217.57/214.42 YES 217.57/214.42 217.57/214.42 DP problem for innermost termination. 217.57/214.42 P = 217.57/214.42 f16#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f15#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 217.57/214.42 f15#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 217.57/214.42 f15#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f3#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 217.57/214.42 f15#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 217.57/214.42 f15#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f8#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 217.57/214.42 f15#(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 217.57/214.42 f15#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f13#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 217.57/214.42 f15#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f12#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 217.57/214.42 f15#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 217.57/214.42 f15#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 217.57/214.42 f15#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 217.57/214.42 f15#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 217.57/214.42 f15#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f4#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 217.57/214.42 f15#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f1#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 217.57/214.42 f15#(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f13#(I176, I177, I178, I179, rnd5, rnd6, rnd7, I175, I176, rnd10, rnd11, rnd12) [rnd12 = rnd7 /\ rnd11 = rnd6 /\ rnd10 = rnd5 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 217.57/214.42 f5#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10#(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3#(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2#(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4#(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f8#(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6#(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 f13#(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259) -> f12#(I256, I257, I258, I259, I260, I261, I254, I255, I256, 0, I262, I263) [I263 = I261 /\ I262 = I260 /\ I261 = I261 /\ I260 = I260] 217.57/214.42 f12#(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11#(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 f12#(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f10#(I288, I289, I290, I291, I292, I285, I286, I287, I288, I289, 0, I293) [I293 = I292 /\ -1 + I288 <= I289 /\ I292 = I292] 217.57/214.42 f11#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12#(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 f10#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9#(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 f10#(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f6#(I332, I333, I334, I335, I328, I329, I330, I331, I332, I333, I334, 0) [-1 + I332 <= I334] 217.57/214.42 f9#(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4#(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f6#(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8#(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 f6#(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371) -> f7#(I368, I369, I370, I371, I364, I365, I366, I367, I368, I369, I370, I371) [-1 + I368 <= I371] 217.57/214.42 f4#(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1#(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4#(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5#(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1#(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3#(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1#(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2#(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 R = 217.57/214.42 f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 217.57/214.42 f15(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 217.57/214.42 f15(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 217.57/214.42 f15(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 217.57/214.42 f15(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f8(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 217.57/214.42 f15(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 217.57/214.42 f15(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 217.57/214.42 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f13(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 217.57/214.42 f15(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f12(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 217.57/214.42 f15(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 217.57/214.42 f15(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 217.57/214.42 f15(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 217.57/214.42 f15(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 217.57/214.42 f15(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 217.57/214.42 f15(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 217.57/214.42 f15(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f13(I176, I177, I178, I179, rnd5, rnd6, rnd7, I175, I176, rnd10, rnd11, rnd12) [rnd12 = rnd7 /\ rnd11 = rnd6 /\ rnd10 = rnd5 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 217.57/214.42 f5(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f8(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 f7(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f14(I238, I239, I240, I241, I242, I243, I244, rnd8, rnd9, I245, I246, I247) [I247 = rnd8 /\ I246 = I244 /\ I245 = I243 /\ rnd9 = I242 /\ rnd8 = rnd8 /\ I244 = I244 /\ I243 = I243 /\ I242 = I242] 217.57/214.42 f13(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259) -> f12(I256, I257, I258, I259, I260, I261, I254, I255, I256, 0, I262, I263) [I263 = I261 /\ I262 = I260 /\ I261 = I261 /\ I260 = I260] 217.57/214.42 f12(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 