$[15$pts$]$ Examine the constraint graph below, which has four variables $(x_1,x_2,x_3$ and $x_4)$ and the following three constraints:

x$1)x4$

$x_1=x4+-2($i$.$e$.,x1$ must be either $2$ more or $2$ less than $x4)$

$x4=x3+-2,($NOTE: Also implies $x4+-2=x3)$

$x2=x1+-2$

In addition, for all Xi $($e$.$g$.,$ X$1,$ X$2,$ X$3,$ X$4),$ the domains are:

$=\{0,1,2,3,4,5,6,7,8,9,10\}$

arc$-$consistency to eliminate domain values. In each row, please place the equation arc$-$consistency uses $($for that row$)$ to remove values in the "Evaluated" column.

It does NOT matter what order vou remove values but be sure to only remove values from one variable from line to line.

b$)$ What did you discover from performing arc$-$consistency in $($a$)?$ Should we pick a new variable to expand? If so$,$ which variable? If not, should we backtrack and what does that mean?