/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE DP problem for innermost termination. P = init#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26#(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26#(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26#(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26#(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26#(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26#(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25#(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25#(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26#(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25#(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25#(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25#(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24#(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14#(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24#(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22#(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21#(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23#(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24#(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22#(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23#(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23#(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24#(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22#(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23#(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21#(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22#(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7#(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21#(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20#(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20#(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20#(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19#(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19#(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20#(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7#(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19#(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7#(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14#(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18#(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18#(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18#(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17#(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17#(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18#(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17#(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16#(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16#(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17#(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6#(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16#(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6#(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14#(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15#(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15#(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15#(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14#(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14#(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15#(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5#(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14#(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13#(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13#(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13#(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12#(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12#(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13#(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5#(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12#(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11#(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11#(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11#(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10#(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10#(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11#(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5#(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10#(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2#(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10#(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9#(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8#(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8#(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9#(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9#(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8#(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8#(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9#(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8#(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5#(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5#(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8#(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6#(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7#(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6#(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7#(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5#(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6#(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5#(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6#(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2#(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5#(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4#(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3#(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3#(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4#(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4#(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3#(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3#(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4#(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3#(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2#(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2#(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3#(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1#(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2#(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] The dependency graph for this problem is: 0 -> 59 1 -> 1, 4 2 -> 2, 3, 4 3 -> 1, 4 4 -> 5, 6 5 -> 1, 2, 3 6 -> 5 7 -> 6 8 -> 31 9 -> 12, 14 10 -> 15 11 -> 7, 8, 9, 10 12 -> 11 13 -> 7, 8, 9, 10 14 -> 13 15 -> 12 16 -> 15 17 -> 17, 18 18 -> 19 19 -> 17, 18 20 -> 19 21 -> 31 22 -> 22, 23 23 -> 24, 25 24 -> 22, 23 25 -> 26 26 -> 24, 25 27 -> 26 28 -> 31 29 -> 29, 30 30 -> 31 31 -> 29, 30 32 -> 31 33 -> 33, 34 34 -> 35 35 -> 33, 34 36 -> 35 37 -> 37, 38 38 -> 39 39 -> 37, 38 40 -> 39 41 -> 39 42 -> 43, 45, 46 43 -> 42, 44 44 -> 43, 46 45 -> 44 46 -> 32, 36, 40, 47, 50, 51 47 -> 43, 45, 46 48 -> 16, 20, 21 49 -> 16, 20, 21 50 -> 27, 28, 48, 49 51 -> 27, 28, 48, 49 52 -> 32, 36, 40, 47, 50, 51 53 -> 56, 57 54 -> 53 55 -> 54, 57 56 -> 55 57 -> 41, 52, 58 58 -> 54, 56, 57 59 -> 41, 52, 58 Where: 0) init#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) 1) f26#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26#(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] 2) f26#(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26#(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] 3) f26#(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26#(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] 4) f26#(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25#(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] 5) f25#(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26#(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] 6) f25#(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25#(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] 7) f24#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25#(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] 8) f24#(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14#(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] 9) f24#(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22#(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] 10) f24#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21#(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] 11) f23#(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24#(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] 12) f22#(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23#(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] 13) f23#(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24#(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] 14) f22#(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23#(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] 15) f21#(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22#(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] 16) f7#(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21#(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] 17) f20#(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20#(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] 18) f20#(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19#(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] 19) f19#(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20#(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] 20) f7#(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19#(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] 21) f7#(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14#(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] 22) f18#(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18#(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] 23) f18#(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17#(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] 24) f17#(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18#(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] 25) f17#(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16#(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] 26) f16#(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17#(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] 27) f6#(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16#(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] 28) f6#(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14#(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] 29) f15#(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15#(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] 30) f15#(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14#(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] 31) f14#(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15#(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] 32) f5#(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14#(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] 33) f13#(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13#(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] 34) f13#(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12#(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] 35) f12#(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13#(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] 36) f5#(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12#(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] 37) f11#(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11#(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] 