10.92/10.87 YES 10.92/10.87 10.92/10.87 DP problem for innermost termination. 10.92/10.87 P = 10.92/10.87 init#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f3#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23, rnd24, rnd25) 10.92/10.87 f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f8#(I25, I1 - 1, 0, 1, 1, I26, I27, I7, I28, I9, I29, I11, 0, I30, 2, I31, I32, I33, I34, I19 + 1, I20 + 1, I35, I36, I37, I24 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I24 - 1 /\ -1 <= I20 - 1 /\ 11 <= I0 - 1 /\ 13 <= I25 - 1 /\ I20 + 5 <= I0 /\ I21 + 9 <= I0 /\ I22 + 9 <= I0 /\ I23 + 9 <= I0 /\ I24 + 3 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15] 10.92/10.87 f8#(I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8#(I63, I39 - 1, I40, I64, I65, I43, I44, I45, I66, I47, I67, I49, I68, I69, I70, I71, I72, I73, I74, I57 + 1, I58 + 1, I75, I76, I77, I62 + 1) [0 <= I39 - 1 /\ -1 <= I78 - 1 /\ 0 <= I43 - 1 /\ 0 <= I40 - 1 /\ -1 <= I57 - 1 /\ I57 <= I78 - 1 /\ 0 <= I47 - 1 /\ 0 <= I41 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I79 - 1 /\ 0 <= I46 - 1 /\ 0 <= I42 - 1 /\ 0 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I56 - 1 /\ 0 <= I54 - 1 /\ 0 <= I52 - 1 /\ 0 <= I53 - 1 /\ -1 <= I62 - 1 /\ -1 <= I58 - 1 /\ 9 <= I38 - 1 /\ 9 <= I63 - 1 /\ I58 + 5 <= I38 /\ I59 + 9 <= I38 /\ I60 + 9 <= I38 /\ I62 + 3 <= I38 /\ I61 + 9 <= I38] 10.92/10.87 f2#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f8#(I105, I80, I92, I90, I86, I91, I85, I106, I82, I93, I84, 0, I83, I87, I88, I89, I94, I95, I96, I98, I99, I107, I108, I109, I102) [I102 + 3 <= I81 /\ I101 + 9 <= I81 /\ I100 + 9 <= I81 /\ I99 + 5 <= I81 /\ 11 <= I105 - 1 /\ 11 <= I81 - 1] 10.92/10.87 f3#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1#(I135, I136, I137, I138, 1, 0, 0, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [7 <= I136 - 1 /\ 0 <= I110 - 1 /\ I136 - 7 <= I110 /\ 0 <= I111 - 1 /\ -1 <= I135 - 1] 10.92/10.87 f7#(I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f7#(I157 + 1, I158, 1, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [I157 <= I158 /\ I204 <= I159 - 1 /\ -1 <= I159 - 1] 10.92/10.87 f7#(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f7#(I205 + 1, I206, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252) [-1 <= I207 - 1 /\ 0 <= I253 - 1 /\ I253 <= I207 - 1 /\ I205 <= I206 /\ I253 <= I230 - 1] 10.92/10.87 f4#(I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278) -> f7#(0, I279, I255, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [-1 <= I302 - 1 /\ I302 + 1 <= I257 - 1 /\ -1 <= I279 - 1 /\ -1 <= I303 - 1 /\ I279 <= y3 - 1 /\ I279 <= I258 - 1 /\ 6 <= I254 - 1 /\ I258 + 5 <= I254 /\ I259 + 7 <= I254 /\ I261 + 3 <= I254 /\ I260 + 7 <= I254] 10.92/10.87 f6#(I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f6#(I304 - 1, I305, 1, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350) [I305 <= I304 - 1 /\ I351 <= I306 - 1 /\ -1 <= I306 - 1] 10.92/10.87 f6#(I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f6#(I352 - 1, I353, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399) [-1 <= I354 - 1 /\ 0 <= I400 - 1 /\ I400 <= I354 - 1 /\ I353 <= I352 - 1 /\ I400 <= I377 - 1] 10.92/10.87 f4#(I401, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f6#(I405, I426, I403, I427, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448) [-1 <= I449 - 1 /\ I449 + 1 <= I404 - 1 /\ -1 <= I426 - 1 /\ -1 <= I450 - 1 /\ I451 <= I426 /\ I426 <= I405 - 1 /\ 6 <= I401 - 1 /\ I405 + 5 <= I401 /\ I406 + 7 <= I401 /\ I408 + 3 <= I401 /\ I407 + 7 <= I401] 10.92/10.87 f5#(I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f4#(I477, I454, I455, I478, I457, I479, I480, I460, I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) [I459 + 7 <= I453 /\ I460 + 3 <= I453 /\ I458 + 7 <= I453 /\ I457 + 5 <= I453 /\ 6 <= I477 - 1 /\ 6 <= I453 - 1 /\ 0 <= I452 - 1] 10.92/10.87 f3#(I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4#(I523, I524, I525, I499, I526, I527, I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I547 - 1 /\ 0 <= I499 - 1 /\ 0 <= I498 - 1 /\ 6 <= I523 - 1] 10.92/10.87 f1#(I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) -> f2#(I548, I573, 0, 0, I551, I574, I575, 0, 0, 0, I576, I577, I578, I579, I550, I550, I551, I580, I552, I553, I581, I582, I554, I583, I584) [I574 = I575 /\ I554 + 3 <= I549 /\ I553 + 5 <= I549 /\ 9 <= I573 - 1 /\ 9 <= I549 - 1] 10.92/10.87 R = 10.92/10.87 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f3(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23, rnd24, rnd25) 10.92/10.87 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I1 - 1, 0, 1, 1, I26, I27, I7, I28, I9, I29, I11, 0, I30, 2, I31, I32, I33, I34, I19 + 1, I20 + 1, I35, I36, I37, I24 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I24 - 1 /\ -1 <= I20 - 1 /\ 11 <= I0 - 1 /\ 13 <= I25 - 1 /\ I20 + 5 <= I0 /\ I21 + 9 <= I0 /\ I22 + 9 <= I0 /\ I23 + 9 <= I0 /\ I24 + 3 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15] 10.92/10.87 f8(I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8(I63, I39 - 1, I40, I64, I65, I43, I44, I45, I66, I47, I67, I49, I68, I69, I70, I71, I72, I73, I74, I57 + 1, I58 + 