An undecidable problem is a problem that is not decidable. Problems that are not decidable are "undecidable". Partially decidable problems and any other problems that are not decidable are called undecidable. In general, being recursively enumerable is a weaker condition than being a decidable set. This subset of higher-order unification is decidable and solvable unification problems have most-general unifiers. The Halting problem is decidable for lossy Turing machine but nonprimitive recursive. For example one may speak of languages decidable on a non-deterministic Turing machine. Unlike Peano arithmetic, Presburger arithmetic is a decidable theory. The following are some decidable problems about context-free grammars. This fact allowed Tarski to prove that Euclidean geometry is decidable. Equivalence is decidable for it, while inclusion is not. The kernel is then solved by the algorithm that proves that the problem is decidable. A decision problem which can be solved by an algorithm is called "decidable". This technique can be used to show that Presburger arithmetic is decidable. Ax proved that the theory is decidable.