It seems that OP's problem is an easy special case of the LCS problem. We have one big string S and 2 substrings (seq1, seq2) with known coordinates within S: 
S:    CTGCCACCGCTGTGTTTCGGCCGGCGAXXXXXXXXXXXXXXXXXXXXX
seq1: CTGCCACCGCTGT (Pos: 0)
seq2:      ACCGCTGTGTTTCGGCCGGCGA (Pos: 5)

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So it's a trivial O(1) algorithm to calculate the overlap with the substring positions and lengths.

In reply to Re^2: Intersecting Two Strings by lima1
in thread Intersecting Two Strings by Anonymous Monk

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