Is it permissible to take back one's wife after divorcing her with a single pronouncement of divorce four years ago, or is this considered an irrevocable divorce?

It is clear that your wife has become irrevocably divorced from you. You are not permitted to take her back except with a new contract and dower, for she is now like any other unrelated woman. This is because her waiting period (iddah) has ended, either by delivering her burden if she was pregnant, or by three menstrual cycles if she was one who menstruates, or by three months if she was young and did not menstruate or elderly and had despaired of menstruation.