32.90/32.45 YES 32.90/32.45 32.90/32.45 DP problem for innermost termination. 32.90/32.45 P = 32.90/32.45 f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f11#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 32.90/32.45 f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7#(I0, I1, I2, I3, I4, I5, I6, I7, I8) 32.90/32.45 f11#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 32.90/32.45 f11#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f9#(I36, I37, I38, I39, I40, I41, I42, I43, I44) 32.90/32.45 f11#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) 32.90/32.45 f11#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f5#(I54, I55, I56, I57, I58, I59, I60, I61, I62) 32.90/32.45 f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f4#(I72, I73, I74, I75, I76, I77, I78, I79, I80) 32.90/32.45 f11#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f2#(I81, I82, I83, I84, I85, I86, I87, I88, I89) 32.90/32.45 f11#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f1#(I90, I91, I92, I93, I94, I95, I96, I97, I98) 32.90/32.45 f11#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f4#(I105, I106, I107, rnd4, rnd5, I104, I105, rnd8, rnd9) [rnd9 = rnd5 /\ rnd8 = rnd4 /\ rnd5 = rnd5 /\ rnd4 = rnd4] 32.90/32.45 f7#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f9#(I127, I128, I129, I130, I131, I126, I127, I132, I133) [I133 = I131 /\ I132 = I130 /\ I131 = I131 /\ I130 = I130] 32.90/32.45 f9#(I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f8#(I155, I156, I157, I158, I159, I154, I155, I160, I161) [I161 = I159 /\ I160 = I158 /\ I155 <= 0 /\ I159 = I159 /\ I158 = I158] 32.90/32.45 f9#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f5#(I168, I169, I170, I171, I172, I167, I168, I173, I174) [I174 = I172 /\ I173 = I171 /\ 1 <= I168 /\ I172 = I172 /\ I171 = I171] 32.90/32.45 f5#(I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f7#(I196, I197, I198, I199, I200, I195, -1 + I196, I201, I202) [I202 = I200 /\ I201 = I199 /\ I200 = I200 /\ I199 = I199] 32.90/32.45 f4#(I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2#(I224, I225, I226, I221, I222, I223, I224, 0, I224) 32.90/32.45 f2#(I227, I228, I229, I230, I231, I232, I233, I234, I235) -> f1#(I233, I234, I235, I230, I231, I232, I233, I234, I235) [0 <= I235] 32.90/32.45 f2#(I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f3#(I242, I243, I244, I239, I240, I241, I242, I243, I244) [1 + I244 <= 0] 32.90/32.45 f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253) -> f2#(I251, I252, I253, I254, I249, I250, I251, I255, -1 + I253) [I255 = I252 + I254 /\ I254 = I254] 32.90/32.45 R = 32.90/32.45 f13(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9) 32.90/32.45 f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I2, I3, I4, I5, I6, I7, I8) 32.90/32.45 f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) 32.90/32.45 f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f10(I18, I19, I20, I21, I22, I23, I24, I25, I26) 32.90/32.45 f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f12(I27, I28, I29, I30, I31, I32, I33, I34, I35) 32.90/32.45 f11(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f9(I36, I37, I38, I39, I40, I41, I42, I43, I44) 32.90/32.45 f11(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 32.90/32.45 f11(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f5(I54, I55, I56, I57, I58, I59, I60, I61, I62) 32.90/32.45 f11(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6(I63, I64, I65, I66, I67, I68, I69, I70, I71) 32.90/32.45 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f4(I72, I73, I74, I75, I76, I77, I78, I79, I80) 32.90/32.45 f11(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f2(I81, I82, I83, I84, I85, I86, I87, I88, I89) 32.90/32.45 f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f1(I90, I91, I92, I93, I94, I95, I96, I97, I98) 32.90/32.45 f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f4(I105, I106, I107, rnd4, rnd5, I104, I105, rnd8, rnd9) [rnd9 = rnd5 /\ rnd8 = rnd4 /\ rnd5 = rnd5 /\ rnd4 = rnd4] 32.90/32.45 f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f12(I114, I115, I116, I117, I118, rnd6, rnd7, I119, I120) [I120 = rnd6 /\ I119 = I118 /\ rnd7 = I117 /\ rnd6 = rnd6 /\ I118 = I118 /\ I117 = I117] 32.90/32.45 f7(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f9(I127, I128, I129, I130, I131, I126, I127, I132, I133) [I133 = I131 /\ I132 = I130 /\ I131 = I131 /\ I130 = I130] 32.90/32.45 f3(I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f10(I140, I141, I142, I143, I144, I145, I146, I147, I148) [I148 = I145 /\ I147 = I144 /\ I146 = I143 /\ I145 = I145 /\ I144 = I144 /\ I143 = I143] 32.90/32.45 f9(I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f8(I155, I156, I157, I158, I159, I154, I155, I160, I161) [I161 = I159 /\ I160 = I158 /\ I155 <= 0 /\ I159 = I159 /\ I158 = I158] 32.90/32.45 f9(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f5(I168, I169, I170, I171, I172, I167, I168, I173, I174) [I174 = I172 /\ I173 = I171 /\ 1 <= I168 /\ I172 = I172 /\ I171 = I171] 32.90/32.45 f8(I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f6(I181, I182, I183, I184, I185, I186, I187, I188, I189) [I189 = I186 /\ I188 = I185 /\ I187 = I184 /\ I186 = I186 /\ I185 = I185 /\ I184 = I184] 32.90/32.45 f5(I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f7(I196, I197, I198, I199, I200, I195, -1 + I196, I201, I202) [I202 = I200 /\ I201 = I199 /\ I200 = I200 /\ I199 = I199] 32.90/32.45 f5(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f6(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I217 = I214 /\ I216 = I213 /\ I215 = I212 /\ I214 = I214 /\ I213 = I213 /\ I212 = I212] 32.90/32.45 f4(I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(I224, I225, I226, I221, I222, I223, I224, 0, I224) 32.90/32.45 f2(I227, I228, I229, I230, I231, I232, I233, I234, I235) -> f1(I233, I234, I235, I230, I231, I232, I233, I234, I235) [0 <= I235] 32.90/32.45 f2(I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f3(I242, I243, I244, I239, I240, I241, I242, I243, I244) [1 + I244 <= 0] 32.90/32.45 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253) -> f2(I251, I252, I253, I254, I249, I250, I251, I255, -1 + I253) [I255 = I252 + I254 /\ I254 = I254] 32.90/32.45 32.90/32.45 The dependency graph for this problem is: 32.90/32.45 0 -> 1, 2, 3, 4, 5, 6, 7, 8, 9 32.90/32.45 1 -> 10 32.90/32.45 2 -> 32.90/32.45 3 -> 11, 12 32.90/32.45 4 -> 32.90/32.45 5 -> 13 32.90/32.45 6 -> 14 32.90/32.45 7 -> 15, 16 32.90/32.45 8 -> 17 32.90/32.45 9 -> 14 32.90/32.45 10 -> 11, 12 32.90/32.45 11 -> 32.90/32.45 12 -> 13 32.90/32.45 13 -> 10 32.90/32.45 14 -> 15, 16 32.90/32.45 15 -> 17 32.90/32.45 16 -> 32.90/32.45 17 -> 15, 16 32.90/32.45 Where: 32.90/32.45 0) f13#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f11#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 32.90/32.45 1) f11#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7#(I0, I1, I2, I3, I4, I5, I6, I7, I8) 32.90/32.45 2) f11#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 32.90/32.45 3) f11#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f9#(I36, I37, I38, I39, I40, I41, I42, I43, I44) 32.90/32.45 4) f11#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) 32.90/32.45 5) f11#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f5#(I54, I55, I56, I57, I58, I59, I60, I61, I62) 32.90/32.45 6) f11#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f4#(I72, I73, I74, I75, I76, I77, I78, I79, I80) 32.90/32.45 7) f11#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f2#(I81, I82, I83, I84, I85, I86, I87, I88, I89) 32.90/32.45 8) f11#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f1#(I90, I91, I92, I93, I94, I95, I96, I97, I98) 32.90/32.45 9) f11#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f4#(I105, I106, I107, rnd4, rnd5, I104, I105, rnd8, rnd9) [rnd9 = rnd5 /\ rnd8 = rnd4 /\ rnd5 = rnd5 /\ rnd4 = rnd4] 32.90/32.45 10) f7#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f9#(I127, I128, I129, I130, I131, I126, I127, I132, I133) [I133 = I131 /\ I132 = I130 /\ I131 = I131 /\ I130 = I130] 32.90/32.45 11) f9#(I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f8#(I155, I156, I157, I158, I159, I154, I155, I160, I161) [I161 = I159 /\ I160 = I158 /\ I155 <= 0 /\ I159 = I159 /\ I158 = I158] 32.90/32.45 