MAYBE
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:
  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))}
  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))}
   SCCS:
    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:
     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))}
     POLY:
      Argument Filtering:
       pi(b) = [], pi(a) = [], pi(f#) = [0,1], pi(f) = [0,1]
      Usable Rules:
       {}
      Interpretation:
       [f#](x0, x1) = x0 + x1,
       [f](x0, x1) = x0 + x1 + 1,
       [b] = 0,
       [a] = 0
      Strict:
       {    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))}
      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))}
      EDG:
       {(f#(f(a(), b()), x) -> f#(a(), f(a(), 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#(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#(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(b(), a()), x) -> f#(b(), f(b(), x)))}
       SCCS:
        Scc:
         {    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))}
        SCC:
         Strict:
          {    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))}
         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))}
         Fail