User blog comment:VoidSansXD/Alpha-Numeral notation/@comment-34422464-20190119191307/@comment-30754445-20190121224414

Yeah.

It's far more interesting to see how this system would look if we set (say) g(n)=n+1. The given notation is actually strong enough to surpass Graham's number while starting from scratch. Something like {3_100(1)} would already be bigger than Graham's number.

Overall, the system as presented does recursion on par of ω+2 in the FGH.

And if you start with Graham's function, which is already at level ω+1, then the final notation would have strength of (ω+1)+(ω+2)=ω2+2, with Graham's function doing half of the work, and the OP's recursion system doing the other half.