Rocket function

This function is based off of a dream I had where I saw its basic idea: x$\rightarrow$x^y, y$\rightarrow$x+y. The name of the function also came in this dream (not a creative name, is it).

The following functions Rocket(x,y,z), Rocket2(x,y,z), Satellite(x,y,z), and Satellite2(x,y,z) have the non-negative integers as their domain.

Defined recursively as follows:

Rocket(0,x,y) = x

Rocket2(0,x,y) = y

Rocket(x+1,y,z) = Rocket(x,y,z)^{Rocket2(x,y,z)}

Rocket2(x+1,y,z) = Rocket(x,y,z)+Rocket2(x,y,z)

Alternate function definition (I'll call this one the Satellite function):

Satellite(0,x,y) = x

Satellite2(0,x,y) = y

Satellite(x+1,y,z) = Satellite2(x,y,z)^{Satellite(x,y,z)}

Satellite2(x+1,y,z) = Satellite(x,y,z)+Satellite2(x,y,z)

First few values of Rocket(x,2,3):

2, 8, 32768, 50216813883093446110686315385661331328818843555712276103168

First few values of Rocket2(x,2,3):

3, 5, 13, 32781, 50216813883093446110686315385661331328818843555712276135949

First few values of Satellite(x,2,3):

2, 9, 1953125

First few values of Satellite2(x,2,3):

3, 5, 14, 1953139

I'll invent some googolisms:

Satellite(10¹⁰⁰,2,3) = Googolsputnik

Satellite(10^{10^100},2,3) = Googolplexsputnik

Or for all googolism with a value of x, suffix -sputnik is for Satellite(x,2,3)

Satellite2(10¹⁰⁰,2,3) = Googolsputniktwo

Satellite2(10^{10^100},2,3) = Googolplexsputniktwo

Or for any googolism with a value of x, suffix -sputniktwo is for Satellite2(x,2,3)

50216813883093446110686315385661331328818843555712276103168 = Triexplorer

Rocket(10¹⁰⁰,2,3) = Googolexplorer

Rocket(10^{10^100},2,3) = Googolplexexplorer

Or for any googolism with a value of x, suffix -explorer is for Rocket(x,2,3)

Rocket2(10¹⁰⁰,2,3) = Googolexplorertwo

Rocket2(10^{10^100},2,3) = Googolplexexplorertwo

Or for any googolism with a value of x, suffix -explorertwo is for Rocket2(x,2,3)