After backtracking, the branch of the search tree that starts with x = 10 has been removed from the search tree. Solver has tried to find a solution in this branch and failed. The next move in the search strategy is to take variable x and assign it the lowest value in the domain of x, which is now [11 12]. Solver takes variable x and assigns it the value 11. Solver then searches for a solution in this branch of the search tree. The "test" or current domain of y includes the following values: 5, 6, and 7.

After this second search move, constraint propagation during search again removes values from the "test" or current domains that violate the constraints.

Examine the constraints. The search strategy has assigned the value 11 to the variable x. You try the value y = 5. This combination of values (x = 11, y = 5) violates the constraint x + y = 17. Solver removes the value y = 5 from the "test" or current domain of y. Next, you try the value y = 6. This combination of values (x = 11, y = 6) satisfies the constraint x + y = 17. This combination of values also satisfies the constraint x - y = 5.