Take Query "A C D" as an example:

             'S1' => [ 'A', 'B', 'C', 'D','H','A' ],
             'S2' => [ 'A', 'C', 'D', 'B','G','J' ],
             'S3' => [ 'C', 'A', 'D', 'H','M','K' ],
             'S4' => [ 'A', 'B', 'I', 'C','I','D' ]  

1. String "A C D" can be found only in S1,S2,S4. 
   Thus, it was array from S1,S2,S4 that is taken for alignment.

2. See, S4->"ABICID" gives the biggest gap compare to S1,S2.
   As shown here:
   S4->"ABICID" gives A[BI]C[I]D, since there are 2 + 1 gaps. 
                                  2 for 'BI', 1 for 'I'
   S1->"ABCDHA" gives A[B]CD, only 1 gaps for [B]
   S2->"ACDBGJ" gives ACD,    without any gaps in between.

3. Then S1,S2 must be align *based* on S4. That means
   the maximum span of S1, S2 is until D ends.
   S1->"ABCD" 
   S2->"ACD"
   These are the two strings we align with S4->"ABICID"

4. Now, lets align S1->"ABCD" with S4->"ABICID"
   In S1, there are 1 gap in ABC in comparison to S4
   like this:
          S1->  AB-C
          S4->  ABIC
   
   There is another 1 gap in CD in comparison to S4
   like this:

          S1-> C-D
          S4-> CID

    Thus the full alignment between S1 and S4 are:

        S1-> AB-C-D
        S4-> ABICID

5. Then align S2->"ACD" with S4->"ABICID"
   In S2, there are 2 gaps in AC in comparison to S4
   like this:
          S2->  A--C
          S4->  ABIC
   
   There is another 1 gap in CD in comparison to S4
   like this:

          S2-> C-D
          S4-> CID

    Thus the full alignment between S1 and S4 are:

        S2-> A--C-D
        S4-> ABICID

6. The final alignment gives:
        S1-> AB-C-D
        S2-> A--C-D
        S4-> ABICID