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

\begin{document}

\sloppy

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

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

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		\vrule width.#3pt}
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\newcommand{\proc}[1]{\mbox{\bf {#1}}}

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

%\section{Problem}

\begin{eqnarray*}
\proc{P}^0 (i) & = &
  \left( \Parallel_{k = 0}^{i - 2} \proc{STOP}_{\alpha (\proc{P}_k)} \right)
  \parallel
  \left( \Choice_{l = 0}^\infty P_{i - 1}.c.Q_l^I \rightarrow
	 P_{i}.r.Q_l^O \rightarrow \proc{STOP} \right)
  \parallel
  \left( \Parallel_{k = i}^\infty \proc{P}_k \right) \\
\proc{P}^1 (i, j) & = &
  \left( \Parallel_{k = 0}^{i - 2} \proc{STOP}_{\alpha (\proc{P}_k)} \right)
  \parallel
  \left( P_i.r.Q_j^O \rightarrow \proc{STOP} \right)
  \parallel
  \left( \Parallel_{k = i}^\infty \proc{P}_k \right) \\
\proc{P}^2 (i) & = &
  \left( \Parallel_{k = 0}^{i - 1} \proc{STOP}_{\alpha (\proc{P}_k)} \right)
  \parallel
  \left( \Parallel_{k = i}^\infty \proc{P}_k \right) \\
\proc{P}^3 (i, j) & = &
  \left( \Parallel_{k = 0}^{i - 1} \proc{STOP}_{\alpha (\proc{P}_k)} \right)
  \parallel
  \proc{P}_i^R (Q_j)
  \parallel
  \left( \Parallel_{k = i + 1}^\infty \proc{P}_k \right) \\
\proc{P}^4 (i, j) & = &
  \left( \Parallel_{k = 0}^{i - 2} \proc{STOP}_{\alpha (\proc{P}_k)} \right)
  \parallel
  \\ & &
  \left( \Choice_{l = 0}^\infty P_{i - 1}.c.Q_l^I \rightarrow
	 P_i.r.Q_l^O \rightarrow \proc{STOP} \right)
  \parallel
  \proc{P}_i^C (Q_{j + 1})
  \parallel
  \left( \Parallel_{k = i + 1}^\infty \proc{P}_k \right) \\
\proc{P}^5 (i, j) & = &
  \left( \Parallel_{k = 0}^{i - 2} \proc{STOP}_{\alpha (\proc{P}_k)} \right)
  \parallel
  \left( P_i.r.Q_j^O \rightarrow \proc{STOP} \right)
  \parallel
  \proc{P}_i^C (Q_{j + 1})
  \parallel
  \left( \Parallel_{k = i + 1}^\infty \proc{P}_k \right) \\
\proc{P}^6 (i, j) & = &
  \left( \Parallel_{k = 0}^{i - 1} \proc{STOP}_{\alpha (\proc{P}_k)} \right)
  \parallel
  \proc{P}_i^C (Q_{j + 1})
  \parallel
  \left( \Parallel_{k = i + 1}^\infty \proc{P}_k \right) \\
\proc{P}^7 (i, j) & = &
  \left( \Parallel_{k = 0}^{i - 1} \proc{STOP}_{\alpha (\proc{P}_k)} \right)
  \parallel
  \left( Q_j.c.P_i^O \rightarrow \proc{P}_i^R (Q_{j + 1}) \right)
  \parallel
  \left( \Parallel_{k = i + 1}^\infty \proc{P}_k \right) \\
\end{eqnarray*}

\begin{displaymath}
\begin{array}{lcl}
\proc{P}^0 (i) / \langle P_{i - 1}.c.Q_j^I    \rangle & = & \proc{P}^1 (i, j) \\
\proc{P}^1 (i, j) / \langle P_i.r.Q_j^O       \rangle & = & \proc{P}^2 (i) \\
\proc{P}^2 (i) / \langle P_i.r.Q_j^I          \rangle & = & \proc{P}^3 (i, j) \\
\proc{P}^3 (i, j) / \langle Q_j.c.P_{i + 1}^O \rangle & = & \proc{P}^0 (i + 1) \\
\\
\proc{P}^0 (i) / \langle P_i.c.Q_{j + 1}^I    \rangle & = & \proc{P}^4 (i, j) \\
\proc{P}^1 (i, j) / \langle P_i.c.Q_{j + 1}^I \rangle & = & \proc{P}^5 (i, j) \\
\proc{P}^2 (i) / \langle P_i.c.Q_{j + 1}^I    \rangle & = & \proc{P}^6 (i, j) \\
\proc{P}^3 (i, j) / \langle P_i.c.Q_{j + 1}^I \rangle & = & \proc{P}^7 (i, j) \\
\\
\proc{P}^4 (i, j) / \langle P_{i - 1}.c.Q_j^I \rangle & = & \proc{P}^5 (i, j) \\
\proc{P}^5 (i, j) / \langle P_i.r.Q_j^O       \rangle & = & \proc{P}^6 (i) \\
\proc{P}^6 (i, j) / \langle P_i.r.Q_j^I       \rangle & = & \proc{P}^7 (i, j) \\
\proc{P}^7 (i, j) / \langle Q_j.c.P_i^O       \rangle & = & \proc{P}^3 (i, j + 1)
\end{array}
\end{displaymath}

