This discussion on the optimality of the factorization algorithm crucially assumes strong equivalence with the source TL-MCTAG G. Of course there might be TL-MCTAGs that are weakly equivalent to G, that is, they generate the same language, and have rank strictly smaller than the rank of G .
finding such structurally different grammars is a task that seems to require techniques quite different from the factorization techniques we have developed in this section.