User blog comment:Ynought/Trying to make the SCG function even quicker/@comment-5529393-20190102052459

What is the precise meaning of "embeddable while removing at most k vertices/edges"? If you mean that G_i is an i minor if G_j if there exists a graph H that is a minor of G_j such that H is G_i with at most i vertices/edges removed, then "i minor" is a weaker condition than the normal minor. (Meaning, there are more pairs (G_i, G_j) that satisfy the relation.) So this can only shorten the length of the longest sequence that avoids the condition.