The optimum cost of an alignment of the strings

x1 x2 x3 x4 ... x_m and y1 y2 y3 ... y_n

will always be greater than the optimum cost of an alignment of

x2 x3 x4 ... x_m and y1 y2 y3 ... y_n

because any alignment of the first pair of strings necessarily contains an alignment of the second pair of strings.

This is NOT correct!

It is NOT true that any alignment of the first pair of strings necessarily contains an alignment of the second pair of strings: For example, let x = CT and let y = CG. It is NOT true that any alignment of these start with x1 = C against a gap, followed by an alignment of x2 against y1 y2 (i.e., an alignment of T against CG). Here is such an alignment:

A T A G

This alignment has cost 1, whereas any alignment that starts with the first A in x against a gap necessarily will have cost at least 2 for that first gap, and optimally has cost 5:

A T - - A G

Is it possible to have a situation in table "opt" where x_i is the same character as y_j and have

opt[ i ][ j ] = 2 + opt[ i+1][ j ] = 2 + opt[ i ][ j+1] = 0 + opt[ i + 1][ j + 1]

(In other words, when creating the alignment, we could have come from ANY of the 3 neighboring squares below and to the right?

can you give me another example of same type?