\begin{frame} \small \begin{theorem}%[Rusinowitch 1987, Middeldorp 1989] \smallskip The disjoint union of terminating TRSs $\RR$ and $\SS$ is terminating if: \begin{itemize} \item $\RR$ and $\SS$ lack collapsing rules, or \item $\RR$ and $\SS$ lack duplicating rules, or \item $\RR$ or $\SS$ lacks both collapsing and duplicating rules. \smallskip \end{itemize} \end{theorem} \bigskip \begin{corollary}<2-> \smallskip Termination is preserved under signature extension. \smallskip \end{corollary} \end{frame}