Another grammar with infinite ambiguity. This one illustrates the difficulty of trying to provide at least one parse for each possible looping path through the tree.

Consider a RHS that generates an infinite set of strings. By the pumping lemma for regular languages, we know that for every sentence longer than some language-dependent length (number of states in the FSA, if I remember correctly), the sentence takes the form uvw, where v can occur zero or more times, so u + v^n + w.

It would be nice to illustrate the set of possible paths, just because. That is, for each set of paths through the RHS of the form u + v^n + w, provide paths for n=0 (u + w) and n=1 (u + v + w).

I don't see a convenient way to do this at the moment, so I currently plan to extend the notion of original NTs to regular languages (or see what H/U call this kind of thing) and return only original parses. But it would be interesting to see if one could exercise each loop in this FSA.