f12(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f10(I288, I289, I290, I291, I292, I285, I286, I287, I288, I289, 0, I293) [I293 = I292 /\ -1 + I288 <= I289 /\ I292 = I292] 217.57/214.42 f11(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 f10(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 f10(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f6(I332, I333, I334, I335, I328, I329, I330, I331, I332, I333, I334, 0) [-1 + I332 <= I334] 217.57/214.42 f9(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f6(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371) -> f7(I368, I369, I370, I371, I364, I365, I366, I367, I368, I369, I370, I371) [-1 + I368 <= I371] 217.57/214.42 f4(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 The dependency graph for this problem is: 217.57/214.42 0 -> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 217.57/214.42 1 -> 15 217.57/214.42 2 -> 16 217.57/214.42 3 -> 17 217.57/214.42 4 -> 18 217.57/214.42 5 -> 217.57/214.42 6 -> 19 217.57/214.42 7 -> 20, 21 217.57/214.42 8 -> 22 217.57/214.42 9 -> 23, 24 217.57/214.42 10 -> 25 217.57/214.42 11 -> 26, 27 217.57/214.42 12 -> 28, 29 217.57/214.42 13 -> 30, 31 217.57/214.42 14 -> 19 217.57/214.42 15 -> 23, 24 217.57/214.42 16 -> 17 217.57/214.42 17 -> 28, 29 217.57/214.42 18 -> 26, 27 217.57/214.42 19 -> 20, 21 217.57/214.42 20 -> 22 217.57/214.42 21 -> 23, 24 217.57/214.42 22 -> 20, 21 217.57/214.42 23 -> 25 217.57/214.42 24 -> 26, 27 217.57/214.42 25 -> 28, 29 217.57/214.42 26 -> 18 217.57/214.42 27 -> 217.57/214.42 28 -> 30, 31 217.57/214.42 29 -> 15 217.57/214.42 30 -> 16 217.57/214.42 31 -> 17 217.57/214.42 Where: 217.57/214.42 0) f16#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f15#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 217.57/214.42 1) f15#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f5#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 217.57/214.42 2) f15#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f3#(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 217.57/214.42 3) f15#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2#(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 217.57/214.42 4) f15#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f8#(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 217.57/214.42 5) f15#(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7#(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 217.57/214.42 6) f15#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f13#(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 217.57/214.42 7) f15#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f12#(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 217.57/214.42 8) f15#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11#(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 217.57/214.42 9) f15#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10#(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 217.57/214.42 10) f15#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9#(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 217.57/214.42 11) f15#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6#(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 217.57/214.42 12) f15#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f4#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 217.57/214.42 13) f15#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f1#(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 217.57/214.42 14) f15#(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f13#(I176, I177, I178, I179, rnd5, rnd6, rnd7, I175, I176, rnd10, rnd11, rnd12) [rnd12 = rnd7 /\ rnd11 = rnd6 /\ rnd10 = rnd5 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 217.57/214.42 15) f5#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10#(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 16) f3#(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2#(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 17) f2#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4#(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 18) f8#(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6#(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 19) f13#(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259) -> f12#(I256, I257, I258, I259, I260, I261, I254, I255, I256, 0, I262, I263) [I263 = I261 /\ I262 = I260 /\ I261 = I261 /\ I260 = I260] 217.57/214.42 20) f12#(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11#(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 21) f12#(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f10#(I288, I289, I290, I291, I292, I285, I286, I287, I288, I289, 0, I293) [I293 = I292 /\ -1 + I288 <= I289 /\ I292 = I292] 217.57/214.42 22) f11#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12#(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 23) f10#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9#(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 24) f10#(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f6#(I332, I333, I334, I335, I328, I329, I330, I331, I332, I333, I334, 0) [-1 + I332 <= I334] 217.57/214.42 25) f9#(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4#(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 26) f6#(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8#(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 27) f6#(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371) -> f7#(I368, I369, I370, I371, I364, I365, I366, I367, I368, I369, I370, I371) [-1 + I368 <= I371] 217.57/214.42 28) f4#(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1#(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 29) f4#(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5#(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 30) f1#(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3#(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 31) f1#(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2#(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 We have the following SCCs. 217.57/214.42 { 20, 22 } 217.57/214.42 { 15, 16, 17, 23, 25, 28, 29, 30, 31 } 217.57/214.42 { 18, 26 } 217.57/214.42 217.57/214.42 DP problem for innermost termination. 