12) f9#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f5#(I168, I169, I170, I171, I172, I167, I168, I173, I174) [I174 = I172 /\ I173 = I171 /\ 1 <= I168 /\ I172 = I172 /\ I171 = I171] 32.90/32.45 13) f5#(I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f7#(I196, I197, I198, I199, I200, I195, -1 + I196, I201, I202) [I202 = I200 /\ I201 = I199 /\ I200 = I200 /\ I199 = I199] 32.90/32.45 14) f4#(I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2#(I224, I225, I226, I221, I222, I223, I224, 0, I224) 32.90/32.45 15) f2#(I227, I228, I229, I230, I231, I232, I233, I234, I235) -> f1#(I233, I234, I235, I230, I231, I232, I233, I234, I235) [0 <= I235] 32.90/32.45 16) f2#(I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f3#(I242, I243, I244, I239, I240, I241, I242, I243, I244) [1 + I244 <= 0] 32.90/32.45 17) f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253) -> f2#(I251, I252, I253, I254, I249, I250, I251, I255, -1 + I253) [I255 = I252 + I254 /\ I254 = I254] 32.90/32.45 32.90/32.45 We have the following SCCs. 32.90/32.45 { 10, 12, 13 } 32.90/32.45 { 15, 17 } 32.90/32.45 32.90/32.45 DP problem for innermost termination. 32.90/32.45 P = 32.90/32.45 f2#(I227, I228, I229, I230, I231, I232, I233, I234, I235) -> f1#(I233, I234, I235, I230, I231, I232, I233, I234, I235) [0 <= I235] 32.90/32.45 f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253) -> f2#(I251, I252, I253, I254, I249, I250, I251, I255, -1 + I253) [I255 = I252 + I254 /\ I254 = I254] 32.90/32.45 R = 32.90/32.45 f13(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9) 32.90/32.45 f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I2, I3, I4, I5, I6, I7, I8) 32.90/32.45 f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) 32.90/32.45 f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f10(I18, I19, I20, I21, I22, I23, I24, I25, I26) 32.90/32.45 f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f12(I27, I28, I29, I30, I31, I32, I33, I34, I35) 32.90/32.45 f11(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f9(I36, I37, I38, I39, I40, I41, I42, I43, I44) 32.90/32.45 f11(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 32.90/32.45 f11(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f5(I54, I55, I56, I57, I58, I59, I60, I61, I62) 32.90/32.45 f11(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6(I63, I64, I65, I66, I67, I68, I69, I70, I71) 32.90/32.45 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f4(I72, I73, I74, I75, I76, I77, I78, I79, I80) 32.90/32.45 f11(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f2(I81, I82, I83, I84, I85, I86, I87, I88, I89) 32.90/32.45 f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f1(I90, I91, I92, I93, I94, I95, I96, I97, I98) 32.90/32.45 f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f4(I105, I106, I107, rnd4, rnd5, I104, I105, rnd8, rnd9) [rnd9 = rnd5 /\ rnd8 = rnd4 /\ rnd5 = rnd5 /\ rnd4 = rnd4] 32.90/32.45 f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f12(I114, I115, I116, I117, I118, rnd6, rnd7, I119, I120) [I120 = rnd6 /\ I119 = I118 /\ rnd7 = I117 /\ rnd6 = rnd6 /\ I118 = I118 /\ I117 = I117] 32.90/32.45 f7(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f9(I127, I128, I129, I130, I131, I126, I127, I132, I133) [I133 = I131 /\ I132 = I130 /\ I131 = I131 /\ I130 = I130] 32.90/32.45 f3(I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f10(I140, I141, I142, I143, I144, I145, I146, I147, I148) [I148 = I145 /\ I147 = I144 /\ I146 = I143 /\ I145 = I145 /\ I144 = I144 /\ I143 = I143] 32.90/32.45 f9(I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f8(I155, I156, I157, I158, I159, I154, I155, I160, I161) [I161 = I159 /\ I160 = I158 /\ I155 <= 0 /\ I159 = I159 /\ I158 = I158] 32.90/32.45 f9(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f5(I168, I169, I170, I171, I172, I167, I168, I173, I174) [I174 = I172 /\ I173 = I171 /\ 1 <= I168 /\ I172 = I172 /\ I171 = I171] 32.90/32.45 f8(I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f6(I181, I182, I183, I184, I185, I186, I187, I188, I189) [I189 = I186 /\ I188 = I185 /\ I187 = I184 /\ I186 = I186 /\ I185 = I185 /\ I184 = I184] 32.90/32.45 f5(I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f7(I196, I197, I198, I199, I200, I195, -1 + I196, I201, I202) [I202 = I200 /\ I201 = I199 /\ I200 = I200 /\ I199 = I199] 32.90/32.45 f5(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f6(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I217 = I214 /\ I216 = I213 /\ I215 = I212 /\ I214 = I214 /\ I213 = I213 /\ I212 = I212] 32.90/32.45 f4(I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(I224, I225, I226, I221, I222, I223, I224, 0, I224) 32.90/32.45 f2(I227, I228, I229, I230, I231, I232, I233, I234, I235) -> f1(I233, I234, I235, I230, I231, I232, I233, I234, I235) [0 <= I235] 32.90/32.45 f2(I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f3(I242, I243, I244, I239, I240, I241, I242, I243, I244) [1 + I244 <= 0] 32.90/32.45 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253) -> f2(I251, I252, I253, I254, I249, I250, I251, I255, -1 + I253) [I255 = I252 + I254 /\ I254 = I254] 32.90/32.45 32.90/32.45 We use the reverse value criterion with the projection function NU: 32.90/32.45 NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = -1 + z9 + -1 * 0 32.90/32.45 NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z9 32.90/32.45 32.90/32.45 This gives the following inequalities: 32.90/32.45 0 <= I235 ==> I235 > -1 + I235 + -1 * 0 with I235 >= 0 32.90/32.45 I255 = I252 + I254 /\ I254 = I254 ==> -1 + I253 + -1 * 0 >= -1 + I253 32.90/32.45 32.90/32.45 We remove all the strictly oriented dependency pairs. 32.90/32.45 32.90/32.45 DP problem for innermost termination. 32.90/32.45 P = 32.90/32.45 f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253) -> f2#(I251, I252, I253, I254, I249, I250, I251, I255, -1 + I253) [I255 = I252 + I254 /\ I254 = I254] 32.90/32.45 R = 32.90/32.45 f13(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9) 32.90/32.45 f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I2, I3, I4, I5, I6, I7, I8) 32.90/32.45 f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) 32.90/32.45 f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f10(I18, I19, I20, I21, I22, I23, I24, I25, I26) 32.90/32.45 f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f12(I27, I28, I29, I30, I31, I32, I33, I34, I35) 32.90/32.45 f11(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f9(I36, I37, I38, I39, I40, I41, I42, I43, I44) 32.90/32.45 f11(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 32.90/32.45 f11(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f5(I54, I55, I56, I57, I58, I59, I60, I61, I62) 32.90/32.45 f11(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6(I63, I64, I65, I66, I67, I68, I69, I70, I71) 32.90/32.45 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f4(I72, I73, I74, I75, I76, I77, I78, I79, I80) 32.90/32.45 f11(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f2(I81, I82, I83, I84, I85, I86, I87, I88, I89) 32.90/32.45 f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f1(I90, I91, I92, I93, I94, I95, I96, I97, I98) 32.90/32.45 f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f4(I105, I106, I107, rnd4, rnd5, I104, I105, rnd8, rnd9) [rnd9 = rnd5 /\ rnd8 = rnd4 /\ rnd5 = rnd5 /\ rnd4 = rnd4] 32.90/32.45 f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f12(I114, I115, I116, I117, I118, rnd6, rnd7, I119, I120) [I120 = rnd6 /\ I119 = I118 /\ rnd7 = I117 /\ rnd6 = rnd6 /\ I118 = I118 /\ I117 = I117] 32.90/32.45 f7(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f9(I127, I128, I129, I130, I131, I126, I127, I132, I133) [I133 = I131 /\ I132 = I130 /\ I131 = I131 /\ I130 = I130] 32.90/32.45 f3(I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f10(I140, I141, I142, I143, I144, I145, I146, I147, I148) [I148 = I145 /\ I147 = I144 /\ I146 = I143 /\ I145 = I145 /\ I144 = I144 /\ I143 = I143] 32.90/32.45 f9(I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f8(I155, I156, I157, I158, I159, I154, I155, I160, I161) [I161 = I159 /\ I160 = I158 /\ I155 <= 0 /\ I159 = I159 /\ I158 = I158] 32.90/32.45 f9(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f5(I168, I169, I170, I171, I172, I167, I168, I173, I174) [I174 = I172 /\ I173 = I171 /\ 1 <= I168 /\ I172 = I172 /\ I171 = I171] 32.90/32.45 