Tree decomposition is a well-known concept from graph theory. Reformulated in terms of binary constraints, a tree decomposition is a tree whose nodes are associated to sets of variables; the scope of each constraint is contained in set of variables of some node, and the subtree of nodes associated to each variable is connected. This is the most general form of decomposition for binary constraints that follows the scheme outlined above, as the conditions imposed on the tree are only the ones that are necessary to guarantee equivalent of the original and new problem.