The possibility of associating a constraint with a node while some of its variables are not effectively associated with the node may produce a width that is less than query width. For example, if a node is associated to formula_19 in a query decomposition, and a constraint formula_20 exists, a hypertree decomposition can associate the same node with constraints formula_21 and variables formula_22. Since only constraints are computed when checking width, this node has width two. The same node has width four when using query decomposition (one constraint and three variables). This width reduction is possible if two or more variables can be replaced with a single constraint, even if this constraint contains a variable that is not associated with the node.