\begin{frame}
\small
\begin{definitions}[Properties of Elements]
Let $\langle A, \to \rangle$ be an ARS. An element $a\in A$ is called:
\begin{itemize}
\item<2->
\makebox[1.5cm][l]{\alert<2>{SN}} \alert<2>{strongly normalizing} \quad or\quad \alert<2>{terminating}\\[1ex]
if $a$ admits no infinite rewrite sequence $a = a_1 \to a_2 \to \ldots$
\smallskip
\item<3->
\makebox[1.5cm][l]{\alert<3>{WN}}\alert<3>{weakly normalizing}\\[1ex]
if $\exists b.\; a \to^! b$
\smallskip
\item<4->
\makebox[1.5cm][l]{\alert<4>{CR}} \alert<4>{confluent} \quad or\quad \alert<4>{Church Rosser}\\[1ex]
if $\forall b,c.\; (c \FromP{*} a \to^* b \;\Rightarrow\; \exists d.\; c \to^* d \FromP{*} b)$
\smallskip
\item<5->
\makebox[1.5cm][l]{\alert<5>{WCR}} \alert<4>{weakly confluent} \quad or\quad \alert<5>{weakly Church Rosser}\\[1ex]
if $\forall b,c.\; (c \from a \to b \;\Rightarrow\; \exists d.\; c \to^* d \FromP{*} b)$
\smallskip
\end{itemize}
\end{definitions}
\onslide<6->
\begin{block}{}
An ARS has the property if all its elements have the respective property.
\end{block}
\end{frame}