\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{braids}

\begin{document}
\begin{tikzpicture}[scale=0.4, every node/.style={scale=0.4}]
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 4,
  name prefix=braid,
] at (-0.25,0) {braid={
s_3^{-1}
s_2^{-1}
s_1^{-1}-s_3^{-1}
s_2^{-1}
s_1^{-1}-s_3^{-1}
s_2^{-1}
s_1^{-1}-s_3^{-1}
s_2^{-1}
s_1^{-1}
111
111111111
}};
\draw[dashed,draw=black, very thick, fill=white] (10-0.5,0-0.25) rectangle ++(2,3.5);
\node at (10.5,-1.6) {\fontsize{40pt}{\baselineskip}\selectfont $=$};
\begin{scope}[shift={(0,-6)}]
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 4,
  name prefix=braid,
] at (-0.25,0) {braid={
111111111
111
s_3^{-1}
s_2^{-1}
s_1^{-1}-s_3^{-1}
s_2^{-1}
s_1^{-1}-s_3^{-1}
s_2^{-1}
s_1^{-1}-s_3^{-1}
s_2^{-1}
s_1^{-1}
}};
\draw[dashed,draw=black, very thick, fill=white] (10-0.5,0-0.25) rectangle ++(2,3.5);
\end{scope}
\end{tikzpicture}
\end{document}