  In this paper, we consider a generalized longest common subsequence problem,
in which a constraining sequence of length $s$ must be included as a substring
and the other constraining sequence of length $t$ must be excluded as a
subsequence of two main sequences and the length of the result must be maximal.
For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and the given
two constraining sequences of length $s$ and $t$, we present an $O(nmst)$ time
dynamic programming algorithm for solving the new generalized longest common
subsequence problem. The time complexity can be reduced further to cubic time
in a more detailed analysis. The correctness of the new algorithm is proved.
