Minimum-tail table for increasing subsequences ($T_{\ell }$)

For a processed prefix $(x_1,\dots ,x_i)$, the minimum-tail table for increasing subsequences storesThere is no slot for an unattainable length. The table records minimum endings, rather than the terms of one longest increasing subsequence. Replacing the value comparisons by $<$ gives the corresponding table for strictly increasing subsequences, whose entries are strictly increasing.