MAYBE

Problem:
 lt(x,0()) -> false()
 lt(0(),s(y)) -> true()
 lt(s(x),s(y)) -> lt(x,y)
 plus(x,0()) -> x
 plus(x,s(y)) -> s(plus(x,y))
 quot(x,s(y)) -> help(x,s(y),0())
 help(x,s(y),c) -> if(lt(c,x),x,s(y),c)
 if(true(),x,s(y),c) -> s(help(x,s(y),plus(c,s(y))))
 if(false(),x,s(y),c) -> 0()

Proof:
 Open