\newpage

\begin{eqnarray*}
\proc{Q}^0 (j) & = &
  \left( \Parallel_{k = 0}^{j - 2} \proc{STOP}_{\alpha (\proc{Q}_k)} \right)
  \parallel
  \left( \Choice_{l = 0}^\infty Q_{j - 1}.c.P_l^I \rightarrow
	 Q_{j}.r.P_l^O \rightarrow \proc{STOP} \right)
  \parallel
  \left( \Parallel_{k = j}^\infty \proc{Q}_k \right) \\
\proc{Q}^1 (j, i) & = &
  \left( \Parallel_{k = 0}^{j - 2} \proc{STOP}_{\alpha (\proc{Q}_k)} \right)
  \parallel
  \left( Q_j.r.P_i^O \rightarrow \proc{STOP} \right)
  \parallel
  \left( \Parallel_{k = j}^\infty \proc{Q}_k \right) \\
\proc{Q}^2 (j) & = &
  \left( \Parallel_{k = 0}^{j - 1} \proc{STOP}_{\alpha (\proc{Q}_k)} \right)
  \parallel
  \left( \Parallel_{k = j}^\infty \proc{Q}_k \right) \\
\proc{Q}^3 (j, i) & = &
  \left( \Parallel_{k = 0}^{j - 1} \proc{STOP}_{\alpha (\proc{Q}_k)} \right)
  \parallel
  \proc{Q}_j^R (P_i)
  \parallel
  \left( \Parallel_{k = j + 1}^\infty \proc{Q}_k \right) \\
\proc{Q}^4 (j, i) & = &
  \left( \Parallel_{k = 0}^{j - 2} \proc{STOP}_{\alpha (\proc{Q}_k)} \right)
  \parallel
  \\ & &
  \left( \Choice_{l = 0}^\infty Q_{j - 1}.c.P_l^I \rightarrow
	 Q_j.r.P_l^O \rightarrow \proc{STOP} \right)
  \parallel
  \proc{Q}_j^C (P_{i + 1})
  \parallel
  \left( \Parallel_{k = j + 1}^\infty \proc{Q}_k \right) \\
\proc{Q}^5 (j, i) & = &
  \left( \Parallel_{k = 0}^{j - 2} \proc{STOP}_{\alpha (\proc{Q}_k)} \right)
  \parallel
  \left( Q_j.r.P_i^O \rightarrow \proc{STOP} \right)
  \parallel
  \proc{Q}_j^C (P_{i + 1})
  \parallel
  \left( \Parallel_{k = j + 1}^\infty \proc{Q}_k \right) \\
\proc{Q}^6 (j, i) & = &
  \left( \Parallel_{k = 0}^{j - 1} \proc{STOP}_{\alpha (\proc{Q}_k)} \right)
  \parallel
  \proc{Q}_j^C (P_{i + 1})
  \parallel
  \left( \Parallel_{k = j + 1}^\infty \proc{Q}_k \right) \\
\proc{Q}^7 (j, i) & = &
  \left( \Parallel_{k = 0}^{j - 1} \proc{STOP}_{\alpha (\proc{Q}_k)} \right)
  \parallel
  \left( P_i.c.Q_j^O \rightarrow \proc{Q}_j^R (P_{i + 1}) \right)
  \parallel
  \left( \Parallel_{k = j + 1}^\infty \proc{Q}_k \right) \\
\end{eqnarray*}

\begin{displaymath}
\begin{array}{lcl}
\proc{Q}^0 (j) / \langle Q_{j - 1}.c.P_i^I    \rangle & = & \proc{Q}^1 (j, i) \\
\proc{Q}^1 (j, i) / \langle Q_j.r.P_i^O       \rangle & = & \proc{Q}^2 (j) \\
\proc{Q}^2 (j) / \langle Q_j.r.P_i^I          \rangle & = & \proc{Q}^3 (j, i) \\
\proc{Q}^3 (j, i) / \langle P_i.c.Q_{j + 1}^O \rangle & = & \proc{Q}^0 (j + 1) \\
\\
\proc{Q}^0 (j) / \langle Q_j.c.P_{i + 1}^I    \rangle & = & \proc{Q}^4 (j, i) \\
\proc{Q}^1 (j, i) / \langle Q_j.c.P_{i + 1}^I \rangle & = & \proc{Q}^5 (j, i) \\
\proc{Q}^2 (j) / \langle Q_j.c.P_{i + 1}^I    \rangle & = & \proc{Q}^6 (j, i) \\
\proc{Q}^3 (j, i) / \langle Q_j.c.P_{i + 1}^I \rangle & = & \proc{Q}^7 (j, i) \\
\\
\proc{Q}^4 (j, i) / \langle Q_{j - 1}.c.P_i^I \rangle & = & \proc{Q}^5 (j, i) \\
\proc{Q}^5 (j, i) / \langle Q_j.r.P_i^O       \rangle & = & \proc{Q}^6 (j) \\
\proc{Q}^6 (j, i) / \langle Q_j.r.P_i^I       \rangle & = & \proc{Q}^7 (j, i) \\
\proc{Q}^7 (j, i) / \langle P_i.c.Q_j^O       \rangle & = & \proc{Q}^3 (j, i + 1)
\end{array}
\end{displaymath}

\end{document}

