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Business process management, service-oriented architectures and software back-engineering heavily rely on the fundamental processes of mining of processes and web service business protocols from log files. Model extraction and mining aim at the (re)discovery of the behavior of a running model implementation using solely its interaction and activity traces, and no a priori information on the target model. This paper presents an approach for correlating messages and extracting the business protocol of a web service in the realistic scenario in which correlation information is entirely absent from interaction and activity logs. Correlation is achieved through deterministic computations that result in an extremely efficient method whose extensive experiments have shown its solid reliability, robustness when dealing with complex structures, and very high performance and scalability. This approach and the underlying algorithms extend what is actually possible to achieve in the web service business protocol mining domain using incomplete and noisy data logs, and opens new horizons in back-engineering of web services. The theoretical and experimental results clearly show the leap forward achieved herein.