Let \(\Sigma \) be a finite alphabet, let \(M\) be a finite Turing machine over \(\Sigma \), and let \(f\) be a total function from strings over \(\Sigma \) to strings over \(\Sigma \). If \(M\) computes \(f\) — on every input \(x\) it halts, after some finite number of steps, with \(f(x)\) on its output tape, with no stated time bound — then there exists a function \(T : \mathbb {N} \to \mathbb {N}\) such that \(M\) computes \(f\) within time \(T\), i.e. on every input \(x\) the machine \(M\) halts with output \(f(x)\) within \(T(\left\lvert x\right\rvert )\) steps, where \(\left\lvert x\right\rvert \) is the length of \(x\). No monotonicity, positivity, or constructibility of \(T\) is claimed.