\begin{frame}[t]
\small
\vspace{-1ex}
\begin{example}
\vspace{-2.5ex}
\GREEN{\begin{xalignat*}{4}
\m{0} + y & \to y &
\m{s}(x) + y &\to \m{s}(x+y) &
\m{0} \times y &\to \m{0} &
\m{s}(x) \times y &\to (x \times y) + y
\end{xalignat*}}
\vspace{-5ex}
\begin{center}
\GREEN{\begin{tikzpicture}[on grid,baseline=(1).baseline]
\small
\matrix[ampersand replacement=\&,row sep=3mm,column sep=0mm]{
\& \& \& \node(0) {$\phantom{0}$};
\& \node (1) {$\makebox[0mm][r]{$\BLACK{t ~= \qquad}$}\alert<2>{+}$};
\& \& \& \& \& \\
\& \node (2) {$\alert<2>{\m{s}}$}; \& \& \& \& \&
\& \node (3) {$+$}; \& \& \& \\
\& \node (4) {$\alert<3>{\times}$}; \& \& \&
\& \node (5) {$\alert<5>{\times}$}; \&
\& \& \& \node (6) {$\alert<4>{+}$}; \& \\
\node (7) {$\alert<3>{0}$}; \& \& \node (8) {$0$}; \&
\& \node (9) {$\alert<5>{0}$};
\& \& \node (10) {$\alert<6>{+}$}; \& \& \node (11) {$\alert<4>{0}$}; \&
\& \node (12) {$\m{s}$}; \\
\& \& \& \& \& \node (13) {$\alert<6>{0}$}; \& \& \node (14) {$\m{s}$};
\& \& \& \node (15) {$0$}; \\
\& \& \& \& \& \& \& \node (16) {$0$}; \& \& \& \\ };
\alert<2>{
\draw (1) node[right] {\BLACK{\alert<2>{$\,{}^\epsilon$}}} -- (2);
\draw (1) -- (3);
\draw (2) -- (4);
}
\draw (3) -- (5);
\draw (3) -- (6);
\alert<3>{
\draw (4) node[left] {\BLACK{\alert<3>{${}^{11}\,$}}} -- (7);
\draw (4) -- (8);
}
\alert<5>{
\draw (5) node[left] {\BLACK{\alert<5>{${}^{21}\,$}}} -- (9);
\draw (5) -- (10);
}
\alert<4>{
\draw (6) node[right] {\BLACK{\alert<4>{$\,{}^{22}$}}} -- (11);
\draw (6) -- (12);
}
\alert<6>{
\draw (10) node[right] {\BLACK{\alert<6>{$\,{}^{212}$}}} -- (13);
\draw (10) -- (14);
}
\draw (12) -- (15);
\draw (14) -- (16);
\end{tikzpicture}
$\stackrel{\BLACK{\alert<1>{21}}}{\longrightarrow}$
\begin{tikzpicture}[on grid,baseline=(1).baseline]
\small
\matrix[ampersand replacement=\&,row sep=3mm,column sep=0mm]{
\& \& \& \node (1) {$\alert<2>{+}\makebox[0mm][l]{$\BLACK{\qquad =~ u}$}$};
\& \& \& \& \\
\& \node (2) {$\alert<2>{\m{s}}$}; \& \& \&
\& \node (3) {$\alert<7>{+}$}; \& \& \\
\& \node (4) {$\alert<3>{\times}$}; \& \&
\& \node (5) {$\alert<7>{0}$}; \& \& \node (6) {$\alert<4>{+}$}; \& \\
\node (7) {$\alert<3>{0}$}; \& \& \node (8) {$0$}; \& \& \&
\node (9) {$\alert<4>{0}$}; \& \& \node (10) {$\m{s}$}; \\
\& \& \& \& \& \& \& \node (11) {$0$}; \\ };
\alert<2>{
\draw (1) node[right] {\BLACK{\alert<2>{$\,{}^\epsilon$}}} -- (2);
\draw (1) -- (3);
\draw (2) -- (4);
}
\alert<7>{
\draw (3) node[right] {\BLACK{\alert<7>{$\,{}^2$}}} -- (5);
\draw (3) -- (6);
}
\alert<3>{
\draw (4) node[left] {\BLACK{\alert<3>{${}^{11}\,$}}} -- (7);
\draw (4) -- (8);
}
\alert<4>{
\draw (6) node[right] {\BLACK{\alert<4>{$\,{}^{22}$}}} -- (9);
\draw (6) -- (10);
}
\draw (10) -- (11);
\end{tikzpicture}}
\end{center}
\vspace{-2ex}
\(
\begin{array}{@{}l@{\hspace{3.2mm}}c|c|c|c|c|c|c}
\text{redex positions in $s$\,:} & \epsilon & 11 & 2 &
\multicolumn{2}{c|}{22} \\
\text{redex positions in $t$\,:} & \alert<2>{\epsilon} &
\alert<3>{11} & \phantom{2} & \alert<6>{212} & \alert<4>{22} &
\alert<5>{21} \onslide<2-> \\
\text{redex positions in $u$\,:} &
\onslide<2->\alert<2>{\epsilon} & \onslide<3->\alert<3>{11} & & &
\onslide<4->\alert<4>{22} & & \onslide<7->\alert<7>{2}
\end{array}
\)
\\[2ex]
\begin{center}
\onslide<6->
redex at position $212$ is \alert<6>{erased} \qquad\qquad
\onslide<7->
redex at position $2$ is \alert<7>{created}
\end{center}
\end{example}
\end{frame}