User blog comment:B1mb0w/Growth Rate of the S Function/@comment-5529393-20160712123611/@comment-10262436-20160712124352

I suggest you work with the equivalent fgh functions to see the 'very similar' structure of S and FGH functions. EG

S(n,T(0),2) == f_w^2(n) = f_w(f_w(n)) = f_{f_w(n)}(f_w(n))

The same convoluted equation will arise with the S and T functions.

I defined the S and T functions specifically to avoid the ambiguous function f_w(w) = S(T(0),T(0),1)

By providing clearly defined ruleset for treating T(m) and T^p(m), I have created a very fast growth rate function. Very keen to understand how fast it does grow...