23/143
\begin{frame}[t,fragile]
\small

\vspace{-1ex}

\mode{
\newcommand{\OfG}[2]{\alert<#1>{\fbox{\GREEN{$#2$}}}}%
}
\mode{
\newcommand{\OfG}[2]{\fbox{\GREEN{$#2$}}}%
}
\begin{example}[cont'd]
\smallskip
\setlength{\fboxrule}{.5pt}%
\setlength{\fboxsep}{2.5pt}%
$$\GREEN{\OfG{2,4,6}{\OfG{0}{0 : \OfG{3,5,7}{1 + 2}} + \OfG{3,7}{3 + 4}} + \OfG{2,3,6,7}{5 + 6}}$$
\setlength{\fboxrule}{4pt}%
\setlength{\fboxsep}{10pt}%

\bigskip

tree representation
\vspace{-2ex}
\begin{center}
\GREEN{\begin{tikzpicture}[scale=.5]
\node (1) at (5.5,8) {$+$};
\node (2) at (3,6)   {$+$} edge (1);
\node (3) at (1,4)   {$:$} edge (2);
\node (4) at (0,2)   {$0$} edge (3);
\node (5) at (2,2)   {$+$} edge (3);
\node (6) at (1,0)   {$1$} edge (5);
\node (7) at (3,0)   {$2$} edge (5);
\node (8) at (5,4)   {$+$} edge (2);
\node (9) at (4,2)   {$3$} edge (8);
\node (10) at (6,2)  {$4$} edge (8);
\node (11) at (8,6)  {$+$} edge (1);
\node (12) at (7,4)  {$5$} edge (11);
\node (13) at (9,4)  {$6$} edge (11);
\draw<1,3,5,7>[rounded corners,draw=black]
(5.north west) -- (6.north west) -- (6.south west) --
(7.south east) -- (7.north east) -- (5.north east) -- cycle;
\only{
\fill<3,5,7>[rounded corners,nearly transparent,fill=orange]
(5.north west) -- (6.north west) -- (6.south west) --
(7.south east) -- (7.north east) -- (5.north east) -- cycle;
}
\draw<1>[rounded corners,draw=black]
(.4,4.5) -- (-.6,2.6) -- (-.6,-.65) -- (3.6,-.65) -- (3.6,.6) --
(1.7,4.5) -- cycle;
\only{
\draw<3,7>[rounded corners,draw=white]
(.4,4.5) -- (-.6,2.6) -- (-.6,-.65) -- (3.6,-.65) -- (3.6,.6) --
(1.7,4.5) -- cycle;
}
\draw<1,2,4,6>[rounded corners,draw=black]
(2.2,6.4) -- (.3,4.8) -- (-.8,2.8) -- (-.8,-.8) -- (6.6,-.8) --
(6.6,2.6) -- (5.6,4.7) -- (3.6,6.4) -- cycle;
\only{
\draw<3,5,7>[rounded corners,draw=white]
(2.2,6.4) -- (.3,4.8) -- (-.8,2.8) -- (-.8,-.8) -- (6.6,-.8) --
(6.6,2.6) -- (5.6,4.7) -- (3.6,6.4) -- cycle;
\fill<2,4,6>[rounded corners,nearly transparent,fill=orange]
(2.2,6.4) -- (.3,4.8) -- (-.8,2.8) -- (-.8,-.8) -- (6.6,-.8) --
(6.6,2.6) -- (5.6,4.7) -- (3.6,6.4) -- cycle;
\draw<5>[rounded corners,draw=white]
(8.north west) -- (9.north west) -- (9.south west) --
(10.south east) -- (10.north east) -- (8.north east) -- cycle;
}
\draw<1,3,7>[rounded corners,draw=black]
(8.north west) -- (9.north west) -- (9.south west) --
(10.south east) -- (10.north east) -- (8.north east) -- cycle;
\only{
\fill<3,7>[rounded corners,nearly transparent,fill=orange]
(8.north west) -- (9.north west) -- (9.south west) --
(10.south east) -- (10.north east) -- (8.north east) -- cycle;
\draw<4,5>[rounded corners,draw=white]
(11.north west) -- (12.north west) -- (12.south west) --
(13.south east) -- (13.north east) -- (11.north east) -- cycle;
}
\draw<1,2,3,6,7>[rounded corners,draw=black]
(11.north west) -- (12.north west) -- (12.south west) --
(13.south east) -- (13.north east) -- (11.north east) -- cycle;
\only{
\fill<2,3,6,7>[rounded corners,nearly transparent,fill=orange]
(11.north west) -- (12.north west) -- (12.south west) --
(13.south east) -- (13.north east) -- (11.north east) -- cycle;
}
\end{tikzpicture}}
\end{center}
\begin{center}
\only{
\alt<4>{leftmost outermost}{
\alt<5>{leftmost innermost}{
\alt<6>{parallel outermost}{
\alt<7>{parallel innermost}{
}}}}}} \makebox[2cm][l]{strategy}}}\strut
}
\only{
\structure{parallel}/\structure{leftmost}
\structure{outermost}/\structure{innermost} strategies\strut
}
\smallskip
\end{center}
\end{example}
\end{frame}