Given a string, find two identical subsequences with consecutive indexes C++

I need to construct an algorithm (not necessarily effective) that given a string finds and prints two identical subsequences (by print I mean color for example). What more, sum of the sets of indexes of these two subsequences has to be a set of consecutive natural numbers.

In mathematics, the thing what I am looking for is called "tight twins", if it helps anything.

Let me give a few examples:

1) consider string 231213231

It has two subsequences I am looking for in the form of "123". To see it better look at this image:

The first subsequence is marked with underlines and the second with overlines. As you can see they have all the properties I need.

2) consider string 12341234

3) consider string 12132344.

Now it gets more complicated:

4) consider string: 13412342

It is also not that easy:

I think that these examples explain well enough what I meant.

I've been thinking a long time about an algorithm that could do that but without success.

For coloring, I wanted to use this piece of code:

HANDLE  hConsole;
    hConsole = GetStdHandle(STD_OUTPUT_HANDLE);
SetConsoleTextAttribute(hConsole, k);

where k is color.

Any help, even hints, would be highly appreciated.