MAYBE
TRS:
 {   ack(s(x), y) -> f(x, x),
  ack(s(x), s(y)) -> ack(x, ack(s(x), y)),
   ack(s(x), 0()) -> ack(x, s(0())),
      ack(0(), y) -> s(y),
          f(x, y) -> ack(x, y),
       f(x, s(y)) -> f(y, x),
       f(s(x), y) -> f(x, s(x))}
 DP:
  Strict:
   {   ack#(s(x), y) -> f#(x, x),
    ack#(s(x), s(y)) -> ack#(x, ack(s(x), y)),
    ack#(s(x), s(y)) -> ack#(s(x), y),
     ack#(s(x), 0()) -> ack#(x, s(0())),
            f#(x, y) -> ack#(x, y),
         f#(x, s(y)) -> f#(y, x),
         f#(s(x), y) -> f#(x, s(x))}
  Weak:
  {   ack(s(x), y) -> f(x, x),
   ack(s(x), s(y)) -> ack(x, ack(s(x), y)),
    ack(s(x), 0()) -> ack(x, s(0())),
       ack(0(), y) -> s(y),
           f(x, y) -> ack(x, y),
        f(x, s(y)) -> f(y, x),
        f(s(x), y) -> f(x, s(x))}
  EDG:
   {(f#(x, y) -> ack#(x, y), ack#(s(x), 0()) -> ack#(x, s(0())))
    (f#(x, y) -> ack#(x, y), ack#(s(x), s(y)) -> ack#(s(x), y))
    (f#(x, y) -> ack#(x, y), ack#(s(x), s(y)) -> ack#(x, ack(s(x), y)))
    (f#(x, y) -> ack#(x, y), ack#(s(x), y) -> f#(x, x))
    (ack#(s(x), y) -> f#(x, x), f#(s(x), y) -> f#(x, s(x)))
    (ack#(s(x), y) -> f#(x, x), f#(x, s(y)) -> f#(y, x))
    (ack#(s(x), y) -> f#(x, x), f#(x, y) -> ack#(x, y))
    (f#(s(x), y) -> f#(x, s(x)), f#(s(x), y) -> f#(x, s(x)))
    (f#(s(x), y) -> f#(x, s(x)), f#(x, s(y)) -> f#(y, x))
    (f#(s(x), y) -> f#(x, s(x)), f#(x, y) -> ack#(x, y))
    (ack#(s(x), s(y)) -> ack#(s(x), y), ack#(s(x), y) -> f#(x, x))
    (ack#(s(x), s(y)) -> ack#(s(x), y), ack#(s(x), s(y)) -> ack#(x, ack(s(x), y)))
    (ack#(s(x), s(y)) -> ack#(s(x), y), ack#(s(x), s(y)) -> ack#(s(x), y))
    (ack#(s(x), s(y)) -> ack#(s(x), y), ack#(s(x), 0()) -> ack#(x, s(0())))
    (f#(x, s(y)) -> f#(y, x), f#(x, y) -> ack#(x, y))
    (f#(x, s(y)) -> f#(y, x), f#(x, s(y)) -> f#(y, x))
    (f#(x, s(y)) -> f#(y, x), f#(s(x), y) -> f#(x, s(x)))
    (ack#(s(x), s(y)) -> ack#(x, ack(s(x), y)), ack#(s(x), y) -> f#(x, x))
    (ack#(s(x), s(y)) -> ack#(x, ack(s(x), y)), ack#(s(x), s(y)) -> ack#(x, ack(s(x), y)))
    (ack#(s(x), s(y)) -> ack#(x, ack(s(x), y)), ack#(s(x), s(y)) -> ack#(s(x), y))
    (ack#(s(x), 0()) -> ack#(x, s(0())), ack#(s(x), y) -> f#(x, x))
    (ack#(s(x), 0()) -> ack#(x, s(0())), ack#(s(x), s(y)) -> ack#(x, ack(s(x), y)))
    (ack#(s(x), 0()) -> ack#(x, s(0())), ack#(s(x), s(y)) -> ack#(s(x), y))}
   SCCS:
    Scc:
     {   ack#(s(x), y) -> f#(x, x),
      ack#(s(x), s(y)) -> ack#(x, ack(s(x), y)),
      ack#(s(x), s(y)) -> ack#(s(x), y),
       ack#(s(x), 0()) -> ack#(x, s(0())),
              f#(x, y) -> ack#(x, y),
           f#(x, s(y)) -> f#(y, x),
           f#(s(x), y) -> f#(x, s(x))}
    SCC:
     Strict:
      {   ack#(s(x), y) -> f#(x, x),
       ack#(s(x), s(y)) -> ack#(x, ack(s(x), y)),
       ack#(s(x), s(y)) -> ack#(s(x), y),
        ack#(s(x), 0()) -> ack#(x, s(0())),
               f#(x, y) -> ack#(x, y),
            f#(x, s(y)) -> f#(y, x),
            f#(s(x), y) -> f#(x, s(x))}
     Weak:
     {   ack(s(x), y) -> f(x, x),
      ack(s(x), s(y)) -> ack(x, ack(s(x), y)),
       ack(s(x), 0()) -> ack(x, s(0())),
          ack(0(), y) -> s(y),
              f(x, y) -> ack(x, y),
           f(x, s(y)) -> f(y, x),
           f(s(x), y) -> f(x, s(x))}
     Fail