38) f11#(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10#(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] 39) f10#(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11#(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] 40) f5#(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10#(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] 41) f2#(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10#(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] 42) f9#(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8#(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] 43) f8#(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9#(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] 44) f9#(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8#(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] 45) f8#(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9#(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] 46) f8#(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5#(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] 47) f5#(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8#(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] 48) f6#(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7#(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] 49) f6#(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7#(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] 50) f5#(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6#(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] 51) f5#(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6#(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] 52) f2#(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5#(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] 53) f4#(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3#(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] 54) f3#(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4#(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] 55) f4#(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3#(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] 56) f3#(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4#(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] 57) f3#(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2#(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] 58) f2#(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3#(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] 59) f1#(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2#(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We have the following SCCs. { 53, 54, 55, 56, 57, 58 } { 42, 43, 44, 45, 46, 47 } { 17, 18, 19 } { 9, 10, 11, 12, 13, 14, 15 } { 1, 2, 3, 4, 5, 6 } { 22, 23, 24, 25, 26 } { 33, 34, 35 } { 29, 30, 31 } { 37, 38, 39 } DP problem for innermost termination. P = f11#(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11#(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11#(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10#(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10#(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11#(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the reverse value criterion with the projection function NU: NU[f10#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z4 - 1 + -1 * z3 NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z5 - 1 + -1 * (z3 + 1) This gives the following inequalities: I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1 ==> I565 - 1 + -1 * (I563 + 1) >= I565 - 1 + -1 * (I563 + 1) 0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578 ==> I582 - 1 + -1 * (I580 + 1) >= I582 - 1 + -1 * (I580 + 1) 0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594 ==> I597 - 1 + -1 * I596 > I597 - 1 + -1 * (I596 + 1) with I597 - 1 + -1 * I596 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f11#(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11#(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11#(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10#(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] The dependency graph for this problem is: 37 -> 37, 38 38 -> Where: 37) f11#(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11#(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] 38) f11#(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10#(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] We have the following SCCs. { 37 } DP problem for innermost termination. P = f11#(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11#(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the reverse value criterion with the projection function NU: NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z5 - 1 + -1 * z4 This gives the following inequalities: I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1 ==> I565 - 1 + -1 * I564 > I565 - 1 + -1 * (I564 + 1) with I565 - 1 + -1 * I564 >= 0 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. DP problem for innermost termination. P = f15#(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15#(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15#(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14#(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14#(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15#(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the reverse value criterion with the projection function NU: NU[f14#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z3 - 1 + -1 * z2 NU[f15#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z4 - 1 + -1 * (z2 + 1) This gives the following inequalities: I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1 ==> I436 - 1 + -1 * (I434 + 1) >= I436 - 1 + -1 * (I434 + 1) 2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449 ==> I452 - 1 + -1 * (I450 + 1) >= I452 - 1 + -1 * (I450 + 1) 