MAYBE

Problem:
 strict:
  Tl(O(x),y) -> Tr(check(x),y)
  Tl(O(x),y) -> Tr(x,check(y))
  Tl(N(x),y) -> Tr(check(x),y)
  Tl(N(x),y) -> Tr(x,check(y))
  Tr(x,O(y)) -> Tl(check(x),y)
  Tr(x,O(y)) -> Tl(x,check(y))
  Tr(x,N(y)) -> Tl(check(x),y)
  Tr(x,N(y)) -> Tl(x,check(y))
  Tl(B(),y) -> Tr(check(B()),y)
  Tl(B(),y) -> Tr(B(),check(y))
  Tr(x,B()) -> Tl(check(x),B())
  Tr(x,B()) -> Tl(x,check(B()))
 weak:
  Tl(O(x),y) -> Tl(check(x),y)
  Tl(O(x),y) -> Tl(x,check(y))
  Tl(N(x),y) -> Tl(check(x),y)
  Tl(N(x),y) -> Tl(x,check(y))
  Tr(x,O(y)) -> Tr(check(x),y)
  Tr(x,O(y)) -> Tr(x,check(y))
  Tr(x,N(y)) -> Tr(check(x),y)
  Tr(x,N(y)) -> Tr(x,check(y))
  B() -> N(B())
  check(O(x)) -> O(x)
  check(O(x)) -> O(check(x))
  check(N(x)) -> N(check(x))

Proof:
 Open