... f'mite set of symbols, so there is only a finite number of strings of given length L, and it has a finite number of rules, so there is only a finite number of possible parse trees of given depth ... Let C a be the set of pairs [A,B] such that A B by a tree of depth n. Clearly C t is the set of pairs [A,B] such that (A ) B) is a rule of G. Also, Cn+ 1 is the set of pairs [A,C] such that ... representation for the set of pairs of ground terms [A,B] such that (A > B) is a rule in the ground grammar of G'. Clearly this representation is just the set of pairs of terms [C,D] such...