190.06/188.55 YES 190.06/188.55 190.06/188.55 DP problem for innermost termination. 190.06/188.55 P = 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 f8#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10#(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 f8#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10#(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8#(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9#(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 f8#(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 f7#(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8#(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 f7#(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7#(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 f1#(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7#(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 f6#(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5#(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6#(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6#(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5#(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5#(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5#(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5#(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6#(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 f4#(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5#(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 f4#(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5#(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 f4#(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4#(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 f2#(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4#(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 f3#(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2#(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 f1#(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2#(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 R = 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 f7(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 f7(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 f1(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 f6(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 f4(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 f4(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 f4(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 f2(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 f3(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 f1(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 190.06/188.55 The dependency graph for this problem is: 190.06/188.55 0 -> 16, 27 190.06/188.55 1 -> 2, 4 190.06/188.55 2 -> 2, 4 190.06/188.55 3 -> 1, 3 190.06/188.55 4 -> 1, 3 190.06/188.55 5 -> 2, 4 190.06/188.55 6 -> 2, 4 190.06/188.55 7 -> 5, 6, 8, 9, 10, 11, 12, 13 190.06/188.55 8 -> 5, 6, 8, 9, 10, 11, 12, 13 190.06/188.55 9 -> 5, 6, 8, 9, 10, 11, 12, 13 190.06/188.55 10 -> 5, 6, 8, 9, 10, 11, 12, 13 190.06/188.55 11 -> 5, 6, 8, 9, 10, 11, 12, 13 190.06/188.55 12 -> 190.06/188.55 13 -> 7 190.06/188.55 14 -> 5, 6, 8, 9, 10, 11, 12, 13 190.06/188.55 15 -> 14, 15 190.06/188.55 16 -> 14, 15 190.06/188.55 17 -> 20, 21 190.06/188.55 18 -> 17, 18, 19 190.06/188.55 19 -> 20, 21 190.06/188.55 20 -> 20, 21 190.06/188.55 21 -> 17, 18, 19 190.06/188.55 22 -> 20, 21 190.06/188.55 23 -> 20, 21 190.06/188.55 24 -> 22, 23, 24 190.06/188.55 25 -> 22, 23, 24 190.06/188.55 26 -> 25 190.06/188.55 27 -> 25 190.06/188.55 Where: 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 5) f8#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10#(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 6) f8#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10#(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 7) f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 12) f8#(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9#(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 13) f8#(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 14) f7#(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8#(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 15) f7#(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7#(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 16) f1#(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7#(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 17) f6#(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5#(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 18) f6#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6#(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 19) f6#(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5#(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 20) f5#(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5#(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 21) f5#(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6#(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 22) f4#(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5#(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 