User blog comment:Edwin Shade/A Question Concerning Ordinals (In Particular, Epsilon-Nought)/@comment-32697988-20171219010144

It's similar to the SGH, so it will take at least 4^^3 steps (Which is bigger than a googol).

\(G_0(n)=0\) \(G_{\alpha+1}(n)=G_\alpha(n)+1\) \(G_\alpha(n)=G_{\alpha[n]}(n)+1\)