User blog comment:DrCeasium/Hyperfactorial array notation: Analysis part 3/@comment-5150073-20130531141516

Trying to make recursive notation look simplier, you shall found more things that can make it ill-defined (but glaringly similar to well-defined) and analysis can get more and more complex.

This is related to the problem of finding busy beavers: for large n, it will be hard to distinguish true champion from just chaotic-looking never-halting TM.