Button in member area

There is a members’ area on our website where you can log in. In this member area, we distinguish between demo users, who only have limited access to content, and users with full access to all content.

We would like to display a button in the navigation only for the demo version so that users have the option to upgrade. For those who have already purchased the full version, this upgrade button should not be visible. (However, the login data is identical for both the demo version and the full version, so it is the same access)

How can this be implemented technically? The two products (demo version and full version) are created products in Digimember.