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