(VAR f x y xs ys)
(RULES
ap(ap(map,f),xs) -> ap(ap(ap(if,ap(isEmpty,xs)),f),xs)
ap(ap(ap(if,true),f),xs) -> nil
ap(ap(ap(if,false),f),xs) -> ap(ap(cons,ap(f,ap(last,xs))),ap(ap(map,f),ap(dropLast,xs)))

ap(isEmpty,nil) -> true
ap(isEmpty,ap(ap(cons,x),xs)) -> false

ap(last,ap(ap(cons,x),nil)) -> x
ap(last,ap(ap(cons,x),ap(ap(cons,y),ys))) -> ap(last,ap(ap(cons,y),ys))

ap(dropLast,nil) -> nil
ap(dropLast,ap(ap(cons,x),nil)) -> nil
ap(dropLast,ap(ap(cons,x),ap(ap(cons,y),ys))) -> ap(ap(cons,x),ap(dropLast,ap(ap(cons,y),ys)))
)