User blog comment:P進大好きbot/New Issue on Traditional Analyses/@comment-36984051-20190823174448/@comment-35470197-20190823224235

Although BM4 is not fully defined, the creator, Bashicu, agreed that it coincides with Koteitan's BM2.3, which has a complete expansion rule. Therefore BM4 is a good choice to use in analysis, as long as you do not intend to show the termination through the analysis. (BM4 is not known to be terminating, and hence analysis through BM4 does not ensure the termination of other systems.)

I note that BM4 is very difficult to use in analysis, and hence we rarely use it in analysis unless we want to analyse variants of BMS. So when we use BM4 in analysis, we tend to analyse an extension of BM4, which is not known to be terminating, either. Therefore we should be careful that if analysis says that a new notation goes beyond BM4, then it does not ensure the notaion terminates up to the limit of BM4.