Before revision:  We show that  the number r \leq n of XBWT-runs upper-bounds the size of the smallest tree attractor and lower-bounds the trie's high-order worst-case entropyH.
After revision:  We show that this natural generalization enjoys several of the useful properties of its counterpart on strings: in particular, the transform natively supports counting occurrences of a query pattern on the trie's paths and its size r captures the number r \leq n of XBWT-runs upper-bounds the size of the smallest tree attractor and lower-bounds the trie's high-order worst-case entropyH.