Problem in our philosophy class... help

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a young woman by the name of jocasta finds a freezer. Inside the freezer she discovers a man frozen alive. She thaws him out and learns that his name is Dum. Dum tells her that he has a books that tells how to build a freezer and preserve humans and how to build a time machine. Jocasta ignored the book but soon they fell in love with each other, got married and had a son called Dee. When Dee grew up, he followed his father and builds a time machine. He asked his father to accompany him into the past taking the book with them. During the trip, they ran out of food and in order to stay alive, Dee kills his father and ate him. Dee then builds a freezer then freezes himself with the book to save himself. Years later, Jocasta finds a freezer and thaws the occupant. To disguise himself, Dee claimed to be Dum. They fell in love, marry and had a son called Dee. Then the cycle continues. Question: Did Jocasta commit a logically possible crime?"