NO

Problem:
 strict:
  top(U(x,y)) -> top(check(D(x,y)))
  D(x,B()) -> U(x,B())
  F(x,U(O(y),z)) -> U(x,F(y,z))
  F(x,U(N(y),z)) -> U(x,F(y,z))
  D(O(x),F(y,z)) -> F(x,D(y,z))
  D(N(x),F(y,z)) -> F(x,D(y,z))
  F(x,U(E(),y)) -> U(x,F(E(),y))
  D(E(),F(x,y)) -> F(E(),D(x,y))
 weak:
  E() -> N(E())
  check(O(x)) -> O(x)
  check(U(x,y)) -> U(check(x),y)
  check(U(x,y)) -> U(x,check(y))
  check(D(x,y)) -> D(check(x),y)
  check(D(x,y)) -> D(x,check(y))
  check(F(x,y)) -> F(check(x),y)
  check(F(x,y)) -> F(x,check(y))
  check(O(x)) -> O(check(x))
  check(N(x)) -> N(check(x))

Proof:
 Unfolding Processor:
  loop length: 3
  terms:
   top(U(x1510,B()))
   top(check(D(x1510,B())))
   top(D(check(x1510),B()))
  context: []
  substitution:
   x1510 -> check(x1510)
  Qed