227.80/224.59 YES 227.80/224.59 227.80/224.59 DP problem for innermost termination. 227.80/224.59 P = 227.80/224.59 init#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.59 f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11#(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.59 f11#(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11#(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.59 f12#(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12#(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.59 f11#(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12#(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.59 f9#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11#(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.59 f9#(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11#(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.59 f10#(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9#(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.59 f9#(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9#(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.59 f9#(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9#(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.59 f9#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9#(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.59 f9#(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9#(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.59 f9#(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10#(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.59 f9#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10#(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.59 f4#(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9#(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.59 f8#(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6#(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.59 f6#(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6#(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.59 f6#(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6#(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.59 f6#(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8#(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.59 f6#(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8#(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.59 f6#(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5#(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.59 f5#(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6#(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.59 f2#(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5#(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.59 f4#(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4#(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.59 f1#(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4#(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.59 f3#(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2#(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.59 f1#(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2#(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.59 R = 227.80/224.59 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.59 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.59 f11(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.59 f12(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.59 f11(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.59 f9(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.59 f9(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.59 f10(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.59 f9(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.59 f9(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.59 f9(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.59 f9(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.59 f9(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.59 f9(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.59 f9(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304) -> f7(I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318) [I292 + 2 <= I294 /\ I307 + 2 <= I294 /\ I298 + 3 <= I291 /\ I297 + 3 <= I291 /\ 0 <= I306 - 1 /\ 0 <= I294 - 1 /\ 3 <= I291 - 1 /\ 1 <= I295 - 1 /\ 1 <= I296 - 1] 227.80/224.59 f4(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.59 f8(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.59 f6(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.59 f6(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.59 f6(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.59 f6(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.59 f6(I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479, I480) -> f7(I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494) [I483 + 2 <= I469 /\ 0 <= I482 - 1 /\ 0 <= I469 - 1 /\ 0 <= I467 - 1 /\ I468 <= I471 - 1 /\ 1 <= I471 - 1] 227.80/224.59 f6(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.59 f5(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.59 f2(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.59 f4(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.59 f1(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.59 f3(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.59 f1(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.59 227.80/224.59 The dependency graph for this problem is: 227.80/224.59 0 -> 24, 26 227.80/224.59 1 -> 2, 4 227.80/224.59 2 -> 2, 4 227.80/224.59 3 -> 1, 3 227.80/224.59 4 -> 1, 3 227.80/224.59 5 -> 2, 4 227.80/224.59 6 -> 2, 4 227.80/224.59 7 -> 5, 6, 8, 9, 10, 11, 12, 13 227.80/224.59 8 -> 5, 6, 8, 9, 10, 11, 12, 13 227.80/224.59 9 -> 5, 6, 8, 9, 10, 11, 12, 13 227.80/224.59 10 -> 5, 6, 8, 9, 10, 11, 12, 13 227.80/224.59 11 -> 5, 6, 8, 9, 10, 11, 12, 13 227.80/224.59 12 -> 227.80/224.59 13 -> 7 227.80/224.59 14 -> 5, 6, 8, 9, 10, 11, 12, 13 227.80/224.59 15 -> 16, 17, 18, 19, 20 227.80/224.59 16 -> 16, 17, 18, 19, 20 227.80/224.59 17 -> 16, 17, 18, 19, 20 227.80/224.59 18 -> 227.80/224.59 19 -> 15 227.80/224.59 20 -> 21 227.80/224.59 21 -> 16, 17, 18, 19, 20 227.80/224.59 22 -> 21 227.80/224.59 23 -> 14, 23 227.80/224.59 24 -> 14, 23 227.80/224.59 25 -> 22 227.80/224.59 26 -> 22 227.80/224.59 Where: 227.80/224.59 0) init#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.59 