This is a question from an exam I did today:
Given $M$, a turing machine, we need to decide the following:
1) $M$ halts on every input
2) The language of $M$ is CFL
My question is, can I prove that this problem is not in $RE$ (recursively enumerable) using Rice's theorem? I understand that Rice's theorem works for languages and not machines, and when first looking at it, number 1 is a property of a machine not the language. But what I said, is that actually it is a property of a language: $M$ halts on every input iff $L(M)$ is decidable! (in $R$), so we can use Rice.
What do you think?