quality:corruption
Halting on all inputs

The universal halting problem, also known (in recursion theory) as totality, is the problem of determining whether a given computer program will halt for every input (the name totality comes from the equivalent question of whether the computed function is total).This problem is not only undecidable, as the halting problem is, but highly undecidable. In terms of the arithmetical hierarchy, it is Π 2 0 {\displaystyle \Pi _{2}^{0}} -complete.

This means, in particular, that it cannot be decided even with an oracle for the halting problem.