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While talking about tetration with my friend the following idea (re)occured.
Equation A
$$f(f(z)) = z , f(\exp(z)) = \exp(f(z)) $$
or variations of it like the weaker
Equation B
$$f(f(f(f(z)))) = z , f(\exp(\exp(z))) = \exp(\exp(f(z))) $$
Now clearly if f satisfies equation A it also satisfies eq...
