/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES DP problem for innermost termination. P = init#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13) f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10#(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f10#(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10#(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] f11#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11#(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] f10#(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11#(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] f8#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10#(I97, I98, I99, 0, I91 + 1, I92, 2 * I90, I90, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I91 + 3 <= I84 /\ 0 <= I99 - 1 /\ 0 <= I98 - 1 /\ 3 <= I97 - 1 /\ -1 <= I87 - 1 /\ 3 <= I84 - 1 /\ I99 - 1 <= I87 /\ I99 + 3 <= I84 /\ I98 - 1 <= I87 /\ I98 + 3 <= I84 /\ I97 - 1 <= I84 /\ I92 <= I91 /\ 0 <= 2 * I90 /\ 1073741824 <= I90 - 1 /\ I86 <= I90 - 1] f8#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10#(I118, I119, I120, 0, I112 + 1, I113, 2 * I111, I111, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I112 + 3 <= I105 /\ 0 <= I120 - 1 /\ 0 <= I119 - 1 /\ 3 <= I118 - 1 /\ -1 <= I108 - 1 /\ 3 <= I105 - 1 /\ I120 - 1 <= I108 /\ I120 + 3 <= I105 /\ I119 - 1 <= I108 /\ I119 + 3 <= I105 /\ I118 - 1 <= I105 /\ I111 <= 1073741823 /\ 0 <= 2 * I111 /\ I113 <= I112 /\ 1 <= I111 - 1 /\ I107 <= I111 - 1] f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] f8#(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8#(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] f8#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8#(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] f8#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8#(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] f8#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8#(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] f8#(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9#(I237, I226, I238, 1, I230, I231, I232, I239, I225, I240, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I231 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I230 - 1 /\ I237 <= I224] f8#(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] f4#(I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302) -> f8#(I303, I304, I305, I306, I292, I293 + 2, I294, I295, I296, I307, I308, I309, I310) [I293 + 1 <= I292 - 1 /\ 1 <= I294 - 1 /\ 0 <= I291 - 1 /\ -1 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I311 - 1 /\ -1 <= y2 - 1 /\ I305 <= I294 - 1 /\ I303 <= I290 /\ 3 <= I290 - 1 /\ 3 <= I303 - 1 /\ -1 <= I306 - 1 /\ I296 + 3 <= I290 /\ I295 + 3 <= I290] f7#(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5#(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] f5#(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5#(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] f5#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5#(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] f5#(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387) -> f7#(I388, I389, I390, 1, I391, I379, I380, I381, I382, I392, I376, I393, I394) [I393 + 4 <= I378 /\ I376 + 2 <= I378 /\ I393 + 4 <= I377 /\ I376 + 2 <= I377 /\ I382 + 3 <= I375 /\ I381 + 3 <= I375 /\ -1 <= I392 - 1 /\ -1 <= I390 - 1 /\ 2 <= I389 - 1 /\ 3 <= I388 - 1 /\ 2 <= I378 - 1 /\ 2 <= I377 - 1 /\ 3 <= I375 - 1 /\ I392 + 2 <= I378 /\ I392 + 2 <= I377 /\ I390 + 2 <= I378 /\ I390 + 2 <= I377 /\ I389 <= I378 /\ I389 <= I377 /\ I388 <= I375 /\ 0 <= I379 - 1 /\ 1 <= I380 - 1] f5#(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7#(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] f5#(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5#(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] f5#(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5#(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] f2#(I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) -> f5#(I498, I499, I500, I501, I502, I487, I488, I489, I503, I504, I505, I506, I507) [I508 <= I486 - 1 /\ 1 <= I487 - 1 /\ -1 <= I508 - 1 /\ -1 <= I509 - 1 /\ 0 <= I486 - 1 /\ y3 <= I487 - 1 /\ I498 <= I485 /\ 3 <= I485 - 1 /\ 3 <= I498 - 1 /\ -1 <= I500 - 1 /\ -1 <= I501 - 1 /\ I489 + 3 <= I485 /\ I488 + 3 <= I485 /\ I508 + 1 = I502] f4#(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4#(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] f1#(I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547) -> f4#(I548, I549, I536, 1, 16, 0, 12, I550, I551, I552, I553, I554, I555) [14 <= I548 - 1 /\ 0 <= I535 - 1 /\ I548 - 14 <= I535 /\ 0 <= I536 - 1 /\ -1 <= I549 - 1] f3#(I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f2#(I569, I570, 16, I560, 12, I571, I572, I573, I574, I575, I576, I577, I578) [12 = I561 /\ 16 = I559 /\ I560 + 3 <= I557 /\ 14 <= I569 - 1 /\ 14 <= I557 - 1 /\ 0 <= I556 - 1 /\ I569 <= I557] f1#(I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f2#(I592, I580, I593, I594, I595, I596, I597, I598, I599, I600, I601, I602, I603) [-1 <= I604 - 1 /\ 0 <= I580 - 1 /\ 0 <= I579 - 1 /\ 3 <= I592 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f10(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] f10(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I91 + 1, I92, 2 * I90, I90, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I91 + 3 <= I84 /\ 0 <= I99 - 1 /\ 0 <= I98 - 1 /\ 3 <= I97 - 1 /\ -1 <= I87 - 1 /\ 3 <= I84 - 1 /\ I99 - 1 <= I87 /\ I99 + 3 <= I84 /\ I98 - 1 <= I87 /\ I98 + 3 <= I84 /\ I97 - 1 <= I84 /\ I92 <= I91 /\ 0 <= 2 * I90 /\ 1073741824 <= I90 - 1 /\ I86 <= I90 - 1] f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I112 + 1, I113, 2 * I111, I111, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I112 + 3 <= I105 /\ 0 <= I120 - 1 /\ 0 <= I119 - 1 /\ 3 <= I118 - 1 /\ -1 <= I108 - 1 /\ 3 <= I105 - 1 /\ I120 - 1 <= I108 /\ I120 + 3 <= I105 /\ I119 - 1 <= I108 /\ I119 + 3 <= I105 /\ I118 - 1 <= I105 /\ I111 <= 1073741823 /\ 0 <= 2 * I111 /\ I113 <= I112 /\ 1 <= I111 - 1 /\ I107 <= I111 - 1] f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] f8(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] f8(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] f8(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I225, I240, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I231 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I230 - 1 /\ I237 <= I224] f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] f8(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f6(I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289) [I265 + 2 <= I267 /\ I279 + 2 <= I267 /\ I272 + 3 <= I264 /\ I271 + 3 <= I264 /\ 0 <= I278 - 1 /\ 0 <= I267 - 1 /\ 1 <= I270 - 1 /\ 3 <= I264 - 1] f4(I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302) -> f8(I303, I304, I305, I306, I292, I293 + 2, I294, I295, I296, I307, I308, I309, I310) [I293 + 1 <= I292 - 1 /\ 1 <= I294 - 1 /\ 0 <= I291 - 1 /\ -1 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I311 - 1 /\ -1 <= y2 - 1 /\ I305 <= I294 - 1 /\ I303 <= I290 /\ 3 <= I290 - 1 /\ 3 <= I303 - 1 /\ -1 <= I306 - 1 /\ I296 + 3 <= I290 /\ I295 + 3 <= I290] f7(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] f5(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] f5(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] f5(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387) -> f7(I388, I389, I390, 1, I391, I379, I380, I381, I382, I392, I376, I393, I394) [I393 + 4 <= I378 /\ I376 + 2 <= I378 /\ I393 + 4 <= I377 /\ I376 + 2 <= I377 /\ I382 + 3 <= I375 /\ I381 + 3 <= I375 /\ -1 <= I392 - 1 /\ -1 <= I390 - 1 /\ 2 <= I389 - 1 /\ 3 <= I388 - 1 /\ 2 <= I378 - 1 /\ 2 <= I377 - 1 /\ 3 <= I375 - 1 /\ I392 + 2 <= I378 /\ I392 + 2 <= I377 /\ I390 + 2 <= I378 /\ I390 + 2 <= I377 /\ I389 <= I378 /\ I389 <= I377 /\ I388 <= I375 /\ 0 <= I379 - 1 /\ 1 <= I380 - 1] f5(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f6(I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440) [I416 + 2 <= I418 /\ I430 + 2 <= I418 /\ I430 + 2 <= I417 /\ I416 + 2 <= I417 /\ I422 + 3 <= I415 /\ I421 + 3 <= I415 /\ 0 <= I429 - 1 /\ 0 <= I418 - 1 /\ 0 <= I417 - 1 /\ 3 <= I415 - 1 /\ 0 <= I419 - 1 /\ 1 <= I420 - 1] f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] f5(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] f2(I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) -> f5(I498, I499, I500, I501, I502, I487, I488, I489, I503, I504, I505, I506, I507) [I508 <= I486 - 1 /\ 1 <= I487 - 1 /\ -1 <= I508 - 1 /\ -1 <= I509 - 1 /\ 0 <= I486 - 1 /\ y3 <= I487 - 1 /\ I498 <= I485 /\ 3 <= I485 - 1 /\ 3 <= I498 - 1 /\ -1 <= I500 - 1 /\ -1 <= I501 - 1 /\ I489 + 3 <= I485 /\ I488 + 3 <= I485 /\ I508 + 1 = I502] f4(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] f1(I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547) -> f4(I548, I549, I536, 1, 16, 0, 12, I550, I551, I552, I553, I554, I555) [14 <= I548 - 1 /\ 0 <= I535 - 1 /\ I548 - 14 <= I535 /\ 0 <= I536 - 1 /\ -1 <= I549 - 1] f3(I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f2(I569, I570, 16, I560, 12, I571, I572, I573, I574, I575, I576, I577, I578) [12 = I561 /\ 16 = I559 /\ I560 + 3 <= I557 /\ 14 <= I569 - 1 /\ 14 <= I557 - 1 /\ 0 <= I556 - 1 /\ I569 <= I557] f1(I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f2(I592, I580, I593, I594, I595, I596, I597, I598, I599, I600, I601, I602, I603) [-1 <= I604 - 1 /\ 0 <= I580 - 1 /\ 0 <= I579 - 1 /\ 3 <= I592 - 1] The dependency graph for this problem is: 0 -> 24, 26 1 -> 2, 4 2 -> 2, 4 3 -> 1, 3 4 -> 1, 3 5 -> 2, 4 6 -> 2, 4 7 -> 5, 6, 8, 9, 10, 11, 12, 13 8 -> 5, 6, 8, 9, 10, 11, 12, 13 9 -> 5, 6, 8, 9, 10, 11, 12, 13 10 -> 5, 6, 8, 9, 10, 11, 12, 13 11 -> 5, 6, 8, 9, 10, 11, 12, 13 12 -> 13 -> 7 14 -> 5, 6, 8, 9, 10, 11, 12, 13 15 -> 16, 17, 18, 19, 20, 21 16 -> 16, 17, 18, 19, 20, 21 17 -> 16, 17, 18, 19, 20, 21 18 -> 19 -> 15 20 -> 16, 17, 18, 19, 20, 21 21 -> 16, 17, 18, 19, 20, 21 22 -> 16, 17, 18, 19, 20, 21 23 -> 14, 23 24 -> 14, 23 25 -> 22 26 -> 22 Where: 0) init#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13) 1) f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10#(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] 2) f10#(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10#(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] 3) f11#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11#(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] 4) f10#(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11#(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] 5) f8#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10#(I97, I98, I99, 0, I91 + 1, I92, 2 * I90, I90, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I91 + 3 <= I84 /\ 0 <= I99 - 1 /\ 0 <= I98 - 1 /\ 3 <= I97 - 1 /\ -1 <= I87 - 1 /\ 3 <= I84 - 1 /\ I99 - 1 <= I87 /\ I99 + 3 <= I84 /\ I98 - 1 <= I87 /\ I98 + 3 <= I84 /\ I97 - 1 <= I84 /\ I92 <= I91 /\ 0 <= 2 * I90 /\ 1073741824 <= I90 - 1 /\ I86 <= I90 - 1] 6) f8#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10#(I118, I119, I120, 0, I112 + 1, I113, 2 * I111, I111, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I112 + 3 <= I105 /\ 0 <= I120 - 1 /\ 0 <= I119 - 1 /\ 3 <= I118 - 1 /\ -1 <= I108 - 1 /\ 3 <= I105 - 1 /\ I120 - 1 <= I108 /\ I120 + 3 <= I105 /\ I119 - 1 <= I108 /\ I119 + 3 <= I105 /\ I118 - 1 <= I105 /\ I111 <= 1073741823 /\ 0 <= 2 * I111 /\ I113 <= I112 /\ 1 <= I111 - 1 /\ I107 <= I111 - 1] 7) f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 8) f8#(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8#(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] 9) f8#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8#(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] 10) f8#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8#(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] 11) f8#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8#(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] 12) f8#(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9#(I237, I226, I238, 1, I230, I231, I232, I239, I225, I240, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I231 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I230 - 1 /\ I237 <= I224] 13) f8#(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] 14) f4#(I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302) -> f8#(I303, I304, I305, I306, I292, I293 + 2, I294, I295, I296, I307, I308, I309, I310) [I293 + 1 <= I292 - 1 /\ 1 <= I294 - 1 /\ 0 <= I291 - 1 /\ -1 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I311 - 1 /\ -1 <= y2 - 1 /\ I305 <= I294 - 1 /\ I303 <= I290 /\ 3 <= I290 - 1 /\ 3 <= I303 - 1 /\ -1 <= I306 - 1 /\ I296 + 3 <= I290 /\ I295 + 3 <= I290] 15) f7#(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5#(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] 16) f5#(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5#(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] 17) f5#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5#(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] 18) f5#(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387) -> f7#(I388, I389, I390, 1, I391, I379, I380, I381, I382, I392, I376, I393, I394) [I393 + 4 <= I378 /\ I376 + 2 <= I378 /\ I393 + 4 <= I377 /\ I376 + 2 <= I377 /\ I382 + 3 <= I375 /\ I381 + 3 <= I375 /\ -1 <= I392 - 1 /\ -1 <= I390 - 1 /\ 2 <= I389 - 1 /\ 3 <= I388 - 1 /\ 2 <= I378 - 1 /\ 2 <= I377 - 1 /\ 3 <= I375 - 1 /\ I392 + 2 <= I378 /\ I392 + 2 <= I377 /\ I390 + 2 <= I378 /\ I390 + 2 <= I377 /\ I389 <= I378 /\ I389 <= I377 /\ I388 <= I375 /\ 0 <= I379 - 1 /\ 1 <= I380 - 1] 19) f5#(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7#(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] 20) f5#(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5#(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] 21) f5#(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5#(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] 22) f2#(I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) -> f5#(I498, I499, I500, I501, I502, I487, I488, I489, I503, I504, I505, I506, I507) [I508 <= I486 - 1 /\ 1 <= I487 - 1 /\ -1 <= I508 - 1 /\ -1 <= I509 - 1 /\ 0 <= I486 - 1 /\ y3 <= I487 - 1 /\ I498 <= I485 /\ 3 <= I485 - 1 /\ 3 <= I498 - 1 /\ -1 <= I500 - 1 /\ -1 <= I501 - 1 /\ I489 + 3 <= I485 /\ I488 + 3 <= I485 /\ I508 + 1 = I502] 23) f4#(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4#(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] 24) f1#(I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547) -> f4#(I548, I549, I536, 1, 16, 0, 12, I550, I551, I552, I553, I554, I555) [14 <= I548 - 1 /\ 0 <= I535 - 1 /\ I548 - 14 <= I535 /\ 0 <= I536 - 1 /\ -1 <= I549 - 1] 25) f3#(I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f2#(I569, I570, 16, I560, 12, I571, I572, I573, I574, I575, I576, I577, I578) [12 = I561 /\ 16 = I559 /\ I560 + 3 <= I557 /\ 14 <= I569 - 1 /\ 14 <= I557 - 1 /\ 0 <= I556 - 1 /\ I569 <= I557] 26) f1#(I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f2#(I592, I580, I593, I594, I595, I596, I597, I598, I599, I600, I601, I602, I603) [-1 <= I604 - 1 /\ 0 <= I580 - 1 /\ 0 <= I579 - 1 /\ 3 <= I592 - 1] We have the following SCCs. { 23 } { 7, 8, 9, 10, 11, 13 } { 1, 2, 3, 4 } { 15, 16, 17, 19, 20, 21 } DP problem for innermost termination. P = f7#(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5#(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] f5#(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5#(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] f5#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5#(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] f5#(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7#(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] f5#(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5#(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] f5#(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5#(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f10(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] f10(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I91 + 1, I92, 2 * I90, I90, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I91 + 3 <= I84 /\ 0 <= I99 - 1 /\ 0 <= I98 - 1 /\ 3 <= I97 - 1 /\ -1 <= I87 - 1 /\ 3 <= I84 - 1 /\ I99 - 1 <= I87 /\ I99 + 3 <= I84 /\ I98 - 1 <= I87 /\ I98 + 3 <= I84 /\ I97 - 1 <= I84 /\ I92 <= I91 /\ 0 <= 2 * I90 /\ 1073741824 <= I90 - 1 /\ I86 <= I90 - 1] f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I112 + 1, I113, 2 * I111, I111, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I112 + 3 <= I105 /\ 0 <= I120 - 1 /\ 0 <= I119 - 1 /\ 3 <= I118 - 1 /\ -1 <= I108 - 1 /\ 3 <= I105 - 1 /\ I120 - 1 <= I108 /\ I120 + 3 <= I105 /\ I119 - 1 <= I108 /\ I119 + 3 <= I105 /\ I118 - 1 <= I105 /\ I111 <= 1073741823 /\ 0 <= 2 * I111 /\ I113 <= I112 /\ 1 <= I111 - 1 /\ I107 <= I111 - 1] f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] f8(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] f8(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] f8(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I225, I240, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I231 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I230 - 1 /\ I237 <= I224] f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] f8(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f6(I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289) [I265 + 2 <= I267 /\ I279 + 2 <= I267 /\ I272 + 3 <= I264 /\ I271 + 3 <= I264 /\ 0 <= I278 - 1 /\ 0 <= I267 - 1 /\ 1 <= I270 - 1 /\ 3 <= I264 - 1] f4(I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302) -> f8(I303, I304, I305, I306, I292, I293 + 2, I294, I295, I296, I307, I308, I309, I310) [I293 + 1 <= I292 - 1 /\ 1 <= I294 - 1 /\ 0 <= I291 - 1 /\ -1 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I311 - 1 /\ -1 <= y2 - 1 /\ I305 <= I294 - 1 /\ I303 <= I290 /\ 3 <= I290 - 1 /\ 3 <= I303 - 1 /\ -1 <= I306 - 1 /\ I296 + 3 <= I290 /\ I295 + 3 <= I290] f7(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] f5(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] f5(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] f5(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387) -> f7(I388, I389, I390, 1, I391, I379, I380, I381, I382, I392, I376, I393, I394) [I393 + 4 <= I378 /\ I376 + 2 <= I378 /\ I393 + 4 <= I377 /\ I376 + 2 <= I377 /\ I382 + 3 <= I375 /\ I381 + 3 <= I375 /\ -1 <= I392 - 1 /\ -1 <= I390 - 1 /\ 2 <= I389 - 1 /\ 3 <= I388 - 1 /\ 2 <= I378 - 1 /\ 2 <= I377 - 1 /\ 3 <= I375 - 1 /\ I392 + 2 <= I378 /\ I392 + 2 <= I377 /\ I390 + 2 <= I378 /\ I390 + 2 <= I377 /\ I389 <= I378 /\ I389 <= I377 /\ I388 <= I375 /\ 0 <= I379 - 1 /\ 1 <= I380 - 1] f5(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f6(I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440) [I416 + 2 <= I418 /\ I430 + 2 <= I418 /\ I430 + 2 <= I417 /\ I416 + 2 <= I417 /\ I422 + 3 <= I415 /\ I421 + 3 <= I415 /\ 0 <= I429 - 1 /\ 0 <= I418 - 1 /\ 0 <= I417 - 1 /\ 3 <= I415 - 1 /\ 0 <= I419 - 1 /\ 1 <= I420 - 1] f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] f5(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] f2(I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) -> f5(I498, I499, I500, I501, I502, I487, I488, I489, I503, I504, I505, I506, I507) [I508 <= I486 - 1 /\ 1 <= I487 - 1 /\ -1 <= I508 - 1 /\ -1 <= I509 - 1 /\ 0 <= I486 - 1 /\ y3 <= I487 - 1 /\ I498 <= I485 /\ 3 <= I485 - 1 /\ 3 <= I498 - 1 /\ -1 <= I500 - 1 /\ -1 <= I501 - 1 /\ I489 + 3 <= I485 /\ I488 + 3 <= I485 /\ I508 + 1 = I502] f4(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] f1(I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547) -> f4(I548, I549, I536, 1, 16, 0, 12, I550, I551, I552, I553, I554, I555) [14 <= I548 - 1 /\ 0 <= I535 - 1 /\ I548 - 14 <= I535 /\ 0 <= I536 - 1 /\ -1 <= I549 - 1] f3(I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f2(I569, I570, 16, I560, 12, I571, I572, I573, I574, I575, I576, I577, I578) [12 = I561 /\ 16 = I559 /\ I560 + 3 <= I557 /\ 14 <= I569 - 1 /\ 14 <= I557 - 1 /\ 0 <= I556 - 1 /\ I569 <= I557] f1(I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f2(I592, I580, I593, I594, I595, I596, I597, I598, I599, I600, I601, I602, I603) [-1 <= I604 - 1 /\ 0 <= I580 - 1 /\ 0 <= I579 - 1 /\ 3 <= I592 - 1] We use the basic value criterion with the projection function NU: NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z4 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z3 This gives the following inequalities: 0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312 ==> I314 (>! \union =) I327 I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1 ==> I336 >! I348 I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1 ==> I357 >! I369 I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1 ==> I398 >! I410 I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441 ==> I444 >! I456 I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463 ==> I466 >! I478 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f7#(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5#(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f10(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] f10(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I91 + 1, I92, 2 * I90, I90, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I91 + 3 <= I84 /\ 0 <= I99 - 1 /\ 0 <= I98 - 1 /\ 3 <= I97 - 1 /\ -1 <= I87 - 1 /\ 3 <= I84 - 1 /\ I99 - 1 <= I87 /\ I99 + 3 <= I84 /\ I98 - 1 <= I87 /\ I98 + 3 <= I84 /\ I97 - 1 <= I84 /\ I92 <= I91 /\ 0 <= 2 * I90 /\ 1073741824 <= I90 - 1 /\ I86 <= I90 - 1] f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I112 + 1, I113, 2 * I111, I111, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I112 + 3 <= I105 /\ 0 <= I120 - 1 /\ 0 <= I119 - 1 /\ 3 <= I118 - 1 /\ -1 <= I108 - 1 /\ 3 <= I105 - 1 /\ I120 - 1 <= I108 /\ I120 + 3 <= I105 /\ I119 - 1 <= I108 /\ I119 + 3 <= I105 /\ I118 - 1 <= I105 /\ I111 <= 1073741823 /\ 0 <= 2 * I111 /\ I113 <= I112 /\ 1 <= I111 - 1 /\ I107 <= I111 - 1] f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] f8(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] f8(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] f8(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I225, I240, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I231 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I230 - 1 /\ I237 <= I224] f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] f8(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f6(I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289) [I265 + 2 <= I267 /\ I279 + 2 <= I267 /\ I272 + 3 <= I264 /\ I271 + 3 <= I264 /\ 0 <= I278 - 1 /\ 0 <= I267 - 1 /\ 1 <= I270 - 1 /\ 3 <= I264 - 1] f4(I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302) -> f8(I303, I304, I305, I306, I292, I293 + 2, I294, I295, I296, I307, I308, I309, I310) [I293 + 1 <= I292 - 1 /\ 1 <= I294 - 1 /\ 0 <= I291 - 1 /\ -1 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I311 - 1 /\ -1 <= y2 - 1 /\ I305 <= I294 - 1 /\ I303 <= I290 /\ 3 <= I290 - 1 /\ 3 <= I303 - 1 /\ -1 <= I306 - 1 /\ I296 + 3 <= I290 /\ I295 + 3 <= I290] f7(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] f5(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] f5(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] f5(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387) -> f7(I388, I389, I390, 1, I391, I379, I380, I381, I382, I392, I376, I393, I394) [I393 + 4 <= I378 /\ I376 + 2 <= I378 /\ I393 + 4 <= I377 /\ I376 + 2 <= I377 /\ I382 + 3 <= I375 /\ I381 + 3 <= I375 /\ -1 <= I392 - 1 /\ -1 <= I390 - 1 /\ 2 <= I389 - 1 /\ 3 <= I388 - 1 /\ 2 <= I378 - 1 /\ 2 <= I377 - 1 /\ 3 <= I375 - 1 /\ I392 + 2 <= I378 /\ I392 + 2 <= I377 /\ I390 + 2 <= I378 /\ I390 + 2 <= I377 /\ I389 <= I378 /\ I389 <= I377 /\ I388 <= I375 /\ 0 <= I379 - 1 /\ 1 <= I380 - 1] f5(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f6(I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440) [I416 + 2 <= I418 /\ I430 + 2 <= I418 /\ I430 + 2 <= I417 /\ I416 + 2 <= I417 /\ I422 + 3 <= I415 /\ I421 + 3 <= I415 /\ 0 <= I429 - 1 /\ 0 <= I418 - 1 /\ 0 <= I417 - 1 /\ 3 <= I415 - 1 /\ 0 <= I419 - 1 /\ 1 <= I420 - 1] f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] f5(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] f2(I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) -> f5(I498, I499, I500, I501, I502, I487, I488, I489, I503, I504, I505, I506, I507) [I508 <= I486 - 1 /\ 1 <= I487 - 1 /\ -1 <= I508 - 1 /\ -1 <= I509 - 1 /\ 0 <= I486 - 1 /\ y3 <= I487 - 1 /\ I498 <= I485 /\ 3 <= I485 - 1 /\ 3 <= I498 - 1 /\ -1 <= I500 - 1 /\ -1 <= I501 - 1 /\ I489 + 3 <= I485 /\ I488 + 3 <= I485 /\ I508 + 1 = I502] f4(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] f1(I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547) -> f4(I548, I549, I536, 1, 16, 0, 12, I550, I551, I552, I553, I554, I555) [14 <= I548 - 1 /\ 0 <= I535 - 1 /\ I548 - 14 <= I535 /\ 0 <= I536 - 1 /\ -1 <= I549 - 1] f3(I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f2(I569, I570, 16, I560, 12, I571, I572, I573, I574, I575, I576, I577, I578) [12 = I561 /\ 16 = I559 /\ I560 + 3 <= I557 /\ 14 <= I569 - 1 /\ 14 <= I557 - 1 /\ 0 <= I556 - 1 /\ I569 <= I557] f1(I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f2(I592, I580, I593, I594, I595, I596, I597, I598, I599, I600, I601, I602, I603) [-1 <= I604 - 1 /\ 0 <= I580 - 1 /\ 0 <= I579 - 1 /\ 3 <= I592 - 1] The dependency graph for this problem is: 15 -> Where: 15) f7#(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5#(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] We have the following SCCs. DP problem for innermost termination. P = f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10#(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f10#(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10#(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] f11#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11#(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] f10#(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11#(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f10(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] f10(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I91 + 1, I92, 2 * I90, I90, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I91 + 3 <= I84 /\ 0 <= I99 - 1 /\ 0 <= I98 - 1 /\ 3 <= I97 - 1 /\ -1 <= I87 - 1 /\ 3 <= I84 - 1 /\ I99 - 1 <= I87 /\ I99 + 3 <= I84 /\ I98 - 1 <= I87 /\ I98 + 3 <= I84 /\ I97 - 1 <= I84 /\ I92 <= I91 /\ 0 <= 2 * I90 /\ 1073741824 <= I90 - 1 /\ I86 <= I90 - 1] f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I112 + 1, I113, 2 * I111, I111, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I112 + 3 <= I105 /\ 0 <= I120 - 1 /\ 0 <= I119 - 1 /\ 3 <= I118 - 1 /\ -1 <= I108 - 1 /\ 3 <= I105 - 1 /\ I120 - 1 <= I108 /\ I120 + 3 <= I105 /\ I119 - 1 <= I108 /\ I119 + 3 <= I105 /\ I118 - 1 <= I105 /\ I111 <= 1073741823 /\ 0 <= 2 * I111 /\ I113 <= I112 /\ 1 <= I111 - 1 /\ I107 <= I111 - 1] f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] f8(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] f8(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] f8(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I225, I240, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I231 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I230 - 1 /\ I237 <= I224] f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] f8(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f6(I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289) [I265 + 2 <= I267 /\ I279 + 2 <= I267 /\ I272 + 3 <= I264 /\ I271 + 3 <= I264 /\ 0 <= I278 - 1 /\ 0 <= I267 - 1 /\ 1 <= I270 - 1 /\ 3 <= I264 - 1] f4(I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302) -> f8(I303, I304, I305, I306, I292, I293 + 2, I294, I295, I296, I307, I308, I309, I310) [I293 + 1 <= I292 - 1 /\ 1 <= I294 - 1 /\ 0 <= I291 - 1 /\ -1 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I311 - 1 /\ -1 <= y2 - 1 /\ I305 <= I294 - 1 /\ I303 <= I290 /\ 3 <= I290 - 1 /\ 3 <= I303 - 1 /\ -1 <= I306 - 1 /\ I296 + 3 <= I290 /\ I295 + 3 <= I290] f7(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] f5(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] f5(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] f5(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387) -> f7(I388, I389, I390, 1, I391, I379, I380, I381, I382, I392, I376, I393, I394) [I393 + 4 <= I378 /\ I376 + 2 <= I378 /\ I393 + 4 <= I377 /\ I376 + 2 <= I377 /\ I382 + 3 <= I375 /\ I381 + 3 <= I375 /\ -1 <= I392 - 1 /\ -1 <= I390 - 1 /\ 2 <= I389 - 1 /\ 3 <= I388 - 1 /\ 2 <= I378 - 1 /\ 2 <= I377 - 1 /\ 3 <= I375 - 1 /\ I392 + 2 <= I378 /\ I392 + 2 <= I377 /\ I390 + 2 <= I378 /\ I390 + 2 <= I377 /\ I389 <= I378 /\ I389 <= I377 /\ I388 <= I375 /\ 0 <= I379 - 1 /\ 1 <= I380 - 1] f5(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f6(I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440) [I416 + 2 <= I418 /\ I430 + 2 <= I418 /\ I430 + 2 <= I417 /\ I416 + 2 <= I417 /\ I422 + 3 <= I415 /\ I421 + 3 <= I415 /\ 0 <= I429 - 1 /\ 0 <= I418 - 1 /\ 0 <= I417 - 1 /\ 3 <= I415 - 1 /\ 0 <= I419 - 1 /\ 1 <= I420 - 1] f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] f5(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] f2(I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) -> f5(I498, I499, I500, I501, I502, I487, I488, I489, I503, I504, I505, I506, I507) [I508 <= I486 - 1 /\ 1 <= I487 - 1 /\ -1 <= I508 - 1 /\ -1 <= I509 - 1 /\ 0 <= I486 - 1 /\ y3 <= I487 - 1 /\ I498 <= I485 /\ 3 <= I485 - 1 /\ 3 <= I498 - 1 /\ -1 <= I500 - 1 /\ -1 <= I501 - 1 /\ I489 + 3 <= I485 /\ I488 + 3 <= I485 /\ I508 + 1 = I502] f4(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] f1(I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547) -> f4(I548, I549, I536, 1, 16, 0, 12, I550, I551, I552, I553, I554, I555) [14 <= I548 - 1 /\ 0 <= I535 - 1 /\ I548 - 14 <= I535 /\ 0 <= I536 - 1 /\ -1 <= I549 - 1] f3(I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f2(I569, I570, 16, I560, 12, I571, I572, I573, I574, I575, I576, I577, I578) [12 = I561 /\ 16 = I559 /\ I560 + 3 <= I557 /\ 14 <= I569 - 1 /\ 14 <= I557 - 1 /\ 0 <= I556 - 1 /\ I569 <= I557] f1(I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f2(I592, I580, I593, I594, I595, I596, I597, I598, I599, I600, I601, I602, I603) [-1 <= I604 - 1 /\ 0 <= I580 - 1 /\ 0 <= I579 - 1 /\ 3 <= I592 - 1] We use the reverse value criterion with the projection function NU: NU[f10#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z8 - 1 + -1 * z4 NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z10 - 1 + -1 * (z3 + 1) This gives the following inequalities: