It is a mixture of both in all cases. All of the cellulose from the asparagus is going to be excreted as feces. but the asparagus, just like any other food, is absolutely full of chemicals that your body can absorb in the intestines and stomach, and those end up in your blood, get processed, and any waste products eventually get excreted in your urine.
With asparagus, it is just that one of the chemicals in it is something your body cannot use, so it excretes it pretty quickly, and it has a distinctive smell.
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