User blog comment:P進大好きbot/Rathjen-type Ordinal Notation/@comment-11227630-20190823085852/@comment-35470197-20190823143727

But Pair Sequence System was so difficult to show the termination, even though its limit is ψ(Ω_ω). The difficulty occurs also when the expansion rule is not quite similar to that of an existing ordinal notation.