... positions in such sub-instances are indexedaccording to the same indexing as of the original strings. That is, the characters in sub-instances of the formsi, jare indexed f rom i to j - 1, and in ... contained in J1,whereitcan be verified that e ither L = J1(if the last index in Iis smaller than the first index in J, as in the example of Figure 8c), or L is an empty interval (in all othercases ... r the computation of α4i,j. Note that the set of all foldings of si,j in which j is unpaired is exactly the set of all foldings of si,j+1,andthusthesumofweights of all such foldings...