\documentclass{rtaloop}
\rtalabel{strong}

\begin{document}
\begin{problem}{Michio Oyamaguchi}{}{June 1993} 

\begin{abstract}
Is any ``strongly'' non-overlapping right-linear term-rewriting system
confluent?
\end{abstract}

Is any ``strongly'' non-overlapping right-linear term-rewriting system
confluent? (``Strong'' in the sense that left-hand sides are non-overlapping
even when the occurrences of variables have been renamed apart
\cite{C81:stoc}.) On the one hand, strongly non-overlapping systems need not
be confluent \cite{H80:jacm}; on the other hand, strongly non-overlapping
right-ground systems are \cite{OO93:ieice}.

\begin{remark}
A partial positive solution is given in \cite{Ohta94}\cite{Toyama94}, namely,
any strongly non-overlapping right-linear term-rewriting system is confluent
if it satisfies the condition that for any rewrite rule, no variables
occurring more than once in the left-hand-side occur in the right-hand-side.
\end{remark}

\end{problem}
\end{document}