2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465 ==> I467 - 1 + -1 * I466 > I467 - 1 + -1 * (I466 + 1) with I467 - 1 + -1 * I466 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f15#(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15#(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15#(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14#(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] The dependency graph for this problem is: 29 -> 29, 30 30 -> Where: 29) f15#(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15#(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] 30) f15#(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14#(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] We have the following SCCs. { 29 } DP problem for innermost termination. P = f15#(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15#(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the reverse value criterion with the projection function NU: NU[f15#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z4 - 1 + -1 * z3 This gives the following inequalities: I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1 ==> I436 - 1 + -1 * I435 > I436 - 1 + -1 * (I435 + 1) with I436 - 1 + -1 * I435 >= 0 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. DP problem for innermost termination. P = f13#(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13#(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13#(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12#(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12#(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13#(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the reverse value criterion with the projection function NU: NU[f12#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z3 - 1 + -1 * z2 NU[f13#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z4 - 1 + -1 * (z2 + 1) This gives the following inequalities: I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1 ==> I499 - 1 + -1 * (I497 + 1) >= I499 - 1 + -1 * (I497 + 1) 2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1 ==> I517 - 1 + -1 * (I515 + 1) >= I517 - 1 + -1 * (I515 + 1) 2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1 ==> I532 - 1 + -1 * I531 > I532 - 1 + -1 * (I531 + 1) with I532 - 1 + -1 * I531 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f13#(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13#(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13#(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12#(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] The dependency graph for this problem is: 33 -> 33, 34 34 -> Where: 33) f13#(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13#(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] 34) f13#(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12#(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] We have the following SCCs. { 33 } DP problem for innermost termination. P = f13#(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13#(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the reverse value criterion with the projection function NU: NU[f13#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z4 - 1 + -1 * z3 This gives the following inequalities: I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1 ==> I499 - 1 + -1 * I498 > I499 - 1 + -1 * (I498 + 1) with I499 - 1 + -1 * I498 >= 0 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. DP problem for innermost termination. P = f18#(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18#(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18#(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17#(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17#(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18#(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17#(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16#(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16#(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17#(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the extended value criterion with the projection function NU: NU[f16#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x1 + x2 - 1 NU[f17#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x1 + x3 - 2 NU[f18#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x1 + x4 - 2 This gives the following inequalities: I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1 ==> -I324 + I327 - 2 >= -I324 + I327 - 2 2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1 ==> -I341 + I344 - 2 >= -I341 + I344 - 2 I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1 ==> -I356 + I358 - 2 >= -I356 + I358 - 2 2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1 ==> -I371 + I373 - 2 >= -(I371 + 1) + I373 - 1 2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1 ==> -I387 + I388 - 1 > -I387 + I388 - 2 with -I387 + I388 - 1 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f18#(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18#(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18#(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17#(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17#(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18#(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17#(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16#(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] The dependency graph for this problem is: 22 -> 22, 23 23 -> 24, 25 24 -> 22, 23 25 -> Where: 22) f18#(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18#(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] 23) f18#(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17#(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] 24) f17#(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18#(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] 25) f17#(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16#(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] We