User blog comment:GamesFan2000/GamesFan's Step Function/@comment-35470197-20181229072816

The growth rate is approximately \(\omega^\omega\) in Hardy hierarchy with respect to a modified Wainer hierarchy \(\alpha[n] = \alpha[2n]_{\textrm{Wainer}}\). Therefore it is roughly between \(\omega\) and \(\omega+1\) in FGH. Sorry if I am incorrect.