Non-termination is a fundamental property of turing machines; after all, if all programs terminate, a halting problem decider is trivial to write. While you cou

Non-termination is a fundamental property of turing machines; after all, if all programs terminate, a halting problem decider is trivial to write. While you could certainly argue that the CSS + human system is a turing-complete system, the CSS is a bit superfluous there; the human could just be doing all the work on their own. As such, when a language or system is proven to be turing complete, it generally has to be shown to emulate another turing-complete system _until termination_ without external assistance.