User blog comment:Boboris02/Boris´s sezration notation/@comment-24920136-20161002204126

[n,n] = cg(n) around  w^2 level

If you scroll down below the cg function you can see Peter Hufords extensions which are much stronger than this, although also more elaborate.

In this ocasion ill actually try to help OP see how it could be stronger, for starters, the base function eats two arguments right off the bat so you have [a,b] drop automagically into a->...->a

at 3 arguments [a,b,c] goes straight into a->a...a->a territory and does not pass [a,b] to collect more power.

in fgh words, you have [a,b] approximately at  f_w*b(a) level

and then [a,b,c] at f_w*(f_w*b(a))(c) level. Sure, f_w*b(a) > b, and so it seems [a,b,c] will produce a huge number, but check what happens when we use a single value n for all the variables:

[n,n,n] = f_w*(f_w*n(n))(n) = f_w^2(f_w^2(n))

the same applies further on

[n,n,n,n] = f_w*(f_w*n(f_w*n(n)))(n) = f_w^2(f_w^2(f_w^2(n)))

and so [a|b|a]  = f^b_(w^2)(a) and finally [n|n|n] = f^n_(w^2)(n) = f(w^2)+1(n)

[n|[n|n|n]|n] =  f^(f^n_(w^2))_(w^2)(n) again, here  f^n_(w^2)(n) > n makes you feel like should be huge increase of power, but

f^(f^n_(w^2)(n))_(w^2)(n) = f(w^2)+1(f(w^2)+1(n))

So you can see

(w^2)+2(n) at the fgh dominates [n|...|n] that is nested into itself n times.