Consider the following constraint satisfaction problem with four variables and three possible

values. Use the AC$3$ algorithm to demonstrate that no solution is possible:

Variables:

$$ X$1$: Domain $=\{1\}$

$$ X$2$: Domain $=\{1,2,3\}$

$$ X$3$: Domain $=\{1,2,3\}$

$$ X$4$: Domain $=\{3\}$

Constraints:

$1.$ X$1$ X$2$

$2.$ X$1$ X$3$

$3.$ X$2$ X$3$

$4.$ X$2$ X$4$

$5.$ X$3$ X$4$

Pop arcs from the queue in rank order:

Queue Arc Resulting Assignment

$1,2,3,4,51$ X$1=\{1\},$ X$2=\{2,3\},$ X$3=\{1,2,3\},$ X$4=\{3\}$

$2,3,4,52$