Given a Turing Machine M and a string $x$ how do we tell whether a the Turing Machine M loops on the string $x$

Let us say there is a Turing Machine $M$ and a string $x$. So now I want to know if $M$ accepts or rejects the string or loops on it. So, I feed the string to $M$. So, if $M$ is accept or reject the string it would halt after a finite time and I would get my answer. But how do I know if the machine loops on the string or not.

One possible way is to see if a configuration repeats itself. However, the machine has no way of knowing if the configuration has occurred before because it cannot store them . So, we would never get an answer. So, how will I be able to tell whether or not $x$ is accpted or rejected or looped upon by $M$.

• This problem refers to the Halting problem . you can never make sure if the machine loops forever on a specific input String. You can only recognize this language , you cannot decide this language. Commented Nov 13, 2016 at 15:25
• Why do you think that your loop-testing TM couldn't store the configurations of the machine being tested? Conceptually, at least, you could store them on another tape. Commented Nov 13, 2016 at 21:41