Functional super-iteration and hierarchy of functional hyper-iterations

[Base-Acid Tetration]

To test the usefulness of this concept, I am now trying to define the hyper-operations in terms of hyper-iteration of the successor operation x+1. to try to see if the levels of hyper operations correspond to the hyper-iterations. if S(a) := a+1, than iteration of this function is addition: \( a+b = [S \operatorname{It}_1 b] (a). \) Problem is, \( [S \operatorname{It}_2 b] (a) \) produces ab+1 instead of ab, so it needs to be written as \( [S \operatorname{It}_2 (b)] (a)-1 \). So to define exponentiation etc... How do I put it in It_3? Don't know how to do this! Dammit!