23) f4#(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5#(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 24) f4#(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4#(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 25) f2#(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4#(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 26) f3#(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2#(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 27) f1#(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2#(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 190.06/188.55 We have the following SCCs. 190.06/188.55 { 15 } 190.06/188.55 { 7, 8, 9, 10, 11, 13 } 190.06/188.55 { 1, 2, 3, 4 } 190.06/188.55 { 24 } 190.06/188.55 { 17, 18, 19, 20, 21 } 190.06/188.55 190.06/188.55 DP problem for innermost termination. 190.06/188.55 P = 190.06/188.55 f6#(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5#(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6#(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6#(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6#(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5#(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5#(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5#(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5#(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6#(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 R = 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 f7(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 f7(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 f1(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 f6(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 f4(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 f4(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 f4(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 f2(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 f3(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 f1(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 190.06/188.55 We use the reverse value criterion with the projection function NU: 190.06/188.55 NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z5 - 1 + -1 * z3 190.06/188.55 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z6 - 1 + -1 * z3 190.06/188.55 190.06/188.55 This gives the following inequalities: 190.06/188.55 I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1 ==> I337 - 1 + -1 * I334 > I337 - 1 + -1 * (I334 + 1) with I337 - 1 + -1 * I334 >= 0 190.06/188.55 I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1 ==> I359 - 1 + -1 * I356 > I359 - 1 + -1 * (I356 + 1) with I359 - 1 + -1 * I356 >= 0 190.06/188.55 I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376 ==> I381 - 1 + -1 * I378 >= I381 - 1 + -1 * I378 190.06/188.55 I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398 ==> I402 - 1 + -1 * I400 >= I402 - 1 + -1 * I400 190.06/188.55 I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420 ==> I424 - 1 + -1 * I422 >= I424 - 1 + -1 * I422 190.06/188.55 190.06/188.55 We remove all the strictly oriented dependency pairs. 190.06/188.55 190.06/188.55 DP problem for innermost termination. 190.06/188.55 P = 190.06/188.55 f6#(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5#(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5#(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5#(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5#(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6#(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 R = 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 f7(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 f7(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 f1(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 f6(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 f4(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 f4(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 f4(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 f2(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 f3(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 f1(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 190.06/188.55 We use the basic value criterion with the projection function NU: 190.06/188.55 NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z2 190.06/188.55 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z2 190.06/188.55 190.06/188.55 This gives the following inequalities: 190.06/188.55 I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376 ==> I377 >! I390 190.06/188.55 I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398 ==> I399 >! I412 190.06/188.55 I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420 ==> I421 >! I434 190.06/188.55 190.06/188.55 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 190.06/188.55 190.06/188.55 DP problem for innermost termination. 