User blog comment:MachineGunSuper/Simple question/@comment-30754445-20180104200524

It can't. Graham is too big.

Each function in your hierarchy repeats the previous one, so this adds "1" to the FGH ordinal of your function (or if your prefer: each function adds a single arrow in knuth notation).

You repeated this process 4 times, and your starting function is a power tower (the factorial doesn't add much). Power towers are comparable to f3(n) (or if you prefer: 10↑↑n). So your final function would be roughly comparable to f3+4(n) = f7(n) (or 10↑↑↑↑↑↑n with 6 arrows)

And this is nowhere near Graham.

To reach Graham with this system, you'll need to create a new function ListX which does "repeat the entire above process n times", and then create another new function ListY which repeats List(X) n times.

If you do this correctly, then Graham would be surpassed by ListY(n) for some reasonable n (the exact value of n depends on your exact definition of ListY).

(I remember already showing you how to do this in a comment on another blog post, but I don't quite remember which one)