For a recursive partitioning of h s g in which the root has children labeled {1, 3} and {2}, Algorithm 2 constructs the LCFRS: Alternatively, if we let Algorithm 2 run on the recursive partitioning of h s g in which the root has children labeled {1, 2} and {3}, then it produces the following LCFRS, which is, in fact, a CFG: Observe that terminals are generated individually by the rules that were constructed from the leaves of the recursive partitioning but not by the structural rules obtained from internal nodes.
the LCFRS that we induce is in general not lexicalized.