190.06/188.55 P = 190.06/188.55 f4#(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4#(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 R = 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 f7(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 f7(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 f1(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 f6(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 f4(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 f4(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 f4(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 f2(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 f3(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 f1(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 190.06/188.55 We use the reverse value criterion with the projection function NU: 190.06/188.55 NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z6 - 1 + -1 * z3 190.06/188.55 190.06/188.55 This gives the following inequalities: 190.06/188.55 I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1 ==> I491 - 1 + -1 * I488 > I491 - 1 + -1 * (I488 + 1) with I491 - 1 + -1 * I488 >= 0 190.06/188.55 190.06/188.55 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 190.06/188.55 190.06/188.55 DP problem for innermost termination. 190.06/188.55 P = 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 R = 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 f7(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 f7(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 f1(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 f6(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 f4(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 f4(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 f4(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 f2(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 f3(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 f1(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 190.06/188.55 We use the reverse value criterion with the projection function NU: 190.06/188.55 NU[f10#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z8 - 1 + -1 * z4 190.06/188.55 NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z10 - 1 + -1 * (z3 + 1) 190.06/188.55 190.06/188.55 This gives the following inequalities: 190.06/188.55 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) 190.06/188.55 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 >= 0 190.06/188.55 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) 190.06/188.55 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 >= 0 190.06/188.55 190.06/188.55 We remove all the strictly oriented dependency pairs. 190.06/188.55 190.06/188.55 DP problem for innermost termination. 190.06/188.55 P = 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 R = 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 f7(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 f7(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 f1(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 f6(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 f4(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 f4(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 f4(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 f2(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 f3(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 f1(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 190.06/188.55 The dependency graph for this problem is: 190.06/188.55 1 -> 190.06/188.55 3 -> 1, 3 190.06/188.55 Where: 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 190.06/188.55 We have the following SCCs. 190.06/188.55 { 3 } 190.06/188.55 190.06/188.55 DP problem for innermost termination. 190.06/188.55 P = 190.06/188.55 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] 190.06/188.55 R = 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 f7(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 f7(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 f1(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 f6(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 f4(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 f4(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 f4(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 f2(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 f3(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 f1(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 190.06/188.55 We use the basic value criterion with the projection function NU: 190.06/188.55 NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z5 190.06/188.55 190.06/188.55 This gives the following inequalities: 190.06/188.55 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 190.06/188.55 190.06/188.55 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 190.06/188.55 190.06/188.55 DP problem for innermost termination. 