
%\documentstyle[11pt,zed]{csart}
\documentstyle{csart}

\begin{document}

\sloppy

\def\dotdot{\mathinner{\ldotp\ldotp}}

\def\parallel{\mathinner{\,\|\,}}

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		\hbox{\vrule width.#3pt height#2pt \kern#1pt
		\vrule width.#3pt}
		\hrule height.#3pt}}}}
\def\choi{\mathchoice\cho5{15}{48}\cho4{12}{45}\cho39{25}\cho26{21}}
\def\Choice{\mathop{\smash\choi\vphantom\sum}}

\def\choice{{\scriptstyle \Choice }}

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\def\leftif{\mathchoice\lefti{2}{\displaystyle|}\lefti{2}{\textstyle|}\lefti{2}{\scriptstyle|}\lefti{1.5}{\scriptscriptstyle|}}

\newcommand{\proc}[1]{\mbox{\bf {#1}}}

\def\lbag{[[}
\def\rbag{]]}

\def\ndchoice{\sqcap}

%\section{Problem}

\begin{eqnarray*}
\proc{C}^{00} (i, j) & = &
  \left( P_{i - 1}.c.Q_j^I \rightarrow C^{01} (i, j) \right) \ndchoice
  \left( Q_{j - 1}.c.P_i^I \rightarrow C^{10} (i, j) \right) \\
\proc{C}^{01} (i, j) & = & 
  \left( P_i.r.Q_j^O \rightarrow C^{02} (i, j) \right) \ndchoice
  \left( Q_{j - 1}.c.P_i^I \rightarrow C^{11} (i, j) \right) \\
\proc{C}^{02} (i, j) & = &
  \left( P_i.r.Q_j^I \rightarrow C^{03} (i, j) \right) \ndchoice
  \left( Q_{j - 1}.c.P_i^I \rightarrow C^{12} (i, j) \right) \\
\proc{C}^{03} (i, j) & = &
  \left( Q_j.c.P_{i + 1}^O \rightarrow C^{04} (i, j) \right) \ndchoice
  \left( Q_{j - 1}.c.P_i^I \rightarrow C^{13} (i, j) \right) \\
\proc{C}^{04} (i, j) & = &
  \left( Q_j.c.P_{i + 1}^I \rightarrow C^{05} (i, j) \right) \ndchoice
  \left( Q_{j - 1}.c.P_i^I \rightarrow C^{14} (i, j) \right) \\
\proc{C}^{05} (i, j) & = &
  \left( Q_{j - 1}.c.P_i^I \rightarrow C^{15} (i, j) \right) \\
\\
\proc{C}^{10} (i, j) & = &
  \left( P_{i - 1}.c.Q_j^I \rightarrow C^{11} (i, j) \right) \ndchoice
  \left( Q_j.r.P_i^O \rightarrow C^{20} (i, j) \right) \\
\proc{C}^{11} (i, j) & = & 
  \left( P_i.r.Q_j^O \rightarrow C^{12} (i, j) \right) \ndchoice
  \left( Q_j.r.P_i^O \rightarrow C^{21} (i, j) \right) \\
\proc{C}^{12} (i, j) & = &
  \left( P_i.r.Q_j^I \rightarrow C^{13} (i, j) \right) \ndchoice
  \left( Q_j.r.P_i^O \rightarrow C^{22} (i, j) \right) \\
\proc{C}^{13} (i, j) & = &
  \left( Q_j.c.P_{i + 1}^O \rightarrow C^{14} (i, j) \right) \ndchoice
  \left( Q_j.r.P_i^O \rightarrow C^{23} (i, j) \right) \\
\proc{C}^{14} (i, j) & = &
  \left( Q_j.c.P_{i + 1}^I \rightarrow C^{15} (i, j) \right) \ndchoice
  \left( Q_j.r.P_i^O \rightarrow C^{24} (i, j) \right) \\
\proc{C}^{15} (i, j) & = &
  \left( Q_j.r.P_i^O \rightarrow C^{25} (i, j) \right) \\
\\
\proc{C}^{20} (i, j) & = &
  \left( P_{i - 1}.c.Q_j^I \rightarrow C^{21} (i, j) \right) \ndchoice
  \left( Q_j.r.P_i^I \rightarrow C^{30} (i, j) \right) \\
