# Colon/Sipma: Practical Methods for Proving Program Termination (VAR x y1 y2 z) (RULES eval_0(x, y1, y2, z) -> eval_1(x, x, 1, z) eval_1(x, y1, y2, z) -> eval_2(x, y1, y2, y1 - 10) :|: y1 > 100 eval_1(x, y1, y2, z) -> eval_3(x, y1, y2, z) :|: y1 <= 100 eval_3(x, y1, y2, z) -> eval_3(x, y1 + 11, y2 + 1, z) :|: y1 <= 100 eval_3(x, y1, y2, z) -> eval_5(x, y1, y2, z) :|: y1 > 100 eval_5(x, y1, y2, z) -> eval_7(x, y1 - 10, y2 - 1, z) :|: y2 > 1 eval_7(x, y1, y2, z) -> eval_5(x, y1, y2, y1 - 10) :|: y1 > 100 && y2 = 1 eval_7(x, y1, y2, z) -> eval_9(x, y1, y2, z) :|: y1 <= 100 || !(y2 = 1) eval_9(x, y1, y2, z) -> eval_11(x, y1 - 10, y2 - 1, z) :|: y1 > 100 eval_9(x, y1, y2, z) -> eval_11(x, y1, y2, z) :|: y1 <= 100 eval_11(x, y1, y2, z) -> eval_5(x, y1 + 11, y2 + 1, z) )
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