I don't assume the *Rule of Two* was followed so strictly, since Sith are the bad guys, they would not always play by the rules... But it seems that it was Sidious's way to have only one apprentice at a time.

As shown in RotJ, the Emperor had no problem in letting Luke kill Vader... He even encouraged him to do so, so he would *take his father's place at his side*... He did the same when Anakin fought Dooku in Episode III...

Had things went differently, and Luke was turned to the dark side, would Sidious just kill Vader, so that it would only have two Sith at a time?

Is there any material that exposes the Emperor's ultimate intentions in his plan of bringing Luke to the dark side, regarding this matter of slaughtering Vader?