What is the ruling on rhyming with verses from the Holy Quran for the purpose of remembrance and filling time, without degradation?

There is no objection to using aids to memorize and master the Quran, such as competitions, memorization tests, and attention to similar verses. This is recommended to solidify and strengthen memorization, and it includes responsive recitations (musaajalaat) which oblige the memorizer to produce a verse that begins with the letter that ended the previous verse.