PHP if $user_ID problem when "WWW."

I have a PHP if script that works when I’m using the same site and WordPress URL (Settings/General), but when I choose to have “WWW.” infront of the URL it stops working and only shows “Login” and “Register”.

Here’s the script:

<?php if ($user_ID) {
echo '<div id="navigation">
<ul>
	<li><a href="https://wp-admin/profile.php">Profile</a></li>
	<li><a href="https://twp-login.php?action=logout">Log out</a></li>
    </ul>
</div>'; }
else {
echo '<div id="navigation">
<ul>
	<li><a href="https://wp-login.php">Login</a></li>
	<li><a href="https://wp-login.php?action=register">Register</a></li>
    </ul>
</div>'; } ?>

And by the way, this problem only occurs with Google Chrome and Firefox, not Internet Explorer.

What’s the problem and how do I solve this?

Thanks,
Skez

EDIT: Sorry, I managed to solve it.