217.57/214.42 P = 217.57/214.42 f8#(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6#(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 f6#(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8#(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 R = 217.57/214.42 f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 217.57/214.42 f15(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 217.57/214.42 f15(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 217.57/214.42 f15(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 217.57/214.42 f15(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f8(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 217.57/214.42 f15(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 217.57/214.42 f15(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 217.57/214.42 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f13(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 217.57/214.42 f15(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f12(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 217.57/214.42 f15(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 217.57/214.42 f15(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 217.57/214.42 f15(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 217.57/214.42 f15(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 217.57/214.42 f15(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 217.57/214.42 f15(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 217.57/214.42 f15(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f13(I176, I177, I178, I179, rnd5, rnd6, rnd7, I175, I176, rnd10, rnd11, rnd12) [rnd12 = rnd7 /\ rnd11 = rnd6 /\ rnd10 = rnd5 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 217.57/214.42 f5(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f8(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 f7(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f14(I238, I239, I240, I241, I242, I243, I244, rnd8, rnd9, I245, I246, I247) [I247 = rnd8 /\ I246 = I244 /\ I245 = I243 /\ rnd9 = I242 /\ rnd8 = rnd8 /\ I244 = I244 /\ I243 = I243 /\ I242 = I242] 217.57/214.42 f13(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259) -> f12(I256, I257, I258, I259, I260, I261, I254, I255, I256, 0, I262, I263) [I263 = I261 /\ I262 = I260 /\ I261 = I261 /\ I260 = I260] 217.57/214.42 f12(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 f12(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f10(I288, I289, I290, I291, I292, I285, I286, I287, I288, I289, 0, I293) [I293 = I292 /\ -1 + I288 <= I289 /\ I292 = I292] 217.57/214.42 f11(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 f10(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 f10(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f6(I332, I333, I334, I335, I328, I329, I330, I331, I332, I333, I334, 0) [-1 + I332 <= I334] 217.57/214.42 f9(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f6(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371) -> f7(I368, I369, I370, I371, I364, I365, I366, I367, I368, I369, I370, I371) [-1 + I368 <= I371] 217.57/214.42 f4(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 We use the reverse value criterion with the projection function NU: 217.57/214.42 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12)] = -1 + z9 + -1 * (1 + z12) 217.57/214.42 NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12)] = -1 + z9 + -1 * (1 + (1 + z12)) 217.57/214.42 217.57/214.42 This gives the following inequalities: 217.57/214.42 ==> -1 + I226 + -1 * (1 + (1 + I229)) >= -1 + I226 + -1 * (1 + (1 + I229)) 217.57/214.42 1 + I359 <= -1 + I356 ==> -1 + I356 + -1 * (1 + I359) > -1 + I356 + -1 * (1 + (1 + I359)) with -1 + I356 + -1 * (1 + I359) >= 0 217.57/214.42 217.57/214.42 We remove all the strictly oriented dependency pairs. 217.57/214.42 217.57/214.42 DP problem for innermost termination. 217.57/214.42 P = 217.57/214.42 f8#(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6#(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 R = 217.57/214.42 f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 217.57/214.42 f15(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 217.57/214.42 f15(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 217.57/214.42 f15(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 217.57/214.42 f15(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f8(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 217.57/214.42 f15(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 217.57/214.42 f15(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 217.57/214.42 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f13(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 217.57/214.42 f15(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f12(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 217.57/214.42 f15(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 217.57/214.42 f15(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 217.57/214.42 f15(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 217.57/214.42 f15(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 217.57/214.42 f15(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 217.57/214.42 f15(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 217.57/214.42 f15(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f13(I176, I177, I178, I179, rnd5, rnd6, rnd7, I175, I176, rnd10, rnd11, rnd12) [rnd12 = rnd7 /\ rnd11 = rnd6 /\ rnd10 = rnd5 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 217.57/214.42 f5(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f8(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 f7(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f14(I238, I239, I240, I241, I242, I243, I244, rnd8, rnd9, I245, I246, I247) [I247 = rnd8 /\ I246 = I244 /\ I245 = I243 /\ rnd9 = I242 /\ rnd8 = rnd8 /\ I244 = I244 /\ I243 = I243 /\ I242 = I242] 217.57/214.42 f13(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259) -> f12(I256, I257, I258, I259, I260, I261, I254, I255, I256, 