Migrating Joomla To WordPress on same server

Hi. I have a Joomla website and want to change it to a WordPress website, and at the same time moving all my posts from the Joomla website. The problem is that I want to do this on the same server, meaning that there is only 1 website, not 2. I know there are several plugins, such as FG Joomla To WordPress, but I believe they work only if you have 2 existent websites, one Joomla and one WordPress. But that would be too easy and I don’t have this option. Is there a way using localhost? Or can I make a full website back-up, save it on my computer, and then install WordPress on the server? Could I import the posts from the back-up or something like that?

I found something that I think it’s related to my problem, but don’t really understand how to do it.

http://www.warriorforum.com/main-internet-marketing-discussion-forum/335218-multiple-joomla-wordpress-one-web-host.html