MAYBE
TRS:
 {     nonZero(0()) -> false(),
      nonZero(s(x)) -> true(),
             p(0()) -> 0(),
            p(s(x)) -> x,
          id_inc(x) -> x,
          id_inc(x) -> s(x),
         rand(x, y) -> if(nonZero(x), x, y),
          random(x) -> rand(x, 0()),
  if(false(), x, y) -> y,
   if(true(), x, y) -> rand(p(x), id_inc(y))}
 DP:
  Strict:
   {      rand#(x, y) -> nonZero#(x),
          rand#(x, y) -> if#(nonZero(x), x, y),
           random#(x) -> rand#(x, 0()),
    if#(true(), x, y) -> p#(x),
    if#(true(), x, y) -> id_inc#(y),
    if#(true(), x, y) -> rand#(p(x), id_inc(y))}
  Weak:
  {     nonZero(0()) -> false(),
       nonZero(s(x)) -> true(),
              p(0()) -> 0(),
             p(s(x)) -> x,
           id_inc(x) -> x,
           id_inc(x) -> s(x),
          rand(x, y) -> if(nonZero(x), x, y),
           random(x) -> rand(x, 0()),
   if(false(), x, y) -> y,
    if(true(), x, y) -> rand(p(x), id_inc(y))}
  EDG:
   {(random#(x) -> rand#(x, 0()), rand#(x, y) -> if#(nonZero(x), x, y))
    (random#(x) -> rand#(x, 0()), rand#(x, y) -> nonZero#(x))
    (rand#(x, y) -> if#(nonZero(x), x, y), if#(true(), x, y) -> p#(x))
    (rand#(x, y) -> if#(nonZero(x), x, y), if#(true(), x, y) -> id_inc#(y))
    (rand#(x, y) -> if#(nonZero(x), x, y), if#(true(), x, y) -> rand#(p(x), id_inc(y)))
    (if#(true(), x, y) -> rand#(p(x), id_inc(y)), rand#(x, y) -> nonZero#(x))
    (if#(true(), x, y) -> rand#(p(x), id_inc(y)), rand#(x, y) -> if#(nonZero(x), x, y))}
   SCCS:
    Scc:
     {      rand#(x, y) -> if#(nonZero(x), x, y),
      if#(true(), x, y) -> rand#(p(x), id_inc(y))}
    SCC:
     Strict:
      {      rand#(x, y) -> if#(nonZero(x), x, y),
       if#(true(), x, y) -> rand#(p(x), id_inc(y))}
     Weak:
     {     nonZero(0()) -> false(),
          nonZero(s(x)) -> true(),
                 p(0()) -> 0(),
                p(s(x)) -> x,
              id_inc(x) -> x,
              id_inc(x) -> s(x),
             rand(x, y) -> if(nonZero(x), x, y),
              random(x) -> rand(x, 0()),
      if(false(), x, y) -> y,
       if(true(), x, y) -> rand(p(x), id_inc(y))}
     Fail