In other words, using the example wiki gives me, what's the difference between deal with the problem and swim in the pool "You must deal with the problem ". The essential difference between a complement of a verb and an adverbial is that obligatory elements are always complements (they are needed to complete the verb phrase), whereas optional elements may be complements or adverbials. In that example, the PP "with the problem" is essential for this sense of "deal", meaning something like 'cope with' or 'put right'.
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Anonymous am a little confuse about 2 and 3.What is the difference between a complement of a verb and an adverb phrase of a verb?In other words, using the example wiki gives me, what's the difference between deal with the problem and swim in the pool"You must deal with the problem".