Similar Child

Given two strings a and b of equal length, what's the longest string (s) that can be constructed such that it is a child of both? A string x is said to be a child of a string y if x can be formed by deleting 0 or more characters from y. For example, ABCD and ABDC has two children with maximum length 3, ABC and ABD. Note that we will not consider ABCD as a common child because C doesn't occur bef