Let s be the given string. We want to find a substring t of s with the maximum self-alignment value . Let s[1, j] be the substring of s that consists of the first j letters. Informally, we use w(i, j) to denote the maximum self-alignment value of a suffix tj of s[1, j] such that there are i letters at the right end of the self-alignment of tj that are aligned with spaces and scored as . Note that, the right end of the self-alignment of tj could contain more than i spaces. However, only the last i spaces are scores as  each and the rest of them are scored as the score for μ(x, Δ).