I don't understand your point. I could run it with memory constrained to, say, 100 KB, and it will quickly produce an OOM condition. I clearly said that the approach I sketched in my first comment is not practically applicable.

Real-life computers have bounded memory, so they don't have any more computational power than, say, regular expressions matchers -- every computational task performed by real computer can be represented by appropriately complicated regular expression. That's why one needs to be especially careful when arguing from computability when talking about real-life problems.

The more serious issue is a treatment of I/O.