How would one go about classifying the time complexity of Ackermann's function, and can we say that all primitive-recursive functions are asymptotically bounded by the complexity of the Ackermann function as an asymptotic upper bound?
Edit: I want to make it clear that I am interested in the time complexity of computing Ackermman's function and whether the time complexity of computing any primitive recursive function is asymptotically bounded by the time complexity of computing Ackermman's function. I am not interested in the actual values of those functions.
I am asking because I remember seeing an assertion of my second question in an old book but no proof was shown and no time complexity for computing Ackermman's function was listed, so the assertion was by no means rigorous.