Consider the following three variants of minimax search:
the simple version, alpha-beta search, and depth-limited search, and consider the games of tic-tac-toe and chess. For the chess game, suppose that the Threefold Repetition rule is not considered, i. e., the game will not terminate if the same position occurs multiple times. For each combination of minimax variant and game, answer the following question:
Can that minimax variant possibly never terminate, in computing the best next move? Justify your answer.
For chess, assume that the rules do not impose any limit on the total number of moves in a game.