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Stream processing has become increasingly important as many emerging applications call for continuous real-time processing over data streams, such as voice-over-IP telephony, security surveillance, and sensor data analysis. In this paper, we propose a composable stream processing system for cooperative peer-to-peer environments. The system can dynamically select and compose stream processing elements located on different peers into user desired applications. We investigate multiple alternative approaches to composing stream applications: 1) global-state-based centralized versus local-state-based distributed algorithms for initially composing stream applications at setup phase. The centralized algorithm performs periodical global state maintenance while the distributed algorithm performs on-demand state collection. 2) Reactive versus proactive failure recovery schemes for maintaining composed stream applications during runtime. The reactive failure recovery algorithm dynamically recomposes a new stream application upon failures while the proactive approach maintains a number of backup compositions for failure recovery. We conduct both theoretical analysis and experimental evaluations to study the properties of different approaches. Our study illustrates the performance and overhead trade-offs among different design alternatives, which can provide important guidance for selecting proper algorithms to compose stream applications in cooperative peer-to-peer environments.