Question $9$:

Simulating a TM with a Semi$-$Thue System. In this problem, consider the Turing machine $M$ with $=\{0,1\},=\{0,1$lrcorner,$\},Q=\{s,q_{\text{a}\text{c}\text{c}\text{e}\text{p}\text{t}},q_{\text{r}\text{e}\text{j}\text{e}\text{c}\text{t}}\}$ and transitions

$s,$ddots,$s,,R$

$s,0,s,0,R$

$s,1,q_{\text{a}\text{c}\text{c}\text{e}\text{p}\text{t}},1,R$

Clearly, $|)$:$\}$ contains a $1$