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 entropy \mathcal H^{wc index able to \emph{locate in pre-order nodes reached by a path labeled with a given pattern.
After 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 entropy \mathcal H^{wc index able to \emph{locate in pre-order nodes reached by a path labeled with a given pattern.