MAYBE

Problem:
 min(0(),y) -> 0()
 min(s(x),0()) -> 0()
 min(s(x),s(y)) -> min(x,y)
 len(nil()) -> 0()
 len(cons(x,xs)) -> s(len(xs))
 sum(x,0()) -> x
 sum(x,s(y)) -> s(sum(x,y))
 le(0(),x) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 take(0(),cons(y,ys)) -> y
 take(s(x),cons(y,ys)) -> take(x,ys)
 addList(x,y) -> if(le(0(),min(len(x),len(y))),0(),x,y,nil())
 if(false(),c,x,y,z) -> z
 if(true(),c,xs,ys,z) ->
 if(le(s(c),min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))

Proof:
 Open