1, I75, I76, I77, I62 + 1) [0 <= I39 - 1 /\ -1 <= I78 - 1 /\ 0 <= I43 - 1 /\ 0 <= I40 - 1 /\ -1 <= I57 - 1 /\ I57 <= I78 - 1 /\ 0 <= I47 - 1 /\ 0 <= I41 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I79 - 1 /\ 0 <= I46 - 1 /\ 0 <= I42 - 1 /\ 0 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I56 - 1 /\ 0 <= I54 - 1 /\ 0 <= I52 - 1 /\ 0 <= I53 - 1 /\ -1 <= I62 - 1 /\ -1 <= I58 - 1 /\ 9 <= I38 - 1 /\ 9 <= I63 - 1 /\ I58 + 5 <= I38 /\ I59 + 9 <= I38 /\ I60 + 9 <= I38 /\ I62 + 3 <= I38 /\ I61 + 9 <= I38] 10.92/10.87 f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f8(I105, I80, I92, I90, I86, I91, I85, I106, I82, I93, I84, 0, I83, I87, I88, I89, I94, I95, I96, I98, I99, I107, I108, I109, I102) [I102 + 3 <= I81 /\ I101 + 9 <= I81 /\ I100 + 9 <= I81 /\ I99 + 5 <= I81 /\ 11 <= I105 - 1 /\ 11 <= I81 - 1] 10.92/10.87 f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1(I135, I136, I137, I138, 1, 0, 0, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [7 <= I136 - 1 /\ 0 <= I110 - 1 /\ I136 - 7 <= I110 /\ 0 <= I111 - 1 /\ -1 <= I135 - 1] 10.92/10.87 f7(I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f7(I157 + 1, I158, 1, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [I157 <= I158 /\ I204 <= I159 - 1 /\ -1 <= I159 - 1] 10.92/10.87 f7(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f7(I205 + 1, I206, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252) [-1 <= I207 - 1 /\ 0 <= I253 - 1 /\ I253 <= I207 - 1 /\ I205 <= I206 /\ I253 <= I230 - 1] 10.92/10.87 f4(I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278) -> f7(0, I279, I255, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [-1 <= I302 - 1 /\ I302 + 1 <= I257 - 1 /\ -1 <= I279 - 1 /\ -1 <= I303 - 1 /\ I279 <= y3 - 1 /\ I279 <= I258 - 1 /\ 6 <= I254 - 1 /\ I258 + 5 <= I254 /\ I259 + 7 <= I254 /\ I261 + 3 <= I254 /\ I260 + 7 <= I254] 10.92/10.87 f6(I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f6(I304 - 1, I305, 1, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350) [I305 <= I304 - 1 /\ I351 <= I306 - 1 /\ -1 <= I306 - 1] 10.92/10.87 f6(I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f6(I352 - 1, I353, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399) [-1 <= I354 - 1 /\ 0 <= I400 - 1 /\ I400 <= I354 - 1 /\ I353 <= I352 - 1 /\ I400 <= I377 - 1] 10.92/10.87 f4(I401, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f6(I405, I426, I403, I427, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448) [-1 <= I449 - 1 /\ I449 + 1 <= I404 - 1 /\ -1 <= I426 - 1 /\ -1 <= I450 - 1 /\ I451 <= I426 /\ I426 <= I405 - 1 /\ 6 <= I401 - 1 /\ I405 + 5 <= I401 /\ I406 + 7 <= I401 /\ I408 + 3 <= I401 /\ I407 + 7 <= I401] 10.92/10.87 f5(I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f4(I477, I454, I455, I478, I457, I479, I480, I460, I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) [I459 + 7 <= I453 /\ I460 + 3 <= I453 /\ I458 + 7 <= I453 /\ I457 + 5 <= I453 /\ 6 <= I477 - 1 /\ 6 <= I453 - 1 /\ 0 <= I452 - 1] 10.92/10.87 f3(I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I524, I525, I499, I526, I527, I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I547 - 1 /\ 0 <= I499 - 1 /\ 0 <= I498 - 1 /\ 6 <= I523 - 1] 10.92/10.87 f1(I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) -> f2(I548, I573, 0, 0, I551, I574, I575, 0, 0, 0, I576, I577, I578, I579, I550, I550, I551, I580, I552, I553, I581, I582, I554, I583, I584) [I574 = I575 /\ I554 + 3 <= I549 /\ I553 + 5 <= I549 /\ 9 <= I573 - 1 /\ 9 <= I549 - 1] 10.92/10.87 10.92/10.87 The dependency graph for this problem is: 10.92/10.87 0 -> 4, 12 10.92/10.87 1 -> 10.92/10.87 2 -> 1, 2 10.92/10.87 3 -> 10.92/10.87 4 -> 13 10.92/10.87 5 -> 5 10.92/10.87 6 -> 5, 6 10.92/10.87 7 -> 5, 6 10.92/10.87 8 -> 8 10.92/10.87 9 -> 8, 9 10.92/10.87 10 -> 8, 9 10.92/10.87 11 -> 7, 10 10.92/10.87 12 -> 7, 10 10.92/10.87 13 -> 3 10.92/10.87 Where: 10.92/10.87 0) init#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f3#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23, rnd24, rnd25) 10.92/10.87 1) f8#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f8#(I25, I1 - 1, 0, 1, 1, I26, I27, I7, I28, I9, I29, I11, 0, I30, 2, I31, I32, I33, I34, I19 + 1, I20 + 1, I35, I36, I37, I24 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I24 - 1 /\ -1 <= I20 - 1 /\ 11 <= I0 - 1 /\ 13 <= I25 - 1 /\ I20 + 5 <= I0 /\ I21 + 9 <= I0 /\ I22 + 9 <= I0 /\ I23 + 9 <= I0 /\ I24 + 3 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15] 10.92/10.87 2) f8#(I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8#(I63, I39 - 1, I40, I64, I65, I43, I44, I45, I66, I47, I67, I49, I68, I69, I70, I71, I72, I73, I74, I57 + 1, I58 + 1, I75, I76, I77, I62 + 1) [0 <= I39 - 1 /\ -1 <= I78 - 1 /\ 0 <= I43 - 1 /\ 0 <= I40 - 1 /\ -1 <= I57 - 1 /\ I57 <= I78 - 1 /\ 0 <= I47 - 1 /\ 0 <= I41 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I79 - 1 /\ 0 <= I46 - 1 /\ 0 <= I42 - 1 /\ 0 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I56 - 1 /\ 0 <= I54 - 1 /\ 0 <= I52 - 1 /\ 0 <= I53 - 1 /\ -1 <= I62 - 1 /\ -1 <= I58 - 1 /\ 9 <= I38 - 1 /\ 9 <= I63 - 1 /\ I58 + 5 <= I38 /\ I59 + 9 <= I38 /\ I60 + 9 <= I38 /\ I62 + 3 <= I38 /\ I61 + 