\proc{C}^{21} (i, j) & = & 
  \left( P_i.r.Q_j^O \rightarrow C^{22} (i, j) \right) \ndchoice
  \left( Q_j.r.P_i^I \rightarrow C^{31} (i, j) \right) \\
\proc{C}^{22} (i, j) & = &
  \left( P_i.r.Q_j^I \rightarrow C^{23} (i, j) \right) \ndchoice
  \left( Q_j.r.P_i^I \rightarrow C^{32} (i, j) \right) \\
\proc{C}^{23} (i, j) & = &
  \left( Q_j.c.P_{i + 1}^O \rightarrow C^{24} (i, j) \right) \ndchoice
  \left( Q_j.r.P_i^I \rightarrow C^{33} (i, j) \right) \\
\proc{C}^{24} (i, j) & = &
  \left( Q_j.c.P_{i + 1}^I \rightarrow C^{25} (i, j) \right) \ndchoice
  \left( Q_j.r.P_i^I \rightarrow C^{34} (i, j) \right) \\
\proc{C}^{25} (i, j) & = &
  \left( Q_j.r.P_i^I \rightarrow C^{35} (i, j) \right) \\
\\
\proc{C}^{30} (i, j) & = &
  \left( P_{i - 1}.c.Q_j^I \rightarrow C^{31} (i, j) \right) \ndchoice
  \left( P_i.c.Q_{j + 1}^O \rightarrow C^{40} (i, j) \right) \\
\proc{C}^{31} (i, j) & = & 
  \left( P_i.r.Q_j^O \rightarrow C^{32} (i, j) \right) \ndchoice
  \left( P_i.c.Q_{j + 1}^O \rightarrow C^{41} (i, j) \right) \\
\proc{C}^{32} (i, j) & = &
  \left( P_i.r.Q_j^I \rightarrow C^{33} (i, j) \right) \ndchoice
  \left( P_i.c.Q_{j + 1}^O \rightarrow C^{42} (i, j) \right) \\
\proc{C}^{33} (i, j) & = &
  \left( Q_j.c.P_{i + 1}^O \rightarrow C^{34} (i, j) \right) \ndchoice
  \left( P_i.c.Q_{j + 1}^O \rightarrow C^{43} (i, j) \right) \\
\proc{C}^{34} (i, j) & = &
  \left( Q_j.c.P_{i + 1}^I \rightarrow C^{35} (i, j) \right) \ndchoice
  \left( P_i.c.Q_{j + 1}^O \rightarrow C^{00} (i + 1, j + 1) \right) \\
\proc{C}^{35} (i, j) & = &
  \left( P_i.c.Q_j^O \rightarrow C^{30} (i + 1, j) \right) \\
\\
\proc{C}^{40} (i, j) & = &
  \left( P_{i - 1}.c.Q_j^I \rightarrow C^{41} (i, j) \right) \ndchoice
  \left( P_i.c.Q_{j + 1}^I \rightarrow C^{50} (i, j) \right) \\
\proc{C}^{41} (i, j) & = & 
  \left( P_i.r.Q_j^O \rightarrow C^{42} (i, j) \right) \ndchoice
  \left( P_i.c.Q_{j + 1}^I \rightarrow C^{51} (i, j) \right) \\
\proc{C}^{42} (i, j) & = &
  \left( P_i.r.Q_j^I \rightarrow C^{43} (i, j) \right) \ndchoice
  \left( P_i.c.Q_{j + 1}^I \rightarrow C^{52} (i, j) \right) \\
\proc{C}^{43} (i, j) & = &
  \left( Q_j.c.P_{i + 1}^O \rightarrow C^{00} (i + 1, j + 1) \right) \ndchoice
  \left( P_i.c.Q_{j + 1}^I \rightarrow C^{53} (i, j) \right) \\
\\
\proc{C}^{50} (i, j) & = &
  \left( P_{i - 1}.c.Q_j^I \rightarrow C^{51} (i, j) \right) \\
\proc{C}^{51} (i, j) & = & 
  \left( P_i.r.Q_j^O \rightarrow C^{52} (i, j) \right) \\
\proc{C}^{52} (i, j) & = &
  \left( P_i.r.Q_j^I \rightarrow C^{53} (i, j) \right) \\
\proc{C}^{53} (i, j) & = &
  \left( Q_j.c.P_i^O \rightarrow C^{03} (i, j + 1) \right)
\end{eqnarray*}

\end{document}

