User blog comment:Mh314159/FOX notation/@comment-39585023-20191205111828

Thank you, P進大好きbot for all the feedback so far. I can see that going further will be a challenge. I may have to be satisfied with w^w, but not stopping yet. As a first attempt, what if I now go back to the beginning and iterate the strongest structure so far using the entire structure? I define:

g0(0) = g(0) = 1

for x > 0, g0(x) = g(x) = f‹X›(x) where X is a string of g(x-1) terms, each term = x

g‹0›(x) = gx(x) Otherwise, g‹n›(x) and g‹S›(x) following the same recursion rules as f How fast is g‹S›(x) compared to f‹S›(x) ? Do I need to recurse f in a more complex way?