112.64/111.39 YES 112.64/111.39 112.64/111.39 DP problem for innermost termination. 112.64/111.39 P = 112.64/111.39 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) 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 f8#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10#(I97, I98, I99, 0, I90 + 1, I91, 2 * I89, I89, I100, I101, I102, I103, I104) [I91 + 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 /\ I91 <= I90 /\ 0 <= 2 * I89 /\ 1073741824 <= I89 - 1 /\ I86 <= I89 - 1] 112.64/111.39 f8#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10#(I118, I119, I120, 0, I111 + 1, I112, 2 * I110, I110, I121, I122, I123, I124, I125) [I112 + 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 /\ I110 <= 1073741823 /\ 0 <= 2 * I110 /\ I112 <= I111 /\ 1 <= I110 - 1 /\ I107 <= I110 - 1] 112.64/111.39 f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 f8#(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8#(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 f8#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8#(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 f8#(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8#(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 f8#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8#(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 f8#(I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9#(I240, I229, I241, 1, I231, I232, I233, I234, I228, I242, I243, I244, I245) [I243 + 4 <= I230 /\ I228 + 2 <= I230 /\ I234 + 3 <= I227 /\ I233 + 3 <= I227 /\ -1 <= I242 - 1 /\ 2 <= I241 - 1 /\ 3 <= I240 - 1 /\ 2 <= I230 - 1 /\ 3 <= I227 - 1 /\ I242 + 2 <= I230 /\ I241 <= I230 /\ I240 <= I227 /\ 1 <= I231 - 1 /\ 1 <= I232 - 1] 112.64/111.39 f8#(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9#(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 f4#(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303) -> f8#(I304, I305, I306, I307, I294 + 2, I295, I296, I297, I308, I309, I310, I311, I312) [I294 + 1 <= I293 - 1 /\ 1 <= I295 - 1 /\ 0 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I294 - 1 /\ -1 <= I313 - 1 /\ -1 <= y2 - 1 /\ I306 <= I295 - 1 /\ I304 <= I291 /\ 3 <= I291 - 1 /\ 3 <= I304 - 1 /\ -1 <= I307 - 1 /\ I297 + 3 <= I291 /\ I296 + 3 <= I291] 112.64/111.39 f7#(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5#(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 f5#(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5#(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 f5#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5#(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 f5#(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5#(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 f5#(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5#(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 f5#(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f7#(I454, 1, I455, I441, I456, I457, I458, I459, I460, I461, I462, I463, I464) [I457 + 4 <= I442 /\ I441 + 2 <= I442 /\ -1 <= I456 - 1 /\ 2 <= I454 - 1 /\ 2 <= I442 - 1 /\ I456 + 2 <= I442 /\ I454 <= I442] 112.64/111.39 f5#(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7#(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 f2#(I515, I516, I517, I518, I519, I520, I521, I522, I523, I524, I525, I526, I527) -> f5#(I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540) [I541 <= I516 - 1 /\ 1 <= I517 - 1 /\ -1 <= I541 - 1 /\ -1 <= I542 - 1 /\ 0 <= I516 - 1 /\ y3 <= I517 - 1 /\ 3 <= I515 - 1 /\ -1 <= I529 - 1 /\ I519 + 3 <= I515 /\ I518 + 3 <= I515] 112.64/111.39 f4#(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4#(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 f1#(I568, I569, I570, I571, I572, I573, I574, I575, I576, I577, I578, I579, I580) -> f4#(I581, I582, I569, 1, 16, 0, 12, I583, I584, I585, I586, I587, I588) [14 <= I581 - 1 /\ 0 <= I568 - 1 /\ I581 - 14 <= I568 /\ 0 <= I569 - 1 /\ -1 <= I582 - 1] 112.64/111.39 f3#(I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) -> f2#(I602, I603, 16, I593, 12, I604, I605, I606, I607, I608, I609, I610, I611) [12 = I594 /\ 16 = I592 /\ I593 + 3 <= I590 /\ 14 <= I602 - 1 /\ 14 <= I590 - 1 /\ 0 <= I589 - 1 /\ I602 <= I590] 112.64/111.39 f1#(I612, I613, I614, I615, I616, I617, I618, I619, I620, I621, I622, I623, I624) -> f2#(I625, I613, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636) [-1 <= I637 - 1 /\ 0 <= I613 - 1 /\ 0 <= I612 - 1 /\ 3 <= I625 - 1] 112.64/111.39 R = 112.64/111.39 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) 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I91, 2 * I89, I89, I100, I101, I102, I103, I104) [I91 + 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 /\ I91 <= I90 /\ 0 <= 2 * I89 /\ 1073741824 <= I89 - 1 /\ I86 <= I89 - 1] 112.64/111.39 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I112, 2 * I110, I110, I121, I122, I123, I124, I125) [I112 + 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 /\ I110 <= 1073741823 /\ 0 <= 2 * I110 /\ I112 <= I111 /\ 1 <= I110 - 1 /\ I107 <= I110 - 1] 112.64/111.39 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 f8(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 f8(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 f8(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 f8(I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I229, I241, 1, I231, I232, I233, I234, I228, I242, I243, I244, I245) [I243 + 4 <= I230 /\ I228 + 2 <= I230 /\ I234 + 3 <= I227 /\ I233 + 3 <= I227 /\ -1 <= I242 - 1 /\ 2 <= I241 - 1 /\ 3 <= I240 - 1 /\ 2 <= I230 - 1 /\ 3 <= I227 - 1 /\ I242 + 2 <= I230 /\ I241 <= I230 /\ I240 <= I227 /\ 1 <= I231 - 1 /\ 1 <= I232 - 1] 112.64/111.39 f8(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 f8(I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290) [I266 + 2 <= I268 /\ I280 + 2 <= I268 /\ I272 + 3 <= I265 /\ I271 + 3 <= I265 /\ 0 <= I279 - 1 /\ 0 <= I268 - 1 /\ 3 <= I265 - 1 /\ 1 <= I269 - 1 /\ 1 <= I270 - 1] 112.64/111.39 f4(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303) -> f8(I304, I305, I306, I307, I294 + 2, I295, I296, I297, I308, I309, I310, I311, I312) [I294 + 1 <= I293 - 1 /\ 1 <= I295 - 1 /\ 0 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I294 - 1 /\ -1 <= I313 - 1 /\ -1 <= y2 - 1 /\ I306 <= I295 - 1 /\ I304 <= I291 /\ 3 <= I291 - 1 /\ 3 <= I304 - 1 /\ -1 <= I307 - 1 /\ I297 + 3 <= I291 /\ I296 + 3 <= I291] 112.64/111.39 f7(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 f5(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 f5(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 f5(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f7(I454, 1, I455, I441, I456, I457, I458, I459, I460, I461, I462, I463, I464) [I457 + 4 <= I442 /\ I441 + 2 <= I442 /\ -1 <= I456 - 1 /\ 2 <= I454 - 1 /\ 2 <= I442 - 1 /\ I456 + 2 <= I442 /\ I454 <= I442] 112.64/111.39 f5(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 