It starts with a common man who just lived his life, but his life has started to fall into pieces. He has two children with his wife, but as requested the children are genetically enhanced and have extremely high IQs. They have left their parents willingly for a special school, and they were even before that not much child-like.
This drove his wife into insanity (or into alcoholism/drugs). On his way home, he finds a body near their apartment and he is afraid of getting convicted for the murder, because he was the first one who is seen by the body.
Later, his wife is executed for the murder, without a trial. She is put to death in a public arena with a laser. (But I think her husband didn’t know this. He isn’t informed. To him, she just has disappeared.)
With his life torn apart, he starts running and on some days he even runs outside the city.
— The whole population lives in cities and most are dependent on a social allowance of some kind of nutrition bars from a local food bank … that are sometimes – whoops – poisonous. Being outside of a city is counted as suspicious behavior. Everything is controlled by a big AI. —
He encounters kind of a resistance to the government outside the city and he joins them, eventually. In German the resistance is called “Renegaten” so maybe the original term is “renegades”.
The resistance owns a big AI, too and during the endgame their AI fights the government AI. I remember the scene in which the renegade AI bids farewell to the main protagonist.
I can’t remember how the book ended but I think the renegade AI ‘died’.
Got solved over at scifi.stackexchange.com.
It is Anvil of the Heart, by Bruce T. Holmes.