$\text{Example}:$ Let $x$ and $y$ be two positive integers represented in unary notation. Construct a Turing machine that will halt in a final state $q_y$ if $x\geq y,$ and that will halt in a nonfinal state $q_n$ if $x < y.$ More specifically, the machine is to perform the computation
$q_0w(x)0w(y) \vdash^* q_yw(x)0w(y)$ if $x\geq y$,
$q_0w(x)0w(y) \vdash^* q_nw(x)0w(y)$ if $x < y$,
Complete all the details in Example
