User blog comment:P進大好きbot/BMOCF/@comment-35870936-20181128002342/@comment-30754445-20181128003533

The fundamental sequences are given by the expansion rules of BM2.3.

For example, for (a) just follow the rules to expand (0,0,0)(1,1,1)(2,0,0)(1,1,1)(2,0,0).

(whether or not the expressions you've given actually corresponds to an ordinal, of-course, depends on the termination of BM2.3)