\end{itemize}
+\subsection{Proof of termination}
+
+$\alg{Rank-Recurse}(\pc)$ recurses but only downwards through the
+finite graph $\hasdirdep$, so it must terminate.
+
+The whole ranking algorithm iterates but each iteration involves
+adding one or more patches to $\allpatches$. Since there are
+finitely many patches and we never remove anything from $\allpatches$
+this must complete eventually.
+
+$\qed$
+
\section{Traversal phase}
-For each patch $C \in \allpatches$ in topological order by $\hasdep$,
+For each patch $\pc \in \allpatches$ in topological order by $\hasdep$,
lowest first:
\begin{enumerate}
-\item Optionally, attempt $\alg{Merge-Base}(\pc)$.
+\item Optionally, attempt
+ $\alg{Merge-Base}(\pc)$. This may or may not succeed.
+
+\item If this didn't succeed, or was not attempted, execute
+ $\alg{Recreate-Base}(\pc)$.
+
+\item Then in any case, execute
+ $\alg{Merge-Tip}(\pc)$.
\end{enumerate}
+After processing each $\pc$
+
+\subsection{$\alg{Merge-Base}(\pc)$}
+
+This algorithm attempts to construct a suitably updated version of the
+base branch $\pcn$.
+
+It should be executed noninteractively. Specifically, if any step
+fails with a merge conflict, the whole thing should be abandoned.
+This avoids asking the user to resolve confusing conflicts. It also
+avoids asking the user to pointlessly resolve conflicts in situations
+where we will later discover that $\alg{Merge-Base}$ wasn't feasible
+after all.
+
+\subsubsection{Bases and sources}
+
+In some order, perhaps interleaving the two kinds of merge:
+
+\begin{enumerate}
+
+\item For each $\pd \isdirdep$
+
+\item
+
+\end{enumerate}
+
+
+
\section{Planning phase}