\documentclass{rtaloop}
\rtalabel{string-onerule-nonlooping-nonterminating}


\begin{document}
\begin{problem}{Hans Zantema}{}{1999}

\begin{abstract}
  Is there a one-rule string rewriting system that is non-terminating
  but also non-looping?
\end{abstract}

Is there a one-rule string rewriting system that is non-terminating
but also non-looping, that is not allowing a rewrite sequence 
$ x \rightarrow^* uxv$ ?
Motivation and examples of two rule string rewriting
systems and a one rule term rewriting system that is non-terminating
and non-looping, can be found in \cite{ZG96}.

This problem is related to \rtaref{one} and \rtaref{string-rewriting}. More
about the history of this problem in the context of the question of one-rule
termination can be found in \cite{Dershowitz05OpenClosed}.
\end{problem}
\end{document}
