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\begin{frame}{Pumping Lemma as a Game}
\begin{goal}{}
To \emph{contradict the pumping lemma}, we prove the negation:
\begin{talign}
\end{talign}
\end{goal}

\begin{block}{Pumping Lemma as a Game}
Given is a language $L$. \pause We want to prove that $L$ is not context-free.
\begin{enumerate}
\pause
\item Opponent picks \alert{$m$}.
\pause
\item We choose a word \alert{$w\in L$} with $|w|\geq m$.
\pause
\item Opponent picks \alert{$u,v,x,y,z$} \\with $w=uvxyz$, $|vxy|\leq m$ and $|vy|\geq 1$.
\pause
\item If we can find \alert{$i\geq 0$} such that \alert{$uv^ixy^iz\not\in L$}, then \emph{we win}.
\end{enumerate}
\pause
If we can always win, then $L$ does not fulfil the pumping lemma!
\end{block}
\end{frame}