User blog comment:Boboris02/MBOT/@comment-30004975-20161219034751/@comment-30754445-20161220204917

Well, the Ackermann function is one of the simplest possible functions that still requires one diagonalization (that is - it isn't primitive recursive).

As such, it is a perfect "small" example to test things. And it will probably be much much easier to polish this one example to perfection, then it would be to try and fix all of MBOT in one bold stroke.

I'll also be interested in seeing the exact inner workings of your other two computable example (specifically: an evaluation of {3,3,3,3} and a detailed explanation of why the claimed ψ(ψᵢ(0))-level system really is ψ(ψᵢ(0))-level), but please don't do these before the Ackermann one. There's little point jumping to these complex levels of recursion when we're not even sure that the first diagonalization works properly.