I'm a bit disappointed that the lengthened URL for http://aaa.aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa... itself doesn't work. That is:

https://aaa.aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa...

EDIT: Uh, I don't know what I did differently, but this one works:

https://aaa.aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa...

EDIT: Looks like the site is actively being updated, there are new option checkboxes, the self-reference link only works with "Use a path instead of an URL" checked

EDIT: I repeatedly lengthened maybe a dozen times, that seems to get it stuck in a loop:

https://aaa.aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa...