MAYBE

Problem:
 strict:
  top(old(x)) -> top(check(x))
  top(new(x)) -> top(check(x))
 weak:
  bot() -> new(bot())
  check(new(x)) -> new(check(x))
  check(old(x)) -> old(check(x))
  check(old(x)) -> old(x)

Proof:
 Open