/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES DP problem for innermost termination. P = f32#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31#(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30#(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31#(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26#(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31#(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23#(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31#(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18#(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31#(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15#(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31#(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13#(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31#(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12#(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31#(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10#(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31#(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8#(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31#(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6#(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31#(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4#(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31#(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5#(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31#(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3#(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31#(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1#(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31#(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14#(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11#(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20#(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29#(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30#(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30#(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28#(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30#(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26#(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28#(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29#(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f24#(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25#(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25#(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23#(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25#(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21#(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23#(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24#(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f20#(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10#(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20#(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6#(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18#(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19#(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19#(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17#(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19#(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15#(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17#(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18#(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f14#(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13#(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13#(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12#(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13#(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8#(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12#(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13#(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10#(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11#(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f4#(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5#(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5#(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3#(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5#(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1#(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3#(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4#(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] The dependency graph for this problem is: 0 -> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 1 -> 26 2 -> 27 3 -> 28, 29 4 -> 30 5 -> 6 -> 31 7 -> 32, 33 8 -> 34 9 -> 10 -> 35, 36 11 -> 37 12 -> 38, 39 13 -> 40 14 -> 15 -> 41 16 -> 42, 43 17 -> 44 18 -> 45 19 -> 20 -> 21 -> 46 22 -> 47, 48 23 -> 49 24 -> 25 -> 41 26 -> 35, 36 27 -> 28, 29 28 -> 30 29 -> 30 -> 27 31 -> 32, 33 32 -> 34 33 -> 34 -> 31 35 -> 45 36 -> 37 -> 38, 39 38 -> 40 39 -> 40 -> 37 41 -> 42, 43 42 -> 44 43 -> 44 -> 42, 43 45 -> 26 46 -> 47, 48 47 -> 49 48 -> 49 -> 46 Where: 0) f32#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) 1) f31#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) 2) f31#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29#(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) 3) f31#(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30#(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 4) f31#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28#(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) 5) f31#(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26#(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) 