I am implementing the dynamic programming algorithm for computing tree alignment distance as described in Alignment of trees  an alternative to tree edit. But I got stuck in lemma 3 on page 141 (page 5 of pdf). The notations are given at the beginning of section 2. The last case in lemma 3 saysHowever, there is no recurrence formula given to compute . How did we obtain this? I don't think the following holds either:?
Computing tree alignment distance
algorithms;trees;dynamic programming
If I understand the paper correctly (and I might not), the solution seems to be described in Section 2.2 of the paper.  It says we have to compute $D(F_1[i],F_2[j_s,j_t])$... and then it goes on to describe a strategy for doing so (namely, the Procedure 1, as described in Figure 2).