1) f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11#(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.59 2) f11#(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11#(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.59 3) f12#(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12#(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.59 4) f11#(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12#(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.59 5) f9#(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11#(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.59 6) f9#(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11#(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.59 7) f10#(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9#(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.59 8) f9#(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9#(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.59 9) f9#(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9#(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.59 10) f9#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9#(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.59 11) f9#(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9#(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.59 12) f9#(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10#(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.59 13) f9#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10#(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.59 14) f4#(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9#(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.59 15) f8#(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6#(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.59 16) f6#(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6#(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.59 17) f6#(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6#(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.59 18) f6#(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8#(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.59 19) f6#(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8#(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.59 20) f6#(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5#(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.59 21) f5#(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6#(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.59 22) f2#(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5#(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.59 23) f4#(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4#(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.59 24) f1#(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4#(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.59 25) f3#(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2#(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.59 26) f1#(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2#(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.59 227.80/224.59 We have the following SCCs. 227.80/224.59 { 23 } 227.80/224.59 { 7, 8, 9, 10, 11, 13 } 227.80/224.59 { 1, 2, 3, 4 } 227.80/224.59 { 15, 16, 17, 19, 20, 21 } 227.80/224.59 227.80/224.59 DP problem for innermost termination. 227.80/224.59 P = 227.80/224.59 f8#(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6#(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.59 f6#(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6#(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.59 f6#(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6#(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.59 f6#(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8#(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.59 f6#(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5#(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.59 f5#(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6#(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.59 R = 227.80/224.59 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.59 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.59 f11(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.59 f12(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.59 f11(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.59 f9(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.59 f9(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.59 f10(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.59 f9(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.59 f9(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.59 f9(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.59 f9(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.59 f9(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.59 f9(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.59 f9(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304) -> f7(I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318) [I292 + 2 <= I294 /\ I307 + 2 <= I294 /\ I298 + 3 <= I291 /\ I297 + 3 <= I291 /\ 0 <= I306 - 1 /\ 0 <= I294 - 1 /\ 3 <= I291 - 1 /\ 1 <= I295 - 1 /\ 1 <= I296 - 1] 227.80/224.59 f4(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.59 f8(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.59 f6(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.59 f6(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.59 f6(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.59 f6(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.59 f6(I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479, I480) -> f7(I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494) [I483 + 2 <= I469 /\ 0 <= I482 - 1 /\ 0 <= I469 - 1 /\ 0 <= I467 - 1 /\ I468 <= I471 - 1 /\ 1 <= I471 - 1] 227.80/224.59 f6(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.59 f5(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.59 f2(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.59 f4(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.59 f1(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.59 f3(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.59 f1(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.59 227.80/224.59 We use the extended value criterion with the projection function NU: 227.80/224.59 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -x1 + x2 - 1 227.80/224.59 