190.06/188.55 P = 190.06/188.55 f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8#(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9#(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 R = 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 f7(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 f7(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 f1(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 f6(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 f4(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 f4(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 f4(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 f2(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 f3(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 f1(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 190.06/188.55 We use the basic value criterion with the projection function NU: 190.06/188.55 NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z4 190.06/188.55 NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z8 190.06/188.55 190.06/188.55 This gives the following inequalities: 190.06/188.55 0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 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 190.06/188.55 I148 + 2 <= I150 /\ I155 + 3 <= I147 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147 ==> I150 >! I161 190.06/188.55 I167 + 2 <= I169 /\ I174 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166 ==> I169 >! I180 190.06/188.55 I198 <= I185 /\ I186 <= y1 - 1 /\ I199 + 1 <= I188 /\ 3 <= I185 - 1 /\ 0 <= I188 - 1 /\ 3 <= I198 - 1 /\ -1 <= I199 - 1 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185 ==> I188 >! I199 190.06/188.55 I217 <= I204 /\ I223 <= I205 - 1 /\ I218 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I217 - 1 /\ -1 <= I218 - 1 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204 ==> I207 >! I218 190.06/188.55 I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244 ==> I247 >! I259 190.06/188.55 190.06/188.55 We remove all the strictly oriented dependency pairs. 190.06/188.55 190.06/188.55 DP problem for innermost termination. 190.06/188.55 P = 190.06/188.55 f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 R = 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 f7(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 f7(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 f1(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 f6(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 f4(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 f4(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 f4(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 f2(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 f3(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 f1(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 190.06/188.55 The dependency graph for this problem is: 190.06/188.55 7 -> 190.06/188.55 Where: 190.06/188.55 7) f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 190.06/188.55 We have the following SCCs. 190.06/188.55 190.06/188.55 190.06/188.55 DP problem for innermost termination. 190.06/188.55 P = 190.06/188.55 f7#(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7#(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 R = 190.06/188.55 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) 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 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] 190.06/188.55 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I92, 2 * I91, I91, I100, I101, I102, I103, I104) [I92 + 3 <= I84 /\ I90 + 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 <= I90 /\ 0 <= 2 * I91 /\ 1073741824 <= I91 - 1 /\ I86 <= I91 - 1] 190.06/188.55 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I113, 2 * I112, I112, I121, I122, I123, I124, I125) [I113 + 3 <= I105 /\ I111 + 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 /\ I112 <= 1073741823 /\ 0 <= 2 * I112 /\ I113 <= I111 /\ 1 <= I112 - 1 /\ I107 <= I112 - 1] 190.06/188.55 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I135, I127, I140, I141, I142, I130, I131, I132, I143, I144, I145, I146) [0 = I129 /\ I135 + 2 <= I128 /\ I134 + 4 <= I128 /\ I132 + 3 <= I126 /\ I130 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I133 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I133 /\ I140 + 2 <= I128 /\ I139 <= I126] 190.06/188.55 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 /\ I153 + 3 <= I147 /\ -1 <= I161 - 1 /\ 3 <= I160 - 1 /\ 2 <= I150 - 1 /\ 3 <= I147 - 1 /\ I161 + 2 <= I150 /\ 1 <= I154 - 1 /\ I160 <= I147] 190.06/188.55 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 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ 1 <= I173 - 1 /\ I179 <= I166] 190.06/188.55 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 /\ I191 + 3 <= I185 /\ I193 + 3 <= I185] 190.06/188.55 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 /\ I210 + 3 <= I204 /\ I212 + 3 <= I204] 190.06/188.55 f8(I224, I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236) -> f9(I237, I226, I238, 1, I230, I231, I232, I239, I240, I225, I241, I242, I243) [I240 + 4 <= I227 /\ I225 + 2 <= I227 /\ I232 + 3 <= I224 /\ I230 + 3 <= I224 /\ -1 <= I239 - 1 /\ 2 <= I238 - 1 /\ 3 <= I237 - 1 /\ 2 <= I227 - 1 /\ 3 <= I224 - 1 /\ I239 + 2 <= I227 /\ I238 <= I227 /\ 1 <= I231 - 1 /\ I237 <= I224] 190.06/188.55 f8(I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256) -> f9(I257, I246, I258, 0, I250, I251, I252, I259, I260, I245, I261, I262, I263) [I260 + 4 <= I247 /\ I245 + 2 <= I247 /\ I252 + 3 <= I244 /\ I250 + 3 <= I244 /\ -1 <= I259 - 1 /\ 2 <= I258 - 1 /\ 3 <= I257 - 1 /\ 2 <= I247 - 1 /\ 3 <= I244 - 1 /\ I259 + 2 <= I247 /\ I258 <= I247 /\ 1 <= I251 - 1 /\ I257 <= I244] 190.06/188.55 