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Mining web access sequences can discover very useful knowledge from web logs with broad applications. By considering non-binary occurrences of web pages as internal utilities in web access sequences, e.g., time spent by each user in a web page, more realistic information can be extracted. However, the existing utility-based approach has many limitations such as considering only forward references of web access sequences, not applicable for incremental mining, suffers in the level-wise candidate generation-and-test methodology, needs several database scans and does not show how to mine web traversal sequences with external utility, i.e., different impacts/significances for different web pages. In this paper, we propose a new approach to solve these problems. Moreover, we propose two novel tree structures, called UWAS-tree (utility-based web access sequence tree), and IUWAS-tree (incremental UWAS tree), for mining web access sequences in static and dynamic databases respectively. Our approach can handle both forward and backward references, static and dynamic data, avoids the level-wise candidate generation-and-test methodology, does not scan databases several times and considers both internal and external utilities of a web page. Extensive performance analyses show that our approach is very efficient for both static and incremental mining of high utility web access sequences.