addlist Cons x xs' Cons S 0 xs Cons S x addlist xs' xs addlist Cons S 0 xs' Cons x xs Cons S x addlist xs' xs addlist Nil ys Nil notEmpty Cons x xs True notEmpty Nil False goal xs ys addlist xs ys addlist 2 Cons 2 S 1 0 0 Nil 0 notEmpty 1 True 0 False 0 goal 2 INNERMOST