Problem $6($Design only$)$

a$.$ Clearly describe in English a plan for a Turing Machine $M$ that accepts

$L=\{win\{a,{\}}^{+}$:$n_3(w)=n{b}_b(w)\}.$ Note that $w=$ bbabaa inL.

b$.$ Illustrate how your TM plan in Part a changes the $\frac{r}{w}$ tape if the input is $w=$ baabab.

Show all main steps. Show that $w=$ baabab is accepted

c$.$ Illustrate how your TM plan in Part a changes the $\frac{r}{w}$ tape if the input is $w=$baaab

Show all main steps. Show that $w=$ baaab is rejected.