Functional super-iteration and hierarchy of functional hyper-iterations

[bo198214]

So to define exponentiation etc... How do I put it in It_3? Don't know how to do this! Dammit!

I dont think they are compatible:
Roughly your hyper-iteration ladder does:
\( f_{n+1} (x) = f^{[x]}(x) \)
while the hyper-operations ladder does:
\( f_{n+1}(x) = f^{[x]}( c) \)
where \( c=0 \) or \( c=1 \).