User blog comment:P進大好きbot/Analysis of 非想非非想 notation/@comment-36957202-20190801181858/@comment-35470197-20190806050455

Both BMS and TON are not known to terminate, although people often state that they obviously terminate. Therefore "analysis" based on comparison to them does not ensure the termination, or does not give a description of the correspondence to ordinals.

Moreover, the expansion rule of BMS is not compatible those of notations associated to OCFs, and hence it is very difficult to compare BMS (even pair sequence system) to an OCF-like notation. It is not good for you to recommend others to compare notation with BMS if you do not know the difficulty well.