0, I262, I263) [I263 = I261 /\ I262 = I260 /\ I261 = I261 /\ I260 = I260] 217.57/214.42 f12(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 f12(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f10(I288, I289, I290, I291, I292, I285, I286, I287, I288, I289, 0, I293) [I293 = I292 /\ -1 + I288 <= I289 /\ I292 = I292] 217.57/214.42 f11(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 f10(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 f10(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f6(I332, I333, I334, I335, I328, I329, I330, I331, I332, I333, I334, 0) [-1 + I332 <= I334] 217.57/214.42 f9(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f6(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371) -> f7(I368, I369, I370, I371, I364, I365, I366, I367, I368, I369, I370, I371) [-1 + I368 <= I371] 217.57/214.42 f4(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 The dependency graph for this problem is: 217.57/214.42 18 -> 217.57/214.42 Where: 217.57/214.42 18) f8#(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6#(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 217.57/214.42 We have the following SCCs. 217.57/214.42 217.57/214.42 217.57/214.42 DP problem for innermost termination. 217.57/214.42 P = 217.57/214.42 f5#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10#(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3#(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2#(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4#(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f10#(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9#(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 f9#(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4#(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f4#(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1#(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4#(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5#(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1#(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3#(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1#(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2#(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 R = 217.57/214.42 f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 217.57/214.42 f15(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 217.57/214.42 f15(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 217.57/214.42 f15(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 217.57/214.42 f15(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f8(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 217.57/214.42 f15(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 217.57/214.42 f15(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 217.57/214.42 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f13(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 217.57/214.42 f15(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f12(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 217.57/214.42 f15(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 217.57/214.42 f15(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 217.57/214.42 f15(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 217.57/214.42 f15(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 217.57/214.42 f15(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 217.57/214.42 f15(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 217.57/214.42 f15(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f13(I176, I177, I178, I179, rnd5, rnd6, rnd7, I175, I176, rnd10, rnd11, rnd12) [rnd12 = rnd7 /\ rnd11 = rnd6 /\ rnd10 = rnd5 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 217.57/214.42 f5(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f8(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 f7(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f14(I238, I239, I240, I241, I242, I243, I244, rnd8, rnd9, I245, I246, I247) [I247 = rnd8 /\ I246 = I244 /\ I245 = I243 /\ rnd9 = I242 /\ rnd8 = rnd8 /\ I244 = I244 /\ I243 = I243 /\ I242 = I242] 217.57/214.42 f13(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259) -> f12(I256, I257, I258, I259, I260, I261, I254, I255, I256, 0, I262, I263) [I263 = I261 /\ I262 = I260 /\ I261 = I261 /\ I260 = I260] 217.57/214.42 f12(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 f12(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f10(I288, I289, I290, I291, I292, I285, I286, I287, I288, I289, 0, I293) [I293 = I292 /\ -1 + I288 <= I289 /\ I292 = I292] 217.57/214.42 f11(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 f10(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 f10(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f6(I332, I333, I334, I335, I328, I329, I330, I331, I332, I333, I334, 0) [-1 + I332 <= I334] 217.57/214.42 f9(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f6(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371) -> f7(I368, I369, I370, I371, I364, I365, I366, I367, I368, I369, I370, I371) [-1 + I368 <= I371] 217.57/214.42 f4(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 We use the extended value criterion with the projection function NU: 217.57/214.42 NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - x10 - 2 217.57/214.42 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - x10 - 2 217.57/214.42 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - x10 - 2 217.57/214.42 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - x10 - 2 217.57/214.42 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - x10 - 2 217.57/214.42 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - x10 - 1 217.57/214.42 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - x10 - 2 217.57/214.42 217.57/214.42 This gives the following inequalities: 217.57/214.42 I193 = I192 /\ I192 = I192 ==> I188 - I190 - 2 >= I188 - (1 + I190) - 1 217.57/214.42 ==> I202 - I204 - 2 >= I202 - I204 - 2 217.57/214.42 ==> I214 - I216 - 2 >= I214 - I216 - 2 217.57/214.42 I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322 ==> I318 - I320 - 1 > I318 - I320 - 2 with I318 - I320 - 1 >= 0 217.57/214.42 ==> I344 - I346 - 2 >= I344 - I346 - 2 217.57/214.42 1 + I383 <= I380 ==> I380 - I382 - 2 >= I380 - I382 - 2 217.57/214.42 I392 <= I395 ==> I392 - I394 - 2 >= I392 - I394 - 2 217.57/214.42 1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408 ==> I404 - I406 - 2 >= I404 - I406 - 2 217.57/214.42 I423 <= I422 /\ I423 = I423 /\ I422 = I422 ==> I418 - I420 - 2 >= I418 - I420 - 2 217.57/214.42 217.57/214.42 We remove all the strictly oriented dependency pairs. 