"Recumbent bike" is just that. It has nothing to do with an exercise bike other than the body position you would be operating it in. Maybe that's why it's called a "Recumbent Exercise Cycle."
If you want to get technical, I guess I'd call it a "stationary" recumbent bike. Because, couldn't any bike be used for exercise? Just as you claim body position has nothing to do with the type of bike, the same thing could be said about "exercise" or "pleasure."
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