f5(I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500, I501) -> f6(I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514) [I489 + 2 <= I490 /\ I504 + 2 <= I490 /\ 0 <= I503 - 1 /\ 0 <= I490 - 1] 112.64/111.39 f2(I515, I516, I517, I518, I519, I520, I521, I522, I523, I524, I525, I526, I527) -> f5(I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540) [I541 <= I516 - 1 /\ 1 <= I517 - 1 /\ -1 <= I541 - 1 /\ -1 <= I542 - 1 /\ 0 <= I516 - 1 /\ y3 <= I517 - 1 /\ 3 <= I515 - 1 /\ -1 <= I529 - 1 /\ I519 + 3 <= I515 /\ I518 + 3 <= I515] 112.64/111.39 f4(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 f1(I568, I569, I570, I571, I572, I573, I574, I575, I576, I577, I578, I579, I580) -> f4(I581, I582, I569, 1, 16, 0, 12, I583, I584, I585, I586, I587, I588) [14 <= I581 - 1 /\ 0 <= I568 - 1 /\ I581 - 14 <= I568 /\ 0 <= I569 - 1 /\ -1 <= I582 - 1] 112.64/111.39 f3(I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) -> f2(I602, I603, 16, I593, 12, I604, I605, I606, I607, I608, I609, I610, I611) [12 = I594 /\ 16 = I592 /\ I593 + 3 <= I590 /\ 14 <= I602 - 1 /\ 14 <= I590 - 1 /\ 0 <= I589 - 1 /\ I602 <= I590] 112.64/111.39 f1(I612, I613, I614, I615, I616, I617, I618, I619, I620, I621, I622, I623, I624) -> f2(I625, I613, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636) [-1 <= I637 - 1 /\ 0 <= I613 - 1 /\ 0 <= I612 - 1 /\ 3 <= I625 - 1] 112.64/111.39 112.64/111.39 The dependency graph for this problem is: 112.64/111.39 0 -> 24, 26 112.64/111.39 1 -> 2, 4 112.64/111.39 2 -> 2, 4 112.64/111.39 3 -> 1, 3 112.64/111.39 4 -> 1, 3 112.64/111.39 5 -> 2, 4 112.64/111.39 6 -> 2, 4 112.64/111.39 7 -> 5, 6, 8, 9, 10, 11, 12, 13 112.64/111.39 8 -> 5, 6, 8, 9, 10, 11, 12, 13 112.64/111.39 9 -> 5, 6, 8, 9, 10, 11, 12, 13 112.64/111.39 10 -> 5, 6, 8, 9, 10, 11, 12, 13 112.64/111.39 11 -> 5, 6, 8, 9, 10, 11, 12, 13 112.64/111.39 12 -> 112.64/111.39 13 -> 7 112.64/111.39 14 -> 5, 6, 8, 9, 10, 11, 12, 13 112.64/111.39 15 -> 16, 17, 18, 19, 20, 21 112.64/111.39 16 -> 16, 17, 18, 19, 20, 21 112.64/111.39 17 -> 16, 17, 18, 19, 20, 21 112.64/111.39 18 -> 16, 17, 18, 19, 20, 21 112.64/111.39 19 -> 16, 17, 18, 19, 20, 21 112.64/111.39 20 -> 112.64/111.39 21 -> 15 112.64/111.39 22 -> 16, 17, 18, 19, 20, 21 112.64/111.39 23 -> 14, 23 112.64/111.39 24 -> 14, 23 112.64/111.39 25 -> 22 112.64/111.39 26 -> 22 112.64/111.39 Where: 112.64/111.39 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) 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 5) f8#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10#(I97, I98, I99, 0, I90 + 1, I91, 2 * I89, I89, I100, I101, I102, I103, I104) [I91 + 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 /\ I91 <= I90 /\ 0 <= 2 * I89 /\ 1073741824 <= I89 - 1 /\ I86 <= I89 - 1] 112.64/111.39 6) f8#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10#(I118, I119, I120, 0, I111 + 1, I112, 2 * I110, I110, I121, I122, I123, I124, I125) [I112 + 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 /\ I110 <= 1073741823 /\ 0 <= 2 * I110 /\ I112 <= I111 /\ 1 <= I110 - 1 /\ I107 <= I110 - 1] 112.64/111.39 7) f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 8) f8#(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8#(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 9) f8#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8#(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 10) f8#(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8#(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 11) f8#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8#(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 12) f8#(I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9#(I240, I229, I241, 1, I231, I232, I233, I234, I228, I242, I243, I244, I245) [I243 + 4 <= I230 /\ I228 + 2 <= I230 /\ I234 + 3 <= I227 /\ I233 + 3 <= I227 /\ -1 <= I242 - 1 /\ 2 <= I241 - 1 /\ 3 <= I240 - 1 /\ 2 <= I230 - 1 /\ 3 <= I227 - 1 /\ I242 + 2 <= I230 /\ I241 <= I230 /\ I240 <= I227 /\ 1 <= I231 - 1 /\ 1 <= I232 - 1] 112.64/111.39 13) f8#(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9#(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 14) f4#(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303) -> f8#(I304, I305, I306, I307, I294 + 2, I295, I296, I297, I308, I309, I310, I311, I312) [I294 + 1 <= I293 - 1 /\ 1 <= I295 - 1 /\ 0 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I294 - 1 /\ -1 <= I313 - 1 /\ -1 <= y2 - 1 /\ I306 <= I295 - 1 /\ I304 <= I291 /\ 3 <= I291 - 1 /\ 3 <= I304 - 1 /\ -1 <= I307 - 1 /\ I297 + 3 <= I291 /\ I296 + 3 <= I291] 112.64/111.39 15) f7#(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5#(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 16) f5#(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5#(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 17) f5#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5#(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 18) f5#(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5#(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 19) f5#(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5#(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 20) f5#(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f7#(I454, 1, I455, I441, I456, I457, I458, I459, I460, I461, I462, I463, I464) [I457 + 4 <= I442 /\ I441 + 2 <= I442 /\ -1 <= I456 - 1 /\ 2 <= I454 - 1 /\ 2 <= I442 - 1 /\ I456 + 2 <= I442 /\ I454 <= I442] 112.64/111.39 21) f5#(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7#(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 22) f2#(I515, I516, I517, I518, I519, I520, I521, I522, I523, I524, I525, I526, I527) -> f5#(I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540) [I541 <= I516 - 1 /\ 1 <= I517 - 1 /\ -1 <= I541 - 1 /\ -1 <= I542 - 1 /\ 0 <= I516 - 1 /\ y3 <= I517 - 1 /\ 3 <= I515 - 1 /\ -1 <= I529 - 1 /\ I519 + 3 <= I515 /\ I518 + 3 <= I515] 112.64/111.39 23) f4#(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4#(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 24) f1#(I568, I569, I570, I571, I572, I573, I574, I575, I576, I577, I578, I579, I580) -> f4#(I581, I582, I569, 1, 16, 0, 12, I583, I584, I585, I586, I587, I588) [14 <= I581 - 1 /\ 0 <= I568 - 1 /\ I581 - 14 <= I568 /\ 0 <= I569 - 1 /\ -1 <= I582 - 1] 112.64/111.39 25) f3#(I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) -> f2#(I602, I603, 16, I593, 12, I604, I605, I606, I607, I608, I609, I610, I611) [12 = I594 /\ 16 = I592 /\ I593 + 3 <= I590 /\ 14 <= I602 - 1 /\ 14 <= I590 - 1 /\ 0 <= I589 - 1 /\ I602 <= I590] 112.64/111.39 26) f1#(I612, I613, I614, I615, I616, I617, I618, I619, I620, I621, I622, I623, I624) -> f2#(I625, I613, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636) [-1 <= I637 - 1 /\ 0 <= I613 - 1 /\ 0 <= I612 - 1 /\ 3 <= I625 - 1] 112.64/111.39 112.64/111.39 We have the following SCCs. 112.64/111.39 { 23 } 112.64/111.39 { 7, 8, 9, 10, 11, 13 } 112.64/111.39 { 1, 2, 3, 4 } 112.64/111.39 { 15, 16, 17, 18, 19, 21 } 112.64/111.39 112.64/111.39 DP problem for innermost termination. 