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -x1 + x4 - 2 227.80/224.59 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13)] = -x1 - x3 + x5 - 2 227.80/224.59 227.80/224.59 This gives the following inequalities: 227.80/224.59 0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344 ==> -I345 - I347 + I349 - 2 >= -I345 + I349 - 2 227.80/224.59 -1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1 ==> -I370 + I373 - 2 >= -I370 + I373 - 2 227.80/224.59 -1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1 ==> -I395 + I398 - 2 >= -I395 + I398 - 2 227.80/224.59 I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1 ==> -I444 + I447 - 2 >= -I444 - 0 + I447 - 2 227.80/224.59 0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495 ==> -I496 + I499 - 2 >= -(I496 + 1) + I499 - 1 227.80/224.59 -1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521 ==> -I522 + I523 - 1 > -I522 + I523 - 2 with -I522 + I523 - 1 >= 0 227.80/224.59 227.80/224.59 We remove all the strictly oriented dependency pairs. 227.80/224.59 227.80/224.59 DP problem for innermost termination. 227.80/224.59 P = 227.80/224.59 f8#(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6#(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.59 f6#(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6#(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.59 f6#(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6#(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.59 f6#(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8#(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.59 f6#(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5#(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.59 R = 227.80/224.59 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.59 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.59 f11(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.59 f12(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.59 f11(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.59 f9(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.59 f9(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.59 f10(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.59 f9(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.59 f9(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.59 f9(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.59 f9(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.59 f9(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.59 f9(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.59 f9(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304) -> f7(I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318) [I292 + 2 <= I294 /\ I307 + 2 <= I294 /\ I298 + 3 <= I291 /\ I297 + 3 <= I291 /\ 0 <= I306 - 1 /\ 0 <= I294 - 1 /\ 3 <= I291 - 1 /\ 1 <= I295 - 1 /\ 1 <= I296 - 1] 227.80/224.59 f4(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.59 f8(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.59 f6(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.59 f6(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.59 f6(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.59 f6(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.59 f6(I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479, I480) -> f7(I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494) [I483 + 2 <= I469 /\ 0 <= I482 - 1 /\ 0 <= I469 - 1 /\ 0 <= I467 - 1 /\ I468 <= I471 - 1 /\ 1 <= I471 - 1] 227.80/224.59 f6(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.59 f5(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.59 f2(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.59 f4(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.59 f1(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.59 f3(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.59 f1(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.59 227.80/224.59 The dependency graph for this problem is: 227.80/224.59 15 -> 16, 17, 19, 20 227.80/224.59 16 -> 16, 17, 19, 20 227.80/224.59 17 -> 16, 17, 19, 20 227.80/224.59 19 -> 15 227.80/224.59 20 -> 227.80/224.59 Where: 227.80/224.59 15) f8#(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6#(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.59 16) f6#(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6#(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.60 17) f6#(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6#(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.60 19) f6#(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8#(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 20) f6#(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5#(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.60 227.80/224.60 We have the following SCCs. 227.80/224.60 { 15, 16, 17, 19 } 227.80/224.60 227.80/224.60 DP problem for innermost termination. 227.80/224.60 P = 227.80/224.60 f8#(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6#(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.60 f6#(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6#(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.60 f6#(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6#(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.60 f6#(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8#(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 R = 227.80/224.60 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.60 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.60 f11(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.60 f12(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 f11(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.60 f9(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.60 f9(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.60 f10(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.60 f9(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.60 f9(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.60 f9(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.60 f9(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.60 f9(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.60 f9(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.60 f9(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304) -> f7(I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318) [I292 + 2 <= I294 /\ I307 + 2 <= I294 /\ I298 + 3 <= I291 /\ I297 + 3 <= I291 /\ 0 <= I306 - 1 /\ 0 <= I294 - 1 /\ 3 <= I291 - 1 /\ 1 <= I295 - 1 /\ 1 <= I296 - 1] 227.80/224.60 f4(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.60 f8(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.60 f6(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.60 f6(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.60 f6(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.60 f6(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 f6(I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479, I480) -> f7(I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494) [I483 + 2 <= I469 /\ 0 <= I482 - 1 /\ 0 <= I469 - 1 /\ 0 <= I467 - 1 /\ I468 <= I471 - 1 /\ 1 <= I471 - 1] 227.80/224.60 f6(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.60 f5(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.60 f2(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.60 f4(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.60 f1(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.60 f3(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.60 f1(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.60 227.80/224.60 We use the basic value criterion with the projection function NU: 227.80/224.60 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = z3 227.80/224.60 NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = z3 227.80/224.60 227.80/224.60 This gives the following inequalities: 227.80/224.60 0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344 ==> I346 >! I359 227.80/224.60 -1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1 ==> I371 >! I384 227.80/224.60 -1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1 ==> I396 >! I409 227.80/224.60 I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1 ==> I445 (>! \union =) I458 227.80/224.60 227.80/224.60 We remove all the strictly oriented dependency pairs. 227.80/224.60 227.80/224.60 DP problem for innermost termination. 227.80/224.60 P = 227.80/224.60 f6#(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8#(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 R = 227.80/224.60 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.60 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.60 f11(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.60 f12(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 f11(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.60 f9(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.60 f9(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.60 f10(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.60 f9(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.60 f9(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.60 f9(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.60 f9(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.60 f9(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.60 f9(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.60 f9(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304) -> f7(I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318) [I292 + 2 <= I294 /\ I307 + 2 <= I294 /\ I298 + 3 <= I291 /\ I297 + 3 <= I291 /\ 0 <= I306 - 1 /\ 0 <= I294 - 1 /\ 3 <= I291 - 1 /\ 1 <= I295 - 1 /\ 1 <= I296 - 1] 227.80/224.60 f4(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.60 f8(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.60 f6(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.60 f6(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.60 f6(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.60 f6(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 f6(I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479, I480) -> f7(I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494) [I483 + 2 <= I469 /\ 0 <= I482 - 1 /\ 0 <= I469 - 1 /\ 0 <= I467 - 1 /\ I468 <= I471 - 1 /\ 1 <= I471 - 1] 227.80/224.60 f6(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.60 f5(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.60 f2(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.60 f4(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.60 f1(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.60 f3(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.60 f1(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.60 227.80/224.60 The dependency graph for this problem is: 227.80/224.60 19 -> 227.80/224.60 Where: 227.80/224.60 19) f6#(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8#(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 227.80/224.60 We have the following SCCs. 227.80/224.60 227.80/224.60 227.80/224.60 DP problem for innermost termination. 227.80/224.60 P = 227.80/224.60 f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11#(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.60 f11#(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11#(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.60 f12#(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12#(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 f11#(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12#(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.60 R = 227.80/224.60 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.60 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.60 f11(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.60 f12(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 f11(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.60 f9(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.60 f9(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.60 f10(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.60 f9(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.60 f9(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.60 f9(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.60 f9(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.60 f9(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.60 f9(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.60 f9(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304) -> f7(I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318) [I292 + 2 <= I294 /\ I307 + 2 <= I294 /\ I298 + 3 <= I291 /\ I297 + 3 <= I291 /\ 0 <= I306 - 1 /\ 0 <= I294 - 1 /\ 3 <= I291 - 1 /\ 1 <= I295 - 1 /\ 1 <= I296 - 1] 227.80/224.60 f4(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.60 f8(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.60 f6(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.60 