$A$

$x$

$y$

$B$

$\tilde{y}$

$\tilde{x}$

$z$

$C=B^{-1}{y}^{-1}zyB$

$A_1={\tau }^2$

${\tau }^2$

${\sigma }^{-1}$

$\tau {\sigma }^2{\tau }^3{\sigma }^3=B_1$

${\sigma }^{-1}$

${\tau }^{-2}$

${\omega }_2^{-1}$

$C_1=B_1^{-1}\sigma {\omega }_2^{-1}{\sigma }^{-1}{B}_1$

$A_2=\text{empty}$

${\tau }^2$

${\sigma }^{-1}$

${\tau }^{-1}{\sigma }^2{\tau }^3{\sigma }^3=B_2$

${\sigma }^{-1}$

${\tau }^{-2}$

${\omega }_2^{-1}$

$C_2=B_2^{-1}\sigma {\omega }_2^{-1}{\sigma }^{-1}{B}_2$

$A_3={\sigma }^{-1}{\tau }^{-2}$

${\tau }^{-1}$

${\sigma }^2$

${\tau }^3{\sigma }^3=B_3$

${\sigma }^{-2}$

${\tau }^{-1}$

${\omega }_5$

$C_3=B_3^{-1}{\sigma }^{-2}{\omega }_5{\sigma }^2{B}_3$

$A_4={\sigma }^{-1}{\tau }^{-1}$

${\tau }^{-1}$

${\sigma }^{-2}$

${\tau }^2{\sigma }^3=B_4$

${\sigma }^2$

${\tau }^{-1}$

${\omega }_4$

$C_4=B_4^{-1}{\sigma }^2{\omega }_4{\sigma }^{-2}{B}_4$

$A_5={\sigma }^{-1}$

${\tau }^{-1}$

${\sigma }^2$

$\tau {\sigma }^3=B_5$

${\sigma }^{-2}$

${\tau }^{-1}$

${\omega }_5$

$C_5=B_5^{-1}{\sigma }^{-2}{\omega }_5{\sigma }^2{B}_5$