112.64/111.39 P = 112.64/111.39 f7#(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5#(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 f5#(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5#(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 f5#(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5#(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 f5#(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5#(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 f5#(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5#(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 f5#(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7#(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 R = 112.64/111.39 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) 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I91, 2 * I89, I89, I100, I101, I102, I103, I104) [I91 + 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 /\ I91 <= I90 /\ 0 <= 2 * I89 /\ 1073741824 <= I89 - 1 /\ I86 <= I89 - 1] 112.64/111.39 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I112, 2 * I110, I110, I121, I122, I123, I124, I125) [I112 + 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 /\ I110 <= 1073741823 /\ 0 <= 2 * I110 /\ I112 <= I111 /\ 1 <= I110 - 1 /\ I107 <= I110 - 1] 112.64/111.39 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 f8(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 f8(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 f8(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 f8(I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I229, I241, 1, I231, I232, I233, I234, I228, I242, I243, I244, I245) [I243 + 4 <= I230 /\ I228 + 2 <= I230 /\ I234 + 3 <= I227 /\ I233 + 3 <= I227 /\ -1 <= I242 - 1 /\ 2 <= I241 - 1 /\ 3 <= I240 - 1 /\ 2 <= I230 - 1 /\ 3 <= I227 - 1 /\ I242 + 2 <= I230 /\ I241 <= I230 /\ I240 <= I227 /\ 1 <= I231 - 1 /\ 1 <= I232 - 1] 112.64/111.39 f8(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 f8(I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290) [I266 + 2 <= I268 /\ I280 + 2 <= I268 /\ I272 + 3 <= I265 /\ I271 + 3 <= I265 /\ 0 <= I279 - 1 /\ 0 <= I268 - 1 /\ 3 <= I265 - 1 /\ 1 <= I269 - 1 /\ 1 <= I270 - 1] 112.64/111.39 f4(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303) -> f8(I304, I305, I306, I307, I294 + 2, I295, I296, I297, I308, I309, I310, I311, I312) [I294 + 1 <= I293 - 1 /\ 1 <= I295 - 1 /\ 0 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I294 - 1 /\ -1 <= I313 - 1 /\ -1 <= y2 - 1 /\ I306 <= I295 - 1 /\ I304 <= I291 /\ 3 <= I291 - 1 /\ 3 <= I304 - 1 /\ -1 <= I307 - 1 /\ I297 + 3 <= I291 /\ I296 + 3 <= I291] 112.64/111.39 f7(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 f5(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 f5(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 f5(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f7(I454, 1, I455, I441, I456, I457, I458, I459, I460, I461, I462, I463, I464) [I457 + 4 <= I442 /\ I441 + 2 <= I442 /\ -1 <= I456 - 1 /\ 2 <= I454 - 1 /\ 2 <= I442 - 1 /\ I456 + 2 <= I442 /\ I454 <= I442] 112.64/111.39 f5(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 f5(I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500, I501) -> f6(I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514) [I489 + 2 <= I490 /\ I504 + 2 <= I490 /\ 0 <= I503 - 1 /\ 0 <= I490 - 1] 112.64/111.39 f2(I515, I516, I517, I518, I519, I520, I521, I522, I523, I524, I525, I526, I527) -> f5(I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540) [I541 <= I516 - 1 /\ 1 <= I517 - 1 /\ -1 <= I541 - 1 /\ -1 <= I542 - 1 /\ 0 <= I516 - 1 /\ y3 <= I517 - 1 /\ 3 <= I515 - 1 /\ -1 <= I529 - 1 /\ I519 + 3 <= I515 /\ I518 + 3 <= I515] 112.64/111.39 f4(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 f1(I568, I569, I570, I571, I572, I573, I574, I575, I576, I577, I578, I579, I580) -> f4(I581, I582, I569, 1, 16, 0, 12, I583, I584, I585, I586, I587, I588) [14 <= I581 - 1 /\ 0 <= I568 - 1 /\ I581 - 14 <= I568 /\ 0 <= I569 - 1 /\ -1 <= I582 - 1] 112.64/111.39 f3(I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) -> f2(I602, I603, 16, I593, 12, I604, I605, I606, I607, I608, I609, I610, I611) [12 = I594 /\ 16 = I592 /\ I593 + 3 <= I590 /\ 14 <= I602 - 1 /\ 14 <= I590 - 1 /\ 0 <= I589 - 1 /\ I602 <= I590] 112.64/111.39 f1(I612, I613, I614, I615, I616, I617, I618, I619, I620, I621, I622, I623, I624) -> f2(I625, I613, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636) [-1 <= I637 - 1 /\ 0 <= I613 - 1 /\ 0 <= I612 - 1 /\ 3 <= I625 - 1] 112.64/111.39 112.64/111.39 We use the basic value criterion with the projection function NU: 112.64/111.39 NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z2 112.64/111.39 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z5 112.64/111.39 112.64/111.39 This gives the following inequalities: 112.64/111.39 0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314 ==> I318 (>! \union =) I327 112.64/111.39 I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340 ==> I340 >! I352 112.64/111.39 I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365 ==> I365 >! I377 112.64/111.39 I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1 ==> I390 >! I402 112.64/111.39 I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1 ==> I416 >! I428 112.64/111.39 I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466 ==> I466 >! I480 112.64/111.39 112.64/111.39 We remove all the strictly oriented dependency pairs. 112.64/111.39 112.64/111.39 DP problem for innermost termination. 112.64/111.39 P = 112.64/111.39 f7#(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5#(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 R = 112.64/111.39 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) 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I91, 2 * I89, I89, I100, I101, I102, I103, I104) [I91 + 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 /\ I91 <= I90 /\ 0 <= 2 * I89 /\ 1073741824 <= I89 - 1 /\ I86 <= I89 - 1] 112.64/111.39 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I112, 2 * I110, I110, I121, I122, I123, I124, I125) [I112 + 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 /\ I110 <= 1073741823 /\ 0 <= 2 * I110 /\ I112 <= I111 /\ 1 <= I110 - 1 /\ I107 <= I110 - 1] 112.64/111.39 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 f8(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 f8(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 f8(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 f8(I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I229, I241, 1, I231, I232, I233, I234, I228, I242, I243, I244, I245) [I243 + 4 <= I230 /\ I228 + 2 <= I230 /\ I234 + 3 <= I227 /\ I233 + 3 <= I227 /\ -1 <= I242 - 1 /\ 2 <= I241 - 1 /\ 3 <= I240 - 1 /\ 2 <= I230 - 1 /\ 3 <= I227 - 1 /\ I242 + 2 <= I230 /\ I241 <= I230 /\ I240 <= I227 /\ 1 <= I231 - 1 /\ 1 <= I232 - 1] 112.64/111.39 f8(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 f8(I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290) [I266 + 2 <= I268 /\ I280 + 2 <= I268 /\ I272 + 3 <= I265 /\ I271 + 3 <= I265 /\ 0 <= I279 - 1 /\ 0 <= I268 - 1 /\ 3 <= I265 - 1 /\ 1 <= I269 - 1 /\ 1 <= I270 - 1] 112.64/111.39 f4(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303) -> f8(I304, I305, I306, I307, I294 + 2, I295, I296, I297, I308, I309, I310, I311, I312) [I294 + 1 <= I293 - 1 /\ 1 <= I295 - 1 /\ 0 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I294 - 1 /\ -1 <= I313 - 1 /\ -1 <= y2 - 1 /\ I306 <= I295 - 1 /\ I304 <= I291 /\ 3 <= I291 - 1 /\ 3 <= I304 - 1 /\ -1 <= I307 - 1 /\ I297 + 3 <= I291 /\ I296 + 3 <= I291] 112.64/111.39 f7(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 f5(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 f5(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 f5(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f7(I454, 1, I455, I441, I456, I457, I458, I459, I460, I461, I462, I463, I464) [I457 + 4 <= I442 /\ I441 + 2 <= I442 /\ -1 <= I456 - 1 /\ 2 <= I454 - 1 /\ 2 <= I442 - 1 /\ I456 + 2 <= I442 /\ I454 <= I442] 112.64/111.39 f5(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 f5(I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500, I501) -> f6(I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514) [I489 + 2 <= I490 /\ I504 + 2 <= I490 /\ 0 <= I503 - 1 /\ 0 <= I490 - 1] 112.64/111.39 f2(I515, I516, I517, I518, I519, I520, I521, I522, I523, I524, I525, I526, I527) -> f5(I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540) [I541 <= I516 - 1 /\ 1 <= I517 - 1 /\ -1 <= I541 - 1 /\ -1 <= I542 - 1 /\ 0 <= I516 - 1 /\ y3 <= I517 - 1 /\ 3 <= I515 - 1 /\ -1 <= I529 - 1 /\ I519 + 3 <= I515 /\ I518 + 3 <= I515] 112.64/111.39 f4(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 f1(I568, I569, I570, I571, I572, I573, I574, I575, I576, I577, I578, I579, I580) -> f4(I581, I582, I569, 1, 16, 0, 12, I583, I584, I585, I586, I587, I588) [14 <= I581 - 1 /\ 0 <= I568 - 1 /\ I581 - 14 <= I568 /\ 0 <= I569 - 1 /\ -1 <= I582 - 1] 112.64/111.39 f3(I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) -> f2(I602, I603, 16, I593, 12, I604, I605, I606, I607, I608, I609, I610, I611) [12 = I594 /\ 16 = I592 /\ I593 + 3 <= I590 /\ 14 <= I602 - 1 /\ 14 <= I590 - 1 /\ 0 <= I589 - 1 /\ I602 <= I590] 112.64/111.39 f1(I612, I613, I614, I615, I616, I617, I618, I619, I620, I621, I622, I623, I624) -> f2(I625, I613, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636) [-1 <= I637 - 1 /\ 0 <= I613 - 1 /\ 0 <= I612 - 1 /\ 3 <= I625 - 1] 112.64/111.39 112.64/111.39 The dependency graph for this problem is: 112.64/111.39 15 -> 112.64/111.39 Where: 112.64/111.39 15) f7#(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5#(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 112.64/111.39 We have the following SCCs. 112.64/111.39 112.64/111.39 112.64/111.39 DP problem for innermost termination. 112.64/111.39 P = 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 R = 112.64/111.39 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) 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I91, 2 * I89, I89, I100, I101, I102, I103, I104) [I91 + 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 /\ I91 <= I90 /\ 0 <= 2 * I89 /\ 1073741824 <= I89 - 1 /\ I86 <= I89 - 1] 112.64/111.39 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I112, 2 * I110, I110, I121, I122, I123, I124, I125) [I112 + 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 /\ I110 <= 1073741823 /\ 0 <= 2 * I110 /\ I112 <= I111 /\ 1 <= I110 - 1 /\ I107 <= I110 - 1] 112.64/111.39 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 f8(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 f8(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 f8(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 f8(I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I229, I241, 1, I231, I232, I233, I234, I228, I242, I243, I244, I245) [I243 + 4 <= I230 /\ I228 + 2 <= I230 /\ I234 + 3 <= I227 /\ I233 + 3 <= I227 /\ -1 <= I242 - 1 /\ 2 <= I241 - 1 /\ 3 <= I240 - 1 /\ 2 <= I230 - 1 /\ 3 <= I227 - 1 /\ I242 + 2 <= I230 /\ I241 <= I230 /\ I240 <= I227 /\ 1 <= I231 - 1 /\ 1 <= I232 - 1] 112.64/111.39 f8(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 f8(I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290) [I266 + 2 <= I268 /\ I280 + 2 <= I268 /\ I272 + 3 <= I265 /\ I271 + 3 <= I265 /\ 0 <= I279 - 1 /\ 0 <= I268 - 1 /\ 3 <= I265 - 1 /\ 1 <= I269 - 1 /\ 1 <= I270 - 1] 112.64/111.39 f4(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303) -> f8(I304, I305, I306, I307, I294 + 2, I295, I296, I297, I308, I309, I310, I311, I312) [I294 + 1 <= I293 - 1 /\ 1 <= I295 - 1 /\ 0 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I294 - 1 /\ -1 <= I313 - 1 /\ -1 <= y2 - 1 /\ I306 <= I295 - 1 /\ I304 <= I291 /\ 3 <= I291 - 1 /\ 3 <= I304 - 1 /\ -1 <= I307 - 1 /\ I297 + 3 <= I291 /\ I296 + 3 <= I291] 112.64/111.39 f7(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 f5(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 f5(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 f5(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f7(I454, 1, I455, I441, I456, I457, I458, I459, I460, I461, I462, I463, I464) [I457 + 4 <= I442 /\ I441 + 2 <= I442 /\ -1 <= I456 - 1 /\ 2 <= I454 - 1 /\ 2 <= I442 - 1 /\ I456 + 2 <= I442 /\ I454 <= I442] 112.64/111.39 f5(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 f5(I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500, I501) -> f6(I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514) [I489 + 2 <= I490 /\ I504 + 2 <= I490 /\ 0 <= I503 - 1 /\ 0 <= I490 - 1] 112.64/111.39 f2(I515, I516, I517, I518, I519, I520, I521, I522, I523, I524, I525, I526, I527) -> f5(I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540) [I541 <= I516 - 1 /\ 1 <= I517 - 1 /\ -1 <= I541 - 1 /\ -1 <= I542 - 1 /\ 0 <= I516 - 1 /\ y3 <= I517 - 1 /\ 3 <= I515 - 1 /\ -1 <= I529 - 1 /\ I519 + 3 <= I515 /\ I518 + 3 <= I515] 112.64/111.39 f4(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 f1(I568, I569, I570, I571, I572, I573, I574, I575, I576, I577, I578, I579, I580) -> f4(I581, I582, I569, 1, 16, 0, 12, I583, I584, I585, I586, I587, I588) [14 <= I581 - 1 /\ 0 <= I568 - 1 /\ I581 - 14 <= I568 /\ 0 <= I569 - 1 /\ -1 <= I582 - 1] 112.64/111.39 f3(I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) -> f2(I602, I603, 16, I593, 12, I604, I605, I606, I607, I608, I609, I610, I611) [12 = I594 /\ 16 = I592 /\ I593 + 3 <= I590 /\ 14 <= I602 - 1 /\ 14 <= I590 - 1 /\ 0 <= I589 - 1 /\ I602 <= I590] 112.64/111.39 f1(I612, I613, I614, I615, I616, I617, I618, I619, I620, I621, I622, I623, I624) -> f2(I625, I613, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636) [-1 <= I637 - 1 /\ 0 <= I613 - 1 /\ 0 <= I612 - 1 /\ 3 <= I625 - 1] 112.64/111.39 112.64/111.39 We use the reverse value criterion with the projection function NU: 112.64/111.39 NU[f10#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z8 - 1 + -1 * z4 112.64/111.39 NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z10 - 1 + -1 * (z3 + 1) 112.64/111.39 112.64/111.39 This gives the following inequalities: 112.64/111.39 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) 112.64/111.39 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 >= 0 112.64/111.39 I53 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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) 112.64/111.39 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 >= 0 112.64/111.39 112.64/111.39 We remove all the strictly oriented dependency pairs. 