Hello all! I have double/triple checked that this notation will work. I want you to find out its growth rate and ways to expand it. Thank you.

T notation, or tower notation, is a way of expressing towers in different notations and ways. The form of the notation is n(t^x)y. The rules are as followed below:

1. n(t)1 is always n

2. n(t)y is defined as a set of an operation done n(t)y-1 amount of times. This builds a tower of y height.

3. In n(t^x)y, if x=1, then cut out the x

4. In n(t^2)y, the y tells you how many side towers to create. A side tower is defined as the following: lets say there is a tower with a value of G, where G can be defined with n(t)y. A single side tower of this particular tower G would have a height of G. A side tower of the second tower would have a height equal to the value of the second tower, and so on.

5. In n(t^3)y, the y tells you how many vertical towers to create. Vertical towers can be defined very similar to side towers, where the amount of side towers to create is equal to the value of another set of side towers. The amount of times to do this is dictated by y until you get to an original set where the amount of side towers is equal to y.

6. In n(t^x)y, the value of x tells you which type of tower to create. It will always be a chain of towers, where the towers it is a chain of are defined by x-1. The tower chains are always nested.

Examples: 10(t)2 = 10^10. 10(t)10 = 10^^10.

I know n(t)y is exponentiation and n(t^2)y is tetration but what is n(t^3)y, or n(t^x)y?