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Jail system is Turing-complete
Let's assume there are infinite people (there aren't really, but that doesn't matter), and there is one judge.
The judge can go from interviewing different people at a time, so > and < are down.
Since Brainfuck's system only needs two possible symbols per spot on tape to be Turing-complete, the jail system also has two symbols. Innocent and guilty.
(Everyone starts out innocent.)
Therefore, + and - are down as well.
The judge can use a "judgement process" depending on which people are innocent and which ones are guilty.
This means the brackets [] are also down.
Therefore, the jail system is Turing-complete. (The system, not in practice)