\subsubsection{Simple Join}
\begin{algorithm}
    \caption{SimpleJoin Algorithm}
    \begin{algorithmic}[1]
        \Procedure{SimpleJoin}{$R$, $S$}
            \For{each tuple $t_R \in R$}
                \For{each tuple $t_S \in S$}
                    \If{$\texttt{pred}(t_R, t_S)$}
                        \State $\texttt{add}\{ t_R, t_S \}$ to the join output
                    \EndIf
                \EndFor
            \EndFor
        \EndProcedure
    \end{algorithmic}
\end{algorithm}
Here, the max output size is $T_R \cdot T_S$, where $T_X$ is the number of tuples for relation $X$.

The cost is obviously \cost{$\texttt{cnt}(R) \cdot \texttt{cnt}(S)$}, with $\texttt{cnt}(X)$ the number of tuples in $X$.