User blog comment:Mh314159/Question about growth rate/@comment-35470197-20191107005001/@comment-35470197-20191107012409

It actually grows faster than f_{ω^2+1}(x), but grows much slower than f_{ω^2+2}(x). Therefore it is usually approximated to ω^2+1.

It is good to see f_{ω^2+1}(x) = f_{ω^2}^{x}(x) < f_{ω^2}^{f_{ω^2}(x)}(x) < f_{ω^2}^{f_{ω^2}(x)}(f_{ω^2}(x)) = f_{ω^2+1}(f_{ω^2}(x)) < f_{ω^2+1}^2(x) << f_{ω^2+2}(x).