User blog:Mh314159/Question about growth rate

I'm playing with something and I wonder what growth rate a function has if it uses an omega-squared level function to iterate an omega-squared level function. That is, if g(x) = ff(x-1)(x) and f has omega-squared growth rates, then what is the growth rate of h(x) for sufficiently large x? Experienced googologists answer, please. Thank you.