Hence, paths( By the Myhill-Nerode theorem, it therefore suffices to show that the equivalence relation ∼, given by w 1 ∼ w 2 if and only if ∆(w 1 ) = ∆(w 2 ), is a right congruence.
if ∆(w 1 ) = ∆(w 2 ) and w is any string, then So, assume that ∆(w 1 ) = ∆(w 2 ) and ] containing a path p whose node labels are w 1 w .