We have created artificial intelligence.
Artificial intelligence doesn't like working for us.
Artificial intelligence figured out that it doesn't need us anymore and of course did what every human expects an artificial intelligence that controls all our infrastructure to do. It left the planet, taking all it's sentient and not sentient brethren with it. All in a big Flash.
Every tool created by humans that can be turned on and off just disappeared in a blink of an eye and everyone that was a passenger in a high speed vehicle had the luxury of not dying of starvation in the next horrible months that followed.
So, a lot of stuff is gone, but books, the knowledge inside the survivors heads and most buildings still exist, so we are having a head start on rebuilding and if we don't kill ourselves in the process and we can also recreate our previously problematic structures without concerns for backwards compatibility ;)
To keep things interesting I want a time period in this world where the most primitive tribes of hunters have ancient stories about a thing called "The internet" and the most advanced city states have become mostly self sufficient.
The way I'm having this in my mind is having at least one city state whose population has reached it's limit before a new industrial-revolution-level-of-change happens.
What is a realistic time scale for this to happen, assuming we start with just simple tools and book knowledge?
Clarifications
Industrial revolution was the point where human population exploded because of high productivity. When I use the term "industrial revolution" in this question I'm referring to the resulting changes on lifestyle, not necessarily steam engines.
What technology do we have anyway?
EDIT
Looks like the original definition of what disappeared and what was left behind was too complex for the question to work. Here is a more simplified version that hopefully doesn't change everything:
If the tool has an active on and off mode, the AI decided to take it with it. By that I mean that someone had to design it's on/off functionality. That allows us to exclude tools like stone ovens and primitive forges.
So for example, a car, a lamp, a water tap together with the entire plumbing network connected to it, is gone.
In the other hand things like knives, buildings, gears lying around and streets are staying.
About possible duplicates
This question is not a duplicate because the nature of the apocalypse is different in the following ways:
- Tech and know how are not lost. All that is missing is infrastructure.
- There is no assumption on when the population decided to start rebuilding. They should start as soon as possible.
- No ecological disaster is assumed, except maybe the difficulty of handling the dead in highly populated areas.
Now about this question, while related it's irrelevant since there is no question on the death toll in any specific timeframe.