A Simple Predicate to Expedite the Termination of a Randomized Consensus Algorithm Consensus is one of the most important problems encountered in fault-tolerant distributed computing. Basically, consensus allows processes to agree on a common value. Unfortunately, no deterministic algorithm can solve this problem in an asynchronous message-passing system prone to process crash failures. One way to circumvent this impossibility, consists in enriching the system with random numbers and design a randomized algorithm. This paper considers such a consensus algorithm and presents a simple predicate that allows to expedite its termination.