217.57/214.42 217.57/214.42 DP problem for innermost termination. 217.57/214.42 P = 217.57/214.42 f5#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10#(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3#(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2#(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4#(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f9#(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4#(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f4#(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1#(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4#(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5#(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1#(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3#(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1#(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2#(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 R = 217.57/214.42 f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 217.57/214.42 f15(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 217.57/214.42 f15(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 217.57/214.42 f15(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 217.57/214.42 f15(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f8(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 217.57/214.42 f15(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 217.57/214.42 f15(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 217.57/214.42 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f13(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 217.57/214.42 f15(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f12(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 217.57/214.42 f15(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 217.57/214.42 f15(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 217.57/214.42 f15(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 217.57/214.42 f15(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 217.57/214.42 f15(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 217.57/214.42 f15(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 217.57/214.42 f15(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f13(I176, I177, I178, I179, rnd5, rnd6, rnd7, I175, I176, rnd10, rnd11, rnd12) [rnd12 = rnd7 /\ rnd11 = rnd6 /\ rnd10 = rnd5 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 217.57/214.42 f5(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f8(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 f7(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f14(I238, I239, I240, I241, I242, I243, I244, rnd8, rnd9, I245, I246, I247) [I247 = rnd8 /\ I246 = I244 /\ I245 = I243 /\ rnd9 = I242 /\ rnd8 = rnd8 /\ I244 = I244 /\ I243 = I243 /\ I242 = I242] 217.57/214.42 f13(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259) -> f12(I256, I257, I258, I259, I260, I261, I254, I255, I256, 0, I262, I263) [I263 = I261 /\ I262 = I260 /\ I261 = I261 /\ I260 = I260] 217.57/214.42 f12(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 f12(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f10(I288, I289, I290, I291, I292, I285, I286, I287, I288, I289, 0, I293) [I293 = I292 /\ -1 + I288 <= I289 /\ I292 = I292] 217.57/214.42 f11(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 f10(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 f10(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f6(I332, I333, I334, I335, I328, I329, I330, I331, I332, I333, I334, 0) [-1 + I332 <= I334] 217.57/214.42 f9(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f6(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371) -> f7(I368, I369, I370, I371, I364, I365, I366, I367, I368, I369, I370, I371) [-1 + I368 <= I371] 217.57/214.42 f4(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 The dependency graph for this problem is: 217.57/214.42 15 -> 217.57/214.42 16 -> 17 217.57/214.42 17 -> 28, 29 217.57/214.42 25 -> 28, 29 217.57/214.42 28 -> 30, 31 217.57/214.42 29 -> 15 217.57/214.42 30 -> 16 217.57/214.42 31 -> 17 217.57/214.42 Where: 217.57/214.42 15) f5#(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10#(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 16) f3#(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2#(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 17) f2#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4#(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 25) f9#(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4#(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 28) f4#(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1#(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 29) f4#(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5#(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 30) f1#(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3#(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 31) f1#(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2#(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 We have the following SCCs. 217.57/214.42 { 16, 17, 28, 30, 31 } 217.57/214.42 217.57/214.42 DP problem for innermost termination. 