6) f31#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24#(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 7) f31#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) 8) f31#(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23#(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) 9) f31#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21#(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) 10) f31#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20#(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) 11) f31#(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18#(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) 12) f31#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19#(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) 13) f31#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17#(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) 14) f31#(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15#(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) 15) f31#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14#(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) 16) f31#(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13#(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) 17) f31#(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12#(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) 18) f31#(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10#(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) 19) f31#(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8#(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) 20) f31#(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6#(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) 21) f31#(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4#(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) 22) f31#(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5#(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) 23) f31#(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3#(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) 24) f31#(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1#(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) 25) f31#(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14#(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] 26) f11#(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20#(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] 27) f29#(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30#(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] 28) f30#(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28#(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] 29) f30#(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26#(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] 30) f28#(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29#(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] 31) f24#(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25#(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] 32) f25#(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23#(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] 33) f25#(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21#(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] 34) f23#(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24#(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] 35) f20#(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10#(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] 36) f20#(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6#(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] 37) f18#(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19#(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] 38) f19#(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17#(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] 39) f19#(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15#(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] 40) f17#(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18#(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] 41) f14#(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13#(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] 42) f13#(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12#(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] 43) f13#(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8#(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] 44) f12#(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13#(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] 45) f10#(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11#(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] 46) f4#(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5#(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) 47) f5#(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3#(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] 48) f5#(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1#(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] 49) f3#(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4#(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) We have the following SCCs. { 27, 28, 30 } { 31, 32, 34 } { 37, 38, 40 } { 42, 44 } { 26, 35, 45 } { 46, 47, 49 } DP problem for innermost termination. P = f4#(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5#(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5#(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3#(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f3#(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4#(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] We use the extended value criterion with the projection function NU: NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = -x10 + x11 - 1 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = -x10 + x11 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = -x10 + x11 This gives the following inequalities: ==> -I1094 + I1095 >= -I1094 + I1095 I1109 <= I1110 ==> -I1109 + I1110 > -I1109 + I1110 - 1 with -I1109 + I1110 >= 0 ==> -I1139 + I1140 - 1 >= -(1 + I1139) + I1140 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f4#(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5#(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f3#(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4#(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] The dependency graph for this problem is: 46 -> 49 -> 46 Where: 46) f4#(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5#(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) 49) f3#(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4#(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) We have the following SCCs. DP problem for innermost termination. P = f11#(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20#(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f20#(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10#(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f10#(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11#(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] We use the extended value criterion with the projection function NU: NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = x10 - x11 - 1 NU[f20#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = x10 - x11 NU[f11#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = x10 - x11 This gives the following inequalities: I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480 ==> I475 - I476 >= I475 - I476 I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743 ==> I738 - I739 > I738 - I739 - 1 with I738 - I739 >= 0 I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003 ==> I998 - I999 - 1 >= (-1 + I998) - I999 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f11#(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20#(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f10#(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11#(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] The dependency graph for this problem is: 26 -> 45 -> 26 Where: 26) f11#(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20#(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] 45) f10#(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11#(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] We have the following SCCs. DP problem for innermost termination. P = f13#(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12#(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f12#(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13#(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] We use the reverse value criterion with the projection function NU: NU[f12#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15)] = z11 + -1 * (1 + (1 + z12)) NU[f13#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15)] = z11 + -1 * (1 + z12) This gives the following inequalities: I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940 ==> I935 + -1 * (1 + I936) > I935 + -1 * (1 + (1 + I936)) with I935 + -1 * (1 + I936) >= 0 I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982 ==> I977 + -1 * (1 + (1 + I978)) >= I977 + -1 * (1 + (1 + I978)) We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f12#(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13#(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] The dependency graph for this problem is: 44 -> Where: 44) f12#(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13#(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] We have the following SCCs. DP problem for innermost termination. P = f18#(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19#(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19#(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17#(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f17#(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18#(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] We use the extended value criterion with the projection function NU: NU[f17#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = -x10 + x11 - 1 NU[f19#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = -x10 + x11 NU[f18#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = -x10 + x11 This gives the following inequalities: I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785 ==> -I780 + I781 >= -I780 + I781 I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806 ==> -I801 + I802 > -I801 + I802 - 1 with -I801 + I802 >= 0 I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848 ==> -I843 + I844 - 1 >= -(1 + I843) + I844 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f18#(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19#(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f17#(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18#(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] The dependency graph for this problem is: 37 -> 40 -> 37 Where: 37) f18#(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19#(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] 40) f17#(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18#(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] We have the following SCCs. DP problem for innermost termination. P = f24#(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25#(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25#(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23#(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f23#(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24#(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] We