YES
Input TRS:
      1: top(ok(new(x))) -> top(check(x))
      2: top(ok(old(x))) -> top(check(x))
      3: bot() ->= new(bot())
      4: check(new(x)) ->= new(check(x))
      5: check(old(x)) ->= old(check(x))
      6: check(old(x)) ->= ok(old(x))
      7: new(ok(x)) ->= ok(new(x))
      8: old(ok(x)) ->= ok(old(x))
Number of strict rules: 2
Direct POLO(bPol) ... removes: 2
      new	w: x1
      top	w: x1
      bot	w: 25907
      check	w: x1 + 21656
      ok	w: x1 + 21656
      old	w: x1 + 1
Number of strict rules: 1
Direct POLO(bPol) ... removes: 8 1 5 7 6
      new	w: 2 * x1
      top	w: x1 + 2240
      bot	w: 0
      check	w: 2 * x1
      ok	w: x1 + 28882
      old	w: 2 * x1 + 28883
Number of strict rules: 0