x, f(x, y)) -> f#(f(x, a()), a()), f#(x, f(x, y)) -> f#(f(x, a()), a()))
    (f#(x, f(x, y)) -> f#(f(x, a()), a()), f#(x, f(x, y)) -> f#(x, a()))
    (f#(y, f(x, f(a(), x))) -> f#(x, a()), f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())))
    (f#(y, f(x, f(a(), x))) -> f#(x, a()), f#(y, f(x, f(a(), x))) -> f#(a(), y))
    (f#(y, f(x, f(a(), x))) -> f#(x, a()), f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)))
    (f#(y, f(x, f(a(), x))) -> f#(x, a()), f#(y, f(x, f(a(), x))) -> f#(x, a()))
    (f#(y, f(x, f(a(), x))) -> f#(x, a()), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
    (f#(y, f(x, f(a(), x))) -> f#(x, a()), f#(x, f(x, y)) -> f#(f(x, a()), a()))
    (f#(y, f(x, f(a(), x))) -> f#(x, a()), f#(x, f(x, y)) -> f#(x, a()))
    (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())))
    (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(a(), y))
    (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)))
    (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(x, a()))
    (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
    (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(x, f(x, y)) -> f#(f(x, a()), a()))
    (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(x, f(x, y)) -> f#(x, a()))
    (f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())), f#(x, f(x, y)) -> f#(x, a()))
    (f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())), f#(x, f(x, y)) -> f#(f(x, a()), a()))
    (f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
    (f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())), f#(y, f(x, f(a(), x))) -> f#(x, a()))
    (f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())), f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)))
    (f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())), f#(y, f(x, f(a(), x))) -> f#(a(), y))
    (f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())), f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())))
    (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(x, f(x, y)) -> f#(x, a()))
    (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(x, f(x, y)) -> f#(f(x, a()), a()))
    (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
    (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(x, a()))
    (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)))
    (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(a(), y))
    (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())))
    (f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()), f#(x, f(x, y)) -> f#(x, a()))
    (f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()), f#(x, f(x, y)) -> f#(f(x, a()), a()))
    (f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
    (f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()), f#(y, f(x, f(a(), x))) -> f#(x, a()))
    (f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()), f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)))
    (f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()), f#(y, f(x, f(a(), x))) -> f#(a(), y))
    (f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()), f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())))
    (f#(x, f(x, y)) -> f#(x, a()), f#(x, f(x, y)) -> f#(x, a()))
    (f#(x, f(x, y)) -> f#(x, a()), f#(x, f(x, y)) -> f#(f(x, a()), a()))
    (f#(x, f(x, y)) -> f#(x, a()), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
    (f#(x, f(x, y)) -> f#(x, a()), f#(y, f(x, f(a(), x))) -> f#(x, a()))
    (f#(x, f(x, y)) -> f#(x, a()), f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)))
    (f#(x, f(x, y)) -> f#(x, a()), f#(y, f(x, f(a(), x))) -> f#(a(), y))
    (f#(x, f(x, y)) -> f#(x, a()), f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())))}
   EDG:
    {(f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())))
     (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(a(), y))
     (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)))
     (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(x, a()))
     (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
     (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(x, f(x, y)) -> f#(f(x, a()), a()))
     (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(x, f(x, y)) -> f#(x, a()))
     (f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())), f#(x, f(x, y)) -> f#(x, a()))
     (f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())), f#(x, f(x, y)) -> f#(f(x, a()), a()))
     (f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
     (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(x, f(x, y)) -> f#(x, a()))
     (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(x, f(x, y)) -> f#(f(x, a()), a()))
     (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
     (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(x, a()))
     (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)))
     (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(a(), y))
     (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())))}
    EDG:
     {(f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())))
      (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(a(), y))
      (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)))
      (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(y, f(x, f(a(), x))) -> f#(x, a()))
      (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
      (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(x, f(x, y)) -> f#(f(x, a()), a()))
      (f#(y, f(x, f(a(), x))) -> f#(a(), y), f#(x, f(x, y)) -> f#(x, a()))
      (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(x, f(x, y)) -> f#(x, a()))
      (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(x, f(x, y)) -> f#(f(x, a()), a()))
      (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(x, f(x, y)) -> f#(f(f(x, a()), a()), a()))
      (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(x, a()))
      (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)))
      (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(a(), y))
      (f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)), f#(y, f(x, f(a(), x))) -> f#(a(), f(x, a())))}
     STATUS:
      arrows: 0.714286
      SCCS (1):
       Scc:
        {f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)),
         f#(y, f(x, f(a(), x))) -> f#(a(), y)}
       
       SCC (2):
        Strict:
         {f#(y, f(x, f(a(), x))) -> f#(f(a(), f(x, a())), f(a(), y)),
          f#(y, f(x, f(a(), x))) -> f#(a(), y)}
        Weak:
        {        f(x, f(x, y)) -> f(f(f(x, a()), a()), a()),
         f(y, f(x, f(a(), x))) -> f(f(a(), f(x, a())), f(a(), y))}
        Open