I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1 ==> I9 - 1 + -1 * (I2 + 1) >= I9 - 1 + -1 * (I2 + 1) I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1 ==> I28 - 1 + -1 * I24 > I28 - 1 + -1 * (I24 + 1) with I28 - 1 + -1 * I24 >= 0 I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1 ==> I51 - 1 + -1 * (I44 + 1) >= I51 - 1 + -1 * (I44 + 1) I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1 ==> I70 - 1 + -1 * I66 > I70 - 1 + -1 * (I66 + 1) with I70 - 1 + -1 * I66 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10#(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f11#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11#(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f10(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] f10(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I91 + 1, I92, 2 * I90, I90, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I91 + 3 <= I84 /\ 0 <= I99 - 1 /\ 0 <= I98 - 1 /\ 3 <= I97 - 1 /\ -1 <= I87 - 1 /\ 3 <= I84 - 1 /\ I99 - 1 <= I87 /\ I99 + 3 <= I84 /\ I98 - 1 <= I87 /\ I98 + 3 <= I84 /\ I97 - 1 <= I84 /\ I92 <= I91 /\ 0 <= 2 * I90 /\ 1073741824 <= I90 - 1 /\ I86 <= I90 - 1] f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I112 + 1, I113, 2 * I111, I111, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I112 + 3 <= I105 /\ 0 <= I120 - 1 /\ 0 <= I119 - 1 /\ 3 <= I118 - 1 /\ -1 <= I108 - 1 /\ 3 <= I105 - 1 /\ I120 - 1 <= I108 /\ I120 + 3 <= I105 /\ I119 - 1 <= I108 /\ I119 + 3 <= I105 /\ I118 - 1 <= I105 /\ I111 <= 1073741823 /\ 0 <= 2 * I111 /\ I113 <= I112 /\ 1 <= I111 - 1 /\ I107 <= I111 - 1] f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] f8(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] f8(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] f8(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I225, I240, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I231 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I230 - 1 /\ I237 <= I224] f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] f8(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f6(I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289) [I265 + 2 <= I267 /\ I279 + 2 <= I267 /\ I272 + 3 <= I264 /\ I271 + 3 <= I264 /\ 0 <= I278 - 1 /\ 0 <= I267 - 1 /\ 1 <= I270 - 1 /\ 3 <= I264 - 1] f4(I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302) -> f8(I303, I304, I305, I306, I292, I293 + 2, I294, I295, I296, I307, I308, I309, I310) [I293 + 1 <= I292 - 1 /\ 1 <= I294 - 1 /\ 0 <= I291 - 1 /\ -1 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I311 - 1 /\ -1 <= y2 - 1 /\ I305 <= I294 - 1 /\ I303 <= I290 /\ 3 <= I290 - 1 /\ 3 <= I303 - 1 /\ -1 <= I306 - 1 /\ I296 + 3 <= I290 /\ I295 + 3 <= I290] f7(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] f5(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] f5(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] f5(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387) -> f7(I388, I389, I390, 1, I391, I379, I380, I381, I382, I392, I376, I393, I394) [I393 + 4 <= I378 /\ I376 + 2 <= I378 /\ I393 + 4 <= I377 /\ I376 + 2 <= I377 /\ I382 + 3 <= I375 /\ I381 + 3 <= I375 /\ -1 <= I392 - 1 /\ -1 <= I390 - 1 /\ 2 <= I389 - 1 /\ 3 <= I388 - 1 /\ 2 <= I378 - 1 /\ 2 <= I377 - 1 /\ 3 <= I375 - 1 /\ I392 + 2 <= I378 /\ I392 + 2 <= I377 /\ I390 + 2 <= I378 /\ I390 + 2 <= I377 /\ I389 <= I378 /\ I389 <= I377 /\ I388 <= I375 /\ 0 <= I379 - 1 /\ 1 <= I380 - 1] f5(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f6(I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440) [I416 + 2 <= I418 /\ I430 + 2 <= I418 /\ I430 + 2 <= I417 /\ I416 + 2 <= I417 /\ I422 + 3 <= I415 /\ I421 + 3 <= I415 /\ 0 <= I429 - 1 /\ 0 <= I418 - 1 /\ 0 <= I417 - 1 /\ 3 <= I415 - 1 /\ 0 <= I419 - 1 /\ 1 <= I420 - 1] f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] f5(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] f2(I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) -> f5(I498, I499, I500, I501, I502, I487, I488, I489, I503, I504, I505, I506, I507) [I508 <= I486 - 1 /\ 1 <= I487 - 1 /\ -1 <= I508 - 1 /\ -1 <= I509 - 1 /\ 0 <= I486 - 1 /\ y3 <= I487 - 1 /\ I498 <= I485 /\ 3 <= I485 - 1 /\ 3 <= I498 - 1 /\ -1 <= I500 - 1 /\ -1 <= I501 - 1 /\ I489 + 3 <= I485 /\ I488 + 3 <= I485 /\ I508 + 1 = I502] f4(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] f1(I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547) -> f4(I548, I549, I536, 1, 16, 0, 12, I550, I551, I552, I553, I554, I555) [14 <= I548 - 1 /\ 0 <= I535 - 1 /\ I548 - 14 <= I535 /\ 0 <= I536 - 1 /\ -1 <= I549 - 1] f3(I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f2(I569, I570, 16, I560, 12, I571, I572, I573, I574, I575, I576, I577, I578) [12 = I561 /\ 16 = I559 /\ I560 + 3 <= I557 /\ 14 <= I569 - 1 /\ 14 <= I557 - 1 /\ 0 <= I556 - 1 /\ I569 <= I557] f1(I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f2(I592, I580, I593, I594, I595, I596, I597, I598, I599, I600, I601, I602, I603) [-1 <= I604 - 1 /\ 0 <= I580 - 1 /\ 0 <= I579 - 1 /\ 3 <= I592 - 1] The dependency graph for this problem is: 1 -> 3 -> 1, 3 Where: 1) f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10#(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] 3) f11#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11#(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] We have the following SCCs. { 3 } DP problem for innermost termination. P = f11#(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11#(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f10(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] f10(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I91 + 1, I92, 2 * I90, I90, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I91 + 3 <= I84 /\ 0 <= I99 - 1 /\ 0 <= I98 - 1 /\ 3 <= I97 - 1 /\ -1 <= I87 - 1 /\ 3 <= I84 - 1 /\ I99 - 1 <= I87 /\ I99 + 3 <= I84 /\ I98 - 1 <= I87 /\ I98 + 3 <= I84 /\ I97 - 1 <= I84 /\ I92 <= I91 /\ 0 <= 2 * I90 /\ 1073741824 <= I90 - 1 /\ I86 <= I90 - 1] f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I112 + 1, I113, 2 * I111, I111, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I112 + 3 <= I105 /\ 0 <= I120 - 1 /\ 0 <= I119 - 1 /\ 3 <= I118 - 1 /\ -1 <= I108 - 1 /\ 3 <= I105 - 1 /\ I120 - 1 <= I108 /\ I120 + 3 <= I105 /\ I119 - 1 <= I108 /\ I119 + 3 <= I105 /\ I118 - 1 <= I105 /\ I111 <= 1073741823 /\ 0 <= 2 * I111 /\ I113 <= I112 /\ 1 <= I111 - 1 /\ I107 <= I111 - 1] f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] f8(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] f8(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] f8(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I225, I240, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I231 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I230 - 1 /\ I237 <= I224] f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] f8(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f6(I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289) [I265 + 2 <= I267 /\ I279 + 2 <= I267 /\ I272 + 3 <= I264 /\ I271 + 3 <= I264 /\ 0 <= I278 - 1 /\ 0 <= I267 - 1 /\ 1 <= I270 - 1 /\ 3 <= I264 - 1] f4(I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302) -> f8(I303, I304, I305, I306, I292, I293 + 2, I294, I295, I296, I307, I308, I309, I310) [I293 + 1 <= I292 - 1 /\ 1 <= I294 - 1 /\ 0 <= I291 - 1 /\ -1 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I311 - 1 /\ -1 <= y2 - 1 /\ I305 <= I294 - 1 /\ I303 <= I290 /\ 3 <= I290 - 1 /\ 3 <= I303 - 1 /\ -1 <= I306 - 1 /\ I296 + 3 <= I290 /\ I295 + 3 <= I290] f7(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] f5(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] f5(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] f5(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387) -> f7(I388, I389, I390, 