User blog comment:Hyp cos/Fundamental Sequences in Taranovsky's Notation/@comment-35470197-20190918031607/@comment-11227630-20190918075607

The "γ=0 and m=1" means successor terms.

Successor terms are terms in the form C(0,x) where x is a term. If a successor term C(0,x) is standard, then it corresponds with a successor ordinal, and the x is also standard and C(0,x)=x+1. If C(0,x) is not standard, then x is not standard. Also, there is no terms with size between x and C(0,x).

In the algorithm, if we find C(0,x) not standard from a previous step 6, then we do not check x. Instead, we check what x reduces to.

And, since a standard successor term means a successor ordinal, we will never use the algorithm for it. If we apply the algorithm on a successor ordinal, the resulting FS will be the one for its predecessor of predecessor of ... until a limit ordinal.