the program, operating on the input, will eventually stop or will continue forever. It is trivial to create an algorithm that can do this for some inputs, but impossible to do this in general. For any characteristic of the program's eventual output, it is impossible to determine whether this characteristic will hold.

This impossibility poses problems when analyzing real-world computer programs. For example, one cannot write a tool that entirely protects programmers from writing infinite loops or protects users from supplying input that