User blog:JTOnstead20/Recursive Recursion Function

I need your help in finding the expansion rate of various things in the following notation before I formally release it. I will release one bit of the notation at a time. I really appreciate your support and guidance:

Recursive Recursion Function (RRF) is a fast growing function that will hopefully use the power of eventual domination to overpower some functions. It tries to accomplish this by an endless supply of recursion using the results from the previous iteration of the notation. The StarThe star is the first portion of RRF and uses a simple recursion depending on the number it multiplies out to. Although RRF can be used on any function, exponentiation is a great way to begin as an introduction to the star. The simple definition is this: x(function)x *1 = x(function)x. Then, x(function)x *2 = (x(function)x) (function) (x(function)x). Let's establish a number as an example throughout this entire page. This number will be 10^10 or ten billion. 10^10 *1 = ten billion. Then we move on to 10^10 *2 = 10^10^10^...10 a 10^10 amount of times. This is equal to 10^^10^10 using up arrow notation. Let's go onto 3: 10^10 *3 = 10^10^10...10 with 10^^10^10 amount of power towers. So we see the star's growth rate is on par with up arrow notation. Lets go on to double stars. 10^10 **2 = ? A double star means the following: 10^10 * 10^10 * 10^10 ... 10^10 with 10^10 amount of times. If a number in stars is equal to up arrow notation, then a single 10^10 * 10^10 would be equal to around 10^10^^^...^^^10^10 with 10^10 amount of up arrows in between. That's only 1 step on the way to 10^10 stars. 10^10 * (10^10^^^...^^^10^10 with 10^10 amount of up arrows) = 10^10 ^^...^^ 10^10 with the number seen in the parenthesis above amount of up arrows. This is easily expressible in chained arrow notation: 10^10 -> 10^10 -> 2 -> 2. The next star would bring us up to  10^10 -> 10^10 -> 3 -> 2. Once we are done, we achieve a number higher than Graham's number: 10^10 -> 10^10 -> 10^10 -> 2.