ID Symbol Reducement 1 $\stackrel{3/2/o=1}{\overbrace{\left\{\mathbb{S}\right\}}}$  2 $\stackrel{2/1}{\overbrace{\left\{\mathbb{S}\right\}}}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}7& \begin{array}{cc}19& \begin{array}{cc}37& \begin{array}{cc}61& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}1& \begin{array}{cc}\begin{array}{c}+1\\ -1\end{array}& \begin{array}{cc}\begin{array}{c}+1\\ -1\end{array}& \cdots \end{array}\end{array}\end{array}\right\}\\ =\left\{\begin{array}{cc}1& \begin{array}{cc}6& \begin{array}{cc}12& \begin{array}{cc}18& \begin{array}{cc}24& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\end{array}$ 3 $\stackrel{1/0}{\overbrace{\left\{\mathbb{S}\right\}}}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}6& \begin{array}{cc}12& \begin{array}{cc}18& \begin{array}{cc}24& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}1& \begin{array}{cc}\begin{array}{c}+1\\ -1\end{array}& \begin{array}{cc}\begin{array}{c}+1\\ -1\end{array}& \cdots \end{array}\end{array}\end{array}\right\}\\ =\left\{\begin{array}{cc}1& \begin{array}{cc}5& \begin{array}{cc}6& \begin{array}{cc}6& \begin{array}{cc}6& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\end{array}$ 4 $\stackrel{0/\text{kernel}}{\overbrace{\left\{\mathbb{S}\right\}}}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}5& \begin{array}{cc}6& \begin{array}{cc}6& \begin{array}{cc}6& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}1& \begin{array}{cc}\begin{array}{c}+1\\ -1\end{array}& \begin{array}{cc}\begin{array}{c}+1\\ -1\end{array}& \cdots \end{array}\end{array}\end{array}\right\}\\ =〈\begin{array}{cc}1& \begin{array}{cc}4& \begin{array}{cc}1& \begin{array}{cc}0& \cdots \end{array}\end{array}\end{array}\end{array}〉\end{array}$ 5 $\stackrel{0/-1}{\overbrace{\left\{\mathbb{S}\right\}}}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}4& \begin{array}{cc}1& \begin{array}{cc}0& \cdots \end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}1& \begin{array}{cc}\begin{array}{c}+1\\ -1\end{array}& \begin{array}{cc}\begin{array}{c}+1\\ -1\end{array}& -1\end{array}\end{array}\end{array}\right\}\\ =\left\{\begin{array}{cc}1& \begin{array}{cc}3& \begin{array}{cc}-3& \begin{array}{cc}-1& \begin{array}{cc}0& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}4& \begin{array}{cc}1& \begin{array}{cc}0& \cdots \end{array}\end{array}\end{array}\end{array}\right\}\end{array}$ 6 $\stackrel{-1/-2}{\overbrace{\left\{\mathbb{S}\right\}}}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}3& \begin{array}{cc}-3& \begin{array}{cc}-1& \begin{array}{cc}0& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\oplus \left\{\begin{array}{cc}1& \begin{array}{cc}\begin{array}{c}+1\\ -1\end{array}& \begin{array}{cc}\begin{array}{c}+1\\ -1\end{array}& \begin{array}{cc}\begin{array}{c}+1\\ -1\end{array}& -1\end{array}\end{array}\end{array}\end{array}\right\}\\ =\left\{\begin{array}{cc}1& \begin{array}{cc}2& \begin{array}{cc}-6& \begin{array}{cc}2& \begin{array}{cc}1& 0\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\end{array}$ 7 $\stackrel{3/\mathrm{ker}}{\overbrace{\left\{\mathbb{S}\right\}}}$ 8 $=\left\{\begin{array}{ccc}0& 8& \begin{array}{ccc}-5& 4& -1\end{array}\end{array}\right\}$