YES
TRS:
 {      perfectp(0()) -> false(),
       perfectp(s(x)) -> f(x, s(0()), s(x), s(x)),
    f(0(), y, 0(), u) -> true(),
   f(0(), y, s(z), u) -> false(),
   f(s(x), 0(), z, u) -> f(x, u, minus(z, s(x)), u),
  f(s(x), s(y), z, u) -> if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u))}
 DP:
  Strict:
   {     perfectp#(s(x)) -> f#(x, s(0()), s(x), s(x)),
     f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u),
    f#(s(x), s(y), z, u) -> f#(x, u, z, u),
    f#(s(x), s(y), z, u) -> f#(s(x), minus(y, x), z, u)}
  Weak:
  {      perfectp(0()) -> false(),
        perfectp(s(x)) -> f(x, s(0()), s(x), s(x)),
     f(0(), y, 0(), u) -> true(),
    f(0(), y, s(z), u) -> false(),
    f(s(x), 0(), z, u) -> f(x, u, minus(z, s(x)), u),
   f(s(x), s(y), z, u) -> if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u))}
  EDG:
   {(f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u), f#(s(x), s(y), z, u) -> f#(s(x), minus(y, x), z, u))
    (f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u), f#(s(x), s(y), z, u) -> f#(x, u, z, u))
    (f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u), f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u))
    (f#(s(x), s(y), z, u) -> f#(x, u, z, u), f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u))
    (f#(s(x), s(y), z, u) -> f#(x, u, z, u), f#(s(x), s(y), z, u) -> f#(x, u, z, u))
    (f#(s(x), s(y), z, u) -> f#(x, u, z, u), f#(s(x), s(y), z, u) -> f#(s(x), minus(y, x), z, u))
    (perfectp#(s(x)) -> f#(x, s(0()), s(x), s(x)), f#(s(x), s(y), z, u) -> f#(x, u, z, u))
    (perfectp#(s(x)) -> f#(x, s(0()), s(x), s(x)), f#(s(x), s(y), z, u) -> f#(s(x), minus(y, x), z, u))}
   SCCS:
    Scc:
     { f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u),
      f#(s(x), s(y), z, u) -> f#(x, u, z, u)}
    SCC:
     Strict:
      { f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u),
       f#(s(x), s(y), z, u) -> f#(x, u, z, u)}
     Weak:
     {      perfectp(0()) -> false(),
           perfectp(s(x)) -> f(x, s(0()), s(x), s(x)),
        f(0(), y, 0(), u) -> true(),
       f(0(), y, s(z), u) -> false(),
       f(s(x), 0(), z, u) -> f(x, u, minus(z, s(x)), u),
      f(s(x), s(y), z, u) -> if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u))}
     SPSC:
      Simple Projection:
       pi(f#) = 0
      Strict:
       {f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u)}
      EDG:
       {(f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u), f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u))}
       SCCS:
        Scc:
         {f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u)}
        SCC:
         Strict:
          {f#(s(x), 0(), z, u) -> f#(x, u, minus(z, s(x)), u)}
         Weak:
         {      perfectp(0()) -> false(),
               perfectp(s(x)) -> f(x, s(0()), s(x), s(x)),
            f(0(), y, 0(), u) -> true(),
           f(0(), y, s(z), u) -> false(),
           f(s(x), 0(), z, u) -> f(x, u, minus(z, s(x)), u),
          f(s(x), s(y), z, u) -> if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u))}
         SPSC:
          Simple Projection:
           pi(f#) = 0
          Strict:
           {}
          Qed