have the following SCCs. { 22, 23, 24 } DP problem for innermost termination. P = f18#(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18#(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18#(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17#(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17#(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18#(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the reverse value criterion with the projection function NU: NU[f17#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z4 - 1 + -1 * z3 NU[f18#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z5 - 1 + -1 * (z3 + 1) This gives the following inequalities: I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1 ==> I327 - 1 + -1 * (I325 + 1) >= I327 - 1 + -1 * (I325 + 1) 2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1 ==> I344 - 1 + -1 * (I342 + 1) >= I344 - 1 + -1 * (I342 + 1) I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1 ==> I358 - 1 + -1 * I357 > I358 - 1 + -1 * (I357 + 1) with I358 - 1 + -1 * I357 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f18#(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18#(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18#(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17#(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] The dependency graph for this problem is: 22 -> 22, 23 23 -> Where: 22) f18#(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18#(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] 23) f18#(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17#(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] We have the following SCCs. { 22 } DP problem for innermost termination. P = f18#(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18#(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the reverse value criterion with the projection function NU: NU[f18#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z5 - 1 + -1 * z4 This gives the following inequalities: I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1 ==> I327 - 1 + -1 * I326 > I327 - 1 + -1 * (I326 + 1) with I327 - 1 + -1 * I326 >= 0 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. DP problem for innermost termination. P = f26#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26#(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26#(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26#(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26#(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26#(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26#(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25#(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25#(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26#(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25#(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25#(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the reverse value criterion with the projection function NU: NU[f25#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z6 - 1 + -1 * z5 NU[f26#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z8 - 1 + -1 * (z4 + 1) This gives the following inequalities: I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1 ==> I7 - 1 + -1 * (I3 + 1) >= I7 - 1 + -1 * (I3 + 1) I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1 ==> I18 - 1 + -1 * (I14 + 1) >= I18 - 1 + -1 * (I14 + 1) I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1 ==> I31 - 1 + -1 * (I27 + 1) >= I31 - 1 + -1 * (I27 + 1) 2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41 ==> I42 - 1 + -1 * (I38 + 1) >= I42 - 1 + -1 * (I38 + 1) 2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1 ==> I53 - 1 + -1 * I52 > I53 - 1 + -1 * (I52 + 1) with I53 - 1 + -1 * I52 >= 0 0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59 ==> I64 - 1 + -1 * I63 > I64 - 1 + -1 * 1 with I64 - 1 + -1 * I63 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f26#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26#(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26#(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26#(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26#(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26#(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26#(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25#(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] The dependency graph for this problem is: 1 -> 1, 4 2 -> 2, 3, 4 3 -> 1, 4 4 -> Where: 1) f26#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26#(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] 2) f26#(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26#(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] 3) f26#(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26#(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] 4) f26#(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25#(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] We have the following SCCs. { 2 } { 1 } DP problem for innermost termination. P = f26#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26#(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the reverse value criterion with the projection function NU: NU[f26#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z8 - 1 + -1 * z7 This gives the following inequalities: I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1 ==> I7 - 1 + -1 * I6 > I7 - 1 + -1 * (I6 + 1) with I7 - 1 + -1 * I6 >= 0 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. DP problem for innermost termination. P = f26#(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26#(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910] We use the reverse value criterion with the projection function NU: NU[f26#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z8 - 1 + -1 * z7 This gives the following inequalities: I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1 ==> I18 - 1 + -1 * I17 > I18 - 1 + -1 * (I17 + 1) with I18 - 1 + -1 * I17 >= 0 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. DP problem for innermost termination. P = f24#(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22#(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21#(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23#(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24#(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22#(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23#(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23#(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24#(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22#(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23#(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21#(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22#(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9) f26(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f26(I9, I1, I10, I3, I4, I5 + 1, I6 + 1, I7, I8) [I1 <= I6 - 1 /\ I6 <= I7 - 1 /\ I4 <= I8 - 1 /\ I3 <= I7 - 1 /\ -1 <= y1 - 1 /\ I6 <= y1 - 1 /\ -1 <= y2 - 1 /\ -1 <= I7 - 1 /\ I5 <= y2 - 1 /\ I9 <= I0 /\ I9 <= I2 /\ I10 <= I0 /\ I10 <= I2 /\ 2 <= I0 - 1 /\ 2 <= I2 - 1 /\ 2 <= I9 - 1 /\ 2 <= I10 - 1] f26(I11, I12, I13, I14, I15, I16, I17, I18, I19) -> f26(I20, I12, I21, I14, I15, I16 + 1, I17 + 1, I18, I19) [I17 <= I12 - 1 /\ I17 <= I18 - 1 /\ I15 <= I19 - 1 /\ I14 <= I18 - 1 /\ -1 <= I22 - 1 /\ I17 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I18 - 1 /\ I16 <= I23 - 1 /\ I20 <= I11 /\ I20 <= I13 /\ I21 <= I11 /\ I21 <= I13 /\ 2 <= I11 - 1 /\ 2 <= I13 - 1 /\ 2 <= I20 - 1 /\ 2 <= I21 - 1] f26(I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f26(I33, I25, I34, I27, I28, I29, I25 + 1, I31, I32) [I25 = I30 /\ 2 <= I34 - 1 /\ 2 <= I33 - 1 /\ 2 <= I26 - 1 /\ 2 <= I24 - 1 /\ I34 <= I26 /\ I34 <= I24 /\ I33 <= I26 /\ I33 <= I24 /\ -1 <= I31 - 1 /\ I25 <= I31 - 1] f26(I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f25(I44, I36, I45, I39 + 1, I38 + 1, I42, I43, I46, I47) [2 <= I45 - 1 /\ 2 <= I44 - 1 /\ 2 <= I37 - 1 /\ 2 <= I35 - 1 /\ I45 <= I37 /\ I45 <= I35 /\ I44 <= I37 /\ I44 <= I35 /\ -1 <= I42 - 1 /\ I42 <= I41] f25(I48, I49, I50, I51, I52, I53, I54, I55, I56) -> f26(I57, I49, I58, I52, I51, 0, 0, I53, I54) [2 <= I58 - 1 /\ 2 <= I57 - 1 /\ 2 <= I50 - 1 /\ 2 <= I48 - 1 /\ I58 <= I50 /\ I58 <= I48 /\ I57 <= I50 /\ I57 <= I48 /\ 0 <= I52 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1] f25(I59, I60, I61, I62, I63, I64, I65, I66, I67) -> f25(I68, I60, I69, I62, 1, I64, I65, I70, I71) [0 = I63 /\ 2 <= I69 - 1 /\ 2 <= I68 - 1 /\ 2 <= I61 - 1 /\ 2 <= I59 - 1 /\ I69 <= I61 /\ I69 <= I59 /\ I68 <= I61 /\ 0 <= I64 - 1 /\ I68 <= I59] f24(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f25(I81, I74, I82, 0, 0, I75, I75 - 1, I83, I84) [I74 <= I75 - 1 /\ 1 <= I75 - 1 /\ I74 <= I85 - 1 /\ -1 <= I85 - 1 /\ I75 - 1 <= I75 - 1 /\ I74 <= I75 - 1 /\ I81 <= I72 /\ I81 - 2 <= I73 /\ I82 <= I72 /\ I82 - 2 <= I73 /\ 2 <= I72 - 1 /\ 0 <= I73 - 1 /\ 2 <= I81 - 1 /\ 2 <= I82 - 1] f24(I86, I87, I88, I89, I90, I91, I92, I93, I94) -> f14(I95, 0, I89 - 1, I96, I97, I98, I99, I100, I101) [I88 <= I89 - 1 /\ 1 <= I89 - 1 /\ I88 <= I102 - 1 /\ -1 <= I102 - 1 /\ I89 - 1 <= I89 - 1 /\ I88 <= I89 - 1 /\ I95 <= I86 /\ I95 - 2 <= I87 /\ 2 <= I86 - 1 /\ 0 <= I87 - 1 /\ 2 <= I95 - 1] f24(I103, I104, I105, I106, I107, I108, I109, I110, I111) -> f22(I112, I105 + 1, I106, I113, I114, I115, I116, I117, I118) [I105 <= I106 - 1 /\ 1 <= I106 - 1 /\ I105 <= I119 - 1 /\ 0 <= I120 - 1 /\ -1 <= I119 - 1 /\ I112 <= I103 /\ I112 - 2 <= I104 /\ 2 <= I103 - 1 /\ 0 <= I104 - 1 /\ 2 <= I112 - 1] f24(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f21(I130, I131, I132, I133, I134, I135, I136, I137, I138) [I123 <= I124 - 1 /\ 0 <= I131 - 1 /\ 1 <= I124 - 1 /\ I123 <= I139 - 1 /\ -1 <= I139 - 1 /\ I130 <= I121 /\ I130 - 2 <= I122 /\ 2 <= I121 - 1 /\ 0 <= I122 - 1 /\ 2 <= I130 - 1] f23(I140, I141, I142, I143, I144, I145, I146, I147, I148) -> f24(I149, I150, I141, I142, I151, I152, I153, I154, I155) [0 <= I142 - 1 /\ I141 <= I142 - 1 /\ I141 - 2 * I156 = 0 /\ I149 <= I140 /\ 2 <= I140 - 1 /\ 2 <= I149 - 1 /\ -1 <= I150 - 1 /\ I141 - 2 * I156 <= 1 /\ 0 <= I141 - 2 * I156] f22(I157, I158, I159, I160, I161, I162, I163, I164, I165) -> f23(I157, I158, I159, I166, I167, I168, I169, I170, I171) [0 <= I159 - 1 /\ I158 <= I159 - 1 /\ I158 - 2 * I172 = 0 /\ I173 <= I157 /\ 2 <= I157 - 1 /\ 2 <= I173 - 1 /\ -1 <= y3 - 1] f23(I174, I175, I176, I177, I178, I179, I180, I181, I182) -> f24(I183, I184, I175, I176, I185, I186, I187, I188, I189) [0 <= I176 - 1 /\ I175 <= I176 - 1 /\ I175 - 2 * I190 = 1 /\ I183 <= I174 /\ 2 <= I174 - 1 /\ 2 <= I183 - 1 /\ -1 <= I184 - 1 /\ I175 - 2 * I190 <= 1 /\ 0 <= I175 - 2 * I190] f22(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f23(I191, I192, I193, I200, I201, I202, I203, I204, I205) [0 <= I193 - 1 /\ I192 <= I193 - 1 /\ I192 - 2 * I206 = 1 /\ I207 <= I191 /\ 2 <= I191 - 1 /\ 2 <= I207 - 1 /\ -1 <= I208 - 1] f21(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f22(I218, 0, I210, I219, I220, I221, I222, I223, I224) [2 <= I218 - 1 /\ 2 <= I209 - 1 /\ 1 <= I210 - 1 /\ I218 <= I209] f7(I225, I226, I227, I228, I229, I230, I231, I232, I233) -> f21(I234, I229, I235, I236, I237, I238, I239, I240, I241) [2 <= I234 - 1 /\ 2 <= I227 - 1 /\ 2 <= I226 - 1 /\ 0 <= I225 - 1 /\ I234 <= I227 /\ I234 <= I226 /\ I234 - 2 <= I225 /\ -1 <= I228 - 1 /\ -1 <= I229 - 1] f20(I242, I243, I244, I245, I246, I247, I248, I249, I250) -> f20(I251, I243 + 1, I244, I245, I252, I253, I254, I255, I256) [I243 <= I244 /\ I244 <= I245 - 1 /\ I243 <= I245 - 1 /\ -1 <= I257 - 1 /\ I244 <= I257 - 1 /\ -1 <= I258 - 1 /\ I243 <= I258 - 1 /\ -1 <= I259 - 1 /\ I243 <= I259 - 1 /\ I244 <= y4 - 1 /\ -1 <= y4 - 1 /\ I251 <= I242 /\ 2 <= I242 - 1 /\ 2 <= I251 - 1] f20(I260, I261, I262, I263, I264, I265, I266, I267, I268) -> f19(I269, I262 + 