If two particles, accelerated by a particle accelerator, collide together when they are individually very close to speed of light, so when they collide their relative speed will be more than the speed of light. So the two particles will collide at a speed more than the speed of $c$. So what will happen?
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As per our currently accepted theories, including SR, no particle can travel faster then light.
In your case, the particles themselves travel near the speed of light each.
AS per SR, their relative speed does not matter. There is no contradiction with SR, since, in your case, no particle travels faster then light.
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