User blog comment:Hyp cos/Fundamental Sequences in Taranovsky's Notation/@comment-35470197-20190918031607/@comment-35470197-20190918052146

Thank you for the explanation. It helps me to understand better, but maybe I am still not understanding the algorithm correctly.

In Step 2, if the case for γ=0 and m=1 is applicable, then the C(0,β_1) is decreased into β_1, and we need to repeat the step 1. After the repetition, the occurrence of β_1 is decreased into a smaller term γ_1. Then according to your explanation, through Step 4 and 5, γ_1 is increased into a bigger term γ_2, which is still smaller than β_1, right? Then we have γ_2 < β_1 < C(0,β_1). If this method actually gives the FS, the limit of γ_2 (for varying k) is C(0,β_1), which is bigger than β_1. It implies that β_1 can never be a standard term, right?