User blog comment:Ynought/Array hierarchy/@comment-35470197-20190124134357/@comment-35470197-20190124231144

Then the limit of the growth is roughly bounded by \(f_{2 + \omega + 1 + \omega}(n)\) with respect to FGH. The rule 4 is good.

I note that the rules 2 and 3 for \((\textrm{$}_1)_k\) do not contribute the growth. It is also good for you to try analysing your own hierarchy so that you grasp what makes the corresponding ordinal greater. It will help you to create a new faster hierarchy.