Let $L=\{win\{a,b{\}}^{+}$:$n_b(w)=2^{**}{n}_a(w)\}$ be a language with $=\{a,b\}.$ Note that

$w=$ bababb and $w=$babinL.

a$)$ Create a Turing Machine plan for a Turing machine that accepts L$.$ Give the

basic steps that the machine uses to accept a string in $L.$ Do not create the

actual machine. $[$Hint: for every a in $w,$ there are $2b\text{'}$s in w $]$

b$)$ To illustrate your Turing Machine design, show how the tape changes at each

major step as $M$ processes the input $w=$ baabbb