On quasi orders of words and the confluence property

We investigate the confluence property, that is, the property of a language to contain, for any two words of it, one which is bigger, with respect to a given quasi order on the respective free monoid, than each of the former two. This property is investigated mainly for regular and context-free languages. As a consequence of our study, we give an answer to an old open problem raised by Haines concerning the effective regularity of the sets of …