# 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)
)