MAYBE

Problem:
 check(0()) -> zero()
 check(s(0())) -> odd()
 check(s(s(0()))) -> even()
 check(s(s(s(x)))) -> check(s(x))
 half(0()) -> 0()
 half(s(0())) -> 0()
 half(s(s(x))) -> s(half(x))
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 times(x,y) -> timesIter(x,y,0())
 timesIter(x,y,z) -> if(check(x),x,y,z,plus(z,y))
 p(s(x)) -> x
 p(0()) -> 0()
 if(zero(),x,y,z,u) -> z
 if(odd(),x,y,z,u) -> timesIter(p(x),y,u)
 if(even(),x,y,z,u) -> plus(timesIter(half(x),y,half(z)),timesIter(half(x),y,half(s(z))))

Proof:
 Open