The state machine approach is a well-known technique for building distributed services requiring high performance and high availability, by replicating servers, and by coordinating client interactions with server replicas using consensus. Indulgent consensus algorithms exist for realistic eventually partially synchronous models, that never violate safety and guarantee liveness once the system becomes synchronous. Unavoidably, these algorithms may never terminate, even when no processor crashes, if the system never becomes synchronous. This paper proposes a mechanism similar to state machine replication, called RC-simulation, that can always make progress, even if the system is never synchronous. Using RC-simulation, the quality of the service will adjust to the current level of asynchrony of the network --- degrading when the system is very asynchronous, and improving when the system becomes more synchronous. RC-simulation generalizes the state machine approach in the following sense: when the system is asynchronous, the system behaves as if k+1 threads were running concurrently, where k is a function of the asynchrony. In order to illustrate how the RC-simulation can be used, we describe a long-lived renaming implementation. By reducing the concurrency down to the asynchrony of the system, RC-simulation enables to obtain a renaming quality that adapts linearly to the asynchrony.