Is one's responsibility discharged and the make-up of prayers waived if it is highly probable that there are no missed prayers?

Whoever has a number of unknown prayers due should make them up until he is reasonably certain that he has fulfilled his obligation. And whoever doubts whether he has performed a prayer must make it up, unless he suffers from obsessive doubts (waswas). According to the Hanafis, if one doubts after the time for the prayer has expired, one is not obligated to make it up. If a worshipper has a strong presumption that he has prayed, this is considered like certainty and absolves him of responsibility. As for the one who suffers from obsessive doubts, no attention should be paid to his doubts.