9 <= I38] 10.92/10.87 3) f2#(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f8#(I105, I80, I92, I90, I86, I91, I85, I106, I82, I93, I84, 0, I83, I87, I88, I89, I94, I95, I96, I98, I99, I107, I108, I109, I102) [I102 + 3 <= I81 /\ I101 + 9 <= I81 /\ I100 + 9 <= I81 /\ I99 + 5 <= I81 /\ 11 <= I105 - 1 /\ 11 <= I81 - 1] 10.92/10.87 4) f3#(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1#(I135, I136, I137, I138, 1, 0, 0, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [7 <= I136 - 1 /\ 0 <= I110 - 1 /\ I136 - 7 <= I110 /\ 0 <= I111 - 1 /\ -1 <= I135 - 1] 10.92/10.87 5) f7#(I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f7#(I157 + 1, I158, 1, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [I157 <= I158 /\ I204 <= I159 - 1 /\ -1 <= I159 - 1] 10.92/10.87 6) f7#(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f7#(I205 + 1, I206, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252) [-1 <= I207 - 1 /\ 0 <= I253 - 1 /\ I253 <= I207 - 1 /\ I205 <= I206 /\ I253 <= I230 - 1] 10.92/10.87 7) f4#(I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278) -> f7#(0, I279, I255, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [-1 <= I302 - 1 /\ I302 + 1 <= I257 - 1 /\ -1 <= I279 - 1 /\ -1 <= I303 - 1 /\ I279 <= y3 - 1 /\ I279 <= I258 - 1 /\ 6 <= I254 - 1 /\ I258 + 5 <= I254 /\ I259 + 7 <= I254 /\ I261 + 3 <= I254 /\ I260 + 7 <= I254] 10.92/10.87 8) f6#(I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f6#(I304 - 1, I305, 1, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350) [I305 <= I304 - 1 /\ I351 <= I306 - 1 /\ -1 <= I306 - 1] 10.92/10.87 9) f6#(I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f6#(I352 - 1, I353, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399) [-1 <= I354 - 1 /\ 0 <= I400 - 1 /\ I400 <= I354 - 1 /\ I353 <= I352 - 1 /\ I400 <= I377 - 1] 10.92/10.87 10) f4#(I401, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f6#(I405, I426, I403, I427, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448) [-1 <= I449 - 1 /\ I449 + 1 <= I404 - 1 /\ -1 <= I426 - 1 /\ -1 <= I450 - 1 /\ I451 <= I426 /\ I426 <= I405 - 1 /\ 6 <= I401 - 1 /\ I405 + 5 <= I401 /\ I406 + 7 <= I401 /\ I408 + 3 <= I401 /\ I407 + 7 <= I401] 10.92/10.87 11) f5#(I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f4#(I477, I454, I455, I478, I457, I479, I480, I460, I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) [I459 + 7 <= I453 /\ I460 + 3 <= I453 /\ I458 + 7 <= I453 /\ I457 + 5 <= I453 /\ 6 <= I477 - 1 /\ 6 <= I453 - 1 /\ 0 <= I452 - 1] 10.92/10.87 12) f3#(I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4#(I523, I524, I525, I499, I526, I527, I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I547 - 1 /\ 0 <= I499 - 1 /\ 0 <= I498 - 1 /\ 6 <= I523 - 1] 10.92/10.87 13) f1#(I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) -> f2#(I548, I573, 0, 0, I551, I574, I575, 0, 0, 0, I576, I577, I578, I579, I550, I550, I551, I580, I552, I553, I581, I582, I554, I583, I584) [I574 = I575 /\ I554 + 3 <= I549 /\ I553 + 5 <= I549 /\ 9 <= I573 - 1 /\ 9 <= I549 - 1] 10.92/10.87 10.92/10.87 We have the following SCCs. 10.92/10.87 { 2 } 10.92/10.87 { 9 } 10.92/10.87 { 8 } 10.92/10.87 { 6 } 10.92/10.87 { 5 } 10.92/10.87 10.92/10.87 DP problem for innermost termination. 10.92/10.87 P = 10.92/10.87 f7#(I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f7#(I157 + 1, I158, 1, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [I157 <= I158 /\ I204 <= I159 - 1 /\ -1 <= I159 - 1] 10.92/10.87 R = 10.92/10.87 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f3(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23, rnd24, rnd25) 10.92/10.87 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I1 - 1, 0, 1, 1, I26, I27, I7, I28, I9, I29, I11, 0, I30, 2, I31, I32, I33, I34, I19 + 1, I20 + 1, I35, I36, I37, I24 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I24 - 1 /\ -1 <= I20 - 1 /\ 11 <= I0 - 1 /\ 13 <= I25 - 1 /\ I20 + 5 <= I0 /\ I21 + 9 <= I0 /\ I22 + 9 <= I0 /\ I23 + 9 <= I0 /\ I24 + 3 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15] 10.92/10.87 f8(I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8(I63, I39 - 1, I40, I64, I65, I43, I44, I45, I66, I47, I67, I49, I68, I69, I70, I71, I72, I73, I74, I57 + 1, I58 + 1, I75, I76, I77, I62 + 1) [0 <= I39 - 1 /\ -1 <= I78 - 1 /\ 0 <= I43 - 1 /\ 0 <= I40 - 1 /\ -1 <= I57 - 1 /\ I57 <= I78 - 1 /\ 0 <= I47 - 1 /\ 0 <= I41 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I79 - 1 /\ 0 <= I46 - 1 /\ 0 <= I42 - 1 /\ 0 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I56 - 1 /\ 0 <= I54 - 1 /\ 0 <= I52 - 1 /\ 0 <= I53 - 1 /\ -1 <= I62 - 1 /\ -1 <= I58 - 1 /\ 9 <= I38 - 1 /\ 9 <= I63 - 1 /\ I58 + 5 <= I38 /\ I59 + 9 <= I38 /\ I60 + 9 <= I38 /\ I62 + 3 <= I38 /\ I61 + 9 <= I38] 10.92/10.87 f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f8(I105, I80, I92, I90, I86, I91, I85, I106, I82, I93, I84, 0, I83, I87, I88, I89, I94, I95, I96, I98, I99, I107, I108, I109, I102) [I102 + 3 <= I81 /\ I101 + 9 <= I81 /\ I100 + 9 <= I81 /\ I99 + 5 <= I81 /\ 11 <= I105 - 1 /\ 11 <= I81 - 1] 10.92/10.87 f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1(I135, I136, I137, I138, 