User blog comment:Edwin Shade/A Complete Analysis of Taranovsky's Notation/@comment-30118230-20180201150715/@comment-34434829-20180201170807

BMS is a flawed system beyond pair-sequences anyway.

BM1 was shown to have infinite loops quite early in the triplets range.

BM2 was never analyzed at all, even at the pair-sequences level. People seem to have accepted on faith that BM1 and BM2 are equivalent up to (0,0,0)(1,1,1) but nobody ever bothered to actually demonstrate this fact (let alone prove it).