217.57/214.42 P = 217.57/214.42 f3#(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2#(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4#(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f4#(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1#(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f1#(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3#(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1#(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2#(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 R = 217.57/214.42 f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 217.57/214.42 f15(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 217.57/214.42 f15(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 217.57/214.42 f15(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 217.57/214.42 f15(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f8(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 217.57/214.42 f15(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 217.57/214.42 f15(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 217.57/214.42 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f13(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 217.57/214.42 f15(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f12(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 217.57/214.42 f15(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 217.57/214.42 f15(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 217.57/214.42 f15(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 217.57/214.42 f15(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 217.57/214.42 f15(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 217.57/214.42 f15(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 217.57/214.42 f15(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f13(I176, I177, I178, I179, rnd5, rnd6, rnd7, I175, I176, rnd10, rnd11, rnd12) [rnd12 = rnd7 /\ rnd11 = rnd6 /\ rnd10 = rnd5 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 217.57/214.42 f5(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f8(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 f7(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f14(I238, I239, I240, I241, I242, I243, I244, rnd8, rnd9, I245, I246, I247) [I247 = rnd8 /\ I246 = I244 /\ I245 = I243 /\ rnd9 = I242 /\ rnd8 = rnd8 /\ I244 = I244 /\ I243 = I243 /\ I242 = I242] 217.57/214.42 f13(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259) -> f12(I256, I257, I258, I259, I260, I261, I254, I255, I256, 0, I262, I263) [I263 = I261 /\ I262 = I260 /\ I261 = I261 /\ I260 = I260] 217.57/214.42 f12(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 f12(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f10(I288, I289, I290, I291, I292, I285, I286, I287, I288, I289, 0, I293) [I293 = I292 /\ -1 + I288 <= I289 /\ I292 = I292] 217.57/214.42 f11(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 f10(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 f10(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f6(I332, I333, I334, I335, I328, I329, I330, I331, I332, I333, I334, 0) [-1 + I332 <= I334] 217.57/214.42 f9(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f6(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371) -> f7(I368, I369, I370, I371, I364, I365, I366, I367, I368, I369, I370, I371) [-1 + I368 <= I371] 217.57/214.42 f4(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 We use the extended value criterion with the projection function NU: 217.57/214.42 NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - x11 - 1 217.57/214.42 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - x11 217.57/214.42 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - x11 - 1 217.57/214.42 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11)] = x8 - x11 - 1 217.57/214.42 217.57/214.42 This gives the following inequalities: 217.57/214.42 ==> I202 - I205 - 1 >= I202 - I205 - 1 217.57/214.42 ==> I214 - I217 - 1 >= I214 - (1 + I217) 217.57/214.42 1 + I383 <= I380 ==> I380 - I383 > I380 - I383 - 1 with I380 - I383 >= 0 217.57/214.42 1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408 ==> I404 - I407 - 1 >= I404 - I407 - 1 217.57/214.42 I423 <= I422 /\ I423 = I423 /\ I422 = I422 ==> I418 - I421 - 1 >= I418 - I421 - 1 217.57/214.42 217.57/214.42 We remove all the strictly oriented dependency pairs. 217.57/214.42 217.57/214.42 DP problem for innermost termination. 217.57/214.42 P = 217.57/214.42 f3#(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2#(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4#(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f1#(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3#(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1#(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2#(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 R = 217.57/214.42 f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 217.57/214.42 f15(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 217.57/214.42 f15(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 217.57/214.42 f15(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 217.57/214.42 f15(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f8(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 217.57/214.42 f15(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 217.57/214.42 f15(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 217.57/214.42 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f13(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 217.57/214.42 f15(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f12(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 217.57/214.42 f15(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 217.57/214.42 f15(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 217.57/214.42 f15(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 217.57/214.42 f15(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 217.57/214.42 f15(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 217.57/214.42 f15(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 217.57/214.42 f15(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f13(I176, I177, I178, I179, rnd5, rnd6, rnd7, I175, I176, rnd10, rnd11, rnd12) [rnd12 = rnd7 /\ rnd11 = rnd6 /\ rnd10 = rnd5 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 217.57/214.42 f5(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f8(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 