MAYBE

Problem:
 nonZero(0()) -> false()
 nonZero(s(x)) -> true()
 p(s(0())) -> 0()
 p(s(s(x))) -> s(p(s(x)))
 id_inc(x) -> x
 id_inc(x) -> s(x)
 random(x) -> rand(x,0())
 rand(x,y) -> if(nonZero(x),x,y)
 if(false(),x,y) -> y
 if(true(),x,y) -> rand(p(x),id_inc(y))

Proof:
 Open