f7(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276) -> f8(I277, I278, I279, I280, I266, I267 + 2, I268, I269, I270, I281, I282, I283, I284) [I267 + 1 <= I266 - 1 /\ 1 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ -1 <= I267 - 1 /\ -1 <= I285 - 1 /\ -1 <= y2 - 1 /\ I279 <= I269 - 1 /\ I277 <= I264 /\ 3 <= I264 - 1 /\ 3 <= I277 - 1 /\ -1 <= I280 - 1 /\ I268 + 3 <= I264 /\ I270 + 3 <= I264] 190.06/188.55 f7(I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298) -> f7(I299, I287 - 1, I288, I289 + 2, I300, I301, I302, I303, I304, I305, I306, I307, I308) [0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286] 190.06/188.55 f1(I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323) -> f7(I324, I325, I312, 1, 0, 16, 12, I326, I327, I328, I329, I330, I331) [14 <= I324 - 1 /\ 0 <= I311 - 1 /\ I324 - 14 <= I311 /\ 0 <= I312 - 1 /\ -1 <= I325 - 1] 190.06/188.55 f6(I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f5(I345, I346, I334 + 1, I335, I337, I336, I347, I348, I349, I350, I351, I352, I353) [I336 + 5 <= I332 /\ I335 + 5 <= I332 /\ I334 + 2 <= I332 /\ 0 <= I346 - 1 /\ 5 <= I345 - 1 /\ 0 <= I333 - 1 /\ I334 <= I337 - 1 /\ 5 <= I332 - 1] 190.06/188.55 f6(I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366) -> f6(I367, I368, I356 + 1, I357, I358, I359, I369, I370, I371, I372, I373, I374, I375) [I358 + 5 <= I354 /\ I357 + 5 <= I354 /\ I356 + 2 <= I354 /\ 0 <= I368 - 1 /\ 5 <= I367 - 1 /\ 0 <= I355 - 1 /\ 5 <= I354 - 1 /\ I368 <= I355 /\ I368 + 5 <= I354 /\ I367 - 1 <= I354 /\ I356 <= I359 - 1 /\ -1 <= I359 - 1] 190.06/188.55 f6(I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) -> f5(I389, I390, I378, I379, I381, I380, I391, I392, I393, I394, I395, I396, I397) [I380 + 5 <= I376 /\ I379 + 5 <= I376 /\ I378 + 2 <= I376 /\ -1 <= I390 - 1 /\ 5 <= I389 - 1 /\ 0 <= I377 - 1 /\ 5 <= I376 - 1 /\ I390 + 1 <= I377 /\ I390 + 6 <= I376 /\ I381 <= I378 /\ I389 <= I376] 190.06/188.55 f5(I398, I399, I400, I401, I402, I403, I404, I405, I406, I407, I408, I409, I410) -> f5(I411, I412, I400, I401, I402, I403, I413, I414, I415, I416, I417, I418, I419) [I403 + 5 <= I398 /\ I401 + 5 <= I398 /\ I400 + 2 <= I398 /\ 0 <= I412 - 1 /\ 5 <= I411 - 1 /\ 2 <= I399 - 1 /\ 5 <= I398 - 1 /\ I412 + 2 <= I399 /\ I412 + 4 <= I398 /\ I411 <= I398] 190.06/188.55 f5(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f6(I433, I434, I422, I423, I425, I424, I435, I436, I437, I438, I439, I440, I441) [I425 + 5 <= I420 /\ I423 + 5 <= I420 /\ I422 + 2 <= I420 /\ 0 <= I434 - 1 /\ 5 <= I433 - 1 /\ 1 <= I421 - 1 /\ 5 <= I420 - 1 /\ I434 + 1 <= I421 /\ I434 + 5 <= I420 /\ -1 <= I424 - 1 /\ I433 <= I420] 190.06/188.55 f4(I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454) -> f5(I455, I456, I444 + 1, I445, I447, I446, I457, I458, I459, I460, I461, I462, I463) [I446 + 5 <= I442 /\ I445 + 5 <= I442 /\ I444 + 2 <= I442 /\ 0 <= I456 - 1 /\ 5 <= I455 - 1 /\ 0 <= I443 - 1 /\ 5 <= I442 - 1 /\ -1 <= I444 - 1 /\ I444 <= I447 - 1] 190.06/188.55 f4(I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f5(I477, I478, I466, I467, I469, I468, I479, I480, I481, I482, I483, I484, I485) [I468 + 5 <= I464 /\ I467 + 5 <= I464 /\ I466 + 2 <= I464 /\ -1 <= I478 - 1 /\ 5 <= I477 - 1 /\ 0 <= I465 - 1 /\ 5 <= I464 - 1 /\ I478 + 1 <= I465 /\ I478 + 6 <= I464 /\ I469 <= I466 /\ I477 <= I464] 190.06/188.55 f4(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498) -> f4(I499, I500, I488 + 1, I489, I490, I491, I501, I502, I503, I504, I505, I506, I507) [I490 + 5 <= I486 /\ I489 + 5 <= I486 /\ I488 + 2 <= I486 /\ 0 <= I500 - 1 /\ 5 <= I499 - 1 /\ 0 <= I487 - 1 /\ 5 <= I486 - 1 /\ I500 <= I487 /\ I500 + 5 <= I486 /\ I499 - 1 <= I486 /\ -1 <= I491 - 1 /\ -1 <= I488 - 1 /\ I488 <= I491 - 1] 190.06/188.55 f2(I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) -> f4(I521, I522, 0, I511, I513, I512, I523, I524, I525, I526, I527, I528, I529) [0 = I510 /\ I513 + 3 <= I509 /\ I511 + 3 <= I509 /\ I513 + 5 <= I508 /\ I511 + 5 <= I508 /\ 0 <= I522 - 1 /\ 5 <= I521 - 1 /\ 3 <= I509 - 1 /\ 5 <= I508 - 1 /\ I522 + 3 <= I509 /\ I522 + 5 <= I508 /\ I521 - 2 <= I509 /\ I521 <= I508 /\ -1 <= I512 - 1 /\ 0 <= I511 - 1] 190.06/188.55 f3(I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542) -> f2(I543, I544, 0, I531, 16, 12, I545, I546, I547, I548, I549, I550, I551) [12 = I533 /\ 16 = I532 /\ I531 + 3 <= I530 /\ 14 <= I544 - 1 /\ 16 <= I543 - 1 /\ 14 <= I530 - 1 /\ I544 <= I530 /\ I543 - 2 <= I530] 190.06/188.55 f1(I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564) -> f2(I565, I566, 0, I567, I568, I569, I570, I571, I572, I573, I574, I575, I576) [-1 <= I577 - 1 /\ 0 <= I553 - 1 /\ 0 <= I552 - 1 /\ 5 <= I565 - 1 /\ 3 <= I566 - 1] 190.06/188.55 190.06/188.55 We use the basic value criterion with the projection function NU: 190.06/188.55 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z2 190.06/188.55 190.06/188.55 This gives the following inequalities: 190.06/188.55 0 <= I287 - 1 /\ I289 + 1 <= I288 - 1 /\ -1 <= I288 - 1 /\ -1 <= I289 - 1 /\ -1 <= I309 - 1 /\ -1 <= I310 - 1 /\ 1 <= I291 - 1 /\ 3 <= I286 - 1 /\ 3 <= I299 - 1 /\ I290 + 3 <= I286 /\ I292 + 3 <= I286 ==> I287 >! I287 - 1 190.06/188.56 190.06/188.56 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 190.06/191.53 EOF