In the cryptarithmetic problem below, the aim is to find a substitution of digits for the letters T, W, O, F, U, and R such that each letter stands for a different digit, and the resulting sum is arithmetically correct. The leading letters T and F cannot be 0. Auxiliary variables x1, x2 and x3 are introduced for representing carry overs. The domains for the variables and the constraints for the problem are specified below.

Domains:
x3 x2 x1 x3, F: {1}
TWO + x1, x2: {0,1}
TWO R: {0,2,4,6,8)
F OUR T: {5,6,7,8,9)
W, 0, U: {0,2,3,4,5,6,7,8,9}
Constraints:
Aldiff (F, T,U, W,R, O)
0 +0 = R + 10 x X1
X1 + W + W = U + 10 x X2
X2 + T + T = 0 + 10

(a) Which variables are the neighbors of variable x1?
(b) Which variables are the neighbors of variable T?
(c) Since x3 and F only have one value in their domain, they will be chosen first by the Backtracking Algorithm for CSP and be assigned the value 1. Use the Most Constrained Variable (Minimum Remaining Value) and Most Constraining Variable (Degree) heuristics to choose the next variable to work on by the Backtracking Algorithm. Assume that the Backtracking Algorithm does not use Forward Checking or the AC-3 algorithm to eliminate values from the variables' domains. Show work.
(d) At which level of the search tree do we expect to find a solution for the problem? (Assume that level 0 is for empty assignment, level 1 is for assigning 1 to variable F and level 2 is for assigning 1 to variable x3.)