User blog comment:KthulhuHimself/Plexation, TaN, and such/@comment-28124748-20150925014745/@comment-25601061-20150925231123

I will give you a proof.

Since n^...^n (n arrows) is comparable to ω in FGH, and that is equal to Z1, then Zn would be fω function nested, so it's comparable to ω+1 in FGH. And since Zn = )n(, then )n( has growth rate ω+1 in FGH.