f6(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.60 f6(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.60 f6(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 f6(I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479, I480) -> f7(I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494) [I483 + 2 <= I469 /\ 0 <= I482 - 1 /\ 0 <= I469 - 1 /\ 0 <= I467 - 1 /\ I468 <= I471 - 1 /\ 1 <= I471 - 1] 227.80/224.60 f6(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.60 f5(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.60 f2(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.60 f4(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.60 f1(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.60 f3(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.60 f1(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.60 227.80/224.60 We use the reverse value criterion with the projection function NU: 227.80/224.60 NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = z8 - 1 + -1 * z4 227.80/224.60 NU[f12#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = z10 - 1 + -1 * (z3 + 1) 227.80/224.60 227.80/224.60 This gives the following inequalities: 227.80/224.60 I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1 ==> I9 - 1 + -1 * (I2 + 1) >= I9 - 1 + -1 * (I2 + 1) 227.80/224.60 I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1 ==> I30 - 1 + -1 * I26 > I30 - 1 + -1 * (I26 + 1) with I30 - 1 + -1 * I26 >= 0 227.80/224.60 I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1 ==> I55 - 1 + -1 * (I48 + 1) >= I55 - 1 + -1 * (I48 + 1) 227.80/224.60 I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1 ==> I76 - 1 + -1 * I72 > I76 - 1 + -1 * (I72 + 1) with I76 - 1 + -1 * I72 >= 0 227.80/224.60 227.80/224.60 We remove all the strictly oriented dependency pairs. 227.80/224.60 227.80/224.60 DP problem for innermost termination. 227.80/224.60 P = 227.80/224.60 f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11#(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.60 f12#(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12#(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 R = 227.80/224.60 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.60 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.60 f11(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.60 f12(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 f11(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.60 f9(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.60 f9(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.60 f10(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.60 f9(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.60 f9(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.60 f9(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.60 f9(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.60 f9(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.60 f9(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.60 f9(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304) -> f7(I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318) [I292 + 2 <= I294 /\ I307 + 2 <= I294 /\ I298 + 3 <= I291 /\ I297 + 3 <= I291 /\ 0 <= I306 - 1 /\ 0 <= I294 - 1 /\ 3 <= I291 - 1 /\ 1 <= I295 - 1 /\ 1 <= I296 - 1] 227.80/224.60 f4(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.60 f8(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.60 f6(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.60 f6(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.60 f6(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.60 f6(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 f6(I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479, I480) -> f7(I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494) [I483 + 2 <= I469 /\ 0 <= I482 - 1 /\ 0 <= I469 - 1 /\ 0 <= I467 - 1 /\ I468 <= I471 - 1 /\ 1 <= I471 - 1] 227.80/224.60 f6(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.60 f5(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.60 f2(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.60 f4(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.60 f1(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.60 f3(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.60 f1(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.60 227.80/224.60 The dependency graph for this problem is: 227.80/224.60 1 -> 227.80/224.60 3 -> 1, 3 227.80/224.60 Where: 227.80/224.60 1) f12#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11#(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.60 3) f12#(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12#(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 227.80/224.60 We have the following SCCs. 227.80/224.60 { 3 } 227.80/224.60 227.80/224.60 DP problem for innermost termination. 227.80/224.60 P = 227.80/224.60 f12#(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12#(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 R = 227.80/224.60 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.60 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.60 f11(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.60 f12(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 f11(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.60 f9(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.60 f9(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.60 f10(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.60 f9(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.60 f9(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.60 f9(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.60 f9(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.60 f9(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.60 f9(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.60 f9(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304) -> f7(I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318) [I292 + 2 <= I294 /\ I307 + 2 <= I294 /\ I298 + 3 <= I291 /\ I297 + 3 <= I291 /\ 0 <= I306 - 1 /\ 0 <= I294 - 1 /\ 3 <= I291 - 1 /\ 1 <= I295 - 1 /\ 1 <= I296 - 1] 227.80/224.60 f4(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.60 f8(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.60 f6(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.60 f6(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.60 f6(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.60 