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For many practical systems that are required to perform critical tasks, it is commonly observed that tasks can be performed multiple times within a limited time to improve task success probability. Such property is referred to as time redundancy. This paper contributes by studying the optimal adaptive maintenance and the task abort strategies of continuously degraded systems considering two kinds of time redundancy to improve system safety and task reliability. The task abort decision is considered dynamically according to the degradation level and the number of task attempts. Task success probability and system survival probability under two kinds of time redundancy are evaluated using an event-based numerical algorithm. The optimal imperfect maintenance and task abort thresholds are investigated dynamically in each attempt to minimize the expected total cost of maintenance, task failure and system failure. The established model in this study is illustrated by numerical results.