f7(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f14(I238, I239, I240, I241, I242, I243, I244, rnd8, rnd9, I245, I246, I247) [I247 = rnd8 /\ I246 = I244 /\ I245 = I243 /\ rnd9 = I242 /\ rnd8 = rnd8 /\ I244 = I244 /\ I243 = I243 /\ I242 = I242] 217.57/214.42 f13(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259) -> f12(I256, I257, I258, I259, I260, I261, I254, I255, I256, 0, I262, I263) [I263 = I261 /\ I262 = I260 /\ I261 = I261 /\ I260 = I260] 217.57/214.42 f12(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 f12(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f10(I288, I289, I290, I291, I292, I285, I286, I287, I288, I289, 0, I293) [I293 = I292 /\ -1 + I288 <= I289 /\ I292 = I292] 217.57/214.42 f11(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 f10(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 f10(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f6(I332, I333, I334, I335, I328, I329, I330, I331, I332, I333, I334, 0) [-1 + I332 <= I334] 217.57/214.42 f9(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f6(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371) -> f7(I368, I369, I370, I371, I364, I365, I366, I367, I368, I369, I370, I371) [-1 + I368 <= I371] 217.57/214.42 f4(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 The dependency graph for this problem is: 217.57/214.42 16 -> 17 217.57/214.42 17 -> 217.57/214.42 30 -> 16 217.57/214.42 31 -> 17 217.57/214.42 Where: 217.57/214.42 16) f3#(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2#(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 17) f2#(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4#(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 30) f1#(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3#(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 31) f1#(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2#(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 We have the following SCCs. 217.57/214.42 217.57/214.42 217.57/214.42 DP problem for innermost termination. 217.57/214.42 P = 217.57/214.42 f12#(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11#(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 f11#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12#(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 R = 217.57/214.42 f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 217.57/214.42 f15(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 217.57/214.42 f15(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 217.57/214.42 f15(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 217.57/214.42 f15(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f8(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 217.57/214.42 f15(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 217.57/214.42 f15(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 217.57/214.42 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f13(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 217.57/214.42 f15(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f12(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 217.57/214.42 f15(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 217.57/214.42 f15(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 217.57/214.42 f15(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 217.57/214.42 f15(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 217.57/214.42 f15(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 217.57/214.42 f15(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 217.57/214.42 f15(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f13(I176, I177, I178, I179, rnd5, rnd6, rnd7, I175, I176, rnd10, rnd11, rnd12) [rnd12 = rnd7 /\ rnd11 = rnd6 /\ rnd10 = rnd5 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 217.57/214.42 f5(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f8(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 f7(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f14(I238, I239, I240, I241, I242, I243, I244, rnd8, rnd9, I245, I246, I247) [I247 = rnd8 /\ I246 = I244 /\ I245 = I243 /\ rnd9 = I242 /\ rnd8 = rnd8 /\ I244 = I244 /\ I243 = I243 /\ I242 = I242] 217.57/214.42 f13(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259) -> f12(I256, I257, I258, I259, I260, I261, I254, I255, I256, 0, I262, I263) [I263 = I261 /\ I262 = I260 /\ I261 = I261 /\ I260 = I260] 217.57/214.42 f12(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 f12(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f10(I288, I289, I290, I291, I292, I285, I286, I287, I288, I289, 0, I293) [I293 = I292 /\ -1 + I288 <= I289 /\ I292 = I292] 217.57/214.42 f11(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 f10(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 f10(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f6(I332, I333, I334, I335, I328, I329, I330, I331, I332, I333, I334, 0) [-1 + I332 <= I334] 217.57/214.42 f9(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f6(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371) -> f7(I368, I369, I370, I371, I364, I365, I366, I367, I368, I369, I370, I371) [-1 + I368 <= I371] 217.57/214.42 f4(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 We use the reverse value criterion with the projection function NU: 217.57/214.42 NU[f11#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12)] = -1 + z9 + -1 * (1 + (1 + z10)) 217.57/214.42 NU[f12#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12)] = -1 + z9 + -1 * (1 + z10) 217.57/214.42 217.57/214.42 This gives the following inequalities: 217.57/214.42 I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276 ==> -1 + I272 + -1 * (1 + I273) > -1 + I272 + -1 * (1 + (1 + I273)) with -1 + I272 + -1 * (1 + I273) >= 0 217.57/214.42 I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306 ==> -1 + I302 + -1 * (1 + (1 + I303)) >= -1 + I302 + -1 * (1 + (1 + I303)) 217.57/214.42 217.57/214.42 We remove all the strictly oriented dependency pairs. 217.57/214.42 217.57/214.42 DP problem for innermost termination. 