1, I391, I379, I380, I381, I382, I392, I376, I393, I394) [I393 + 4 <= I378 /\ I376 + 2 <= I378 /\ I393 + 4 <= I377 /\ I376 + 2 <= I377 /\ I382 + 3 <= I375 /\ I381 + 3 <= I375 /\ -1 <= I392 - 1 /\ -1 <= I390 - 1 /\ 2 <= I389 - 1 /\ 3 <= I388 - 1 /\ 2 <= I378 - 1 /\ 2 <= I377 - 1 /\ 3 <= I375 - 1 /\ I392 + 2 <= I378 /\ I392 + 2 <= I377 /\ I390 + 2 <= I378 /\ I390 + 2 <= I377 /\ I389 <= I378 /\ I389 <= I377 /\ I388 <= I375 /\ 0 <= I379 - 1 /\ 1 <= I380 - 1] f5(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f6(I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440) [I416 + 2 <= I418 /\ I430 + 2 <= I418 /\ I430 + 2 <= I417 /\ I416 + 2 <= I417 /\ I422 + 3 <= I415 /\ I421 + 3 <= I415 /\ 0 <= I429 - 1 /\ 0 <= I418 - 1 /\ 0 <= I417 - 1 /\ 3 <= I415 - 1 /\ 0 <= I419 - 1 /\ 1 <= I420 - 1] f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] f5(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] f2(I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) -> f5(I498, I499, I500, I501, I502, I487, I488, I489, I503, I504, I505, I506, I507) [I508 <= I486 - 1 /\ 1 <= I487 - 1 /\ -1 <= I508 - 1 /\ -1 <= I509 - 1 /\ 0 <= I486 - 1 /\ y3 <= I487 - 1 /\ I498 <= I485 /\ 3 <= I485 - 1 /\ 3 <= I498 - 1 /\ -1 <= I500 - 1 /\ -1 <= I501 - 1 /\ I489 + 3 <= I485 /\ I488 + 3 <= I485 /\ I508 + 1 = I502] f4(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] f1(I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547) -> f4(I548, I549, I536, 1, 16, 0, 12, I550, I551, I552, I553, I554, I555) [14 <= I548 - 1 /\ 0 <= I535 - 1 /\ I548 - 14 <= I535 /\ 0 <= I536 - 1 /\ -1 <= I549 - 1] f3(I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f2(I569, I570, 16, I560, 12, I571, I572, I573, I574, I575, I576, I577, I578) [12 = I561 /\ 16 = I559 /\ I560 + 3 <= I557 /\ 14 <= I569 - 1 /\ 14 <= I557 - 1 /\ 0 <= I556 - 1 /\ I569 <= I557] f1(I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f2(I592, I580, I593, I594, I595, I596, I597, I598, I599, I600, I601, I602, I603) [-1 <= I604 - 1 /\ 0 <= I580 - 1 /\ 0 <= I579 - 1 /\ 3 <= I592 - 1] We use the basic value criterion with the projection function NU: NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z5 This gives the following inequalities: I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1 ==> I46 >! I58 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. DP problem for innermost termination. P = f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] f8#(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8#(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] f8#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8#(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] f8#(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8#(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] f8#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8#(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] f8#(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f10(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] f10(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I91 + 1, I92, 2 * I90, I90, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I91 + 3 <= I84 /\ 0 <= I99 - 1 /\ 0 <= I98 - 1 /\ 3 <= I97 - 1 /\ -1 <= I87 - 1 /\ 3 <= I84 - 1 /\ I99 - 1 <= I87 /\ I99 + 3 <= I84 /\ I98 - 1 <= I87 /\ I98 + 3 <= I84 /\ I97 - 1 <= I84 /\ I92 <= I91 /\ 0 <= 2 * I90 /\ 1073741824 <= I90 - 1 /\ I86 <= I90 - 1] f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I112 + 1, I113, 2 * I111, I111, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I112 + 3 <= I105 /\ 0 <= I120 - 1 /\ 0 <= I119 - 1 /\ 3 <= I118 - 1 /\ -1 <= I108 - 1 /\ 3 <= I105 - 1 /\ I120 - 1 <= I108 /\ I120 + 3 <= I105 /\ I119 - 1 <= I108 /\ I119 + 3 <= I105 /\ I118 - 1 <= I105 /\ I111 <= 1073741823 /\ 0 <= 2 * I111 /\ I113 <= I112 /\ 1 <= I111 - 1 /\ I107 <= I111 - 1] f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] f8(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] f8(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] f8(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I225, I240, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I231 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I230 - 1 /\ I237 <= I224] f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] f8(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f6(I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289) [I265 + 2 <= I267 /\ I279 + 2 <= I267 /\ I272 + 3 <= I264 /\ I271 + 3 <= I264 /\ 0 <= I278 - 1 /\ 0 <= I267 - 1 /\ 1 <= I270 - 1 /\ 3 <= I264 - 1] f4(I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302) -> f8(I303, I304, I305, I306, I292, I293 + 2, I294, I295, I296, I307, I308, I309, I310) [I293 + 1 <= I292 - 1 /\ 1 <= I294 - 1 /\ 0 <= I291 - 1 /\ -1 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I311 - 1 /\ -1 <= y2 - 1 /\ I305 <= I294 - 1 /\ I303 <= I290 /\ 3 <= I290 - 1 /\ 3 <= I303 - 1 /\ -1 <= I306 - 1 /\ I296 + 3 <= I290 /\ I295 + 3 <= I290] f7(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] f5(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] f5(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] f5(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387) -> f7(I388, I389, I390, 1, I391, I379, I380, I381, I382, I392, I376, I393, I394) [I393 + 4 <= I378 /\ I376 + 2 <= I378 /\ I393 + 4 <= I377 /\ I376 + 2 <= I377 /\ I382 + 3 <= I375 /\ I381 + 3 <= I375 /\ -1 <= I392 - 1 /\ -1 <= I390 - 1 /\ 2 <= I389 - 1 /\ 3 <= I388 - 1 /\ 2 <= I378 - 1 /\ 2 <= I377 - 1 /\ 3 <= I375 - 1 /\ I392 + 2 <= I378 /\ I392 + 2 <= I377 /\ I390 + 2 <= I378 /\ I390 + 2 <= I377 /\ I389 <= I378 /\ I389 <= I377 /\ I388 <= I375 /\ 0 <= I379 - 1 /\ 1 <= I380 - 1] f5(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f6(I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440) [I416 + 2 <= I418 /\ I430 + 2 <= I418 /\ I430 + 2 <= I417 /\ I416 + 2 <= I417 /\ I422 + 3 <= I415 /\ I421 + 3 <= I415 /\ 0 <= I429 - 1 /\ 0 <= I418 - 1 /\ 0 <= I417 - 1 /\ 3 <= I415 - 1 /\ 0 <= I419 - 1 /\ 1 <= I420 - 1] f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] f5(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] f2(I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) -> f5(I498, I499, I500, I501, I502, I487, I488, I489, I503, I504, I505, I506, I507) [I508 <= I486 - 1 /\ 1 <= I487 - 1 /\ -1 <= I508 - 1 /\ -1 <= I509 - 1 /\ 0 <= I486 - 1 /\ y3 <= I487 - 1 /\ I498 <= I485 /\ 3 <= I485 - 1 /\ 3 <= I498 - 1 /\ -1 <= I500 - 1 /\ -1 <= I501 - 1 /\ I489 + 3 <= I485 /\ I488 + 3 <= I485 /\ I508 + 1 = I502] f4(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] f1(I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547) -> f4(I548, I549, I536, 1, 16, 0, 12, I550, I551, I552, I553, I554, I555) [14 <= I548 - 1 /\ 0 <= I535 - 1 /\ I548 - 14 <= I535 /\ 0 <= I536 - 1 /\ -1 <= I549 - 1] f3(I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f2(I569, I570, 16, I560, 12, I571, I572, I573, I574, I575, I576, I577, I578) [12 = I561 /\ 16 = I559 /\ I560 + 3 <= I557 /\ 14 <= I569 - 1 /\ 14 <= I557 - 1 /\ 0 <= I556 - 1 /\ I569 <= I557] f1(I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f2(I592, I580, I593, I594, I595, I596, I597, I598, I599, I600, I601, I602, I603) [-1 <= I604 - 1 /\ 0 <= I580 - 1 /\ 0 <= I579 - 1 /\ 3 <= I592 - 1] We use the basic value criterion with the projection function NU: NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z4 NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z8 This gives the following inequalities: 0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126 ==> I133 (>! \union =) I140 I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147 ==> I150 >! I161 