112.64/111.39 112.64/111.39 DP problem for innermost termination. 112.64/111.39 P = 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 R = 112.64/111.39 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) 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I91, 2 * I89, I89, I100, I101, I102, I103, I104) [I91 + 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 /\ I91 <= I90 /\ 0 <= 2 * I89 /\ 1073741824 <= I89 - 1 /\ I86 <= I89 - 1] 112.64/111.39 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I112, 2 * I110, I110, I121, I122, I123, I124, I125) [I112 + 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 /\ I110 <= 1073741823 /\ 0 <= 2 * I110 /\ I112 <= I111 /\ 1 <= I110 - 1 /\ I107 <= I110 - 1] 112.64/111.39 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 f8(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 f8(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 f8(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 f8(I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I229, I241, 1, I231, I232, I233, I234, I228, I242, I243, I244, I245) [I243 + 4 <= I230 /\ I228 + 2 <= I230 /\ I234 + 3 <= I227 /\ I233 + 3 <= I227 /\ -1 <= I242 - 1 /\ 2 <= I241 - 1 /\ 3 <= I240 - 1 /\ 2 <= I230 - 1 /\ 3 <= I227 - 1 /\ I242 + 2 <= I230 /\ I241 <= I230 /\ I240 <= I227 /\ 1 <= I231 - 1 /\ 1 <= I232 - 1] 112.64/111.39 f8(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 f8(I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290) [I266 + 2 <= I268 /\ I280 + 2 <= I268 /\ I272 + 3 <= I265 /\ I271 + 3 <= I265 /\ 0 <= I279 - 1 /\ 0 <= I268 - 1 /\ 3 <= I265 - 1 /\ 1 <= I269 - 1 /\ 1 <= I270 - 1] 112.64/111.39 f4(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303) -> f8(I304, I305, I306, I307, I294 + 2, I295, I296, I297, I308, I309, I310, I311, I312) [I294 + 1 <= I293 - 1 /\ 1 <= I295 - 1 /\ 0 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I294 - 1 /\ -1 <= I313 - 1 /\ -1 <= y2 - 1 /\ I306 <= I295 - 1 /\ I304 <= I291 /\ 3 <= I291 - 1 /\ 3 <= I304 - 1 /\ -1 <= I307 - 1 /\ I297 + 3 <= I291 /\ I296 + 3 <= I291] 112.64/111.39 f7(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 f5(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 f5(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 f5(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f7(I454, 1, I455, I441, I456, I457, I458, I459, I460, I461, I462, I463, I464) [I457 + 4 <= I442 /\ I441 + 2 <= I442 /\ -1 <= I456 - 1 /\ 2 <= I454 - 1 /\ 2 <= I442 - 1 /\ I456 + 2 <= I442 /\ I454 <= I442] 112.64/111.39 f5(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 f5(I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500, I501) -> f6(I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514) [I489 + 2 <= I490 /\ I504 + 2 <= I490 /\ 0 <= I503 - 1 /\ 0 <= I490 - 1] 112.64/111.39 f2(I515, I516, I517, I518, I519, I520, I521, I522, I523, I524, I525, I526, I527) -> f5(I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540) [I541 <= I516 - 1 /\ 1 <= I517 - 1 /\ -1 <= I541 - 1 /\ -1 <= I542 - 1 /\ 0 <= I516 - 1 /\ y3 <= I517 - 1 /\ 3 <= I515 - 1 /\ -1 <= I529 - 1 /\ I519 + 3 <= I515 /\ I518 + 3 <= I515] 112.64/111.39 f4(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 f1(I568, I569, I570, I571, I572, I573, I574, I575, I576, I577, I578, I579, I580) -> f4(I581, I582, I569, 1, 16, 0, 12, I583, I584, I585, I586, I587, I588) [14 <= I581 - 1 /\ 0 <= I568 - 1 /\ I581 - 14 <= I568 /\ 0 <= I569 - 1 /\ -1 <= I582 - 1] 112.64/111.39 f3(I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) -> f2(I602, I603, 16, I593, 12, I604, I605, I606, I607, I608, I609, I610, I611) [12 = I594 /\ 16 = I592 /\ I593 + 3 <= I590 /\ 14 <= I602 - 1 /\ 14 <= I590 - 1 /\ 0 <= I589 - 1 /\ I602 <= I590] 112.64/111.39 f1(I612, I613, I614, I615, I616, I617, I618, I619, I620, I621, I622, I623, I624) -> f2(I625, I613, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636) [-1 <= I637 - 1 /\ 0 <= I613 - 1 /\ 0 <= I612 - 1 /\ 3 <= I625 - 1] 112.64/111.39 112.64/111.39 The dependency graph for this problem is: 112.64/111.39 1 -> 112.64/111.39 3 -> 1, 3 112.64/111.39 Where: 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 112.64/111.39 We have the following SCCs. 112.64/111.39 { 3 } 112.64/111.39 112.64/111.39 DP problem for innermost termination. 112.64/111.39 P = 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 R = 112.64/111.39 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) 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I91, 2 * I89, I89, I100, I101, I102, I103, I104) [I91 + 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 /\ I91 <= I90 /\ 0 <= 2 * I89 /\ 1073741824 <= I89 - 1 /\ I86 <= I89 - 1] 112.64/111.39 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I112, 2 * I110, I110, I121, I122, I123, I124, I125) [I112 + 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 /\ I110 <= 1073741823 /\ 0 <= 2 * I110 /\ I112 <= I111 /\ 1 <= I110 - 1 /\ I107 <= I110 - 1] 112.64/111.39 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 f8(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 f8(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 f8(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 f8(I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I229, I241, 1, I231, I232, I233, I234, I228, I242, I243, I244, I245) [I243 + 4 <= I230 /\ I228 + 2 <= I230 /\ I234 + 3 <= I227 /\ I233 + 3 <= I227 /\ -1 <= I242 - 1 /\ 2 <= I241 - 1 /\ 3 <= I240 - 1 /\ 2 <= I230 - 1 /\ 3 <= I227 - 1 /\ I242 + 2 <= I230 /\ I241 <= I230 /\ I240 <= I227 /\ 1 <= I231 - 1 /\ 1 <= I232 - 1] 112.64/111.39 f8(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 f8(I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290) [I266 + 2 <= I268 /\ I280 + 2 <= I268 /\ I272 + 3 <= I265 /\ I271 + 3 <= I265 /\ 0 <= I279 - 1 /\ 0 <= I268 - 1 /\ 3 <= I265 - 1 /\ 1 <= I269 - 1 /\ 1 <= I270 - 1] 112.64/111.39 f4(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303) -> f8(I304, I305, I306, I307, I294 + 2, I295, I296, I297, I308, I309, I310, I311, I312) [I294 + 1 <= I293 - 1 /\ 1 <= I295 - 1 /\ 0 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I294 - 1 /\ -1 <= I313 - 1 /\ -1 <= y2 - 1 /\ I306 <= I295 - 1 /\ I304 <= I291 /\ 3 <= I291 - 1 /\ 3 <= I304 - 1 /\ -1 <= I307 - 1 /\ I297 + 3 <= I291 /\ I296 + 3 <= I291] 112.64/111.39 f7(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 f5(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 f5(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 f5(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f7(I454, 1, I455, I441, I456, I457, I458, I459, I460, I461, I462, I463, I464) [I457 + 4 <= I442 /\ I441 + 2 <= I442 /\ -1 <= I456 - 1 /\ 2 <= I454 - 1 /\ 2 <= I442 - 1 /\ I456 + 2 <= I442 /\ I454 <= I442] 112.64/111.39 f5(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 f5(I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500, I501) -> f6(I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514) [I489 + 2 <= I490 /\ I504 + 2 <= I490 /\ 0 <= I503 - 1 /\ 0 <= I490 - 1] 112.64/111.39 f2(I515, I516, I517, I518, I519, I520, I521, I522, I523, I524, I525, I526, I527) -> f5(I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540) [I541 <= I516 - 1 /\ 1 <= I517 - 1 /\ -1 <= I541 - 1 /\ -1 <= I542 - 1 /\ 0 <= I516 - 1 /\ y3 <= I517 - 1 /\ 3 <= I515 - 1 /\ -1 <= I529 - 1 /\ I519 + 3 <= I515 /\ I518 + 3 <= I515] 112.64/111.39 f4(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 f1(I568, I569, I570, I571, I572, I573, I574, I575, I576, I577, I578, I579, I580) -> f4(I581, I582, I569, 1, 16, 0, 12, I583, I584, I585, I586, I587, I588) [14 <= I581 - 1 /\ 0 <= I568 - 1 /\ I581 - 14 <= I568 /\ 0 <= I569 - 1 /\ -1 <= I582 - 1] 112.64/111.39 f3(I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) -> f2(I602, I603, 16, I593, 12, I604, I605, I606, I607, I608, I609, I610, I611) [12 = I594 /\ 16 = I592 /\ I593 + 3 <= I590 /\ 14 <= I602 - 1 /\ 14 <= I590 - 1 /\ 0 <= I589 - 1 /\ I602 <= I590] 112.64/111.39 f1(I612, I613, I614, I615, I616, I617, I618, I619, I620, I621, I622, I623, I624) -> f2(I625, I613, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636) [-1 <= I637 - 1 /\ 0 <= I613 - 1 /\ 0 <= I612 - 1 /\ 3 <= I625 - 1] 112.64/111.39 112.64/111.39 We use the basic value criterion with the projection function NU: 112.64/111.39 NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z5 112.64/111.39 112.64/111.39 This gives the following inequalities: 112.64/111.39 I53 + 2 <= I46 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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 112.64/111.39 112.64/111.39 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 112.64/111.39 112.64/111.39 DP problem for innermost termination. 112.64/111.39 P = 112.64/111.39 f9#(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8#(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 f8#(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8#(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 f8#(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8#(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 f8#(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8#(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 f8#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8#(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 f8#(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9#(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 R = 112.64/111.39 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) 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I91, 2 * I89, I89, I100, I101, I102, I103, I104) [I91 + 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 /\ I91 <= I90 /\ 0 <= 2 * I89 /\ 1073741824 <= I89 - 1 /\ I86 <= I89 - 1] 112.64/111.39 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I112, 2 * I110, I110, I121, I122, I123, I124, I125) [I112 + 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 /\ I110 <= 1073741823 /\ 0 <= 2 * I110 /\ I112 <= I111 /\ 1 <= I110 - 1 /\ I107 <= I110 - 1] 112.64/111.39 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 f8(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 f8(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 f8(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 f8(I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I229, I241, 1, I231, I232, I233, I234, I228, I242, I243, I244, I245) [I243 + 4 <= I230 /\ I228 + 2 <= I230 /\ I234 + 3 <= I227 /\ I233 + 3 <= I227 /\ -1 <= I242 - 1 /\ 2 <= I241 - 1 /\ 3 <= I240 - 1 /\ 2 <= I230 - 1 /\ 3 <= I227 - 1 /\ I242 + 2 <= I230 /\ I241 <= I230 /\ I240 <= I227 /\ 1 <= I231 - 1 /\ 1 <= I232 - 1] 112.64/111.39 f8(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 f8(I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290) [I266 + 2 <= I268 /\ I280 + 2 <= I268 /\ I272 + 3 <= I265 /\ I271 + 3 <= I265 /\ 0 <= I279 - 1 /\ 0 <= I268 - 1 /\ 3 <= I265 - 1 /\ 1 <= I269 - 1 /\ 1 <= I270 - 1] 112.64/111.39 f4(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303) -> f8(I304, I305, I306, I307, I294 + 2, I295, I296, I297, I308, I309, I310, I311, I312) [I294 + 1 <= I293 - 1 /\ 1 <= I295 - 1 /\ 0 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I294 - 1 /\ -1 <= I313 - 1 /\ -1 <= y2 - 1 /\ I306 <= I295 - 1 /\ I304 <= I291 /\ 3 <= I291 - 1 /\ 3 <= I304 - 1 /\ -1 <= I307 - 1 /\ I297 + 3 <= I291 /\ I296 + 3 <= I291] 112.64/111.39 f7(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 f5(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 f5(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 f5(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f7(I454, 1, I455, I441, I456, I457, I458, I459, I460, I461, I462, I463, I464) [I457 + 4 <= I442 /\ I441 + 2 <= I442 /\ -1 <= I456 - 1 /\ 2 <= I454 - 1 /\ 2 <= I442 - 1 /\ I456 + 2 <= I442 /\ I454 <= I442] 112.64/111.39 f5(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 f5(I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500, I501) -> f6(I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514) [I489 + 2 <= I490 /\ I504 + 2 <= I490 /\ 0 <= I503 - 1 /\ 0 <= I490 - 1] 112.64/111.39 f2(I515, I516, I517, I518, I519, I520, I521, I522, I523, I524, I525, I526, I527) -> f5(I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540) [I541 <= I516 - 1 /\ 1 <= I517 - 1 /\ -1 <= I541 - 1 /\ -1 <= I542 - 1 /\ 0 <= I516 - 1 /\ y3 <= I517 - 1 /\ 3 <= I515 - 1 /\ -1 <= I529 - 1 /\ I519 + 3 <= I515 /\ I518 + 3 <= I515] 112.64/111.39 f4(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 f1(I568, I569, I570, I571, I572, I573, I574, I575, I576, I577, I578, I579, I580) -> f4(I581, I582, I569, 1, 16, 0, 12, I583, I584, I585, I586, I587, I588) [14 <= I581 - 1 /\ 0 <= I568 - 1 /\ I581 - 14 <= I568 /\ 0 <= I569 - 1 /\ -1 <= I582 - 1] 112.64/111.39 f3(I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) -> f2(I602, I603, 16, I593, 12, I604, I605, I606, I607, I608, I609, I610, I611) [12 = I594 /\ 16 = I592 /\ I593 + 3 <= I590 /\ 14 <= I602 - 1 /\ 14 <= I590 - 1 /\ 0 <= I589 - 1 /\ I602 <= I590] 112.64/111.39 f1(I612, I613, I614, I615, I616, I617, I618, I619, I620, I621, I622, I623, I624) -> f2(I625, I613, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636) [-1 <= I637 - 1 /\ 0 <= I613 - 1 /\ 0 <= I612 - 1 /\ 3 <= I625 - 1] 112.64/111.39 112.64/111.39 We use the basic value criterion with the projection function NU: 112.64/111.39 NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z4 112.64/111.39 NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z3 112.64/111.39 112.64/111.39 This gives the following inequalities: 112.64/111.39 0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126 ==> I128 >! I140 112.64/111.39 I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1 ==> I149 >! I160 112.64/111.39 I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1 ==> I169 >! I180 112.64/111.39 I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186 ==> I189 >! I200 112.64/111.39 I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206 ==> I209 >! I220 112.64/111.39 I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1 ==> I249 (>! \union =) I260 112.64/111.39 112.64/111.39 We remove all the strictly oriented dependency pairs. 