Add to ORKGInternational audienceBroken triangles constitute an important concept not only for solving constraint satisfaction problems in polynomial time, but also for variable elimination or domain reduction by merging domain values. Specifically, for a given variable in a binary arc-consistent CSP, if no broken triangle occurs on any pair of values, then this variable can be eliminated while preserving satisfiability. More recently, it has been shown that even when this rule cannot be applied, it could be possible that for a given pair of values no broken triangle occurs. In this case, we can apply a domain-reduction operation which consists in merging these values while preserving satisfiability. In this paper we show that under certain conditi...