Complete the proof that the yraph $B G_{\mathrm{a}}$ /defined in the proof of Theorem 5.13; is indeed a buffer graph, i.e., for eacil path $P \in \mathcal{P}$ there exists a guaranteed path with image $P$ Show that, as claimed, $f b$ and $n b$ do undeed describe a path in $B G_{\mathrm{a}}$.