Stream reasoning is an emerging research area focused on providing continuous reasoning solutions for data streams. The exponential growth in the availability of streaming data on the Web has seriously hindered the applicability of state-of-the-art expressive reasoners, limiting their applicability to process streaming information in a scalable way. In this scenario, in order to reduce the amount of data to reason upon at each iteration, we can leverage advances in continuous query processing over Semantic Web streams. Following this principle, in previous work we have combined semantic query processing and nonmonotonic reasoning over data streams in the StreamRule system. In the approach, we specifically focused on the scalability of a rule layer based on a fragment of Answer Set Programming (ASP). We recently expanded on this approach by designing an algorithm to analyze input dependency so as to enable parallel execution and combine the results. In this paper, we expand on this solution by providing i) a proof of correctness for the approach, ii) an extensive experimental evaluation for different levels of complexity of the input program, and iii) a clear characterization of all the algorithms involved in generating and splitting the graph and identifying heuristics for node duplication, as well as partitioning the reasoning process via input splitting and combining the results.