MAYBE

Problem:
 division(x,y) -> div(x,y,0())
 div(x,y,z) -> if(lt(x,y),x,y,inc(z))
 if(true(),x,y,z) -> z
 if(false(),x,s(y),z) -> div(minus(x,s(y)),s(y),z)
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 lt(x,0()) -> false()
 lt(0(),s(y)) -> true()
 lt(s(x),s(y)) -> lt(x,y)
 inc(0()) -> s(0())
 inc(s(x)) -> s(inc(x))

Proof:
 Open