Solver has found a solution to the problem using a search strategy and constraint propagation during search. The combination of values (x = 11, y = 6) satisfies both constraints. There is no need to further explore the search tree because a solution has been found.

This simple example demonstrates the basic concepts of search strategies and constraint propagation. To summarize, solving a problem consists of finding a value for each decision variable while simultaneously satisfying the constraints. Solver uses two techniques to find a solution: search strategies and constraint propagation. Additionally, Solver performs two types of constraint propagation: initial constraint propagation and constraint propagation during search.

The initial constraint propagation removes all values from domains that will not take part in any solution. After initial constraint propagation, the search space is greatly reduced. This remaining part of the search space, where Solver will use a search strategy to search for a solution, is called the search tree. A search strategy is a way to "try" a value for a variable to see if this will lead to a solution. Solver performs constraint propagation during search. Constraint propagation during search removes all values from the current or "test" domains that violate the constraints. If Solver cannot find a solution in one branch of the search tree, Solver backtracks up the search tree. Backtracking gives Solver the flexibility to make search moves that can be wrong. An alternative can be tried and, if it does not succeed, can be reversed. Solver continues to search using the search strategy and constraint propagation during search until a solution is found.