Can anybody tell me the growth rate (in the fast-growing hierarchy) of this function?

The function is defined at

https://googology.wikia.com/wiki/User_blog:MilkyWay90/Yet_another_attempt_at_making_a_fast-growing_functionThere are comments to the old version (where I used Peano Arithmetic, but then it wasn't well-defined), but not to the new version.

Can anybody help?