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The goal of high-utility sequential pattern mining (HUSPM) is to efficiently discover profitable or useful sequential patterns in a large number of sequences. However, simply being aware of utility-eligible patterns is insufficient for making predictions. To compensate for this deficiency, high-utility sequential rule mining (HUSRM) is designed to explore the confidence or probability of predicting the occurrence of consequence sequential patterns based on the appearance of premise sequential patterns. It has numerous applications, such as product recommendation and weather prediction. However, the existing algorithm, known as HUSRM, is limited to extracting all eligible rules while neglecting the correlation between the generated sequential rules. To address this issue, we propose a novel algorithm called correlated high-utility sequential rule miner (CoUSR) to integrate the concept of correlation into HUSRM. The proposed algorithm requires not only that each rule be correlated but also that the patterns in the antecedent and consequent of the high-utility sequential rule be correlated. The algorithm adopts a utility-list structure to avoid multiple database scans. Additionally, several pruning strategies are used to improve the algorithm's efficiency and performance. Based on several real-world datasets, subsequent experiments demonstrated that CoUSR is effective and efficient in terms of operation time and memory consumption.