MAYBE
Time: 0.036068
TRS:
 {    f(x, f(y, z)) -> f(f(x, y), z),
  f(f(a(), b()), x) -> f(a(), f(a(), x)),
  f(f(b(), a()), x) -> f(b(), f(b(), x))}
 DP:
  DP:
   {    f#(x, f(y, z)) -> f#(x, y),
        f#(x, f(y, z)) -> f#(f(x, y), z),
    f#(f(a(), b()), x) -> f#(a(), x),
    f#(f(a(), b()), x) -> f#(a(), f(a(), x)),
    f#(f(b(), a()), x) -> f#(b(), x),
    f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
  TRS:
  {    f(x, f(y, z)) -> f(f(x, y), z),
   f(f(a(), b()), x) -> f(a(), f(a(), x)),
   f(f(b(), a()), x) -> f(b(), f(b(), x))}
  UR:
   {    f(x, f(y, z)) -> f(f(x, y), z),
    f(f(a(), b()), x) -> f(a(), f(a(), x)),
    f(f(b(), a()), x) -> f(b(), f(b(), x))}
   EDG:
    {(f#(f(b(), a()), x) -> f#(b(), f(b(), x)), f#(x, f(y, z)) -> f#(f(x, y), z))
     (f#(f(b(), a()), x) -> f#(b(), f(b(), x)), f#(x, f(y, z)) -> f#(x, y))
     (f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(b(), a()), x) -> f#(b(), f(b(), x)))
     (f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(b(), a()), x) -> f#(b(), x))
     (f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(a(), b()), x) -> f#(a(), f(a(), x)))
     (f#(x, f(y, z)) -> f#(f(x, y), z), f#(f(a(), b()), x) -> f#(a(), x))
     (f#(x, f(y, z)) -> f#(f(x, y), z), f#(x, f(y, z)) -> f#(f(x, y), z))
     (f#(x, f(y, z)) -> f#(f(x, y), z), f#(x, f(y, z)) -> f#(x, y))
     (f#(f(b(), a()), x) -> f#(b(), x), f#(x, f(y, z)) -> f#(f(x, y), z))
     (f#(f(b(), a()), x) -> f#(b(), x), f#(x, f(y, z)) -> f#(x, y))
     (f#(f(a(), b()), x) -> f#(a(), x), f#(x, f(y, z)) -> f#(x, y))
     (f#(f(a(), b()), x) -> f#(a(), x), f#(x, f(y, z)) -> f#(f(x, y), z))
     (f#(x, f(y, z)) -> f#(x, y), f#(x, f(y, z)) -> f#(x, y))
     (f#(x, f(y, z)) -> f#(x, y), f#(x, f(y, z)) -> f#(f(x, y), z))
     (f#(x, f(y, z)) -> f#(x, y), f#(f(a(), b()), x) -> f#(a(), x))
     (f#(x, f(y, z)) -> f#(x, y), f#(f(a(), b()), x) -> f#(a(), f(a(), x)))
     (f#(x, f(y, z)) -> f#(x, y), f#(f(b(), a()), x) -> f#(b(), x))
     (f#(x, f(y, z)) -> f#(x, y), f#(f(b(), a()), x) -> f#(b(), f(b(), x)))
     (f#(f(a(), b()), x) -> f#(a(), f(a(), x)), f#(x, f(y, z)) -> f#(x, y))
     (f#(f(a(), b()), x) -> f#(a(), f(a(), x)), f#(x, f(y, z)) -> f#(f(x, y), z))}
    STATUS:
     arrows: 0.444444
     SCCS (1):
      Scc:
       {    f#(x, f(y, z)) -> f#(x, y),
            f#(x, f(y, z)) -> f#(f(x, y), z),
        f#(f(a(), b()), x) -> f#(a(), x),
        f#(f(a(), b()), x) -> f#(a(), f(a(), x)),
        f#(f(b(), a()), x) -> f#(b(), x),
        f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
      
      SCC (6):
       Strict:
        {    f#(x, f(y, z)) -> f#(x, y),
             f#(x, f(y, z)) -> f#(f(x, y), z),
         f#(f(a(), b()), x) -> f#(a(), x),
         f#(f(a(), b()), x) -> f#(a(), f(a(), x)),
         f#(f(b(), a()), x) -> f#(b(), x),
         f#(f(b(), a()), x) -> f#(b(), f(b(), x))}
       Weak:
       {    f(x, f(y, z)) -> f(f(x, y), z),
        f(f(a(), b()), x) -> f(a(), f(a(), x)),
        f(f(b(), a()), x) -> f(b(), f(b(), x))}
       Open