1, I263, I270, I271, I272, I273, I274, I275) [2 <= I269 - 1 /\ 2 <= I260 - 1 /\ I269 <= I260 /\ I262 <= I261 - 1 /\ -1 <= I263 - 1] f19(I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f20(I285, 0, I277, I278, I286, I287, I288, I289, I290) [2 <= I285 - 1 /\ 2 <= I276 - 1 /\ I277 <= I278 - 1 /\ I285 <= I276] f7(I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f19(I300, 0, I296, I301, I302, I303, I304, I305, I306) [2 <= I300 - 1 /\ 2 <= I293 - 1 /\ 2 <= I292 - 1 /\ 0 <= I291 - 1 /\ I300 <= I293 /\ I300 <= I292 /\ I300 - 2 <= I291 /\ -1 <= I294 - 1 /\ -1 <= I296 - 1] f7(I307, I308, I309, I310, I311, I312, I313, I314, I315) -> f14(I316, 0, I312, I317, I318, I319, I320, I321, I322) [2 <= I316 - 1 /\ 2 <= I309 - 1 /\ 2 <= I308 - 1 /\ 0 <= I307 - 1 /\ I316 <= I309 /\ I316 <= I308 /\ I316 - 2 <= I307 /\ -1 <= I310 - 1 /\ -1 <= I312 - 1] f18(I323, I324, I325, I326, I327, I328, I329, I330, I331) -> f18(I332, I324, I325, I326 + 1, I327, I333, I334, I335, I336) [I326 <= I327 - 1 /\ I324 <= I327 - 1 /\ -1 <= I337 - 1 /\ I325 <= I337 - 1 /\ -1 <= I338 - 1 /\ I326 <= I338 - 1 /\ -1 <= I339 - 1 /\ I325 <= I339 - 1 /\ -1 <= I327 - 1 /\ I332 <= I323 /\ 2 <= I323 - 1 /\ 2 <= I332 - 1] f18(I340, I341, I342, I343, I344, I345, I346, I347, I348) -> f17(I349, I341, I342 + 1, I344, I350, I351, I352, I353, I354) [2 <= I349 - 1 /\ 2 <= I340 - 1 /\ I349 <= I340 /\ I344 <= I343 /\ -1 <= I344 - 1] f17(I355, I356, I357, I358, I359, I360, I361, I362, I363) -> f18(I364, I356, I357, 0, I358, I365, I366, I367, I368) [I357 <= I358 - 1 /\ I356 <= I358 - 1 /\ -1 <= I369 - 1 /\ -1 <= I358 - 1 /\ I357 <= I369 - 1 /\ I364 <= I355 /\ 2 <= I355 - 1 /\ 2 <= I364 - 1] f17(I370, I371, I372, I373, I374, I375, I376, I377, I378) -> f16(I379, I371 + 1, I373, I380, I381, I382, I383, I384, I385) [2 <= I379 - 1 /\ 2 <= I370 - 1 /\ I379 <= I370 /\ I373 <= I372 /\ -1 <= I373 - 1] f16(I386, I387, I388, I389, I390, I391, I392, I393, I394) -> f17(I395, I387, 0, I388, I396, I397, I398, I399, I400) [2 <= I395 - 1 /\ 2 <= I386 - 1 /\ I395 <= I386 /\ -1 <= I388 - 1 /\ I387 <= I388 - 1] f6(I401, I402, I403, I404, I405, I406, I407, I408, I409) -> f16(I410, 0, I405, I411, I412, I413, I414, I415, I416) [I405 = I406 /\ 2 <= I410 - 1 /\ 2 <= I403 - 1 /\ 2 <= I402 - 1 /\ 0 <= I401 - 1 /\ I410 <= I403 /\ I410 <= I402 /\ I410 - 2 <= I401 /\ -1 <= I405 - 1 /\ -1 <= I404 - 1] f6(I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f14(I426, 0, I421, I427, I428, I429, I430, I431, I432) [2 <= I426 - 1 /\ 2 <= I419 - 1 /\ 2 <= I418 - 1 /\ 0 <= I417 - 1 /\ I426 <= I419 /\ I426 <= I418 /\ I426 - 2 <= I417 /\ -1 <= I420 - 1 /\ -1 <= I421 - 1] f15(I433, I434, I435, I436, I437, I438, I439, I440, I441) -> f15(I442, I434, I435 + 1, I436, I443, I444, I445, I446, I447) [I435 <= I436 - 1 /\ I434 <= I436 - 1 /\ I435 <= I448 - 1 /\ -1 <= I448 - 1 /\ I442 <= I433 /\ 2 <= I433 - 1 /\ 2 <= I442 - 1] f15(I449, I450, I451, I452, I453, I454, I455, I456, I457) -> f14(I458, I450 + 1, I452, I459, I460, I461, I462, I463, I464) [2 <= I458 - 1 /\ 2 <= I449 - 1 /\ I452 <= I451 /\ I458 <= I449] f14(I465, I466, I467, I468, I469, I470, I471, I472, I473) -> f15(I474, I466, 0, I467, I475, I476, I477, I478, I479) [2 <= I474 - 1 /\ 2 <= I465 - 1 /\ I466 <= I467 - 1 /\ I474 <= I465] f5(I480, I481, I482, I483, I484, I485, I486, I487, I488) -> f14(I489, 0, I483, I490, I491, I492, I493, I494, I495) [2 <= I489 - 1 /\ 0 <= I481 - 1 /\ 2 <= I480 - 1 /\ I489 - 2 <= I481 /\ I489 <= I480 /\ I484 <= I482 /\ -1 <= I484 - 1 /\ -1 <= I483 - 1] f13(I496, I497, I498, I499, I500, I501, I502, I503, I504) -> f13(I505, I497, I498 + 1, I499, I506, I507, I508, I509, I510) [I498 <= I499 - 1 /\ I497 <= I499 - 1 /\ -1 <= I511 - 1 /\ I498 <= I511 - 1 /\ -1 <= I512 - 1 /\ I498 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I499 - 1 /\ I498 <= I513 - 1 /\ I505 <= I496 /\ 2 <= I496 - 1 /\ 2 <= I505 - 1] f13(I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f12(I523, I515 + 1, I517, I524, I525, I526, I527, I528, I529) [2 <= I523 - 1 /\ 2 <= I514 - 1 /\ I523 <= I514 /\ I517 <= I516 /\ -1 <= I517 - 1] f12(I530, I531, I532, I533, I534, I535, I536, I537, I538) -> f13(I539, I531, 0, I532, I540, I541, I542, I543, I544) [2 <= I539 - 1 /\ 2 <= I530 - 1 /\ I539 <= I530 /\ -1 <= I532 - 1 /\ I531 <= I532 - 1] f5(I545, I546, I547, I548, I549, I550, I551, I552, I553) -> f12(I554, 0, I548, I555, I556, I557, I558, I559, I560) [2 <= I554 - 1 /\ 0 <= I546 - 1 /\ 2 <= I545 - 1 /\ I554 - 2 <= I546 /\ I554 <= I545 /\ I549 <= I547 /\ -1 <= I549 - 1 /\ -1 <= I548 - 1] f11(I561, I562, I563, I564, I565, I566, I567, I568, I569) -> f11(I570, I571, I563, I564 + 1, I565, I572, I573, I574, I575) [I564 <= I565 - 1 /\ I563 <= I565 - 1 /\ -1 <= I576 - 1 /\ I564 <= I576 - 1 /\ I564 <= I577 - 1 /\ -1 <= I577 - 1 /\ I570 <= I561 /\ I570 - 2 <= I562 /\ I571 + 2 <= I561 /\ I571 <= I562 /\ 2 <= I561 - 1 /\ 0 <= I562 - 1 /\ 2 <= I570 - 1 /\ 0 <= I571 - 1] f11(I578, I579, I580, I581, I582, I583, I584, I585, I586) -> f10(I587, I588, I580 + 1, I582, I589, I590, I591, I592, I593) [0 <= I588 - 1 /\ 2 <= I587 - 1 /\ 0 <= I579 - 1 /\ 2 <= I578 - 1 /\ I588 <= I579 /\ I588 + 2 <= I578 /\ I587 - 2 <= I579 /\ I582 <= I581 /\ I587 <= I578] f10(I594, I595, I596, I597, I598, I599, I600, I601, I602) -> f11(I603, I604, I596, 0, I597, I605, I606, I607, I608) [0 <= I604 - 1 /\ 2 <= I603 - 1 /\ 0 <= I595 - 1 /\ 2 <= I594 - 1 /\ I604 <= I595 /\ I604 + 2 <= I594 /\ I603 - 2 <= I595 /\ I596 <= I597 - 1 /\ I603 <= I594] f5(I609, I610, I611, I612, I613, I614, I615, I616, I617) -> f10(I618, I619, 0, I613, I620, I621, I622, I623, I624) [0 <= I619 - 1 /\ 2 <= I618 - 1 /\ 0 <= I610 - 1 /\ 2 <= I609 - 1 /\ I619 <= I610 /\ I619 + 2 <= I609 /\ I618 - 2 <= I610 /\ I618 <= I609 /\ -1 <= I613 - 1 /\ I613 <= I611] f2(I625, I626, I627, I628, I629, I630, I631, I632, I633) -> f10(I634, I635, 0, I627, I636, I637, I638, I639, I640) [0 <= I635 - 1 /\ 2 <= I634 - 1 /\ 0 <= I625 - 1 /\ I635 <= I625 /\ I634 - 2 <= I625 /\ -1 <= I627 - 1 /\ I627 <= I626] f9(I641, I642, I643, I644, I645, I646, I647, I648, I649) -> f8(I650, I651, I643, I644 + 1, I645, I646, I652, I653, I654) [0 <= I643 + I644 - 3 * I655 - 1 /\ -1 <= I643 - 1 /\ -1 <= I644 - 1 /\ I644 <= I646 - 1 /\ 0 <= I646 - 1 /\ I643 <= I646 - 1 /\ I644 <= I656 - 1 /\ -1 <= I656 - 1 /\ I650 <= I641 /\ I650 - 2 <= I642 /\ I651 + 2 <= I641 /\ I651 <= I642 /\ 2 <= I641 - 1 /\ 0 <= I642 - 1 /\ 2 <= I650 - 1 /\ 0 <= I651 - 1 /\ I643 + I644 - 3 * I655 <= 2] f8(I657, I658, I659, I660, I661, I662, I663, I664, I665) -> f9(I657, I658, I659, I660, I661, I662, I666, I667, I668) [-1 <= I659 - 1 /\ -1 <= I660 - 1 /\ I660 <= I662 - 1 /\ 0 <= I659 + I660 - 3 * I669 - 1 /\ 0 <= I662 - 1 /\ I659 <= I662 - 1 /\ I660 <= I670 - 1 /\ -1 <= I670 - 1 /\ I671 <= I657 /\ I671 - 2 <= I658 /\ I672 + 2 <= I657 /\ I672 <= I658 /\ 2 <= I657 - 1 /\ 0 <= I658 - 1 /\ 2 <= I671 - 1 /\ 0 <= I672 - 1] f9(I673, I674, I675, I676, I677, I678, I679, I680, I681) -> f8(I682, I683, I675, I676 + 1, I677, I678, I684, I685, I686) [-1 <= I675 - 1 /\ -1 <= I676 - 1 /\ I676 <= I678 - 1 /\ I675 + I676 - 3 * I687 = 0 /\ I675 <= I678 - 1 /\ I676 <= I688 - 1 /\ -1 <= I688 - 1 /\ I682 <= I673 /\ I682 - 2 <= I674 /\ I683 + 2 <= I673 /\ I683 <= I674 /\ 2 <= I673 - 1 /\ 0 <= I674 - 1 /\ 2 <= I682 - 1 /\ 0 <= I683 - 1 /\ I675 + I676 - 3 * I687 <= 2 /\ 0 <= I675 + I676 - 3 * I687] f8(I689, I690, I691, I692, I693, I694, I695, I696, I697) -> f9(I689, I690, I691, I692, I693, I694, I698, I699, I700) [-1 <= I691 - 1 /\ -1 <= I692 - 1 /\ I692 <= I694 - 1 /\ I691 + I692 - 3 * I701 = 0 /\ I691 <= I694 - 1 /\ I692 <= I702 - 1 /\ -1 <= I702 - 1 /\ I703 <= I689 /\ I703 - 2 <= I690 /\ I704 + 2 <= I689 /\ I704 <= I690 /\ 2 <= I689 - 1 /\ 0 <= I690 - 1 /\ 2 <= I703 - 1 /\ 0 <= I704 - 1] f8(I705, I706, I707, I708, I709, I710, I711, I712, I713) -> f5(I714, I715, I707 + 1, I709, I710, I716, I717, I718, I719) [0 <= I715 - 1 /\ 2 <= I714 - 1 /\ 0 <= I706 - 1 /\ 2 <= I705 - 1 /\ I715 <= I706 /\ I715 + 2 <= I705 /\ I714 - 2 <= I706 /\ I710 <= I708 /\ I714 <= I705] f5(I720, I721, I722, I723, I724, I725, I726, I727, I728) -> f8(I729, I730, I722, 0, I723, I724, I731, I732, I733) [0 <= I730 - 1 /\ 2 <= I729 - 1 /\ 0 <= I721 - 1 /\ 2 <= I720 - 1 /\ I730 <= I721 /\ I730 + 2 <= I720 /\ I729 - 2 <= I721 /\ I722 <= I724 - 1 /\ I729 <= I720] f6(I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f7(I743, I744, I745, I737, I738, I738, I746, I747, I748) [I738 = I739 /\ 2 <= I745 - 1 /\ 2 <= I744 - 1 /\ 0 <= I743 - 1 /\ 2 <= I736 - 1 /\ 2 <= I735 - 1 /\ 0 <= I734 - 1 /\ I745 <= I736 /\ I745 <= I735 /\ I745 - 2 <= I734 /\ I744 <= I736 /\ I744 <= I735 /\ I744 - 2 <= I734 /\ I743 + 2 <= I736 /\ I743 + 2 <= I735 /\ -1 <= I737 - 1 /\ I743 <= I734] f6(I749, I750, I751, I752, I753, I754, I755, I756, I757) -> f7(I758, I759, I760, I752, I754, I753, I761, I762, I763) [2 <= I760 - 1 /\ 2 <= I759 - 1 /\ 0 <= I758 - 1 /\ 2 <= I751 - 1 /\ 2 <= I750 - 1 /\ 0 <= I749 - 1 /\ I760 <= I751 /\ I760 <= I750 /\ I760 - 2 <= I749 /\ I759 <= I751 /\ I759 <= I750 /\ I759 - 2 <= I749 /\ I758 + 2 <= I751 /\ I758 + 2 <= I750 /\ -1 <= I752 - 1 /\ I758 <= I749] f5(I764, I765, I766, I767, I768, I769, I770, I771, I772) -> f6(I773, I774, I775, I768, I767, I767, I776, I777, I778) [2 <= I775 - 1 /\ 2 <= I774 - 1 /\ 0 <= I773 - 1 /\ 0 <= I765 - 1 /\ 2 <= I764 - 1 /\ I775 - 2 <= I765 /\ I775 <= I764 /\ I774 - 2 <= I765 /\ I774 <= I764 /\ I773 <= I765 /\ I773 + 2 <= I764 /\ -1 <= I768 - 1 /\ I768 <= I766] f5(I779, I780, I781, I782, I783, I784, I785, I786, I787) -> f6(I788, I789, I790, I783, I782, I791, I792, I793, I794) [2 <= I790 - 1 /\ 2 <= I789 - 1 /\ 0 <= I788 - 1 /\ 0 <= I780 - 1 /\ 2 <= I779 - 1 /\ I790 - 2 <= I780 /\ I790 <= I779 /\ I789 - 2 <= I780 /\ I789 <= I779 /\ I788 <= I780 /\ I788 + 2 <= I779 /\ -1 <= I783 - 1 /\ I783 <= I781] f2(I795, I796, I797, I798, I799, I800, I801, I802, I803) -> f5(I804, I805, 0, I806, I797, I807, I808, I809, I810) [0 <= I805 - 1 /\ 2 <= I804 - 1 /\ 0 <= I795 - 1 /\ I805 <= I795 /\ I804 - 2 <= I795 /\ -1 <= I797 - 1 /\ I797 <= I796] f4(I811, I812, I813, I814, I815, I816, I817, I818, I819) -> f3(I820, I812, I813 + 1, I814, I821, I822, I823, I824, I825) [-1 <= I812 - 1 /\ -1 <= I813 - 1 /\ I813 <= I814 - 1 /\ I812 + I813 - 2 * I826 = 0 /\ 0 <= I814 - 1 /\ I812 <= I814 - 1 /\ I813 <= I827 - 1 /\ -1 <= I827 - 1 /\ I820 <= I811 /\ 0 <= I811 - 1 /\ 0 <= I820 - 1 /\ I812 + I813 - 2 * I826 <= 1 /\ 0 <= I812 + I813 - 2 * I826] f3(I828, I829, I830, I831, I832, I833, I834, I835, I836) -> f4(I828, I829, I830, I831, I837, I838, I839, I840, I841) [-1 <= I829 - 1 /\ -1 <= I830 - 1 /\ I830 <= I831 - 1 /\ I829 + I830 - 2 * I842 = 0 /\ 0 <= I831 - 1 /\ I829 <= I831 - 1 /\ I830 <= I843 - 1 /\ -1 <= I843 - 1 /\ I844 <= I828 /\ 0 <= I828 - 1 /\ 0 <= I844 - 1] f4(I845, I846, I847, I848, I849, I850, I851, I852, I853) -> f3(I854, I846, I847 + 1, I848, I855, I856, I857, I858, I859) [-1 <= I846 - 1 /\ -1 <= I847 - 1 /\ I847 <= I848 - 1 /\ I846 + I847 - 2 * I860 = 1 /\ I846 <= I848 - 1 /\ I847 <= I861 - 1 /\ -1 <= I861 - 1 /\ I854 <= I845 /\ 0 <= I845 - 1 /\ 0 <= I854 - 1 /\ I846 + I847 - 2 * I860 <= 1 /\ 0 <= I846 + I847 - 2 * I860] f3(I862, I863, I864, I865, I866, I867, I868, I869, I870) -> f4(I862, I863, I864, I865, I871, I872, I873, I874, I875) [-1 <= I863 - 1 /\ -1 <= I864 - 1 /\ I864 <= I865 - 1 /\ I863 + I864 - 2 * I876 = 1 /\ I863 <= I865 - 1 /\ I864 <= I877 - 1 /\ -1 <= I877 - 1 /\ I878 <= I862 /\ 0 <= I862 - 1 /\ 0 <= I878 - 1] f3(I879, I880, I881, I882, I883, I884, I885, I886, I887) -> f2(I888, I880 + 1, I882, I889, I890, I891, I892, I893, I894) [0 <= I888 - 1 /\ 0 <= I879 - 1 /\ I882 <= I881 /\ I888 <= I879] f2(I895, I896, I897, I898, I899, I900, I901, I902, I903) -> f3(I904, I896, 0, I897, I905, I906, I907, I908, I909) [0 <= I904 - 1 /\ 0 <= I895 - 1 /\ I896 <= I897 - 1 /\ I904 <= I895] f1(I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f2(I919, 0, I911, I920, I921, I922, I923, I924, I925) [0 <= I919 - 1 /\ 0 <= I910 - 1 /\ -1 <= I911 - 1 /\ I919 <= I910]