MAYBE
TRS:
 {          minus(x, 0()) -> x,
            minus(0(), y) -> 0(),
        minus(s(x), s(y)) -> minus(x, y),
             plus(0(), y) -> y,
            plus(s(x), y) -> plus(x, s(y)),
                zero(0()) -> true(),
               zero(s(x)) -> false(),
                  p(s(x)) -> x,
            quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))),
                div(x, y) -> quot(x, y, 0()),
  if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z),
      if(true(), x, y, z) -> p(z)}
 DP:
  Strict:
   {      minus#(s(x), s(y)) -> minus#(x, y),
              plus#(s(x), y) -> plus#(x, s(y)),
              quot#(x, y, z) -> plus#(z, s(0())),
              quot#(x, y, z) -> zero#(x),
              quot#(x, y, z) -> if#(zero(x), x, y, plus(z, s(0()))),
                  div#(x, y) -> quot#(x, y, 0()),
    if#(false(), x, s(y), z) -> minus#(x, s(y)),
    if#(false(), x, s(y), z) -> quot#(minus(x, s(y)), s(y), z),
        if#(true(), x, y, z) -> p#(z)}
  Weak:
  {          minus(x, 0()) -> x,
             minus(0(), y) -> 0(),
         minus(s(x), s(y)) -> minus(x, y),
              plus(0(), y) -> y,
             plus(s(x), y) -> plus(x, s(y)),
                 zero(0()) -> true(),
                zero(s(x)) -> false(),
                   p(s(x)) -> x,
             quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))),
                 div(x, y) -> quot(x, y, 0()),
   if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z),
       if(true(), x, y, z) -> p(z)}
  EDG:
   {(div#(x, y) -> quot#(x, y, 0()), quot#(x, y, z) -> if#(zero(x), x, y, plus(z, s(0()))))
    (div#(x, y) -> quot#(x, y, 0()), quot#(x, y, z) -> zero#(x))
    (div#(x, y) -> quot#(x, y, 0()), quot#(x, y, z) -> plus#(z, s(0())))
    (if#(false(), x, s(y), z) -> quot#(minus(x, s(y)), s(y), z), quot#(x, y, z) -> if#(zero(x), x, y, plus(z, s(0()))))
    (if#(false(), x, s(y), z) -> quot#(minus(x, s(y)), s(y), z), quot#(x, y, z) -> zero#(x))
    (if#(false(), x, s(y), z) -> quot#(minus(x, s(y)), s(y), z), quot#(x, y, z) -> plus#(z, s(0())))
    (quot#(x, y, z) -> plus#(z, s(0())), plus#(s(x), y) -> plus#(x, s(y)))
    (plus#(s(x), y) -> plus#(x, s(y)), plus#(s(x), y) -> plus#(x, s(y)))
    (if#(false(), x, s(y), z) -> minus#(x, s(y)), minus#(s(x), s(y)) -> minus#(x, y))
    (minus#(s(x), s(y)) -> minus#(x, y), minus#(s(x), s(y)) -> minus#(x, y))
    (quot#(x, y, z) -> if#(zero(x), x, y, plus(z, s(0()))), if#(false(), x, s(y), z) -> minus#(x, s(y)))
    (quot#(x, y, z) -> if#(zero(x), x, y, plus(z, s(0()))), if#(false(), x, s(y), z) -> quot#(minus(x, s(y)), s(y), z))
    (quot#(x, y, z) -> if#(zero(x), x, y, plus(z, s(0()))), if#(true(), x, y, z) -> p#(z))}
   SCCS:
    Scc:
     {          quot#(x, y, z) -> if#(zero(x), x, y, plus(z, s(0()))),
      if#(false(), x, s(y), z) -> quot#(minus(x, s(y)), s(y), z)}
    Scc:
     {plus#(s(x), y) -> plus#(x, s(y))}
    Scc:
     {minus#(s(x), s(y)) -> minus#(x, y)}
    SCC:
     Strict:
      {          quot#(x, y, z) -> if#(zero(x), x, y, plus(z, s(0()))),
       if#(false(), x, s(y), z) -> quot#(minus(x, s(y)), s(y), z)}
     Weak:
     {          minus(x, 0()) -> x,
                minus(0(), y) -> 0(),
            minus(s(x), s(y)) -> minus(x, y),
                 plus(0(), y) -> y,
                plus(s(x), y) -> plus(x, s(y)),
                    zero(0()) -> true(),
                   zero(s(x)) -> false(),
                      p(s(x)) -> x,
                quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))),
                    div(x, y) -> quot(x, y, 0()),
      if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z),
          if(true(), x, y, z) -> p(z)}
     Fail
    SCC:
     Strict:
      {plus#(s(x), y) -> plus#(x, s(y))}
     Weak:
     {          minus(x, 0()) -> x,
                minus(0(), y) -> 0(),
            minus(s(x), s(y)) -> minus(x, y),
                 plus(0(), y) -> y,
                plus(s(x), y) -> plus(x, s(y)),
                    zero(0()) -> true(),
                   zero(s(x)) -> false(),
                      p(s(x)) -> x,
                quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))),
                    div(x, y) -> quot(x, y, 0()),
      if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z),
          if(true(), x, y, z) -> p(z)}
     SPSC:
      Simple Projection:
       pi(plus#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {minus#(s(x), s(y)) -> minus#(x, y)}
     Weak:
     {          minus(x, 0()) -> x,
                minus(0(), y) -> 0(),
            minus(s(x), s(y)) -> minus(x, y),
                 plus(0(), y) -> y,
                plus(s(x), y) -> plus(x, s(y)),
                    zero(0()) -> true(),
                   zero(s(x)) -> false(),
                      p(s(x)) -> x,
                quot(x, y, z) -> if(zero(x), x, y, plus(z, s(0()))),
                    div(x, y) -> quot(x, y, 0()),
      if(false(), x, s(y), z) -> quot(minus(x, s(y)), s(y), z),
          if(true(), x, y, z) -> p(z)}
     SPSC:
      Simple Projection:
       pi(minus#) = 0
      Strict:
       {}
      Qed