use the extended value criterion with the projection function NU: NU[f23#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = -x10 + x11 NU[f25#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = -x10 + x11 + 1 NU[f24#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = -x10 + x11 + 1 This gives the following inequalities: I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617 ==> -I612 + I613 + 1 >= -I612 + I613 + 1 I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636 ==> -I631 + I632 + 1 > -I631 + I632 with -I631 + I632 + 1 >= 0 I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674 ==> -I669 + I670 >= -(1 + I669) + I670 + 1 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f24#(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25#(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f23#(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24#(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] The dependency graph for this problem is: 31 -> 34 -> 31 Where: 31) f24#(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25#(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] 34) f23#(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24#(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] We have the following SCCs. DP problem for innermost termination. P = f29#(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30#(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30#(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28#(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f28#(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29#(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] We use the extended value criterion with the projection function NU: NU[f28#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = x10 - x11 - 1 NU[f30#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = x10 - x11 NU[f29#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14)] = x10 - x11 This gives the following inequalities: I502 = I501 /\ I501 = I501 ==> I496 - I497 >= I496 - I497 I519 = I518 /\ I514 <= I513 /\ I518 = I518 ==> I513 - I514 > I513 - I514 - 1 with I513 - I514 >= 0 I553 = I552 /\ I552 = I552 ==> I547 - I548 - 1 >= (-1 + I547) - I548 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f29#(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30#(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f28#(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29#(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] R = f32(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> f31(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) f31(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) -> f11(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14) f31(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) -> f2(I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29) f31(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f29(I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44) f31(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f30(I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) f31(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) -> f28(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71, I72, I73, I74) f31(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f26(I75, I76, I77, I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88, I89) f31(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f27(I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) f31(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f24(I105, I106, I107, I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) f31(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f25(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) f31(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) -> f23(I135, I136, I137, I138, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149) f31(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) -> f21(I150, I151, I152, I153, I154, I155, I156, I157, I158, I159, I160, I161, I162, I163, I164) f31(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f20(I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) f31(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) -> f22(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194) f31(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) -> f18(I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205, I206, I207, I208, I209) f31(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) -> f19(I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224) f31(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) -> f17(I225, I226, I227, I228, I229, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239) f31(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) -> f15(I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252, I253, I254) f31(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) -> f16(I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269) f31(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) -> f14(I270, I271, I272, I273, I274, I275, I276, I277, I278, I279, I280, I281, I282, I283, I284) f31(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) -> f13(I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299) f31(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) -> f12(I300, I301, I302, I303, I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314) f31(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) -> f10(I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328, I329) f31(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) -> f8(I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344) f31(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f9(I345, I346, I347, I