1, 0, 0, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [7 <= I136 - 1 /\ 0 <= I110 - 1 /\ I136 - 7 <= I110 /\ 0 <= I111 - 1 /\ -1 <= I135 - 1] 10.92/10.87 f7(I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f7(I157 + 1, I158, 1, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [I157 <= I158 /\ I204 <= I159 - 1 /\ -1 <= I159 - 1] 10.92/10.87 f7(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f7(I205 + 1, I206, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252) [-1 <= I207 - 1 /\ 0 <= I253 - 1 /\ I253 <= I207 - 1 /\ I205 <= I206 /\ I253 <= I230 - 1] 10.92/10.87 f4(I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278) -> f7(0, I279, I255, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [-1 <= I302 - 1 /\ I302 + 1 <= I257 - 1 /\ -1 <= I279 - 1 /\ -1 <= I303 - 1 /\ I279 <= y3 - 1 /\ I279 <= I258 - 1 /\ 6 <= I254 - 1 /\ I258 + 5 <= I254 /\ I259 + 7 <= I254 /\ I261 + 3 <= I254 /\ I260 + 7 <= I254] 10.92/10.87 f6(I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f6(I304 - 1, I305, 1, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350) [I305 <= I304 - 1 /\ I351 <= I306 - 1 /\ -1 <= I306 - 1] 10.92/10.87 f6(I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f6(I352 - 1, I353, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399) [-1 <= I354 - 1 /\ 0 <= I400 - 1 /\ I400 <= I354 - 1 /\ I353 <= I352 - 1 /\ I400 <= I377 - 1] 10.92/10.87 f4(I401, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f6(I405, I426, I403, I427, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448) [-1 <= I449 - 1 /\ I449 + 1 <= I404 - 1 /\ -1 <= I426 - 1 /\ -1 <= I450 - 1 /\ I451 <= I426 /\ I426 <= I405 - 1 /\ 6 <= I401 - 1 /\ I405 + 5 <= I401 /\ I406 + 7 <= I401 /\ I408 + 3 <= I401 /\ I407 + 7 <= I401] 10.92/10.87 f5(I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f4(I477, I454, I455, I478, I457, I479, I480, I460, I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) [I459 + 7 <= I453 /\ I460 + 3 <= I453 /\ I458 + 7 <= I453 /\ I457 + 5 <= I453 /\ 6 <= I477 - 1 /\ 6 <= I453 - 1 /\ 0 <= I452 - 1] 10.92/10.87 f3(I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I524, I525, I499, I526, I527, I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I547 - 1 /\ 0 <= I499 - 1 /\ 0 <= I498 - 1 /\ 6 <= I523 - 1] 10.92/10.87 f1(I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) -> f2(I548, I573, 0, 0, I551, I574, I575, 0, 0, 0, I576, I577, I578, I579, I550, I550, I551, I580, I552, I553, I581, I582, I554, I583, I584) [I574 = I575 /\ I554 + 3 <= I549 /\ I553 + 5 <= I549 /\ 9 <= I573 - 1 /\ 9 <= I549 - 1] 10.92/10.87 10.92/10.87 We use the reverse value criterion with the projection function NU: 10.92/10.87 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25)] = z2 + -1 * z1 10.92/10.87 10.92/10.87 This gives the following inequalities: 10.92/10.87 I157 <= I158 /\ I204 <= I159 - 1 /\ -1 <= I159 - 1 ==> I158 + -1 * I157 > I158 + -1 * (I157 + 1) with I158 + -1 * I157 >= 0 10.92/10.87 10.92/10.87 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 10.92/10.87 10.92/10.87 DP problem for innermost termination. 10.92/10.87 P = 10.92/10.87 f7#(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f7#(I205 + 1, I206, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252) [-1 <= I207 - 1 /\ 0 <= I253 - 1 /\ I253 <= I207 - 1 /\ I205 <= I206 /\ I253 <= I230 - 1] 10.92/10.87 R = 10.92/10.87 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f3(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23, rnd24, rnd25) 10.92/10.87 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I1 - 1, 0, 1, 1, I26, I27, I7, I28, I9, I29, I11, 0, I30, 2, I31, I32, I33, I34, I19 + 1, I20 + 1, I35, I36, I37, I24 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I24 - 1 /\ -1 <= I20 - 1 /\ 11 <= I0 - 1 /\ 13 <= I25 - 1 /\ I20 + 5 <= I0 /\ I21 + 9 <= I0 /\ I22 + 9 <= I0 /\ I23 + 9 <= I0 /\ I24 + 3 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15] 10.92/10.87 f8(I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8(I63, I39 - 1, I40, I64, I65, I43, I44, I45, I66, I47, I67, I49, I68, I69, I70, I71, I72, I73, I74, I57 + 1, I58 + 1, I75, I76, I77, I62 + 1) [0 <= I39 - 1 /\ -1 <= I78 - 1 /\ 0 <= I43 - 1 /\ 0 <= I40 - 1 /\ -1 <= I57 - 1 /\ I57 <= I78 - 1 /\ 0 <= I47 - 1 /\ 0 <= I41 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I79 - 1 /\ 0 <= I46 - 1 /\ 0 <= I42 - 1 /\ 0 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I56 - 1 /\ 0 <= I54 - 1 /\ 0 <= I52 - 1 /\ 0 <= I53 - 1 /\ -1 <= I62 - 1 /\ -1 <= I58 - 1 /\ 9 <= I38 - 1 /\ 9 <= I63 - 1 /\ I58 + 5 <= I38 /\ I59 + 9 <= I38 /\ I60 + 9 <= I38 /\ I62 + 3 <= I38 /\ I61 + 9 <= I38] 10.92/10.87 f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f8(I105, I80, I92, I90, I86, I91, I85, I106, I82, I93, I84, 0, I83, I87, I88, I89, I94, I95, I96, I98, I99, I107, I108, I109, I102) [I102 + 3 <= I81 /\ I101 + 9 <= I81 /\ I100 + 9 <= I81 /\ I99 + 5 <= I81 /\ 11 <= I105 - 1 /\ 11 <= I81 - 1] 10.92/10.87 f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1(I135, I136, I137, I138, 1, 0, 0, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [7 <= I136 - 1 /\ 0 <= I110 - 1 /\ I136 - 7 <= I110 /\ 0 <= I111 - 1 /\ -1 <= I135 - 1] 10.92/10.87 f7(I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f7(I157 + 1, I158, 1, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [I157 <= I158 /\ I204 <= I159 - 1 /\ -1 <= I159 - 1] 10.92/10.87 f7(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f7(I205 + 1, I206, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252) [-1 <= I207 - 1 /\ 0 <= I253 - 1 /\ I253 <= I207 - 1 /\ I205 <= I206 /\ I253 <= I230 - 1] 10.92/10.87 f4(I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278) -> f7(0, I279, I255, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [-1 <= I302 - 1 /\ I302 + 1 <= I257 - 1 /\ -1 <= I279 - 1 /\ -1 <= I303 - 1 /\ I279 <= y3 - 1 /\ I279 <= I258 - 1 /\ 6 <= I254 - 1 /\ I258 + 5 <= I254 /\ I259 + 7 <= I254 /\ I261 + 3 <= I254 /\ I260 + 7 <= I254] 10.92/10.87 f6(I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f6(I304 - 1, I305, 1, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350) [I305 <= I304 - 1 /\ I351 <= I306 - 1 /\ -1 <= I306 - 1] 10.92/10.87 f6(I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f6(I352 - 1, I353, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399) [-1 <= I354 - 1 /\ 0 <= I400 - 1 /\ I400 <= I354 - 1 /\ I353 <= I352 - 1 /\ I400 <= I377 - 1] 10.92/10.87 f4(I401, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f6(I405, I426, I403, I427, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448) [-1 <= I449 - 1 /\ I449 + 1 <= I404 - 1 /\ -1 <= I426 - 1 /\ -1 <= I450 - 1 /\ I451 <= I426 /\ I426 <= I405 - 1 /\ 6 <= I401 - 1 /\ I405 + 5 <= I401 /\ I406 + 7 <= I401 /\ I408 + 3 <= I401 /\ I407 + 7 <= I401] 10.92/10.87 f5(I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f4(I477, I454, I455, I478, I457, I479, I480, I460, I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) [I459 + 7 <= I453 /\ I460 + 3 <= I453 /\ I458 + 7 <= I453 /\ I457 + 5 <= I453 /\ 6 <= I477 - 1 /\ 6 <= I453 - 1 /\ 0 <= I452 - 1] 10.92/10.87 f3(I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I524, I525, I499, I526, I527, I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I547 - 1 /\ 0 <= I499 - 1 /\ 0 <= I498 - 1 /\ 6 <= I523 - 1] 10.92/10.87 f1(I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) -> f2(I548, I573, 0, 0, I551, I574, I575, 0, 0, 0, I576, I577, I578, I579, I550, I550, I551, I580, I552, I553, I581, I582, I554, I583, I584) [I574 = I575 /\ I554 + 3 <= I549 /\ I553 + 5 <= I549 /\ 9 <= I573 - 1 /\ 9 <= I549 - 1] 10.92/10.87 10.92/10.87 We use the reverse value criterion with the projection function NU: 10.92/10.87 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25)] = z2 + -1 * z1 10.92/10.87 10.92/10.87 This gives the following inequalities: 10.92/10.87 -1 <= I207 - 1 /\ 0 <= I253 - 1 /\ I253 <= I207 - 1 /\ I205 <= I206 /\ I253 <= I230 - 1 ==> I206 + -1 * I205 > I206 + -1 * (I205 + 1) with I206 + -1 * I205 >= 0 10.92/10.87 10.92/10.87 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 10.92/10.87 10.92/10.87 DP problem for innermost termination. 10.92/10.87 P = 10.92/10.87 f6#(I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f6#(I304 - 1, I305, 1, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350) [I305 <= I304 - 1 /\ I351 <= I306 - 1 /\ -1 <= I306 - 1] 10.92/10.87 R = 10.92/10.87 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f3(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23, rnd24, rnd25) 10.92/10.87 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I1 - 1, 0, 1, 1, I26, I27, I7, I28, I9, I29, I11, 0, I30, 2, I31, I32, I33, I34, I19 + 1, I20 + 1, I35, I36, I37, I24 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I24 - 1 /\ -1 <= I20 - 1 /\ 11 <= I0 - 1 /\ 13 <= I25 - 1 /\ I20 + 5 <= I0 /\ I21 + 9 <= I0 /\ I22 + 9 <= I0 /\ I23 + 9 <= I0 /\ I24 + 3 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15] 10.92/10.87 f8(I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8(I63, I39 - 1, I40, I64, I65, I43, I44, I45, I66, I47, I67, I49, I68, I69, I70, I71, I72, I73, I74, I57 + 1, I58 + 1, I75, I76, I77, I62 + 1) [0 <= I39 - 1 /\ -1 <= I78 - 1 /\ 0 <= I43 - 1 /\ 0 <= I40 - 1 /\ -1 <= I57 - 1 /\ I57 <= I78 - 1 /\ 0 <= I47 - 1 /\ 0 <= I41 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I79 - 1 /\ 0 <= I46 - 1 /\ 0 <= I42 - 1 /\ 0 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I56 - 1 /\ 0 <= I54 - 1 /\ 0 <= I52 - 1 /\ 0 <= I53 - 1 /\ -1 <= I62 - 1 /\ -1 <= I58 - 1 /\ 9 <= I38 - 1 /\ 9 <= I63 - 1 /\ I58 + 5 <= I38 /\ I59 + 9 <= I38 /\ I60 + 9 <= I38 /\ I62 + 3 <= I38 /\ I61 + 9 <= I38] 10.92/10.87 f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f8(I105, I80, I92, I90, I86, I91, I85, I106, I82, I93, I84, 0, I83, I87, I88, I89, I94, I95, I96, I98, I99, I107, I108, I109, I102) [I102 + 3 <= I81 /\ I101 + 9 <= I81 /\ I100 + 9 <= I81 /\ I99 + 5 <= I81 /\ 11 <= I105 - 1 /\ 11 <= I81 - 1] 10.92/10.87 f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1(I135, I136, I137, I138, 1, 0, 0, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [7 <= I136 - 1 /\ 0 <= I110 - 1 /\ I136 - 7 <= I110 /\ 0 <= I111 - 1 /\ -1 <= I135 - 1] 10.92/10.87 f7(I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f7(I157 + 1, I158, 1, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [I157 <= I158 /\ I204 <= I159 - 1 /\ -1 <= I159 - 1] 10.92/10.87 f7(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f7(I205 + 1, I206, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252) [-1 <= I207 - 1 /\ 0 <= I253 - 1 /\ I253 <= I207 - 1 /\ I205 <= I206 /\ I253 <= I230 - 1] 10.92/10.87 f4(I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278) -> f7(0, I279, I255, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [-1 <= I302 - 1 /\ I302 + 1 <= I257 - 1 /\ -1 <= I279 - 1 /\ -1 <= I303 - 1 /\ I279 <= y3 - 1 /\ I279 <= I258 - 1 /\ 6 <= I254 - 1 /\ I258 + 5 <= I254 /\ I259 + 7 <= I254 /\ I261 + 3 <= I254 /\ I260 + 7 <= I254] 10.92/10.87 f6(I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f6(I304 - 1, I305, 1, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350) [I305 <= I304 - 1 /\ I351 <= I306 - 1 /\ -1 <= I306 - 1] 10.92/10.87 f6(I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f6(I352 - 1, I353, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399) [-1 <= I354 - 1 /\ 0 <= I400 - 1 /\ I400 <= I354 - 1 /\ I353 <= I352 - 1 /\ I400 <= I377 - 1] 10.92/10.87 f4(I401, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f6(I405, I426, I403, I427, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448) [-1 <= I449 - 1 /\ I449 + 1 <= I404 - 1 /\ -1 <= I426 - 1 /\ -1 <= I450 - 1 /\ I451 <= I426 /\ I426 <= I405 - 1 /\ 6 <= I401 - 1 /\ I405 + 5 <= I401 /\ I406 + 7 <= I401 /\ I408 + 3 <= I401 /\ I407 + 7 <= I401] 10.92/10.87 f5(I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f4(I477, I454, I455, I478, I457, I479, I480, I460, I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) [I459 + 7 <= I453 /\ I460 + 3 <= I453 /\ I458 + 7 <= I453 /\ I457 + 5 <= I453 /\ 6 <= I477 - 1 /\ 6 <= I453 - 1 /\ 0 <= I452 - 1] 10.92/10.87 f3(I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I524, I525, I499, I526, I527, I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I547 - 1 /\ 0 <= I499 - 1 /\ 0 <= I498 - 1 /\ 6 <= I523 - 1] 10.92/10.87 f1(I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) -> f2(I548, I573, 0, 0, I551, I574, I575, 0, 0, 0, I576, I577, I578, I579, I550, I550, I551, I580, I552, I553, I581, I582, I554, I583, I584) [I574 = I575 /\ I554 + 3 <= I549 /\ I553 + 5 <= I549 /\ 9 <= I573 - 1 /\ 9 <= I549 - 1] 10.92/10.87 10.92/10.87 We use the reverse value criterion with the projection function NU: 10.92/10.87 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25)] = z1 - 1 + -1 * z2 10.92/10.87 10.92/10.87 This gives the following inequalities: 10.92/10.87 I305 <= I304 - 1 /\ I351 <= I306 - 1 /\ -1 <= I306 - 1 ==> I304 - 1 + -1 * I305 > I304 - 1 - 1 + -1 * I305 with I304 - 1 + -1 * I305 >= 0 10.92/10.87 10.92/10.87 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 10.92/10.87 10.92/10.87 DP problem for innermost termination. 10.92/10.87 P = 10.92/10.87 f6#(I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f6#(I352 - 1, I353, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399) [-1 <= I354 - 1 /\ 0 <= I400 - 1 /\ I400 <= I354 - 1 /\ I353 <= I352 - 1 /\ I400 <= I377 - 1] 10.92/10.87 R = 10.92/10.87 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f3(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23, rnd24, rnd25) 10.92/10.87 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I1 - 1, 0, 1, 1, I26, I27, I7, I28, I9, I29, I11, 0, I30, 2, I31, I32, I33, I34, I19 + 1, I20 + 1, I35, I36, I37, I24 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I24 - 1 /\ -1 <= I20 - 1 /\ 11 <= I0 - 1 /\ 13 <= I25 - 1 /\ I20 + 5 <= I0 /\ I21 + 9 <= I0 /\ I22 + 9 <= I0 /\ I23 + 9 <= I0 /\ I24 + 3 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15] 10.92/10.87 f8(I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8(I63, I39 - 1, I40, I64, I65, I43, I44, I45, I66, I47, I67, I49, I68, I69, I70, I71, I72, I73, I74, I57 + 1, I58 + 1, I75, I76, I77, I62 + 1) [0 <= I39 - 1 /\ -1 <= I78 - 1 /\ 0 <= I43 - 1 /\ 0 <= I40 - 1 /\ -1 <= I57 - 1 /\ I57 <= I78 - 1 /\ 0 <= I47 - 1 /\ 0 <= I41 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I79 - 1 /\ 0 <= I46 - 1 /\ 0 <= I42 - 1 /\ 0 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I56 - 1 /\ 0 <= I54 - 1 /\ 0 <= I52 - 1 /\ 0 <= I53 - 1 /\ -1 <= I62 - 1 /\ -1 <= I58 - 1 /\ 9 <= I38 - 1 /\ 9 <= I63 - 1 /\ I58 + 5 <= I38 /\ I59 + 9 <= I38 /\ I60 + 9 <= I38 /\ I62 + 3 <= I38 /\ I61 + 9 <= I38] 10.92/10.87 f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f8(I105, I80, I92, I90, I86, I91, I85, I106, I82, I93, I84, 0, I83, I87, I88, I89, I94, I95, I96, I98, I99, I107, I108, I109, I102) [I102 + 3 <= I81 /\ I101 + 9 <= I81 /\ I100 + 9 <= I81 /\ I99 + 5 <= I81 /\ 11 <= I105 - 1 /\ 11 <= I81 - 1] 10.92/10.87 f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1(I135, I136, I137, I138, 1, 0, 0, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [7 <= I136 - 1 /\ 0 <= I110 - 1 /\ I136 - 7 <= I110 /\ 0 <= I111 - 1 /\ -1 <= I135 - 1] 10.92/10.87 f7(I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f7(I157 + 1, I158, 1, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [I157 <= I158 /\ I204 <= I159 - 1 /\ -1 <= I159 - 1] 10.92/10.87 