{"id":"water-bottles-loop-terminates","text":"The water bottles simulation loop terminates for all valid inputs because `empties` strictly decreases each iteration when `numExchange >= 2`.","truth_value":"IN","source":"entries/2026/06/06/water-bottles-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"water-bottles-loop-terminates","truth_value":"IN","reason":"premise"}]}}