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