112.64/111.39 112.64/111.39 DP problem for innermost termination. 112.64/111.39 P = 112.64/111.39 f8#(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9#(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 R = 112.64/111.39 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) 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I91, 2 * I89, I89, I100, I101, I102, I103, I104) [I91 + 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 /\ I91 <= I90 /\ 0 <= 2 * I89 /\ 1073741824 <= I89 - 1 /\ I86 <= I89 - 1] 112.64/111.39 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I112, 2 * I110, I110, I121, I122, I123, I124, I125) [I112 + 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 /\ I110 <= 1073741823 /\ 0 <= 2 * I110 /\ I112 <= I111 /\ 1 <= I110 - 1 /\ I107 <= I110 - 1] 112.64/111.39 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 f8(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 f8(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 f8(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 f8(I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I229, I241, 1, I231, I232, I233, I234, I228, I242, I243, I244, I245) [I243 + 4 <= I230 /\ I228 + 2 <= I230 /\ I234 + 3 <= I227 /\ I233 + 3 <= I227 /\ -1 <= I242 - 1 /\ 2 <= I241 - 1 /\ 3 <= I240 - 1 /\ 2 <= I230 - 1 /\ 3 <= I227 - 1 /\ I242 + 2 <= I230 /\ I241 <= I230 /\ I240 <= I227 /\ 1 <= I231 - 1 /\ 1 <= I232 - 1] 112.64/111.39 f8(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 f8(I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290) [I266 + 2 <= I268 /\ I280 + 2 <= I268 /\ I272 + 3 <= I265 /\ I271 + 3 <= I265 /\ 0 <= I279 - 1 /\ 0 <= I268 - 1 /\ 3 <= I265 - 1 /\ 1 <= I269 - 1 /\ 1 <= I270 - 1] 112.64/111.39 f4(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303) -> f8(I304, I305, I306, I307, I294 + 2, I295, I296, I297, I308, I309, I310, I311, I312) [I294 + 1 <= I293 - 1 /\ 1 <= I295 - 1 /\ 0 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I294 - 1 /\ -1 <= I313 - 1 /\ -1 <= y2 - 1 /\ I306 <= I295 - 1 /\ I304 <= I291 /\ 3 <= I291 - 1 /\ 3 <= I304 - 1 /\ -1 <= I307 - 1 /\ I297 + 3 <= I291 /\ I296 + 3 <= I291] 112.64/111.39 f7(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 f5(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 f5(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 f5(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f7(I454, 1, I455, I441, I456, I457, I458, I459, I460, I461, I462, I463, I464) [I457 + 4 <= I442 /\ I441 + 2 <= I442 /\ -1 <= I456 - 1 /\ 2 <= I454 - 1 /\ 2 <= I442 - 1 /\ I456 + 2 <= I442 /\ I454 <= I442] 112.64/111.39 f5(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 f5(I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500, I501) -> f6(I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514) [I489 + 2 <= I490 /\ I504 + 2 <= I490 /\ 0 <= I503 - 1 /\ 0 <= I490 - 1] 112.64/111.39 f2(I515, I516, I517, I518, I519, I520, I521, I522, I523, I524, I525, I526, I527) -> f5(I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540) [I541 <= I516 - 1 /\ 1 <= I517 - 1 /\ -1 <= I541 - 1 /\ -1 <= I542 - 1 /\ 0 <= I516 - 1 /\ y3 <= I517 - 1 /\ 3 <= I515 - 1 /\ -1 <= I529 - 1 /\ I519 + 3 <= I515 /\ I518 + 3 <= I515] 112.64/111.39 f4(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 f1(I568, I569, I570, I571, I572, I573, I574, I575, I576, I577, I578, I579, I580) -> f4(I581, I582, I569, 1, 16, 0, 12, I583, I584, I585, I586, I587, I588) [14 <= I581 - 1 /\ 0 <= I568 - 1 /\ I581 - 14 <= I568 /\ 0 <= I569 - 1 /\ -1 <= I582 - 1] 112.64/111.39 f3(I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) -> f2(I602, I603, 16, I593, 12, I604, I605, I606, I607, I608, I609, I610, I611) [12 = I594 /\ 16 = I592 /\ I593 + 3 <= I590 /\ 14 <= I602 - 1 /\ 14 <= I590 - 1 /\ 0 <= I589 - 1 /\ I602 <= I590] 112.64/111.39 f1(I612, I613, I614, I615, I616, I617, I618, I619, I620, I621, I622, I623, I624) -> f2(I625, I613, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636) [-1 <= I637 - 1 /\ 0 <= I613 - 1 /\ 0 <= I612 - 1 /\ 3 <= I625 - 1] 112.64/111.39 112.64/111.39 The dependency graph for this problem is: 112.64/111.39 13 -> 112.64/111.39 Where: 112.64/111.39 13) f8#(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9#(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 112.64/111.39 We have the following SCCs. 112.64/111.39 112.64/111.39 112.64/111.39 DP problem for innermost termination. 112.64/111.39 P = 112.64/111.39 f4#(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4#(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 R = 112.64/111.39 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) 112.64/111.39 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] 112.64/111.39 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] 112.64/111.39 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 /\ I62 + 4 <= I46 /\ I61 + 4 <= I46 /\ I52 + 2 <= 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] 112.64/111.39 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] 112.64/111.39 f8(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96) -> f10(I97, I98, I99, 0, I90 + 1, I91, 2 * I89, I89, I100, I101, I102, I103, I104) [I91 + 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 /\ I91 <= I90 /\ 0 <= 2 * I89 /\ 1073741824 <= I89 - 1 /\ I86 <= I89 - 1] 112.64/111.39 f8(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117) -> f10(I118, I119, I120, 0, I111 + 1, I112, 2 * I110, I110, I121, I122, I123, I124, I125) [I112 + 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 /\ I110 <= 1073741823 /\ 0 <= 2 * I110 /\ I112 <= I111 /\ 1 <= I110 - 1 /\ I107 <= I110 - 1] 112.64/111.39 f9(I126, I127, I128, I129, I130, I131, I132, I133, I134, I135, I136, I137, I138) -> f8(I139, I134, I127, I140, I130, I131, I132, I133, I141, I142, I143, I144, I145) [0 = I129 /\ I136 + 4 <= I128 /\ I134 + 2 <= I128 /\ I133 + 3 <= I126 /\ I132 + 3 <= I126 /\ -1 <= I140 - 1 /\ 3 <= I139 - 