f7(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f7(I205 + 1, I206, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252) [-1 <= I207 - 1 /\ 0 <= I253 - 1 /\ I253 <= I207 - 1 /\ I205 <= I206 /\ I253 <= I230 - 1] 10.92/10.87 f4(I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278) -> f7(0, I279, I255, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [-1 <= I302 - 1 /\ I302 + 1 <= I257 - 1 /\ -1 <= I279 - 1 /\ -1 <= I303 - 1 /\ I279 <= y3 - 1 /\ I279 <= I258 - 1 /\ 6 <= I254 - 1 /\ I258 + 5 <= I254 /\ I259 + 7 <= I254 /\ I261 + 3 <= I254 /\ I260 + 7 <= I254] 10.92/10.87 f6(I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f6(I304 - 1, I305, 1, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350) [I305 <= I304 - 1 /\ I351 <= I306 - 1 /\ -1 <= I306 - 1] 10.92/10.87 f6(I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f6(I352 - 1, I353, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399) [-1 <= I354 - 1 /\ 0 <= I400 - 1 /\ I400 <= I354 - 1 /\ I353 <= I352 - 1 /\ I400 <= I377 - 1] 10.92/10.87 f4(I401, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f6(I405, I426, I403, I427, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448) [-1 <= I449 - 1 /\ I449 + 1 <= I404 - 1 /\ -1 <= I426 - 1 /\ -1 <= I450 - 1 /\ I451 <= I426 /\ I426 <= I405 - 1 /\ 6 <= I401 - 1 /\ I405 + 5 <= I401 /\ I406 + 7 <= I401 /\ I408 + 3 <= I401 /\ I407 + 7 <= I401] 10.92/10.87 f5(I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f4(I477, I454, I455, I478, I457, I479, I480, I460, I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) [I459 + 7 <= I453 /\ I460 + 3 <= I453 /\ I458 + 7 <= I453 /\ I457 + 5 <= I453 /\ 6 <= I477 - 1 /\ 6 <= I453 - 1 /\ 0 <= I452 - 1] 10.92/10.87 f3(I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I524, I525, I499, I526, I527, I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I547 - 1 /\ 0 <= I499 - 1 /\ 0 <= I498 - 1 /\ 6 <= I523 - 1] 10.92/10.87 f1(I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) -> f2(I548, I573, 0, 0, I551, I574, I575, 0, 0, 0, I576, I577, I578, I579, I550, I550, I551, I580, I552, I553, I581, I582, I554, I583, I584) [I574 = I575 /\ I554 + 3 <= I549 /\ I553 + 5 <= I549 /\ 9 <= I573 - 1 /\ 9 <= I549 - 1] 10.92/10.87 10.92/10.87 We use the reverse value criterion with the projection function NU: 10.92/10.87 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25)] = z1 - 1 + -1 * z2 10.92/10.87 10.92/10.87 This gives the following inequalities: 10.92/10.87 -1 <= I354 - 1 /\ 0 <= I400 - 1 /\ I400 <= I354 - 1 /\ I353 <= I352 - 1 /\ I400 <= I377 - 1 ==> I352 - 1 + -1 * I353 > I352 - 1 - 1 + -1 * I353 with I352 - 1 + -1 * I353 >= 0 10.92/10.87 10.92/10.87 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 10.92/10.87 10.92/10.87 DP problem for innermost termination. 10.92/10.87 P = 10.92/10.87 f8#(I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8#(I63, I39 - 1, I40, I64, I65, I43, I44, I45, I66, I47, I67, I49, I68, I69, I70, I71, I72, I73, I74, I57 + 1, I58 + 1, I75, I76, I77, I62 + 1) [0 <= I39 - 1 /\ -1 <= I78 - 1 /\ 0 <= I43 - 1 /\ 0 <= I40 - 1 /\ -1 <= I57 - 1 /\ I57 <= I78 - 1 /\ 0 <= I47 - 1 /\ 0 <= I41 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I79 - 1 /\ 0 <= I46 - 1 /\ 0 <= I42 - 1 /\ 0 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I56 - 1 /\ 0 <= I54 - 1 /\ 0 <= I52 - 1 /\ 0 <= I53 - 1 /\ -1 <= I62 - 1 /\ -1 <= I58 - 1 /\ 9 <= I38 - 1 /\ 9 <= I63 - 1 /\ I58 + 5 <= I38 /\ I59 + 9 <= I38 /\ I60 + 9 <= I38 /\ I62 + 3 <= I38 /\ I61 + 9 <= I38] 10.92/10.87 R = 10.92/10.87 init(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25) -> f3(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7, rnd8, rnd9, rnd10, rnd11, rnd12, rnd13, rnd14, rnd15, rnd16, rnd17, rnd18, rnd19, rnd20, rnd21, rnd22, rnd23, rnd24, rnd25) 10.92/10.87 f8(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I1 - 1, 0, 1, 1, I26, I27, I7, I28, I9, I29, I11, 0, I30, 2, I31, I32, I33, I34, I19 + 1, I20 + 1, I35, I36, I37, I24 + 1) [0 <= I1 - 1 /\ -1 <= y1 - 1 /\ 0 <= I5 - 1 /\ 0 <= I2 - 1 /\ -1 <= I19 - 1 /\ I19 <= y1 - 1 /\ 0 <= I9 - 1 /\ 0 <= I11 - 1 /\ -1 <= y2 - 1 /\ 0 <= I17 - 1 /\ 0 <= I18 - 1 /\ 0 <= I16 - 1 /\ 0 <= I7 - 1 /\ -1 <= I24 - 1 /\ -1 <= I20 - 1 /\ 11 <= I0 - 1 /\ 13 <= I25 - 1 /\ I20 + 5 <= I0 /\ I21 + 9 <= I0 /\ I22 + 9 <= I0 /\ I23 + 9 <= I0 /\ I24 + 3 <= I0 /\ I7 = I8 /\ I9 = I10 /\ I11 = I12 /\ I6 = I15] 10.92/10.87 f8(I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f8(I63, I39 - 1, I40, I64, I65, I43, I44, I45, I66, I47, I67, I49, I68, I69, I70, I71, I72, I73, I74, I57 + 1, I58 + 1, I75, I76, I77, I62 + 1) [0 <= I39 - 1 /\ -1 <= I78 - 1 /\ 0 <= I43 - 1 /\ 0 <= I40 - 1 /\ -1 <= I57 - 1 /\ I57 <= I78 - 1 /\ 0 <= I47 - 1 /\ 0 <= I41 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I79 - 1 /\ 0 <= I46 - 1 /\ 0 <= I42 - 1 /\ 0 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I56 - 1 /\ 0 <= I54 - 1 /\ 0 <= I52 - 1 /\ 0 <= I53 - 1 /\ -1 <= I62 - 1 /\ -1 <= I58 - 1 /\ 9 <= I38 - 1 /\ 9 <= I63 - 1 /\ I58 + 5 <= I38 /\ I59 + 9 <= I38 /\ I60 + 9 <= I38 /\ I62 + 3 <= I38 /\ I61 + 9 <= I38] 10.92/10.87 