It's a constrained variation of the longest common subsequence problem.

Anything you do can be easily defeated unless you set some parameters since it's not merely as simple as the trivial example you describe above. For example, what if on two consecutive days you issue the same exact commands. You'd end up with 100% overlap. What is it you're trying to do because your problem description doesn't seem to match up realistically with your contrived overlap example.

And if the files are differentiated by date already, what's the point of even trying to match them up like this?

Update: Using your contrived example where there is true overlap and no repeated elements out of order, then you could iterate over both files in order, each line becomes a key in a Tie::Hash::Indexed tie'd hash (++'d to maintain count). Then all the keys with values of 2 can be taken as the area of overlap. But as I said above, this will not work if there are any repeated lines above or below. So it won't work for you. I do think your problem is ill defined and ambigous. Even your second example has more than one solution based on what you want.