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\title{Relative Normalization \\
in Higher-Order Rewriting Systems}
\author{John Glauert \\
School of Information Systems, UEA \\
Norwich NR4 7TJ England \\
J.Glauert@uea.ac.uk
\and
Zurab Khasidashvili   \\
NTT Basic Research Laboratories \\
Atsugi, Kanagawa 243-01 Japan \\
zurab@theory.brl.ntt.jp
\thanks{Part of this work was supported by the Engineering and Physical Sciences
Research Council of Great Britain under grant GR/H 41300.}
}

\date{}

\maketitle

\begin{abstract}

The Abstract.

\end{abstract}



\section{Picture}

Consider an OTRS $R=\{f(x)\ar g(x,h(x)),\,h(x)\ar c,\,a\ar b\}$ and a
term (redex) $u=f(a)$:
\begin{diagram}
f(a)   && \rTo^f    &             & g(a,h(a))  &         & \rTo^f &         & g(a,c) \\
       &&           & \ldTo^a     &            & \rdTo^a &        & \ruTo^h & \\
\dTo^a && g(b,h(a)) &             &            &         & g(a,h(b)) &   & \dTo_a \\
       &&           & \rdTo_{a} \rdTo(6,2)^h & & \ldTo_a &        &         & \\
f(b)   && \rTo_f    &             & g(b,h(b))  &         & \rTo_h &         & g(b,c) \\
\end{diagram}

Consider an OTRS $R=\{f(x)\ar g(x,h(x)),\,h(x)\ar c,\,a\ar b\}$ and a
term (redex) $u=f(a)$:
\begin{diagram}
f(a)    & \rTo  &           &             & g(a,h(a)) &       &        \\
\dTo    &       &           & \ldTo       & \dTo      & \rdTo &        \\
        &       & g(b,h(a)) &             & g(a,h(b)) & \rTo  & g(a,c) \\
        &       & \dTo      & \rdTo \ldTo &           & \ldTo &        \\
f(b)    & \rTo  & g(b,h(b)) & \rTo        & g(b,c)    &       &        \\
\end{diagram}


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