"Parallel reduction arrow": -//->

I would use my favourite \mathcenterto{#1}{#2} construct which allows you to center #1 over #2. One additional \mathclap makes the right-side slash centered and the left-side one adjacent to it.

\documentclass{article}

\pagestyle{empty}

\usepackage{mathtools}

\newcommand*\mathcenterto[2]{\mathclap{\phantom{#2}\mathclap{#1}}{#2}}
\newcommand*\rpbeta{\mathrel{\mathcenterto{\mathclap{/}/}{\longrightarrow}}_\beta}

\begin{document}

\[
A \rpbeta B
_{A \rpbeta B
_{A \rpbeta B
_{A \rpbeta B
}}}\]

\end{document}

You can emulate the working of \centernot:

\documentclass{article}

\makeatletter
\newcommand{\rpgeneric}[1]{\mathpalette\rp@generic{#1}}
\newcommand{\rp@generic}[2]{%
  \mathrel{%
    \rlap{%
      \settowidth\dimen@{$\m@th#1{\longrightarrow}$}%
      \kern.55\dimen@
      \settowidth\dimen@{$\m@th#1=$}%
      \kern-.53\dimen@
      $\m@th#1\not$%
      \kern-.3\dimen@
      $\m@th#1\not$%
    }%
    {\longrightarrow_{#2}}%
  }%
}
\makeatother
\newcommand{\rpbeta}{\rpgeneric{\beta}}

\begin{document}

$\rpbeta_{\rpbeta}$

\end{document}

In addition to the mathtools package, I would use amsmath.txfonts with the following code (however the fonts could create some other problems elesewhere in the text...)

\documentclass{article}
\usepackage{amsmath,txfonts}
\usepackage{mathtools}
\begin{document}
$\mathrlap{\longrightarrow}\varparallel$
\end{document}