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The completion time of the MongoDB Aggregate pipeline depends on various factors such as the size of the data being processed, the number of stages in the pipeline, the complexity of the queries used, and the resources available on the server where the pipeline is being executed. It is not possible to provide a specific time frame for the completion of the pipeline as it varies from case to case. However, MongoDB's aggregate pipeline uses highly optimized algorithms for processing data, and with proper indexing and query optimization, the pipeline can process large datasets in a matter of seconds.