1 /\ -1 <= I135 - 1 /\ 2 <= I128 - 1 /\ 3 <= I126 - 1 /\ I140 <= I135 /\ I140 + 2 <= I128 /\ I139 <= I126] 112.64/111.39 f8(I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156, I157, I158) -> f8(I159, I147, I148, I160, I150, I151, I152, I153, I161, I162, I163, I164, I165) [I147 + 2 <= I149 /\ I153 + 3 <= I146 /\ I152 + 3 <= I146 /\ -1 <= I160 - 1 /\ 3 <= I159 - 1 /\ 2 <= I149 - 1 /\ 3 <= I146 - 1 /\ I160 + 2 <= I149 /\ I159 <= I146 /\ 1 <= I150 - 1 /\ 1 <= I151 - 1] 112.64/111.39 f8(I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178) -> f8(I179, I167, I168, I180, I170, I171, I172, I173, I181, I182, I183, I184, I185) [I167 + 2 <= I169 /\ I173 + 3 <= I166 /\ I172 + 3 <= I166 /\ -1 <= I180 - 1 /\ 3 <= I179 - 1 /\ 1 <= I169 - 1 /\ 3 <= I166 - 1 /\ I180 + 2 <= I169 /\ I179 <= I166 /\ 1 <= I170 - 1 /\ 1 <= I171 - 1] 112.64/111.39 f8(I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f8(I199, I187, I188, I200, I190, I191, I192, I193, I201, I202, I203, I204, I205) [I199 <= I186 /\ I187 <= y1 - 1 /\ I200 + 1 <= I189 /\ 3 <= I186 - 1 /\ 0 <= I189 - 1 /\ 3 <= I199 - 1 /\ -1 <= I200 - 1 /\ I192 + 3 <= I186 /\ I193 + 3 <= I186] 112.64/111.39 f8(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218) -> f8(I219, I207, I208, I220, I210, I211, I212, I213, I221, I222, I223, I224, I225) [I219 <= I206 /\ I226 <= I207 - 1 /\ I220 + 1 <= I209 /\ 3 <= I206 - 1 /\ 0 <= I209 - 1 /\ 3 <= I219 - 1 /\ -1 <= I220 - 1 /\ I212 + 3 <= I206 /\ I213 + 3 <= I206] 112.64/111.39 f8(I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I229, I241, 1, I231, I232, I233, I234, I228, I242, I243, I244, I245) [I243 + 4 <= I230 /\ I228 + 2 <= I230 /\ I234 + 3 <= I227 /\ I233 + 3 <= I227 /\ -1 <= I242 - 1 /\ 2 <= I241 - 1 /\ 3 <= I240 - 1 /\ 2 <= I230 - 1 /\ 3 <= I227 - 1 /\ I242 + 2 <= I230 /\ I241 <= I230 /\ I240 <= I227 /\ 1 <= I231 - 1 /\ 1 <= I232 - 1] 112.64/111.39 f8(I246, I247, I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258) -> f9(I259, I248, I260, 0, I250, I251, I252, I253, I247, I261, I262, I263, I264) [I262 + 4 <= I249 /\ I247 + 2 <= I249 /\ I253 + 3 <= I246 /\ I252 + 3 <= I246 /\ -1 <= I261 - 1 /\ 2 <= I260 - 1 /\ 3 <= I259 - 1 /\ 2 <= I249 - 1 /\ 3 <= I246 - 1 /\ I261 + 2 <= I249 /\ I260 <= I249 /\ I259 <= I246 /\ 1 <= I250 - 1 /\ 1 <= I251 - 1] 112.64/111.39 f8(I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277) -> f6(I278, I279, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290) [I266 + 2 <= I268 /\ I280 + 2 <= I268 /\ I272 + 3 <= I265 /\ I271 + 3 <= I265 /\ 0 <= I279 - 1 /\ 0 <= I268 - 1 /\ 3 <= I265 - 1 /\ 1 <= I269 - 1 /\ 1 <= I270 - 1] 112.64/111.39 f4(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303) -> f8(I304, I305, I306, I307, I294 + 2, I295, I296, I297, I308, I309, I310, I311, I312) [I294 + 1 <= I293 - 1 /\ 1 <= I295 - 1 /\ 0 <= I292 - 1 /\ -1 <= I293 - 1 /\ -1 <= I294 - 1 /\ -1 <= I313 - 1 /\ -1 <= y2 - 1 /\ I306 <= I295 - 1 /\ I304 <= I291 /\ 3 <= I291 - 1 /\ 3 <= I304 - 1 /\ -1 <= I307 - 1 /\ I297 + 3 <= I291 /\ I296 + 3 <= I291] 112.64/111.39 f7(I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326) -> f5(I317, I327, I328, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338) [0 = I315 /\ I319 + 4 <= I314 /\ I317 + 2 <= I314 /\ -1 <= I327 - 1 /\ -1 <= I318 - 1 /\ 2 <= I314 - 1 /\ I327 <= I318 /\ I327 + 2 <= I314] 112.64/111.39 f5(I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350, I351) -> f5(I339, I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363) [I339 + 2 <= I340 /\ -1 <= I352 - 1 /\ 2 <= I340 - 1 /\ I352 + 2 <= I340] 112.64/111.39 f5(I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f5(I364, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388) [I364 + 2 <= I365 /\ -1 <= I377 - 1 /\ 1 <= I365 - 1 /\ I377 + 2 <= I365] 112.64/111.39 f5(I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401) -> f5(I389, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413) [I402 + 1 <= I390 /\ I389 <= I414 - 1 /\ 0 <= I390 - 1 /\ -1 <= I402 - 1] 112.64/111.39 f5(I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425, I426, I427) -> f5(I415, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439) [I428 + 1 <= I416 /\ I440 <= I415 - 1 /\ 0 <= I416 - 1 /\ -1 <= I428 - 1] 112.64/111.39 f5(I441, I442, I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453) -> f7(I454, 1, I455, I441, I456, I457, I458, I459, I460, I461, I462, I463, I464) [I457 + 4 <= I442 /\ I441 + 2 <= I442 /\ -1 <= I456 - 1 /\ 2 <= I454 - 1 /\ 2 <= I442 - 1 /\ I456 + 2 <= I442 /\ I454 <= I442] 112.64/111.39 f5(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477) -> f7(I478, 0, I479, I465, I480, I481, I482, I483, I484, I485, I486, I487, I488) [I481 + 4 <= I466 /\ I465 + 2 <= I466 /\ -1 <= I480 - 1 /\ 2 <= I478 - 1 /\ 2 <= I466 - 1 /\ I480 + 2 <= I466 /\ I478 <= I466] 112.64/111.39 f5(I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500, I501) -> f6(I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514) [I489 + 2 <= I490 /\ I504 + 2 <= I490 /\ 0 <= I503 - 1 /\ 0 <= I490 - 1] 112.64/111.39 f2(I515, I516, I517, I518, I519, I520, I521, I522, I523, I524, I525, I526, I527) -> f5(I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540) [I541 <= I516 - 1 /\ 1 <= I517 - 1 /\ -1 <= I541 - 1 /\ -1 <= I542 - 1 /\ 0 <= I516 - 1 /\ y3 <= I517 - 1 /\ 3 <= I515 - 1 /\ -1 <= I529 - 1 /\ I519 + 3 <= I515 /\ I518 + 3 <= I515] 112.64/111.39 f4(I543, I544, I545, I546, I547, I548, I549, I550, I551, I552, I553, I554, I555) -> f4(I556, I544 - 1, I545, I546 + 2, I557, I558, I559, I560, I561, I562, I563, I564, I565) [0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543] 112.64/111.39 f1(I568, I569, I570, I571, I572, I573, I574, I575, I576, I577, I578, I579, I580) -> f4(I581, I582, I569, 1, 16, 0, 12, I583, I584, I585, I586, I587, I588) [14 <= I581 - 1 /\ 0 <= I568 - 1 /\ I581 - 14 <= I568 /\ 0 <= I569 - 1 /\ -1 <= I582 - 1] 112.64/111.39 f3(I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) -> f2(I602, I603, 16, I593, 12, I604, I605, I606, I607, I608, I609, I610, I611) [12 = I594 /\ 16 = I592 /\ I593 + 3 <= I590 /\ 14 <= I602 - 1 /\ 14 <= I590 - 1 /\ 0 <= I589 - 1 /\ I602 <= I590] 112.64/111.39 f1(I612, I613, I614, I615, I616, I617, I618, I619, I620, I621, I622, I623, I624) -> f2(I625, I613, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636) [-1 <= I637 - 1 /\ 0 <= I613 - 1 /\ 0 <= I612 - 1 /\ 3 <= I625 - 1] 112.64/111.39 112.64/111.39 We use the basic value criterion with the projection function NU: 112.64/111.39 NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13)] = z2 112.64/111.39 112.64/111.39 This gives the following inequalities: 112.64/111.39 0 <= I544 - 1 /\ I546 + 1 <= I545 - 1 /\ -1 <= I545 - 1 /\ -1 <= I546 - 1 /\ -1 <= I566 - 1 /\ -1 <= I567 - 1 /\ 1 <= I547 - 1 /\ 3 <= I543 - 1 /\ 3 <= I556 - 1 /\ I549 + 3 <= I543 /\ I548 + 3 <= I543 ==> I544 >! I544 - 1 112.64/111.39 112.64/111.39 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 112.64/114.37 EOF