User blog comment:PsiCubed2/My own version of BMS/@comment-35470197-20181120231600/@comment-35470197-20181121144609

> This version only popped into my head on the same day I've written this blog post. The other version is far more complicated, and proving the equivalence of the two is not at all obvious.

Uh-huh. So you verified the termination or something like that for the complicated one. I see. I am looking forward to the proof.

> And in the mean time, you can help out by telling me whether you think the rule-set I've given actually works or not. Should I put my effort into trying to prove that it works, or into searching for a counter example?

I think that PSS with respect to your version works in the same way as other versions whose PSS are not broken. I am sorry if I am incorrect (I note that I have just read the definition of BM1 by koteitan's classification, and hence am not so familiar with the expansion rule of BM1).

If you spend time to write down the proof using Buchholz's psi, then I guess that you will need as many months as I spent because the difference between the expansion rule of PS and the fundamental sequence of Buchholz's ordinal notation system yields tiresome ramifications of arguments. Also, it would be good to show the conversion map before you start writing proofs of its properties in order to avoid minour mistakes which will possibly ruin your efforts. At least for me, the conversion map was sufficiently complicated.