User blog comment:P進大好きbot/Please Help me on study of Pair Sequence System (2-rowed Bashicu Matrix System)/@comment-30754445-20180813155654/@comment-35392788-20180813172900

a) There are indeed a lot of BMS versions, but it turns out that pretty much all of the ones which have not been proven to terminate (that is, BM2, BM2.3, BM3.1 and BM3. 2; BM2.2 sucks, and a couple of BM2.x versions are actually just BM2.3 in disguise) all behave the same way in pair sequences, so it's a bit irrelevant here.

b) Bashicu never intended for BMS to evolve like this. In the beginning, it was just a system for large number programs​​​​​​. The original source for nearly all BMS versions is a BASIC program with syntax errors. The only reliable source of information is the BMS calculator, whose behaviour has been checked by Bashicu, but that guarantees nothing. So if you want us to only look at well-defined stuff, we should give up on BMS altogether.

c) Harass Nish about it, he started to make such a proof, but he never finishes what he starts

d) Yes indeed it has not proven, the only thing we have is a lot of heuristic evidence, and I mean a lot. It's not just "hoping it'll work a third time", and it's not like we pull these patterns out for no reason whatsoever. I would legit give you IRL money if you manage to show a counterexample to PSS corresponding to Bucholz psi expressions as I explained in a response on this thread.