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At 11 you're allowed to take your Pokemon into gyms and battle official league trainers for badges. Literally from Pokemon Red and Blue you were battling little kids and their Weedles and schoolgirls with their Nidorian who were definitely older than the player character. Anything else would fall under Japanese laws.
Japanese age of majority is 20, and under 13 is a go directly to jail card (with pedos complaining about recent efforts to raise it to 16)
