I want to prove that the problem described here
Of course it is in NP, but what problem would be appropriate to reduce to prove NP-Hardness? And how would that work?
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The question you link to shows that the problem can be solved in polynomial time. If the problem was NP-complete, then this would prove that P = NP. Of course, it's a famous open problem to prove that P = NP or P != NP. Therefore, you shouldn't expect anyone to know of any such proof.
Also, many computer scientists expect P != NP; if they're right, then the problem you list is not NP-complete.