We consider the consensus problem in a message-passing system where processes can crash: Each process has an input, and each correct process must decide on an output, such that all correct processes decide on the same output, and this output is the input of one of the processes. Consensus is an important building block for fault-tolerant systems. It is well-known that consensus is not solvable in an asynchronous model even if only one process can crash [7.13]. However, real systems are not completely asynchronous. Some partially synchronous models [7.12], [7.10] where consensus is solvable better approximate real systems.We consider a partial synchronymodel defined as follows [7.12]¹: (1) processes have bounded drift clocks; (2) there are known bounds on processing times and message delays; and (3) less than half of the processes can crash. In addition, this model allows the system to be unstable, where the bounds in (2) do not hold for an unbounded but finite period, but it must eventually enter a stableperiod where the bounds do hold.A consensus algorithm for the partial synchrony model never violates safety, and guarantees liveness once the system becomes stable. Algorithms for this model are called indulgent in [7.16]. What can we say about the running time of consensus algorithms in a partial synchrony model? Unfortunately, even in the absence of failures, any consensus algorithm in this model is bound to have unbounded running times, by [7.13].