f6(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 f6(I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479, I480) -> f7(I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494) [I483 + 2 <= I469 /\ 0 <= I482 - 1 /\ 0 <= I469 - 1 /\ 0 <= I467 - 1 /\ I468 <= I471 - 1 /\ 1 <= I471 - 1] 227.80/224.60 f6(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.60 f5(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.60 f2(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.60 f4(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.60 f1(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.60 f3(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.60 f1(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.60 227.80/224.60 We use the basic value criterion with the projection function NU: 227.80/224.60 NU[f12#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = z5 227.80/224.60 227.80/224.60 This gives the following inequalities: 227.80/224.60 I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1 ==> I50 >! I63 227.80/224.60 227.80/224.60 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 227.80/224.60 227.80/224.60 DP problem for innermost termination. 227.80/224.60 P = 227.80/224.60 f10#(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9#(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.60 f9#(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9#(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.60 f9#(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9#(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.60 f9#(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9#(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.60 f9#(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9#(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.60 f9#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10#(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.60 R = 227.80/224.60 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.60 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.60 f11(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.60 f12(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 f11(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.60 f9(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.60 f9(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.60 f10(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.60 f9(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.60 f9(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.60 f9(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.60 f9(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.60 f9(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.60 f9(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.60 f9(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304) -> f7(I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318) [I292 + 2 <= I294 /\ I307 + 2 <= I294 /\ I298 + 3 <= I291 /\ I297 + 3 <= I291 /\ 0 <= I306 - 1 /\ 0 <= I294 - 1 /\ 3 <= I291 - 1 /\ 1 <= I295 - 1 /\ 1 <= I296 - 1] 227.80/224.60 f4(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.60 f8(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.60 f6(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.60 f6(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.60 f6(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.60 f6(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 f6(I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479, I480) -> f7(I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494) [I483 + 2 <= I469 /\ 0 <= I482 - 1 /\ 0 <= I469 - 1 /\ 0 <= I467 - 1 /\ I468 <= I471 - 1 /\ 1 <= I471 - 1] 227.80/224.60 f6(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.60 f5(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.60 f2(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.60 f4(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.60 f1(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.60 f3(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.60 f1(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.60 227.80/224.60 We use the basic value criterion with the projection function NU: 227.80/224.60 NU[f9#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = z4 227.80/224.60 NU[f10#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = z3 227.80/224.60 227.80/224.60 This gives the following inequalities: 227.80/224.60 0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138 ==> I140 >! I153 227.80/224.60 I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1 ==> I163 >! I175 227.80/224.60 I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1 ==> I185 >! I197 227.80/224.60 I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204 ==> I207 >! I219 227.80/224.60 I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226 ==> I229 >! I241 227.80/224.60 I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1 ==> I273 (>! \union =) I285 227.80/224.60 227.80/224.60 We remove all the strictly oriented dependency pairs. 227.80/224.60 227.80/224.60 DP problem for innermost termination. 227.80/224.60 P = 227.80/224.60 f9#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10#(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.60 R = 227.80/224.60 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.60 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.60 f11(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.60 f12(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 f11(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.60 f9(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.60 f9(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.60 f10(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.60 f9(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.60 f9(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.60 f9(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.60 f9(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.60 f9(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.60 f9(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.60 f9(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304) -> f7(I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318) [I292 + 2 <= I294 /\ I307 + 2 <= I294 /\ I298 + 3 <= I291 /\ I297 + 3 <= I291 /\ 0 <= I306 - 1 /\ 0 <= I294 - 1 /\ 3 <= I291 - 1 /\ 1 <= I295 - 1 /\ 1 <= I296 - 1] 227.80/224.60 f4(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.60 