Yes, definitely. But then the next task is just to solve the incompleteness problem on the level of the higher algorithm, because there must always be incomplet

Yes, definitely. But then the next task is just to solve the incompleteness problem on the level of the higher algorithm, because there must always be incompleteness. Hofstaedter discusses this at length in his book Gödel, Escher, Bach if you are interested in this topic.