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Who knows? Perhaps Aragorn's healing powers extend to mental healing. Denethor has been a good Steward in his time. His son's death and the Palantir between them have helped drive him over the edge, though, yes, he does have a long, long resentment.
In any case, I can't see Aragorn executing him. I find it easier to imagine the healing hands of the King managing to heal his mind.
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