f8(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.60 f6(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.60 f6(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.60 f6(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.60 f6(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 f6(I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479, I480) -> f7(I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494) [I483 + 2 <= I469 /\ 0 <= I482 - 1 /\ 0 <= I469 - 1 /\ 0 <= I467 - 1 /\ I468 <= I471 - 1 /\ 1 <= I471 - 1] 227.80/224.60 f6(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.60 f5(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.60 f2(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.60 f4(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.60 f1(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.60 f3(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.60 f1(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.60 227.80/224.60 The dependency graph for this problem is: 227.80/224.60 13 -> 227.80/224.60 Where: 227.80/224.60 13) f9#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10#(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.60 227.80/224.60 We have the following SCCs. 227.80/224.60 227.80/224.60 227.80/224.60 DP problem for innermost termination. 227.80/224.60 P = 227.80/224.60 f4#(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4#(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.60 R = 227.80/224.60 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14) 227.80/224.60 f12(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13) -> f11(I14, I15, I16, I2 + 1, I7, I8, I13, I9, I17, I18, I19, I20, I21, I22) [I12 + 2 <= I4 /\ I11 + 2 <= I4 /\ I10 + 2 <= I4 /\ I8 + 3 <= I0 /\ I7 + 3 <= I0 /\ 0 <= I16 - 1 /\ 0 <= I15 - 1 /\ 3 <= I14 - 1 /\ 0 <= I5 - 1 /\ 1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 3 <= I0 - 1 /\ I16 <= I5 /\ I16 + 1 <= I4 /\ I16 - 1 <= I3 /\ I16 <= I1 /\ I16 + 3 <= I0 /\ I15 <= I5 /\ I15 + 1 <= I4 /\ I15 - 1 <= I3 /\ I15 <= I1 /\ I15 + 3 <= I0 /\ I14 <= I0 /\ I6 <= I13 - 1 /\ -1 <= I9 - 1] 227.80/224.60 f11(I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36) -> f11(I37, I38, I39, I26 + 1, I27, I28, I29, I30, I40, I41, I42, I43, I44, I45) [I28 + 3 <= I23 /\ I27 + 3 <= I23 /\ 0 <= I39 - 1 /\ 0 <= I38 - 1 /\ 3 <= I37 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1 /\ 3 <= I23 - 1 /\ I39 <= I25 /\ I39 <= I24 /\ I39 + 3 <= I23 /\ I38 <= I25 /\ I38 <= I24 /\ I38 + 3 <= I23 /\ I37 <= I23 /\ I26 <= I30 - 1 /\ -1 <= I30 - 1] 227.80/224.60 f12(I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f12(I60, I61, I48, I62, I63, I64, I65, I53, I54, I55, I66, I67, I68, I59) [I58 + 2 <= I50 /\ I57 + 2 <= I50 /\ I68 + 4 <= I50 /\ I67 + 4 <= I50 /\ I66 + 4 <= I50 /\ I56 + 2 <= I50 /\ I68 + 2 <= I49 /\ I67 + 2 <= I49 /\ I66 + 2 <= I49 /\ I54 + 3 <= I46 /\ I53 + 3 <= I46 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ -1 <= I62 - 1 /\ 0 <= I61 - 1 /\ 3 <= I60 - 1 /\ 0 <= I51 - 1 /\ 2 <= I50 - 1 /\ 0 <= I49 - 1 /\ 0 <= I47 - 1 /\ 3 <= I46 - 1 /\ I64 <= I51 /\ I64 + 2 <= I50 /\ I64 <= I49 /\ I64 <= I47 /\ I64 + 3 <= I46 /\ I63 + 2 <= I50 /\ I63 <= I49 /\ I62 + 3 <= I50 /\ I62 + 1 <= I49 /\ I61 <= I51 /\ I61 + 2 <= I50 /\ I61 <= I49 /\ I61 <= I47 /\ I61 + 3 <= I46 /\ I60 <= I46 /\ 0 <= I59 - 1 /\ I52 <= I59 - 1] 227.80/224.60 f11(I69, I70, I71, I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82) -> f12(I83, I84, I72, I85, I86, I87, I88, I73, I74, I76, I89, I90, I91, I75) [I74 + 3 <= I69 /\ I73 + 3 <= I69 /\ 0 <= I87 - 1 /\ 0 <= I86 - 1 /\ -1 <= I85 - 1 /\ 0 <= I84 - 1 /\ 3 <= I83 - 1 /\ 0 <= I71 - 1 /\ 0 <= I70 - 1 /\ 3 <= I69 - 1 /\ I87 <= I71 /\ I87 <= I70 /\ I87 + 3 <= I69 /\ I84 <= I71 /\ I84 <= I70 /\ I84 + 3 <= I69 /\ I83 <= I69 /\ I72 <= I76 - 1 /\ 0 <= I75 - 1] 227.80/224.60 f9(I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104, I105) -> f11(I106, I107, I108, 0, I98 + 1, I99, 2 * I97, I97, I109, I110, I111, I112, I113, I114) [I99 + 3 <= I92 /\ I98 + 3 <= I92 /\ 0 <= I108 - 1 /\ 0 <= I107 - 1 /\ 3 <= I106 - 1 /\ -1 <= I95 - 1 /\ 3 <= I92 - 1 /\ I108 - 1 <= I95 /\ I108 + 3 <= I92 /\ I107 - 1 <= I95 /\ I107 + 3 <= I92 /\ I106 - 1 <= I92 /\ I99 <= I98 /\ 0 <= 2 * I97 /\ 1073741824 <= I97 - 1 /\ I94 <= I97 - 1] 227.80/224.60 f9(I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128) -> f11(I129, I130, I131, 0, I121 + 1, I122, 2 * I120, I120, I132, I133, I134, I135, I136, I137) [I122 + 3 <= I115 /\ I121 + 3 <= I115 /\ 0 <= I131 - 1 /\ 0 <= I130 - 1 /\ 3 <= I129 - 1 /\ -1 <= I118 - 1 /\ 3 <= I115 - 1 /\ I131 - 1 <= I118 /\ I131 + 3 <= I115 /\ I130 - 1 <= I118 /\ I130 + 3 <= I115 /\ I129 - 1 <= I115 /\ I120 <= 1073741823 /\ 0 <= 2 * I120 /\ I122 <= I121 /\ 1 <= I120 - 1 /\ I117 <= I120 - 1] 227.80/224.60 f10(I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151) -> f9(I152, I148, I139, I153, I142, I143, I144, I145, I154, I155, I156, I157, I158, I159) [0 = I141 /\ I149 + 4 <= I140 /\ I148 + 2 <= I140 /\ I146 + 2 <= I140 /\ I145 + 3 <= I138 /\ I144 + 3 <= I138 /\ -1 <= I153 - 1 /\ 3 <= I152 - 1 /\ -1 <= I147 - 1 /\ 2 <= I140 - 1 /\ 3 <= I138 - 1 /\ I153 <= I147 /\ I153 + 2 <= I140 /\ I152 <= I138] 227.80/224.60 f9(I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173) -> f9(I174, I161, I162, I175, I164, I165, I166, I167, I176, I177, I178, I179, I180, I181) [I161 + 2 <= I163 /\ I167 + 3 <= I160 /\ I166 + 3 <= I160 /\ -1 <= I175 - 1 /\ 3 <= I174 - 1 /\ 2 <= I163 - 1 /\ 3 <= I160 - 1 /\ I175 + 2 <= I163 /\ I174 <= I160 /\ 1 <= I164 - 1 /\ 1 <= I165 - 1] 227.80/224.60 f9(I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195) -> f9(I196, I183, I184, I197, I186, I187, I188, I189, I198, I199, I200, I201, I202, I203) [I183 + 2 <= I185 /\ I189 + 3 <= I182 /\ I188 + 3 <= I182 /\ -1 <= I197 - 1 /\ 3 <= I196 - 1 /\ 1 <= I185 - 1 /\ 3 <= I182 - 1 /\ I197 + 2 <= I185 /\ I196 <= I182 /\ 1 <= I186 - 1 /\ 1 <= I187 - 1] 227.80/224.60 f9(I204, I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f9(I218, I205, I206, I219, I208, I209, I210, I211, I220, I221, I222, I223, I224, I225) [I218 <= I204 /\ I205 <= y1 - 1 /\ I219 + 1 <= I207 /\ 3 <= I204 - 1 /\ 0 <= I207 - 1 /\ 3 <= I218 - 1 /\ -1 <= I219 - 1 /\ I210 + 3 <= I204 /\ I211 + 3 <= I204] 227.80/224.60 f9(I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f9(I240, I227, I228, I241, I230, I231, I232, I233, I242, I243, I244, I245, I246, I247) [I240 <= I226 /\ I248 <= I227 - 1 /\ I241 + 1 <= I229 /\ 3 <= I226 - 1 /\ 0 <= I229 - 1 /\ 3 <= I240 - 1 /\ -1 <= I241 - 1 /\ I232 + 3 <= I226 /\ I233 + 3 <= I226] 227.80/224.60 f9(I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259, I260, I261, I262) -> f10(I263, I251, I264, 1, I253, I254, I255, I256, I265, I266, I250, I267, I268, I269) [I267 + 4 <= I252 /\ I250 + 2 <= I252 /\ I265 + 2 <= I252 /\ I256 + 3 <= I249 /\ I255 + 3 <= I249 /\ -1 <= I266 - 1 /\ 2 <= I264 - 1 /\ 3 <= I263 - 1 /\ 2 <= I252 - 1 /\ 3 <= I249 - 1 /\ I266 + 2 <= I252 /\ I264 <= I252 /\ I263 <= I249 /\ 1 <= I253 - 1 /\ 1 <= I254 - 1] 227.80/224.60 f9(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283) -> f10(I284, I272, I285, 0, I274, I275, I276, I277, I286, I287, I271, I288, I289, I290) [I288 + 4 <= I273 /\ I271 + 2 <= I273 /\ I286 + 2 <= I273 /\ I277 + 3 <= I270 /\ I276 + 3 <= I270 /\ -1 <= I287 - 1 /\ 2 <= I285 - 1 /\ 3 <= I284 - 1 /\ 2 <= I273 - 1 /\ 3 <= I270 - 1 /\ I287 + 2 <= I273 /\ I285 <= I273 /\ I284 <= I270 /\ 1 <= I274 - 1 /\ 1 <= I275 - 1] 227.80/224.60 f9(I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304) -> f7(I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318) [I292 + 2 <= I294 /\ I307 + 2 <= I294 /\ I298 + 3 <= I291 /\ I297 + 3 <= I291 /\ 0 <= I306 - 1 /\ 0 <= I294 - 1 /\ 3 <= I291 - 1 /\ 1 <= I295 - 1 /\ 1 <= I296 - 1] 227.80/224.60 f4(I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329, I330, I331, I332) -> f9(I333, I334, I335, I336, I322 + 2, I323, I324, I325, I337, I338, I339, I340, I341, I342) [I322 + 1 <= I321 - 1 /\ 1 <= I323 - 1 /\ 0 <= I320 - 1 /\ -1 <= I321 - 1 /\ -1 <= I322 - 1 /\ -1 <= I343 - 1 /\ -1 <= y2 - 1 /\ I335 <= I323 - 1 /\ I333 <= I319 /\ 3 <= I319 - 1 /\ 3 <= I333 - 1 /\ -1 <= I336 - 1 /\ I325 + 3 <= I319 /\ I324 + 3 <= I319] 227.80/224.60 f8(I344, I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357) -> f6(I358, I345, I359, I348, I349, I360, I361, I362, I363, I364, I365, I366, I367, I368) [0 = I347 /\ I353 + 2 <= I346 /\ I352 + 2 <= I346 /\ I350 + 4 <= I346 /\ -1 <= I359 - 1 /\ 0 <= I358 - 1 /\ -1 <= I351 - 1 /\ 2 <= I346 - 1 /\ 0 <= I344 - 1 /\ I359 <= I351 /\ I359 + 2 <= I346 /\ I358 - 1 <= I351 /\ I358 + 2 <= I346 /\ I358 <= I344] 227.80/224.60 f6(I369, I370, I371, I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382) -> f6(I383, I370, I384, I372, I373, I385, I386, I387, I388, I389, I390, I391, I392, I393) [-1 <= I384 - 1 /\ 0 <= I383 - 1 /\ 2 <= I371 - 1 /\ 0 <= I369 - 1 /\ I384 + 2 <= I371 /\ I383 + 2 <= I371 /\ I383 <= I369 /\ I370 <= I373 - 1 /\ 1 <= I373 - 1] 227.80/224.60 f6(I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f6(I408, I395, I409, I397, I398, I410, I411, I412, I413, I414, I415, I416, I417, I418) [-1 <= I409 - 1 /\ 0 <= I408 - 1 /\ 1 <= I396 - 1 /\ 0 <= I394 - 1 /\ I409 + 2 <= I396 /\ I408 + 1 <= I396 /\ I408 <= I394 /\ I395 <= I398 - 1 /\ 1 <= I398 - 1] 227.80/224.60 f6(I419, I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432) -> f8(I433, I420, I434, 1, I422, I423, I435, I436, I437, I438, I439, I440, I441, I442) [I437 + 2 <= I421 /\ I438 + 2 <= I421 /\ I435 + 4 <= I421 /\ -1 <= I436 - 1 /\ 2 <= I434 - 1 /\ 0 <= I433 - 1 /\ 2 <= I421 - 1 /\ 0 <= I419 - 1 /\ I436 + 2 <= I421 /\ I434 <= I421 /\ I433 + 2 <= I421 /\ I433 <= I419 /\ I420 <= I423 - 1 /\ 1 <= I423 - 1] 227.80/224.60 f6(I443, I444, I445, I446, I447, I448, I449, I450, I451, I452, I453, I454, I455, I456) -> f8(I457, I444, I458, 0, I446, I447, I459, I460, I461, I462, I463, I464, I465, I466) [I461 + 2 <= I445 /\ I462 + 2 <= I445 /\ I459 + 4 <= I445 /\ -1 <= I460 - 1 /\ 2 <= I458 - 1 /\ 0 <= I457 - 1 /\ 2 <= I445 - 1 /\ 0 <= I443 - 1 /\ I460 + 2 <= I445 /\ I458 <= I445 /\ I457 + 2 <= I445 /\ I457 <= I443 /\ I444 <= I447 - 1 /\ 1 <= I447 - 1] 227.80/224.60 f6(I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479, I480) -> f7(I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494) [I483 + 2 <= I469 /\ 0 <= I482 - 1 /\ 0 <= I469 - 1 /\ 0 <= I467 - 1 /\ I468 <= I471 - 1 /\ 1 <= I471 - 1] 227.80/224.60 f6(I495, I496, I497, I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508) -> f5(I509, I496 + 1, I499, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520) [0 <= I509 - 1 /\ -1 <= I497 - 1 /\ 0 <= I495 - 1 /\ I509 - 1 <= I497 /\ -1 <= I499 - 1 /\ I509 <= I495] 227.80/224.60 f5(I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f6(I535, I522, I536, I537, I523, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I536 - 1 /\ 0 <= I535 - 1 /\ 0 <= I521 - 1 /\ I522 <= I523 - 1 /\ I535 <= I521] 227.80/224.60 f2(I547, I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560) -> f5(I561, 0, I549, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) [I573 <= I548 - 1 /\ 1 <= I549 - 1 /\ -1 <= I573 - 1 /\ -1 <= I574 - 1 /\ 0 <= I548 - 1 /\ I561 + 3 <= I547 /\ 3 <= I547 - 1 /\ 0 <= I561 - 1 /\ I551 + 3 <= I547 /\ I550 + 3 <= I547] 227.80/224.60 f4(I575, I576, I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588) -> f4(I589, I576 - 1, I577, I578 + 2, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599) [0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575] 227.80/224.60 f1(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615) -> f4(I616, I617, I603, 1, 16, 0, 12, I618, I619, I620, I621, I622, I623, I624) [14 <= I616 - 1 /\ 0 <= I602 - 1 /\ I616 - 14 <= I602 /\ 0 <= I603 - 1 /\ -1 <= I617 - 1] 227.80/224.60 f3(I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635, I636, I637, I638) -> f2(I639, I640, 16, I629, 12, I641, I642, I643, I644, I645, I646, I647, I648, I649) [12 = I630 /\ 16 = I628 /\ I629 + 3 <= I626 /\ 14 <= I639 - 1 /\ 14 <= I626 - 1 /\ 0 <= I625 - 1 /\ I639 <= I626] 227.80/224.60 f1(I650, I651, I652, I653, I654, I655, I656, I657, I658, I659, I660, I661, I662, I663) -> f2(I664, I651, I665, I666, I667, I668, I669, I670, I671, I672, I673, I674, I675, I676) [-1 <= I677 - 1 /\ 0 <= I651 - 1 /\ 0 <= I650 - 1 /\ 3 <= I664 - 1] 227.80/224.60 227.80/224.60 We use the basic value criterion with the projection function NU: 227.80/224.60 NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14)] = z2 227.80/224.60 227.80/224.60 This gives the following inequalities: 227.80/224.60 0 <= I576 - 1 /\ I578 + 1 <= I577 - 1 /\ -1 <= I577 - 1 /\ -1 <= I578 - 1 /\ -1 <= I600 - 1 /\ -1 <= I601 - 1 /\ 1 <= I579 - 1 /\ 3 <= I575 - 1 /\ 3 <= I589 - 1 /\ I581 + 3 <= I575 /\ I580 + 3 <= I575 ==> I576 >! I576 - 1 227.80/224.60 227.80/224.60 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 227.80/227.58 EOF