Rational Tangles

In this playful arcade game, you control the movements of four “soldiers” standing in a square, holding the ends of two ropes.  By repeatedly executing two moves, a clockwise “Twist,” and a clockwise “Rotate,” the soldiers create what may appear to be a hopeless tangle.  Can you help them untangle the ropes, not by reversing the moves (not allowed!), but by adding more twists and rotations?

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