I have to find out whether the language $J_1=\{0^n1^n0^n \mid n \in \mathbb{N}\}$ and $J^{c}_{1}$ is recursively enumerable.I already know that $J_1$ is RE, because I have found Turing machine which accepts $J_1$.I would also like to prove this for  $J^{c}_{1}$ by using the following theorem:$J\in RE \wedge J^{c} \in RE \Leftrightarrow J \in Rec$.So I have to prove that $J_1 \in Rec$. I have already tried but I am stuck. Can anybody please help me?
Is the language $0^n 1^n 0^n$ recursive?
formal languages;computability