should in conditional sentence

[Unregistered]

Is it possible to use "should" in the main clause of conditional sentences type 1?

If she likes doing this, I should do this, too.

Thany you for your help.

[philo2009]

Although your chosen example is not especially natural, it is perfectly possible for 'should' to stand as the finite verb of the main clause of a conditional sentence, e.g.

If you are interested in learning more about local history, you should visit the town library.

However, a paradigmatic 'first conditional' is generally understood to refer to an if-sentence whose finite verb is 'will' (or possibly 'shall', as a BrE speaker might use). The sentence above, very similar but different in terms of one vital defining feature, would then be classed as a variant first conditional.