User blog comment:Boboris02/MBOT/@comment-24920136-20161219043958/@comment-30754445-20161219172152

The phrase "Since their definitions aren't well-defind that leaves them open for any definition that you can set,respecting the conditions above..." does not make the system either weak or strong.

It makes it ill-defined. At least until the part of "respecting the conditions above" is rigorously defined.

And diagonalization can happen in many ways, not all of them obvious. How does a 20-state Turing Machine diagonalize and create a number bigger than Graham's number? How does BEAF diagonalize? A quick glance at the expansion rules of (say) {3,3,3,3} doesn't hint at the power of the notation, unless we are already familiar with similar constructs.

In short, I don't see how a quick look at an ill-defined system can tell you how strong (or weak) it might be once the ambiguity is removed. There's simply no way to know.