It’s not necessary to use recursion. Simple logic solves it. If a or c are true, that implies a and c are not true. If b is true, that implies b isn’t true. If d is true, that implies d isn’t true. No recursion needed and this is complete. You could take a recursive approach, but it doesn’t halt, like you said, so it doesn’t give a result.

(Also, the halting problem is determining if something halts, not what the value is at the end. This problem does not halt, if done recursively. The halting problem is easy to resolve for this particular problem.)