217.57/214.42 P = 217.57/214.42 f11#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12#(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 R = 217.57/214.42 f16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) 217.57/214.42 f15(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) -> f5(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10, I11) 217.57/214.42 f15(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23) 217.57/214.42 f15(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f2(I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35) 217.57/214.42 f15(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) -> f8(I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47) 217.57/214.42 f15(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) -> f7(I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59) 217.57/214.42 f15(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70, I71) 217.57/214.42 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) -> f13(I72, I73, I74, I75, I76, I77, I78, I79, I80, I81, I82, I83) 217.57/214.42 f15(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) -> f12(I84, I85, I86, I87, I88, I89, I90, I91, I92, I93, I94, I95) 217.57/214.42 f15(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I96, I97, I98, I99, I100, I101, I102, I103, I104, I105, I106, I107) 217.57/214.42 f15(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) -> f10(I108, I109, I110, I111, I112, I113, I114, I115, I116, I117, I118, I119) 217.57/214.42 f15(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) -> f9(I120, I121, I122, I123, I124, I125, I126, I127, I128, I129, I130, I131) 217.57/214.42 f15(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f6(I132, I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) 217.57/214.42 f15(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154, I155) 217.57/214.42 f15(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) -> f1(I156, I157, I158, I159, I160, I161, I162, I163, I164, I165, I166, I167) 217.57/214.42 f15(I168, I169, I170, I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f13(I176, I177, I178, I179, rnd5, rnd6, rnd7, I175, I176, rnd10, rnd11, rnd12) [rnd12 = rnd7 /\ rnd11 = rnd6 /\ rnd10 = rnd5 /\ rnd7 = rnd7 /\ rnd6 = rnd6 /\ rnd5 = rnd5] 217.57/214.42 f5(I180, I181, I182, I183, I184, I185, I186, I187, I188, I189, I190, I191) -> f10(I188, I189, I190, I191, I192, I185, I186, I187, I188, I189, 1 + I190, I193) [I193 = I192 /\ I192 = I192] 217.57/214.42 f3(I194, I195, I196, I197, I198, I199, I200, I201, I202, I203, I204, I205) -> f2(I202, I203, I204, I205, I198, I199, I200, I201, I202, I203, I204, I205) 217.57/214.42 f2(I206, I207, I208, I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f4(I214, I215, I216, I217, I210, I211, I212, I213, I214, I215, I216, 1 + I217) 217.57/214.42 f8(I218, I219, I220, I221, I222, I223, I224, I225, I226, I227, I228, I229) -> f6(I226, I227, I228, I229, I222, I223, I224, I225, I226, I227, I228, 1 + I229) 217.57/214.42 f7(I230, I231, I232, I233, I234, I235, I236, I237, I238, I239, I240, I241) -> f14(I238, I239, I240, I241, I242, I243, I244, rnd8, rnd9, I245, I246, I247) [I247 = rnd8 /\ I246 = I244 /\ I245 = I243 /\ rnd9 = I242 /\ rnd8 = rnd8 /\ I244 = I244 /\ I243 = I243 /\ I242 = I242] 217.57/214.42 f13(I248, I249, I250, I251, I252, I253, I254, I255, I256, I257, I258, I259) -> f12(I256, I257, I258, I259, I260, I261, I254, I255, I256, 0, I262, I263) [I263 = I261 /\ I262 = I260 /\ I261 = I261 /\ I260 = I260] 217.57/214.42 f12(I264, I265, I266, I267, I268, I269, I270, I271, I272, I273, I274, I275) -> f11(I272, I273, I274, I275, I276, I277, I270, I271, I272, I273, I278, I279) [I279 = I277 /\ I278 = I276 /\ 1 + I273 <= -1 + I272 /\ I277 = I277 /\ I276 = I276] 217.57/214.42 f12(I280, I281, I282, I283, I284, I285, I286, I287, I288, I289, I290, I291) -> f10(I288, I289, I290, I291, I292, I285, I286, I287, I288, I289, 0, I293) [I293 = I292 /\ -1 + I288 <= I289 /\ I292 = I292] 217.57/214.42 f11(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 f10(I310, I311, I312, I313, I314, I315, I316, I317, I318, I319, I320, I321) -> f9(I318, I319, I320, I321, I322, I315, I316, I317, I318, I319, I320, I323) [I323 = I322 /\ 1 + I320 <= -1 + I318 /\ I322 = I322] 217.57/214.42 f10(I324, I325, I326, I327, I328, I329, I330, I331, I332, I333, I334, I335) -> f6(I332, I333, I334, I335, I328, I329, I330, I331, I332, I333, I334, 0) [-1 + I332 <= I334] 217.57/214.42 f9(I336, I337, I338, I339, I340, I341, I342, I343, I344, I345, I346, I347) -> f4(I344, I345, I346, I347, I340, I341, I342, I343, I344, I345, I346, 1 + I346) 217.57/214.42 f6(I348, I349, I350, I351, I352, I353, I354, I355, I356, I357, I358, I359) -> f8(I356, I357, I358, I359, I352, I353, I354, I355, I356, I357, I358, I359) [1 + I359 <= -1 + I356] 217.57/214.42 f6(I360, I361, I362, I363, I364, I365, I366, I367, I368, I369, I370, I371) -> f7(I368, I369, I370, I371, I364, I365, I366, I367, I368, I369, I370, I371) [-1 + I368 <= I371] 217.57/214.42 f4(I372, I373, I374, I375, I376, I377, I378, I379, I380, I381, I382, I383) -> f1(I380, I381, I382, I383, I376, I377, I378, I379, I380, I381, I382, I383) [1 + I383 <= I380] 217.57/214.42 f4(I384, I385, I386, I387, I388, I389, I390, I391, I392, I393, I394, I395) -> f5(I392, I393, I394, I395, I388, I389, I390, I391, I392, I393, I394, I395) [I392 <= I395] 217.57/214.42 f1(I396, I397, I398, I399, I400, I401, I402, I403, I404, I405, I406, I407) -> f3(I404, I405, I406, I407, I408, I409, I402, I403, I404, I405, I406, I407) [1 + I408 <= I409 /\ I409 = I409 /\ I408 = I408] 217.57/214.42 f1(I410, I411, I412, I413, I414, I415, I416, I417, I418, I419, I420, I421) -> f2(I418, I419, I420, I421, I422, I423, I416, I417, I418, I419, I420, I421) [I423 <= I422 /\ I423 = I423 /\ I422 = I422] 217.57/214.42 217.57/214.42 The dependency graph for this problem is: 217.57/214.42 22 -> 217.57/214.42 Where: 217.57/214.42 22) f11#(I294, I295, I296, I297, I298, I299, I300, I301, I302, I303, I304, I305) -> f12#(I302, I303, I304, I305, I306, I307, I300, I301, I302, 1 + I303, I308, I309) [I309 = I307 /\ I308 = I306 /\ I307 = I307 /\ I306 = I306] 217.57/214.42 217.57/214.42 We have the following SCCs. 217.57/214.42 217.57/217.38 EOF