regular expression "contains" another regular expression

Question

Is there a way to test if a regular expression "contains" another regular expression?
For example:

RegEX1 = "a.*b";
RegEx2 = "a1.*b";

RegEX1 "contains" RegEX2.

As far as I know - this can't be done, am I wrong?

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OK, joel.neely has shown that it can be done (haven't read it yet...) academically.

Can it be done in a programming language, say C# ?
How effective will that be? How long will it take to test 1000 pairs?

Answer 1

Yes.

This paper contains a detailed discussion of the topic (see section 4.4).