This also makes our grammar weakly equivalent to an inversion transduction grammar (Wu 1997), although the conversion would create a very large number of new nonterminal symbols.
note that the τ(s j )'s only differ at nodes below n. Let z[in(n)] be the vector consisting of the variables at nodes below n (that is, contained in subtrees rooted at n, or "inside" n) in the forest, and let z[in(n)] be the vector consisting of variables not under node n. the vectors z[in(n)] and z[in(n)] partition the complete vector z.