Seeing your example does make me wonder if the an AI of that level is truly out of reach. It's well known that human reasoning is flawed by cheap heuristics thrown in by nature and/or selection.
Looking at your examples you'd think that just throwing enough memory/speed/power at a simple bruteforce/search approach would solve trivial examples.
Not to mention that when a programmer analyses code he's actually executing it inside his head. Perhaps not all the loops, but looking at a loop he will follow the steps in the code. So in a sense he is executing a piece of code inside his head, thus not violating and/or disproving the halting problem(?).
Looking at your examples you'd think that just throwing enough memory/speed/power at a simple bruteforce/search approach would solve trivial examples.
Not to mention that when a programmer analyses code he's actually executing it inside his head. Perhaps not all the loops, but looking at a loop he will follow the steps in the code. So in a sense he is executing a piece of code inside his head, thus not violating and/or disproving the halting problem(?).