As people said, a turning machine has infinite memory and program space. Just checking for context and program position doesn’t solve all cases of never halting

As people said, a turning machine has infinite memory and program space. Just checking for context and program position doesn’t solve all cases of never halting. Take for example a program that attempts to calculate the https://en.m.wikipedia.org/wiki/Collatz_conjecture https://en.m.wikipedia.org/wiki/Collatz_conjecture Some inputs would rapidly get answered. Most won’t. If you can prove it’s halt-able for all inputs, you’ve won a Nobel and will be well off for life. Good luck.