User blog comment:Eners49/New Notation Idea? (Attempt 2)/@comment-25601061-20180712033049

Sorry, but that's now how recursion works. When evaluating {a,b}, you want to nest {x,b-1}s, not {x}s. If we just do recursion on a specific function and not on the previous function, we get something similar to the Hardy Hierarchy (HH), which can weaken your function's growth rate in FGH if your notation doesn't have a growth rate in HH of the form εx, especially if your notation has a growth rate in HH below ε0.