# Heapsort # Cousot/Halbwachs: Automatic Discovery of Linear Restraints Among Variables of a Program (POPL 1978) (VAR i j l r n) (RULES eval_1(i, j, l, r, n) -> eval_2(i, j, l - 1, r, n) :|: l >= 2 eval_1(i, j, l, r, n) -> eval_2(i, j, l, r - 1, n) :|: 2 > l eval_2(i, j, l, r, n) -> eval_3(l, 2 * l, l, r, n) :|: r >= 2 eval_3(i, j, l, r, n) -> eval_4(i, j, l, r, n) :|: r >= j && r - 1 >= j eval_3(i, j, l, r, n) -> eval_4(i, j + 1, l, r, n) :|: r >= j && r - 1 >= j eval_3(i, j, l, r, n) -> eval_3(j, 2 * j, l, r, n) :|: r >= j && r - 1 >= j && j >= 1 eval_3(i, j, l, r, n) -> eval_3(j + 1, 2 * j + 2, l, r, n) :|: r >= j && r - 1 >= j && j >= 1 eval_3(i, j, l, r, n) -> eval_4(i, j, l, r, n) :|: r >= j && j > r - 1 eval_3(i, j, l, r, n) -> eval_3(j, 2 * j, l, r, n) :|: r >= j && j > r - 1 && j >= 1 eval_4(i, j, l, r, n) -> eval_2(i, j, l - 1, r, n) :|: l >= 2 && l >= 1 && r >= 2 eval_4(i, j, l, r, n) -> eval_2(i, j, l, r - 1, n) :|: 2 > l && l >= 1 && r >= 2 )
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