SEQUENCE ALLIGNMENT

	y	T	A	A	G	G	T	C	A	-
x		0	1	2	3	4	5	6	7	8
A	0	7	8	10	12	13	15	16	18	20
A	1	6	6	8	10	11	13	14	16	18
C	2	6	5	6	8	9	11	12	14	16
A	3	7	5	4	6	7	9	11	12	14
G	4	9	7	5	4	5	7	9	10	12
T	5	8	8	6	4	4	5	7	8	10
T	6	9	8	7	5	3	3	5	6	8
A	7	11	9	7	6	4	2	3	4	6
C	8	13	11	9	7	5	3	1	3	4
C	9	14	12	10	8	6	4	2	1	2
-	10	16	14	12	10	8	6	4	2	0

Find strings x and y such that in the completed "opt" table (where opt[i][j] = optimum cost of aligning x0 x1 x2 ... x_{m-1} with y0 y1 y2 ... y_{n-1}), there exist (provide them) values i and j such that the following holds:

x_i == y_j and opt[ i ][ j ] = 2 + opt[ i+1][ j ] = 2 + opt[ i ][ j+1] = 0 + opt[ i + 1][ j + 1].

or

prove that this cannot happen for ANY strings x and y.