\documentclass{rtaloop}
\rtalabel{decreasing}

\begin{document}
\begin{problem}{V. van Oostrom}{}{June 1993}

\begin{abstract}
Does the Church-Rosser property of abstract reduction systems
imply decreasing Church-Rosser?
\end{abstract}

An abstract reduction system is ``decreasing Church-Rosser'', if there exists
a labelling of the reduction relation by a well-founded set of labels, such
that all local divergences can be completed to form a ``decreasing diagram''
(see \cite{Oost:91} for precise definitions). Does the Church-Rosser property
imply decreasing Church-Rosser? That is, is it always possible to localize the
Church-Rosser property? This is known to be the case for (weakly) normalizing
and finite systems.

\begin{remark}
It is now known to hold for countable systems 
\cite{Mano:93},\cite[Cor. 2.3.30]{Oost:94}.
\end{remark}

\end{problem}
\end{document}