\begin{frame} \frametitle{Termination of $\trslex$ and $\trsllex$} Hence we have proven: \begin{theorem} \centerline{$\airew{{\itrsllex{\arel}}}$ is terminating} \end{theorem} \bigskip \pause \begin{corollary} \centerline{$\reltra{\airew{\trslex}}$ is terminating on $\trmover{\setsum{\asig}{\aTrmvar}}$} \end{corollary} \bigskip {\bf Proof.} $\reltra{\airew{\trslex}}$ and $\reltra{\airew{\trsllex}}$ coincide on $\trmover{\setsum{\asig}{\aTrmvar}}$ \end{frame}