NO

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

Proof:
 Unfolding Processor:
  loop length: 5
  terms:
   top(ok(U(O(x426584),B())))
   top(check(D(O(x426584),B())))
   top(D(check(O(x426584)),B()))
   top(U(check(O(x426584)),B()))
   top(U(ok(O(x426584)),B()))
  context: []
  substitution:
   x426584 -> x426584
  Qed