User blog comment:DrCeasium/Hyperfactorial array notation: Analysis part 3/@comment-5529393-20130530121945/@comment-5529393-20130530171803

Well, it looks like neither of us are going to convince the other here. My point is that you cannot simply use rule-of-thumbs in analyzing these arrays, you have to get down and dirty and evaluate how they reduce. I hope to show that your initial rule regarding (\omega\) is wrong, and I believe I showed that [1...1,2] w/ [1,1,2] was \(\phi(\omega,0)+1\), not \(\phi(\omega^2,0)\) as your rule-of-thumb suggested, but you are changing your rules, so I will wait. (I still think that my point is made, because under the rules you outlined in a previous comment, [1...1,2] w/ [1,1,2]  is indeed at level \(\phi(\omega,0)+1\), while your [n] = \(\omega\) argument should still apply.)