Is it permissible to be content with performing the obligatory prayer once and making the extra prayers supererogatory, after the worshiper used to perform the obligatory prayer twice as compensation for missed prayers and then neglected that?

Prayer is of great importance, and abandoning it is a major sin. One must repent from any negligence in it and make up all missed prayers, whether missed intentionally or unintentionally. If the number of missed prayers is unknown, then one should make up what is most likely the number of those missed. If you have performed what you predominantly believe to be the amount due from you, then you have fulfilled your obligation, and there is no impediment to engaging in supererogatory prayers. If a predominant belief is not achieved, then continue making up prayers until it is.