I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166 ==> I169 >! I180 I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185 ==> I188 >! I199 I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204 ==> I207 >! I218 I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244 ==> I247 >! I259 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f10(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] f10(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I91 + 1, I92, 2 * I90, I90, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I91 + 3 <= I84 /\ 0 <= I99 - 1 /\ 0 <= I98 - 1 /\ 3 <= I97 - 1 /\ -1 <= I87 - 1 /\ 3 <= I84 - 1 /\ I99 - 1 <= I87 /\ I99 + 3 <= I84 /\ I98 - 1 <= I87 /\ I98 + 3 <= I84 /\ I97 - 1 <= I84 /\ I92 <= I91 /\ 0 <= 2 * I90 /\ 1073741824 <= I90 - 1 /\ I86 <= I90 - 1] f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I112 + 1, I113, 2 * I111, I111, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I112 + 3 <= I105 /\ 0 <= I120 - 1 /\ 0 <= I119 - 1 /\ 3 <= I118 - 1 /\ -1 <= I108 - 1 /\ 3 <= I105 - 1 /\ I120 - 1 <= I108 /\ I120 + 3 <= I105 /\ I119 - 1 <= I108 /\ I119 + 3 <= I105 /\ I118 - 1 <= I105 /\ I111 <= 1073741823 /\ 0 <= 2 * I111 /\ I113 <= I112 /\ 1 <= I111 - 1 /\ I107 <= I111 - 1] f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] f8(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] f8(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] f8(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I225, I240, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I231 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I230 - 1 /\ I237 <= I224] f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] f8(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f6(I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289) [I265 + 2 <= I267 /\ I279 + 2 <= I267 /\ I272 + 3 <= I264 /\ I271 + 3 <= I264 /\ 0 <= I278 - 1 /\ 0 <= I267 - 1 /\ 1 <= I270 - 1 /\ 3 <= I264 - 1] f4(I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302) -> f8(I303, I304, I305, I306, I292, I293 + 2, I294, I295, I296, I307, I308, I309, I310) [I293 + 1 <= I292 - 1 /\ 1 <= I294 - 1 /\ 0 <= I291 - 1 /\ -1 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I311 - 1 /\ -1 <= y2 - 1 /\ I305 <= I294 - 1 /\ I303 <= I290 /\ 3 <= I290 - 1 /\ 3 <= I303 - 1 /\ -1 <= I306 - 1 /\ I296 + 3 <= I290 /\ I295 + 3 <= I290] f7(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] f5(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] f5(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] f5(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387) -> f7(I388, I389, I390, 1, I391, I379, I380, I381, I382, I392, I376, I393, I394) [I393 + 4 <= I378 /\ I376 + 2 <= I378 /\ I393 + 4 <= I377 /\ I376 + 2 <= I377 /\ I382 + 3 <= I375 /\ I381 + 3 <= I375 /\ -1 <= I392 - 1 /\ -1 <= I390 - 1 /\ 2 <= I389 - 1 /\ 3 <= I388 - 1 /\ 2 <= I378 - 1 /\ 2 <= I377 - 1 /\ 3 <= I375 - 1 /\ I392 + 2 <= I378 /\ I392 + 2 <= I377 /\ I390 + 2 <= I378 /\ I390 + 2 <= I377 /\ I389 <= I378 /\ I389 <= I377 /\ I388 <= I375 /\ 0 <= I379 - 1 /\ 1 <= I380 - 1] f5(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f6(I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440) [I416 + 2 <= I418 /\ I430 + 2 <= I418 /\ I430 + 2 <= I417 /\ I416 + 2 <= I417 /\ I422 + 3 <= I415 /\ I421 + 3 <= I415 /\ 0 <= I429 - 1 /\ 0 <= I418 - 1 /\ 0 <= I417 - 1 /\ 3 <= I415 - 1 /\ 0 <= I419 - 1 /\ 1 <= I420 - 1] f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] f5(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] f2(I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) -> f5(I498, I499, I500, I501, I502, I487, I488, I489, I503, I504, I505, I506, I507) [I508 <= I486 - 1 /\ 1 <= I487 - 1 /\ -1 <= I508 - 1 /\ -1 <= I509 - 1 /\ 0 <= I486 - 1 /\ y3 <= I487 - 1 /\ I498 <= I485 /\ 3 <= I485 - 1 /\ 3 <= I498 - 1 /\ -1 <= I500 - 1 /\ -1 <= I501 - 1 /\ I489 + 3 <= I485 /\ I488 + 3 <= I485 /\ I508 + 1 = I502] f4(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] f1(I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547) -> f4(I548, I549, I536, 1, 16, 0, 12, I550, I551, I552, I553, I554, I555) [14 <= I548 - 1 /\ 0 <= I535 - 1 /\ I548 - 14 <= I535 /\ 0 <= I536 - 1 /\ -1 <= I549 - 1] f3(I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f2(I569, I570, 16, I560, 12, I571, I572, I573, I574, I575, I576, I577, I578) [12 = I561 /\ 16 = I559 /\ I560 + 3 <= I557 /\ 14 <= I569 - 1 /\ 14 <= I557 - 1 /\ 0 <= I556 - 1 /\ I569 <= I557] f1(I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f2(I592, I580, I593, I594, I595, I596, I597, I598, I599, I600, I601, I602, I603) [-1 <= I604 - 1 /\ 0 <= I580 - 1 /\ 0 <= I579 - 1 /\ 3 <= I592 - 1] The dependency graph for this problem is: 7 -> Where: 7) f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] We have the following SCCs. DP problem for innermost termination. P = f4#(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4#(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] R = init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13) f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12) -> f10(I13, I14, I15, I2 + 1, I7, I8, I12, I9, I16, I17, I18, I19, I20) [I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I15 - 1 /\ 0 <= I14 - 1 /\ 3 <= I13 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I5 /\ I14 + 1 <= I4 /\ I14 - 1 <= I3 /\ I14 <= I1 /\ I14 + 3 <= I0 /\ I13 <= I0 /\ I6 <= I12 - 1 /\ -1 <= I9 - 1] f10(I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33) -> f10(I34, I35, I36, I24 + 1, I25, I26, I27, I28, I37, I38, I39, I40, I41) [I26 + 3 <= I21 /\ I25 + 3 <= I21 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 3 <= I34 - 1 /\ 0 <= I23 - 1 /\ 0 <= I22 - 1 /\ 3 <= I21 - 1 /\ I36 <= I23 /\ I36 <= I22 /\ I36 + 3 <= I21 /\ I35 <= I23 /\ I35 <= I22 /\ I35 + 3 <= I21 /\ I34 <= I21 /\ I24 <= I28 - 1 /\ -1 <= I28 - 1] f11(I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f11(I55, I56, I44, I57, I58, I59, I60, I49, I50, I51, I61, I62, I54) [I53 + 2 <= I46 /\ I52 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I62 + 2 <= I45 /\ I61 + 2 <= I45 /\ I50 + 3 <= I42 /\ I49 + 3 <= I42 /\ 0 <= I59 - 1 /\ 0 <= I58 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ 3 <= I55 - 1 /\ 0 <= I47 - 1 /\ 2 <= I46 - 1 /\ 0 <= I45 - 1 /\ 0 <= I43 - 1 /\ 3 <= I42 - 1 /\ I59 <= I47 /\ I59 + 2 <= I46 /\ I59 <= I45 /\ I59 <= I43 /\ I59 + 3 <= I42 /\ I58 + 2 <= I46 /\ I58 <= I45 /\ I57 + 3 <= I46 /\ I57 + 1 <= I45 /\ I56 <= I47 /\ I56 + 2 <= I46 /\ I56 <= I45 /\ I56 <= I43 /\ I56 + 3 <= I42 /\ I55 <= I42 /\ 0 <= I54 - 1 /\ I48 <= I54 - 1] f10(I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74, I75) -> f11(I76, I77, I66, I78, I79, I80, I81, I67, I68, I70, I82, I83, I69) [I68 + 3 <= I63 /\ I67 + 3 <= I63 /\ 0 <= I80 - 1 /\ 0 <= I79 - 1 /\ -1 <= I78 - 1 /\ 0 <= I77 - 1 /\ 3 <= I76 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1 /\ 3 <= I63 - 1 /\ I80 <= I65 /\ I80 <= I64 /\ I80 + 3 <= I63 /\ I77 <= I65 /\ I77 <= I64 /\ I77 + 3 <= I63 /\ I76 <= I63 /\ I66 <= I70 - 1 /\ 0 <= I69 - 1] f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I91 + 1, I92, 2 * I90, I90, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I91 + 3 <= I84 /\ 0 <= I99 - 1 /\ 0 <= I98 - 1 /\ 3 <= I97 - 1 /\ -1 <= I87 - 1 /\ 3 <= I84 - 1 /\ I99 - 1 <= I87 /\ I99 + 3 <= I84 /\ I98 - 1 <= I87 /\ I98 + 3 <= I84 /\ I97 - 1 <= I84 /\ I92 <= I91 /\ 0 <= 2 * I90 /\ 1073741824 <= I90 - 1 /\ I86 <= I90 - 1] f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I112 + 1, I113, 2 * I111, I111, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I112 + 3 <= I105 /\ 0 <= I120 - 1 /\ 0 <= I119 - 1 /\ 3 <= I118 - 1 /\ -1 <= I108 - 1 /\ 3 <= I105 - 1 /\ I120 - 1 <= I108 /\ I120 + 3 <= I105 /\ I119 - 1 <= I108 /\ I119 + 3 <= I105 /\ I118 - 1 <= I105 /\ I111 <= 1073741823 /\ 0 <= 2 * I111 /\ I113 <= I112 /\ 1 <= I111 - 1 /\ I107 <= I111 - 1] f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 4 <= I128 /\ I134 + 2 <= I128 /\ I132 + 3 <= I126 /\ I131 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] f8(I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158, I159) -> f8(I160, I148, I149, I161, I151, I152, I153, I154, I155, I162, I163, I164, I165) [I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I154 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I153 - 1 /\ I160 <= I147] f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I174, I181, I182, I183, I184) [I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I173 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I172 - 1 /\ I179 <= I166] f8(I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197) -> f8(I198, I186, I187, I199, I189, I190, I191, I192, I193, I200, I201, I202, I203) [I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I192 + 3 <= I185 /\ I193 + 3 <= I185] f8(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216) -> f8(I217, I205, I206, I218, I208, I209, I210, I211, I212, I219, I220, I221, I222) [I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I211 + 3 <= I204 /\ I212 + 3 <= I204] f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I225, I240, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I231 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I230 - 1 /\ I237 <= I224] f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I245, I260, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I251 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I250 - 1 /\ I257 <= I244] f8(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f6(I277, I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289) [I265 + 2 <= I267 /\ I279 + 2 <= I267 /\ I272 + 3 <= I264 /\ I271 + 3 <= I264 /\ 0 <= I278 - 1 /\ 0 <= I267 - 1 /\ 1 <= I270 - 1 /\ 3 <= I264 - 1] f4(I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302) -> f8(I303, I304, I305, I306, I292, I293 + 2, I294, I295, I296, I307, I308, I309, I310) [I293 + 1 <= I292 - 1 /\ 1 <= I294 - 1 /\ 0 <= I291 - 1 /\ -1 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I311 - 1 /\ -1 <= y2 - 1 /\ I305 <= I294 - 1 /\ I303 <= I290 /\ 3 <= I290 - 1 /\ 3 <= I303 - 1 /\ -1 <= I306 - 1 /\ I296 + 3 <= I290 /\ I295 + 3 <= I290] f7(I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324) -> f5(I325, I322, I326, I327, I317, I318, I319, I320, I328, I329, I330, I331, I332) [0 = I315 /\ I323 + 4 <= I313 /\ I322 + 2 <= I313 /\ I320 + 3 <= I312 /\ I319 + 3 <= I312 /\ -1 <= I327 - 1 /\ -1 <= I326 - 1 /\ 3 <= I325 - 1 /\ -1 <= I321 - 1 /\ -1 <= I314 - 1 /\ 2 <= I313 - 1 /\ 3 <= I312 - 1 /\ I327 <= I321 /\ I327 <= I314 /\ I327 + 2 <= I313 /\ I326 <= I321 /\ I326 <= I314 /\ I326 + 2 <= I313 /\ I325 <= I312] f5(I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345) -> f5(I346, I334, I347, I348, I337, I338, I339, I340, I349, I350, I351, I352, I353) [I334 + 2 <= I336 /\ I334 + 2 <= I335 /\ I340 + 3 <= I333 /\ I339 + 3 <= I333 /\ -1 <= I348 - 1 /\ -1 <= I347 - 1 /\ 3 <= I346 - 1 /\ 2 <= I336 - 1 /\ 2 <= I335 - 1 /\ 3 <= I333 - 1 /\ I348 + 2 <= I336 /\ I348 + 2 <= I335 /\ I347 + 2 <= I336 /\ I347 + 2 <= I335 /\ I346 <= I333 /\ 0 <= I337 - 1 /\ 1 <= I338 - 1] f5(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f5(I367, I355, I368, I369, I358, I359, I360, I361, I370, I371, I372, I373, I374) [I355 + 2 <= I357 /\ I355 + 2 <= I356 /\ I361 + 3 <= I354 /\ I360 + 3 <= I354 /\ -1 <= I369 - 1 /\ -1 <= I368 - 1 /\ 3 <= I367 - 1 /\ 1 <= I357 - 1 /\ 1 <= I356 - 1 /\ 3 <= I354 - 1 /\ I369 + 2 <= I357 /\ I369 + 2 <= I356 /\ I368 + 2 <= I357 /\ I368 + 2 <= I356 /\ I367 <= I354 /\ 0 <= I358 - 1 /\ 1 <= I359 - 1] f5(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387) -> f7(I388, I389, I390, 1, I391, I379, I380, I381, I382, I392, I376, I393, I394) [I393 + 4 <= I378 /\ I376 + 2 <= I378 /\ I393 + 4 <= I377 /\ I376 + 2 <= I377 /\ I382 + 3 <= I375 /\ I381 + 3 <= I375 /\ -1 <= I392 - 1 /\ -1 <= I390 - 1 /\ 2 <= I389 - 1 /\ 3 <= I388 - 1 /\ 2 <= I378 - 1 /\ 2 <= I377 - 1 /\ 3 <= I375 - 1 /\ I392 + 2 <= I378 /\ I392 + 2 <= I377 /\ I390 + 2 <= I378 /\ I390 + 2 <= I377 /\ I389 <= I378 /\ I389 <= I377 /\ I388 <= I375 /\ 0 <= I379 - 1 /\ 1 <= I380 - 1] f5(I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f7(I408, I409, I410, 0, I411, I399, I400, I401, I402, I412, I396, I413, I414) [I413 + 4 <= I398 /\ I396 + 2 <= I398 /\ I413 + 4 <= I397 /\ I396 + 2 <= I397 /\ I402 + 3 <= I395 /\ I401 + 3 <= I395 /\ -1 <= I412 - 1 /\ -1 <= I410 - 1 /\ 2 <= I409 - 1 /\ 3 <= I408 - 1 /\ 2 <= I398 - 1 /\ 2 <= I397 - 1 /\ 3 <= I395 - 1 /\ I412 + 2 <= I398 /\ I412 + 2 <= I397 /\ I410 + 2 <= I398 /\ I410 + 2 <= I397 /\ I409 <= I398 /\ I409 <= I397 /\ I408 <= I395 /\ 0 <= I399 - 1 /\ 1 <= I400 - 1] f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f6(I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440) [I416 + 2 <= I418 /\ I430 + 2 <= I418 /\ I430 + 2 <= I417 /\ I416 + 2 <= I417 /\ I422 + 3 <= I415 /\ I421 + 3 <= I415 /\ 0 <= I429 - 1 /\ 0 <= I418 - 1 /\ 0 <= I417 - 1 /\ 3 <= I415 - 1 /\ 0 <= I419 - 1 /\ 1 <= I420 - 1] f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f5(I454, I442, I455, I456, I445, I446, I447, I448, I457, I458, I459, I460, I461) [I454 <= I441 /\ I442 <= I462 - 1 /\ I455 + 1 <= I443 /\ I455 + 1 <= I444 /\ I456 + 1 <= I443 /\ I456 + 1 <= I444 /\ 3 <= I441 - 1 /\ 0 <= I443 - 1 /\ 0 <= I444 - 1 /\ 3 <= I454 - 1 /\ -1 <= I455 - 1 /\ -1 <= I456 - 1 /\ I447 + 3 <= I441 /\ I448 + 3 <= I441] f5(I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475) -> f5(I476, I464, I477, I478, I467, I468, I469, I470, I479, I480, I481, I482, I483) [I476 <= I463 /\ I484 <= I464 - 1 /\ I477 + 1 <= I465 /\ I477 + 1 <= I466 /\ I478 + 1 <= I465 /\ I478 + 1 <= I466 /\ 3 <= I463 - 1 /\ 0 <= I465 - 1 /\ 0 <= I466 - 1 /\ 3 <= I476 - 1 /\ -1 <= I477 - 1 /\ -1 <= I478 - 1 /\ I469 + 3 <= I463 /\ I470 + 3 <= I463] f2(I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) -> f5(I498, I499, I500, I501, I502, I487, I488, I489, I503, I504, I505, I506, I507) [I508 <= I486 - 1 /\ 1 <= I487 - 1 /\ -1 <= I508 - 1 /\ -1 <= I509 - 1 /\ 0 <= I486 - 1 /\ y3 <= I487 - 1 /\ I498 <= I485 /\ 3 <= I485 - 1 /\ 3 <= I498 - 1 /\ -1 <= I500 - 1 /\ -1 <= I501 - 1 /\ I489 + 3 <= I485 /\ I488 + 3 <= I485 /\ I508 + 1 = I502] f4(I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I511 - 1, I512, I513 + 2, I524, I525, I526, I527, I528, I529, I530, I531, I532) [0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510] f1(I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547) -> f4(I548, I549, I536, 1, 16, 0, 12, I550, I551, I552, I553, I554, I555) [14 <= I548 - 1 /\ 0 <= I535 - 1 /\ I548 - 14 <= I535 /\ 0 <= I536 - 1 /\ -1 <= I549 - 1] f3(I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f2(I569, I570, 16, I560, 12, I571, I572, I573, I574, I575, I576, I577, I578) [12 = I561 /\ 16 = I559 /\ I560 + 3 <= I557 /\ 14 <= I569 - 1 /\ 14 <= I557 - 1 /\ 0 <= I556 - 1 /\ I569 <= I557] f1(I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f2(I592, I580, I593, I594, I595, I596, I597, I598, I599, I600, I601, I602, I603) [-1 <= I604 - 1 /\ 0 <= I580 - 1 /\ 0 <= I579 - 1 /\ 3 <= I592 - 1] We use the basic value criterion with the projection function NU: NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z2 This gives the following inequalities: 0 <= I511 - 1 /\ I513 + 1 <= I512 - 1 /\ -1 <= I512 - 1 /\ -1 <= I513 - 1 /\ -1 <= I533 - 1 /\ -1 <= I534 - 1 /\ 1 <= I514 - 1 /\ 3 <= I510 - 1 /\ 3 <= I523 - 1 /\ I516 + 3 <= I510 /\ I515 + 3 <= I510 ==> I511 >! I511 - 1 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.