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) f31(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) -> f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374) f31(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) -> f7(I375, I376, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389) f31(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) -> f4(I390, I391, I392, I393, I394, I395, I396, I397, I398, I399, I400, I401, I402, I403, I404) f31(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) -> f5(I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419) f31(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) -> f3(I420, I421, I422, I423, I424, I425, I426, I427, I428, I429, I430, I431, I432, I433, I434) f31(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) -> f1(I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448, I449) f31(I450, I451, I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464) -> f14(I460, I461, I462, I463, I464, rnd6, rnd7, rnd8, rnd9, I459, I460, rnd12, rnd13, rnd14, rnd15) [rnd15 = rnd9 /\ rnd14 = rnd8 /\ rnd13 = rnd7 /\ rnd12 = rnd6 /\ rnd9 = rnd9 /\ rnd8 = rnd8 /\ rnd7 = rnd7 /\ rnd6 = rnd6] f11(I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476, I477, I478, I479) -> f20(I475, I476, I477, I478, I479, I480, I481, I482, I473, I474, I475, I476, I483, I484, I485) [I485 = I482 /\ I484 = I481 /\ I483 = I480 /\ I482 = I482 /\ I481 = I481 /\ I480 = I480] f29(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] f30(I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517) -> f28(I513, I514, I515, I516, I517, I518, I509, I510, I511, I512, I513, I514, I515, I516, I519) [I519 = I518 /\ I514 <= I513 /\ I518 = I518] f30(I520, I521, I522, I523, I524, I525, I526, I527, I528, I529, I530, I531, I532, I533, I534) -> f26(I530, I531, I532, I533, I534, I535, I526, I527, I528, I529, I530, I531, I532, I533, I536) [I536 = I535 /\ 1 + I530 <= I531 /\ I535 = I535] f28(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] f28(I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568) -> f27(I564, I565, I566, I567, I568, I569, I570, I571, I572, rnd10, rnd11, I573, I574, I575, I576) [I576 = rnd10 /\ I575 = I572 /\ I574 = I571 /\ I573 = I570 /\ rnd11 = I569 /\ rnd10 = rnd10 /\ I572 = I572 /\ I571 = I571 /\ I570 = I570 /\ I569 = I569] f26(I577, I578, I579, I580, I581, I582, I583, I584, I585, I586, I587, I588, I589, I590, I591) -> f27(I587, I588, I589, I590, I591, I592, I593, I594, I595, I596, I597, I598, I599, I600, I601) [I601 = I596 /\ I600 = I595 /\ I599 = I594 /\ I598 = I593 /\ I597 = I592 /\ I596 = I596 /\ I595 = I595 /\ I594 = I594 /\ I593 = I593 /\ I592 = I592] f24(I602, I603, I604, I605, I606, I607, I608, I609, I610, I611, I612, I613, I614, I615, I616) -> f25(I612, I613, I614, I615, I616, I617, I618, I609, I610, I611, I612, I613, I614, I619, I620) [I620 = I618 /\ I619 = I617 /\ I618 = I618 /\ I617 = I617] f25(I621, I622, I623, I624, I625, I626, I627, I628, I629, I630, I631, I632, I633, I634, I635) -> f23(I631, I632, I633, I634, I635, I636, I637, I628, I629, I630, I631, I632, I633, I638, I639) [I639 = I637 /\ I638 = I636 /\ I631 <= I632 /\ I637 = I637 /\ I636 = I636] f25(I640, I641, I642, I643, I644, I645, I646, I647, I648, I649, I650, I651, I652, I653, I654) -> f21(I650, I651, I652, I653, I654, I655, I656, I647, I648, I649, I650, I651, I652, I657, I658) [I658 = I656 /\ I657 = I655 /\ 1 + I651 <= I650 /\ I656 = I656 /\ I655 = I655] f23(I659, I660, I661, I662, I663, I664, I665, I666, I667, I668, I669, I670, I671, I672, I673) -> f24(I669, I670, I671, I672, I673, I674, I675, I666, I667, I668, 1 + I669, I670, I671, I676, I677) [I677 = I675 /\ I676 = I674 /\ I675 = I675 /\ I674 = I674] f23(I678, I679, I680, I681, I682, I683, I684, I685, I686, I687, I688, I689, I690, I691, I692) -> f22(I688, I689, I690, I691, I692, I693, I694, I695, I696, I697, I698, I699, I700, I701, I702) [I702 = I697 /\ I701 = I696 /\ I700 = I695 /\ I699 = I694 /\ I698 = I693 /\ I697 = I697 /\ I696 = I696 /\ I695 = I695 /\ I694 = I694 /\ I693 = I693] f21(I703, I704, I705, I706, I707, I708, I709, I710, I711, I712, I713, I714, I715, I716, I717) -> f22(I713, I714, I715, I716, I717, I718, I719, I720, I721, I722, I723, I724, I725, I726, I727) [I727 = I722 /\ I726 = I721 /\ I725 = I720 /\ I724 = I719 /\ I723 = I718 /\ I722 = I722 /\ I721 = I721 /\ I720 = I720 /\ I719 = I719 /\ I718 = I718] f20(I728, I729, I730, I731, I732, I733, I734, I735, I736, I737, I738, I739, I740, I741, I742) -> f10(I738, I739, I740, I741, I742, I743, I744, I745, I736, I737, I738, I739, I746, I747, I748) [I748 = I745 /\ I747 = I744 /\ I746 = I743 /\ I739 <= I738 /\ I745 = I745 /\ I744 = I744 /\ I743 = I743] f20(I749, I750, I751, I752, I753, I754, I755, I756, I757, I758, I759, I760, I761, I762, I763) -> f6(I759, I760, I761, I762, I763, I764, I765, I766, I757, I758, I759, I760, I767, I768, I769) [I769 = I766 /\ I768 = I765 /\ I767 = I764 /\ 1 + I759 <= I760 /\ I766 = I766 /\ I765 = I765 /\ I764 = I764] f18(I770, I771, I772, I773, I774, I775, I776, I777, I778, I779, I780, I781, I782, I783, I784) -> f19(I780, I781, I782, I783, I784, I785, I786, I787, I778, I779, I780, I781, I788, I789, I790) [I790 = I787 /\ I789 = I786 /\ I788 = I785 /\ I787 = I787 /\ I786 = I786 /\ I785 = I785] f19(I791, I792, I793, I794, I795, I796, I797, I798, I799, I800, I801, I802, I803, I804, I805) -> f17(I801, I802, I803, I804, I805, I806, I807, I808, I799, I800, I801, I802, I809, I810, I811) [I811 = I808 /\ I810 = I807 /\ I809 = I806 /\ I801 <= I802 /\ I808 = I808 /\ I807 = I807 /\ I806 = I806] f19(I812, I813, I814, I815, I816, I817, I818, I819, I820, I821, I822, I823, I824, I825, I826) -> f15(I822, I823, I824, I825, I826, I827, I828, I829, I820, I821, I822, I823, I830, I831, I832) [I832 = I829 /\ I831 = I828 /\ I830 = I827 /\ 1 + I823 <= I822 /\ I829 = I829 /\ I828 = I828 /\ I827 = I827] f17(I833, I834, I835, I836, I837, I838, I839, I840, I841, I842, I843, I844, I845, I846, I847) -> f18(I843, I844, I845, I846, I847, I848, I849, I850, I841, I842, 1 + I843, I844, I851, I852, I853) [I853 = I850 /\ I852 = I849 /\ I851 = I848 /\ I850 = I850 /\ I849 = I849 /\ I848 = I848] f17(I854, I855, I856, I857, I858, I859, I860, I861, I862, I863, I864, I865, I866, I867, I868) -> f16(I864, I865, I866, I867, I868, I869, I870, I871, I872, I873, I874, I875, I876, I877, I878) [I878 = I873 /\ I877 = I872 /\ I876 = I871 /\ I875 = I870 /\ I874 = I869 /\ I873 = I873 /\ I872 = I872 /\ I871 = I871 /\ I870 = I870 /\ I869 = I869] f15(I879, I880, I881, I882, I883, I884, I885, I886, I887, I888, I889, I890, I891, I892, I893) -> f16(I889, I890, I891, I892, I893, I894, I895, I896, I897, I898, I899, I900, I901, I902, I903) [I903 = I898 /\ I902 = I897 /\ I901 = I896 /\ I900 = I895 /\ I899 = I894 /\ I898 = I898 /\ I897 = I897 /\ I896 = I896 /\ I895 = I895 /\ I894 = I894] f14(I904, I905, I906, I907, I908, I909, I910, I911, I912, I913, I914, I915, I916, I917, I918) -> f13(I914, I915, I916, I917, I918, I919, I920, I921, I912, I913, I914, 0, I922, I923, I924) [I924 = I921 /\ I923 = I920 /\ I922 = I919 /\ I921 = I921 /\ I920 = I920 /\ I919 = I919] f13(I925, I926, I927, I928, I929, I930, I931, I932, I933, I934, I935, I936, I937, I938, I939) -> f12(I935, I936, I937, I938, I939, I940, I941, I942, I933, I934, I935, I936, I943, I944, I945) [I945 = I942 /\ I944 = I941 /\ I943 = I940 /\ 1 + I936 <= I935 /\ I942 = I942 /\ I941 = I941 /\ I940 = I940] f13(I946, I947, I948, I949, I950, I951, I952, I953, I954, I955, I956, I957, I958, I959, I960) -> f8(I956, I957, I958, I959, I960, I961, I962, I963, I954, I955, I956, I957, I964, I965, I966) [I966 = I963 /\ I965 = I962 /\ I964 = I961 /\ I956 <= I957 /\ I963 = I963 /\ I962 = I962 /\ I961 = I961] f12(I967, I968, I969, I970, I971, I972, I973, I974, I975, I976, I977, I978, I979, I980, I981) -> f13(I977, I978, I979, I980, I981, I982, I983, I984, I975, I976, I977, 1 + I978, I985, I986, I987) [I987 = I984 /\ I986 = I983 /\ I985 = I982 /\ I984 = I984 /\ I983 = I983 /\ I982 = I982] f10(I988, I989, I990, I991, I992, I993, I994, I995, I996, I997, I998, I999, I1000, I1001, I1002) -> f11(I998, I999, I1000, I1001, I1002, I1003, I1004, I1005, I996, I997, -1 + I998, I999, I1006, I1007, I1008) [I1008 = I1005 /\ I1007 = I1004 /\ I1006 = I1003 /\ I1005 = I1005 /\ I1004 = I1004 /\ I1003 = I1003] f10(I1009, I1010, I1011, I1012, I1013, I1014, I1015, I1016, I1017, I1018, I1019, I1020, I1021, I1022, I1023) -> f7(I1019, I1020, I1021, I1022, I1023, I1024, I1025, I1026, I1027, I1028, I1029, I1030, I1031, I1032, I1033) [I1033 = I1028 /\ I1032 = I1027 /\ I1031 = I1026 /\ I1030 = I1025 /\ I1029 = I1024 /\ I1028 = I1028 /\ I1027 = I1027 /\ I1026 = I1026 /\ I1025 = I1025 /\ I1024 = I1024] f8(I1034, I1035, I1036, I1037, I1038, I1039, I1040, I1041, I1042, I1043, I1044, I1045, I1046, I1047, I1048) -> f9(I1044, I1045, I1046, I1047, I1048, I1049, I1050, I1051, I1052, I1053, I1054, I1055, I1056, I1057, I1058) [I1058 = I1053 /\ I1057 = I1052 /\ I1056 = I1051 /\ I1055 = I1050 /\ I1054 = I1049 /\ I1053 = I1053 /\ I1052 = I1052 /\ I1051 = I1051 /\ I1050 = I1050 /\ I1049 = I1049] f6(I1059, I1060, I1061, I1062, I1063, I1064, I1065, I1066, I1067, I1068, I1069, I1070, I1071, I1072, I1073) -> f7(I1069, I1070, I1071, I1072, I1073, I1074, I1075, I1076, I1077, I1078, I1079, I1080, I1081, I1082, I1083) [I1083 = I1078 /\ I1082 = I1077 /\ I1081 = I1076 /\ I1080 = I1075 /\ I1079 = I1074 /\ I1078 = I1078 /\ I1077 = I1077 /\ I1076 = I1076 /\ I1075 = I1075 /\ I1074 = I1074] f4(I1084, I1085, I1086, I1087, I1088, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) -> f5(I1094, I1095, I1096, I1097, I1098, I1089, I1090, I1091, I1092, I1093, I1094, I1095, I1096, I1097, I1098) f5(I1099, I1100, I1101, I1102, I1103, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) -> f3(I1109, I1110, I1111, I1112, I1113, I1104, I1105, I1106, I1107, I1108, I1109, I1110, I1111, I1112, I1113) [I1109 <= I1110] f5(I1114, I1115, I1116, I1117, I1118, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) -> f1(I1124, I1125, I1126, I1127, I1128, I1119, I1120, I1121, I1122, I1123, I1124, I1125, I1126, I1127, I1128) [1 + I1125 <= I1124] f3(I1129, I1130, I1131, I1132, I1133, I1134, I1135, I1136, I1137, I1138, I1139, I1140, I1141, I1142, I1143) -> f4(I1139, I1140, I1141, I1142, I1143, I1134, I1135, I1136, I1137, I1138, 1 + I1139, I1140, I1141, I1142, I1143) f3(I1144, I1145, I1146, I1147, I1148, I1149, I1150, I1151, I1152, I1153, I1154, I1155, I1156, I1157, I1158) -> f2(I1154, I1155, I1156, I1157, I1158, I1159, I1160, I1161, I1162, I1163, I1164, I1165, I1166, I1167, I1168) [I1168 = I1163 /\ I1167 = I1162 /\ I1166 = I1161 /\ I1165 = I1160 /\ I1164 = I1159 /\ I1163 = I1163 /\ I1162 = I1162 /\ I1161 = I1161 /\ I1160 = I1160 /\ I1159 = I1159] f1(I1169, I1170, I1171, I1172, I1173, I1174, I1175, I1176, I1177, I1178, I1179, I1180, I1181, I1182, I1183) -> f2(I1179, I1180, I1181, I1182, I1183, I1184, I1185, I1186, I1187, I1188, I1189, I1190, I1191, I1192, I1193) [I1193 = I1188 /\ I1192 = I1187 /\ I1191 = I1186 /\ I1190 = I1185 /\ I1189 = I1184 /\ I1188 = I1188 /\ I1187 = I1187 /\ I1186 = I1186 /\ I1185 = I1185 /\ I1184 = I1184] The dependency graph for this problem is: 27 -> 30 -> 27 Where: 27) f29#(I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497, I498, I499, I500) -> f30#(I496, I497, I498, I499, I500, I501, I492, I493, I494, I495, I496, I497, I498, I499, I502) [I502 = I501 /\ I501 = I501] 30) f28#(I537, I538, I539, I540, I541, I542, I543, I544, I545, I546, I547, I548, I549, I550, I551) -> f29#(I547, I548, I549, I550, I551, I552, I543, I544, I545, I546, -1 + I547, I548, I549, I550, I553) [I553 = I552 /\ I552 = I552] We have the following SCCs.