Step 3

Again, only those gaps of a_k are inserted into t_k and t_k+1 that are not already present in t_k. Since each gap of sequence a_k that is considered is inserted into both, t_k and t_k+1, the score of this alignment is still optimal, as gap against gap scores zero. In Figure 9 the down arrows correspond to this step. The dark rectangles represent the inserted gaps. After those two steps the partial score of the MSA and the score between sequences a_k and a_k+1 are both still optimal.