MAYBE

Problem:
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(minus(),x),0()) -> x
 app(app(minus(),app(s(),x)),app(s(),y)) ->
 app(app(minus(),app(p(),app(s(),x))),app(p(),app(s(),y)))
 app(p(),app(s(),x)) -> x
 app(app(div(),0()),app(s(),y)) -> 0()
 app(app(div(),app(s(),x)),app(s(),y)) ->
 app(s(),app(app(div(),app(app(minus(),x),app(id(),y))),app(s(),y)))
 app(id(),x) -> x
 app(id(),x) -> app(s(),app(s(),app(s(),x)))
 app(id(),app(p(),x)) -> app(id(),app(s(),app(id(),x)))

Proof:
 Open