User blog:MilkyWay90/Extension to the Up-Arrow Notation

Here is my Extended Uparrow Notation.

define F(a, b, c) = a ^...^ c with b ^s (normal arrow notation)

define F(a, b, ..., c, d + 1) = F(a, b, ..., F(a, b, ..., c, d))

F(a, b, ..., c, 1) = F(a, b, ..., c)

A few questions for you:

What is the growth rate of this function?

How can I extend it further?

Please leave the answers and/or any comments on the extended notation in the comments below.