In a quantitative sequential database, numerous efficient algorithms have been developed for high-utility sequential pattern mining (HUSPM). HUSPM establishes a relationship between frequency and significance in the real world and reflects more crucial information than frequent pattern mining. However, high average-utility sequential pattern mining (HAUSPM) is deemed fairer and more valuable than HUSPM. It provides a reasonable measure for longer patterns by considering their length. In contrast to scenarios in retail business analysis, some pattern mining applications, such as cybersecurity or artificial intelligence (AI), often involve much longer sequences. Consequently, pruning strategies can exert a more pronounced impact on efficiency. This paper proposes a novel algorithm named HAUSP-PG, which adopts two complementary strategies to independently process pattern prefixes and remaining sequences, thereby achieving a dual pruning effect. Additionally, the proposed method calculates average utility upper bounds without requiring item sorting, significantly reducing computational time and memory consumption compared to alternative approaches. Through experiments conducted on both real-life and synthetic datasets, we demonstrate that the proposed algorithm could achieve satisfactory performance.