User blog comment:VoidSansXD/Letter notation (Part 1?)/@comment-37483899-20190310002304

Interesting! Steps one through three are isomorphic to the Fast-growing hierarchy, meaning the growth of Ax is actually exactly equal to fx-1(n). Now, step four seems to diagonalize over this, placing it's growth-rate at about fω(n). Granted the rules are slightly different so it's not a carbon copy of the FGH but it's extremely close.

Now, in rule five I think you've reiterated the function introduced in rule four, producing a function with a growth rate of about fω+1(n) in the FGH.

Rule six is difficult to read unfortunately (try to describe functions without using "..."'s for future reference), but from what I gather it can't be more powerful than fω+2(n).

All in all, then, I'd say there's some need to be a more efficient and less vague with your descriptions, but the idea is there for sure, and that's good.