\newcommand{\Nats}[0]{\ensuremath{\mathbb{N}}}

\begin{Theorem}{}
  Given an initial  configuration $X^0 =  (X_1^0, \ldots, X_n^0)$  and a
  strategy  $(J^t)^{t  \in \Nats}$.   If chaotic iterations with  strategy
  $(J^t)^{t \in \Nats}$ converge to some fixed-point, then mixed iterations with
  uniform delays  with the same strategy  $(J^t)^{t \in \Nats}$  converge to the
  same fixed-point.
\end{Theorem}
\begin{Proof}
\begin{itemize}
\item Element renaming wrt. a partial order
\item Induction on the SCC index  
\end{itemize}
\end{Proof}