System to validate run time complexity requirements TL;DR: Do you know of a method/system that can determine the run time complexity of code automatically?

At our university we have a system in place that allows students to submit their code and get feedback on whether or not they satisfy the functional requirements of the exercise.
This is excellent and works well for many of our courses, especially the introductory courses.

We also use it for courses that teach more advanced algorithmic concepts, focusing on run time. We have exercises that ask them to implement for example dynamic programming solutions in $O(n^2)$ time.
Currently we use the automated tests to check for the functional requirements and have some tests with larger datasets and a time out to hopefully distinguish between $O(n^3)$ and $O(n^2)$ solutions.

Perhaps to nobody's surprise this system is not perfect, with some students optimising the wrong parts of their code to hand in an $O(n^3)$ (or worse) solution and get it through the tests. Thus for the graded assignments our TAs also check all of these by hand to make sure the solution is really $O(n^2)$ and they deduct some points if it is not.

My question is, do you know of systems or methods that can automatically check the run time complexity of code (in terms of big-O), rather than the actual run time (in seconds)?

In case this is relevant: the programming language used at our university is Java.

(NB: I've seen this question and appreciate the concerns about including this in grading. For introductory courses I would not do this. For the courses that focus on finding the most efficient algorithm to solve problems however it is one of the learning objectives :))
Buffy is provably correct (no risk needed!) that it is impossible to do it with automated code analysis, as this is an attempt to figure out when a program will finish (i.e. the halting problem.)

You can get a very good guess, however, by using a few (very) differently sized input data sets, run the program on each one multiple times, and observe the results on a graph.  This is fairly trivial for a human, and takes very little time.  It may be less trivial for an automated statistical analysis, but I will defer to other who know more about such things to decide whether that is possible or not.