NP-hard is the class of problems that are at least as hard as NP. The halting problem is in there, but it isn't decidable _at all_. Just that its NP-hard doesn

NP-hard is the class of problems that are at least as hard as NP. The halting problem is in there, but it isn't decidable _at all_. Just that its NP-hard doesn't mean it's as hard as the halting problem, it could be easily decidable in exponential time. Complexity analysis is all about the size of the input, it doesn't ignore it.