f2(I80, I81, I82, I83, I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99, I100, I101, I102, I103, I104) -> f8(I105, I80, I92, I90, I86, I91, I85, I106, I82, I93, I84, 0, I83, I87, I88, I89, I94, I95, I96, I98, I99, I107, I108, I109, I102) [I102 + 3 <= I81 /\ I101 + 9 <= I81 /\ I100 + 9 <= I81 /\ I99 + 5 <= I81 /\ 11 <= I105 - 1 /\ 11 <= I81 - 1] 10.92/10.87 f3(I110, I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f1(I135, I136, I137, I138, 1, 0, 0, I139, I140, I141, I142, I143, I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155, I156) [7 <= I136 - 1 /\ 0 <= I110 - 1 /\ I136 - 7 <= I110 /\ 0 <= I111 - 1 /\ -1 <= I135 - 1] 10.92/10.87 f7(I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167, I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f7(I157 + 1, I158, 1, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191, I192, I193, I194, I195, I196, I197, I198, I199, I200, I201, I202, I203) [I157 <= I158 /\ I204 <= I159 - 1 /\ -1 <= I159 - 1] 10.92/10.87 f7(I205, I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217, I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f7(I205 + 1, I206, I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241, I242, I243, I244, I245, I246, I247, I248, I249, I250, I251, I252) [-1 <= I207 - 1 /\ 0 <= I253 - 1 /\ I253 <= I207 - 1 /\ I205 <= I206 /\ I253 <= I230 - 1] 10.92/10.87 f4(I254, I255, I256, I257, I258, I259, I260, I261, I262, I263, I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275, I276, I277, I278) -> f7(0, I279, I255, I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291, I292, I293, I294, I295, I296, I297, I298, I299, I300, I301) [-1 <= I302 - 1 /\ I302 + 1 <= I257 - 1 /\ -1 <= I279 - 1 /\ -1 <= I303 - 1 /\ I279 <= y3 - 1 /\ I279 <= I258 - 1 /\ 6 <= I254 - 1 /\ I258 + 5 <= I254 /\ I259 + 7 <= I254 /\ I261 + 3 <= I254 /\ I260 + 7 <= I254] 10.92/10.87 f6(I304, I305, I306, I307, I308, I309, I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321, I322, I323, I324, I325, I326, I327, I328) -> f6(I304 - 1, I305, 1, I329, I330, I331, I332, I333, I334, I335, I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347, I348, I349, I350) [I305 <= I304 - 1 /\ I351 <= I306 - 1 /\ -1 <= I306 - 1] 10.92/10.87 f6(I352, I353, I354, I355, I356, I357, I358, I359, I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371, I372, I373, I374, I375, I376) -> f6(I352 - 1, I353, I377, I378, I379, I380, I381, I382, I383, I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395, I396, I397, I398, I399) [-1 <= I354 - 1 /\ 0 <= I400 - 1 /\ I400 <= I354 - 1 /\ I353 <= I352 - 1 /\ I400 <= I377 - 1] 10.92/10.87 f4(I401, I402, I403, I404, I405, I406, I407, I408, I409, I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421, I422, I423, I424, I425) -> f6(I405, I426, I403, I427, I428, I429, I430, I431, I432, I433, I434, I435, I436, I437, I438, I439, I440, I441, I442, I443, I444, I445, I446, I447, I448) [-1 <= I449 - 1 /\ I449 + 1 <= I404 - 1 /\ -1 <= I426 - 1 /\ -1 <= I450 - 1 /\ I451 <= I426 /\ I426 <= I405 - 1 /\ 6 <= I401 - 1 /\ I405 + 5 <= I401 /\ I406 + 7 <= I401 /\ I408 + 3 <= I401 /\ I407 + 7 <= I401] 10.92/10.87 f5(I452, I453, I454, I455, I456, I457, I458, I459, I460, I461, I462, I463, I464, I465, I466, I467, I468, I469, I470, I471, I472, I473, I474, I475, I476) -> f4(I477, I454, I455, I478, I457, I479, I480, I460, I481, I482, I483, I484, I485, I486, I487, I488, I489, I490, I491, I492, I493, I494, I495, I496, I497) [I459 + 7 <= I453 /\ I460 + 3 <= I453 /\ I458 + 7 <= I453 /\ I457 + 5 <= I453 /\ 6 <= I477 - 1 /\ 6 <= I453 - 1 /\ 0 <= I452 - 1] 10.92/10.87 f3(I498, I499, I500, I501, I502, I503, I504, I505, I506, I507, I508, I509, I510, I511, I512, I513, I514, I515, I516, I517, I518, I519, I520, I521, I522) -> f4(I523, I524, I525, I499, I526, I527, I528, I529, I530, I531, I532, I533, I534, I535, I536, I537, I538, I539, I540, I541, I542, I543, I544, I545, I546) [-1 <= I547 - 1 /\ 0 <= I499 - 1 /\ 0 <= I498 - 1 /\ 6 <= I523 - 1] 10.92/10.87 f1(I548, I549, I550, I551, I552, I553, I554, I555, I556, I557, I558, I559, I560, I561, I562, I563, I564, I565, I566, I567, I568, I569, I570, I571, I572) -> f2(I548, I573, 0, 0, I551, I574, I575, 0, 0, 0, I576, I577, I578, I579, I550, I550, I551, I580, I552, I553, I581, I582, I554, I583, I584) [I574 = I575 /\ I554 + 3 <= I549 /\ I553 + 5 <= I549 /\ 9 <= I573 - 1 /\ 9 <= I549 - 1] 10.92/10.87 10.92/10.87 We use the basic value criterion with the projection function NU: 10.92/10.87 NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25)] = z2 10.92/10.87 10.92/10.87 This gives the following inequalities: 10.92/10.87 0 <= I39 - 1 /\ -1 <= I78 - 1 /\ 0 <= I43 - 1 /\ 0 <= I40 - 1 /\ -1 <= I57 - 1 /\ I57 <= I78 - 1 /\ 0 <= I47 - 1 /\ 0 <= I41 - 1 /\ 0 <= I50 - 1 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ -1 <= I79 - 1 /\ 0 <= I46 - 1 /\ 0 <= I42 - 1 /\ 0 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I56 - 1 /\ 0 <= I54 - 1 /\ 0 <= I52 - 1 /\ 0 <= I53 - 1 /\ -1 <= I62 - 1 /\ -1 <= I58 - 1 /\ 9 <= I38 - 1 /\ 9 <= I63 - 1 /\ I58 + 5 <= I38 /\ I59 + 9 <= I38 /\ I60 + 9 <= I38 /\ I62 + 3 <= I38 /\ I61 + 9 <= I38 ==> I39 >! I39 - 1 10.92/10.87 10.92/10.87 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 10.92/13.85 EOF