MAYBE
TRS:
 {        min(x, 0()) -> 0(),
          min(0(), y) -> 0(),
      min(s(x), s(y)) -> s(min(x, y)),
          max(x, 0()) -> x,
          max(0(), y) -> y,
      max(s(x), s(y)) -> s(max(x, y)),
              p(s(x)) -> x,
         f(x, y, 0()) -> max(x, y),
         f(x, 0(), z) -> max(x, z),
         f(0(), y, z) -> max(y, z),
  f(s(x), s(y), s(z)) -> f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))}
 DP:
  Strict:
   {    min#(s(x), s(y)) -> min#(x, y),
        max#(s(x), s(y)) -> max#(x, y),
           f#(x, y, 0()) -> max#(x, y),
           f#(x, 0(), z) -> max#(x, z),
           f#(0(), y, z) -> max#(y, z),
    f#(s(x), s(y), s(z)) -> min#(s(y), s(z)),
    f#(s(x), s(y), s(z)) -> min#(s(x), min(s(y), s(z))),
    f#(s(x), s(y), s(z)) -> min#(s(x), max(s(y), s(z))),
    f#(s(x), s(y), s(z)) -> max#(s(y), s(z)),
    f#(s(x), s(y), s(z)) -> max#(s(x), max(s(y), s(z))),
    f#(s(x), s(y), s(z)) -> p#(min(s(x), max(s(y), s(z)))),
    f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))}
  Weak:
  {        min(x, 0()) -> 0(),
           min(0(), y) -> 0(),
       min(s(x), s(y)) -> s(min(x, y)),
           max(x, 0()) -> x,
           max(0(), y) -> y,
       max(s(x), s(y)) -> s(max(x, y)),
               p(s(x)) -> x,
          f(x, y, 0()) -> max(x, y),
          f(x, 0(), z) -> max(x, z),
          f(0(), y, z) -> max(y, z),
   f(s(x), s(y), s(z)) -> f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))}
  EDG:
   {(f#(s(x), s(y), s(z)) -> max#(s(y), s(z)), max#(s(x), s(y)) -> max#(x, y))
    (f#(x, 0(), z) -> max#(x, z), max#(s(x), s(y)) -> max#(x, y))
    (f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))), f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))))
    (f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))), f#(s(x), s(y), s(z)) -> p#(min(s(x), max(s(y), s(z)))))
    (f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))), f#(s(x), s(y), s(z)) -> max#(s(x), max(s(y), s(z))))
    (f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))), f#(s(x), s(y), s(z)) -> max#(s(y), s(z)))
    (f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))), f#(s(x), s(y), s(z)) -> min#(s(x), max(s(y), s(z))))
    (f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))), f#(s(x), s(y), s(z)) -> min#(s(x), min(s(y), s(z))))
    (f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))), f#(s(x), s(y), s(z)) -> min#(s(y), s(z)))
    (f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))), f#(0(), y, z) -> max#(y, z))
    (f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))), f#(x, 0(), z) -> max#(x, z))
    (f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z)))), f#(x, y, 0()) -> max#(x, y))
    (max#(s(x), s(y)) -> max#(x, y), max#(s(x), s(y)) -> max#(x, y))
    (f#(s(x), s(y), s(z)) -> min#(s(x), min(s(y), s(z))), min#(s(x), s(y)) -> min#(x, y))
    (f#(s(x), s(y), s(z)) -> max#(s(x), max(s(y), s(z))), max#(s(x), s(y)) -> max#(x, y))
    (f#(s(x), s(y), s(z)) -> min#(s(x), max(s(y), s(z))), min#(s(x), s(y)) -> min#(x, y))
    (f#(x, y, 0()) -> max#(x, y), max#(s(x), s(y)) -> max#(x, y))
    (min#(s(x), s(y)) -> min#(x, y), min#(s(x), s(y)) -> min#(x, y))
    (f#(0(), y, z) -> max#(y, z), max#(s(x), s(y)) -> max#(x, y))
    (f#(s(x), s(y), s(z)) -> min#(s(y), s(z)), min#(s(x), s(y)) -> min#(x, y))}
   SCCS:
    Scc:
     {f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))}
    Scc:
     {max#(s(x), s(y)) -> max#(x, y)}
    Scc:
     {min#(s(x), s(y)) -> min#(x, y)}
    SCC:
     Strict:
      {f#(s(x), s(y), s(z)) -> f#(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))}
     Weak:
     {        min(x, 0()) -> 0(),
              min(0(), y) -> 0(),
          min(s(x), s(y)) -> s(min(x, y)),
              max(x, 0()) -> x,
              max(0(), y) -> y,
          max(s(x), s(y)) -> s(max(x, y)),
                  p(s(x)) -> x,
             f(x, y, 0()) -> max(x, y),
             f(x, 0(), z) -> max(x, z),
             f(0(), y, z) -> max(y, z),
      f(s(x), s(y), s(z)) -> f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))}
     Fail
    SCC:
     Strict:
      {max#(s(x), s(y)) -> max#(x, y)}
     Weak:
     {        min(x, 0()) -> 0(),
              min(0(), y) -> 0(),
          min(s(x), s(y)) -> s(min(x, y)),
              max(x, 0()) -> x,
              max(0(), y) -> y,
          max(s(x), s(y)) -> s(max(x, y)),
                  p(s(x)) -> x,
             f(x, y, 0()) -> max(x, y),
             f(x, 0(), z) -> max(x, z),
             f(0(), y, z) -> max(y, z),
      f(s(x), s(y), s(z)) -> f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))}
     SPSC:
      Simple Projection:
       pi(max#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {min#(s(x), s(y)) -> min#(x, y)}
     Weak:
     {        min(x, 0()) -> 0(),
              min(0(), y) -> 0(),
          min(s(x), s(y)) -> s(min(x, y)),
              max(x, 0()) -> x,
              max(0(), y) -> y,
          max(s(x), s(y)) -> s(max(x, y)),
                  p(s(x)) -> x,
             f(x, y, 0()) -> max(x, y),
             f(x, 0(), z) -> max(x, z),
             f(0(), y, z) -> max(y, z),
      f(s(x), s(y), s(z)) -> f(max(s(x), max(s(y), s(z))), p(min(s(x), max(s(y), s(z)))), min(s(x), min(s(y), s(z))))}
     SPSC:
      Simple Projection:
       pi(min#) = 0
      Strict:
       {}
      Qed