Halting problem
If running R and making it look at a copy of itself runs forever, then Q answered "no, if we run this program and make it look at a copy of itself it will not run forever". But Q said this when looking at R itself. So what Q actually said is: "no, if we run R and make it look at a copy of itself it will not run forever". So: If R running on a copy of itself runs forever, then it does not run forever. This is also impossible.