f8(I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f6(I181, I182, I183, I184, I185, I186, I187, I188, I189) [I189 = I186 /\ I188 = I185 /\ I187 = I184 /\ I186 = I186 /\ I185 = I185 /\ I184 = I184] 32.90/32.45 f5(I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f7(I196, I197, I198, I199, I200, I195, -1 + I196, I201, I202) [I202 = I200 /\ I201 = I199 /\ I200 = I200 /\ I199 = I199] 32.90/32.45 f5(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f6(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I217 = I214 /\ I216 = I213 /\ I215 = I212 /\ I214 = I214 /\ I213 = I213 /\ I212 = I212] 32.90/32.45 f4(I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(I224, I225, I226, I221, I222, I223, I224, 0, I224) 32.90/32.45 f2(I227, I228, I229, I230, I231, I232, I233, I234, I235) -> f1(I233, I234, I235, I230, I231, I232, I233, I234, I235) [0 <= I235] 32.90/32.45 f2(I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f3(I242, I243, I244, I239, I240, I241, I242, I243, I244) [1 + I244 <= 0] 32.90/32.45 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253) -> f2(I251, I252, I253, I254, I249, I250, I251, I255, -1 + I253) [I255 = I252 + I254 /\ I254 = I254] 32.90/32.45 32.90/32.45 The dependency graph for this problem is: 32.90/32.45 17 -> 32.90/32.45 Where: 32.90/32.45 17) f1#(I245, I246, I247, I248, I249, I250, I251, I252, I253) -> f2#(I251, I252, I253, I254, I249, I250, I251, I255, -1 + I253) [I255 = I252 + I254 /\ I254 = I254] 32.90/32.45 32.90/32.45 We have the following SCCs. 32.90/32.45 32.90/32.45 32.90/32.45 DP problem for innermost termination. 32.90/32.45 P = 32.90/32.45 f7#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f9#(I127, I128, I129, I130, I131, I126, I127, I132, I133) [I133 = I131 /\ I132 = I130 /\ I131 = I131 /\ I130 = I130] 32.90/32.45 f9#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f5#(I168, I169, I170, I171, I172, I167, I168, I173, I174) [I174 = I172 /\ I173 = I171 /\ 1 <= I168 /\ I172 = I172 /\ I171 = I171] 32.90/32.45 f5#(I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f7#(I196, I197, I198, I199, I200, I195, -1 + I196, I201, I202) [I202 = I200 /\ I201 = I199 /\ I200 = I200 /\ I199 = I199] 32.90/32.45 R = 32.90/32.45 f13(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9) 32.90/32.45 f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I2, I3, I4, I5, I6, I7, I8) 32.90/32.45 f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) 32.90/32.45 f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f10(I18, I19, I20, I21, I22, I23, I24, I25, I26) 32.90/32.45 f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f12(I27, I28, I29, I30, I31, I32, I33, I34, I35) 32.90/32.45 f11(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f9(I36, I37, I38, I39, I40, I41, I42, I43, I44) 32.90/32.45 f11(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 32.90/32.45 f11(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f5(I54, I55, I56, I57, I58, I59, I60, I61, I62) 32.90/32.45 f11(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6(I63, I64, I65, I66, I67, I68, I69, I70, I71) 32.90/32.45 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f4(I72, I73, I74, I75, I76, I77, I78, I79, I80) 32.90/32.45 f11(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f2(I81, I82, I83, I84, I85, I86, I87, I88, I89) 32.90/32.45 f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f1(I90, I91, I92, I93, I94, I95, I96, I97, I98) 32.90/32.45 f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f4(I105, I106, I107, rnd4, rnd5, I104, I105, rnd8, rnd9) [rnd9 = rnd5 /\ rnd8 = rnd4 /\ rnd5 = rnd5 /\ rnd4 = rnd4] 32.90/32.45 f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f12(I114, I115, I116, I117, I118, rnd6, rnd7, I119, I120) [I120 = rnd6 /\ I119 = I118 /\ rnd7 = I117 /\ rnd6 = rnd6 /\ I118 = I118 /\ I117 = I117] 32.90/32.45 f7(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f9(I127, I128, I129, I130, I131, I126, I127, I132, I133) [I133 = I131 /\ I132 = I130 /\ I131 = I131 /\ I130 = I130] 32.90/32.45 f3(I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f10(I140, I141, I142, I143, I144, I145, I146, I147, I148) [I148 = I145 /\ I147 = I144 /\ I146 = I143 /\ I145 = I145 /\ I144 = I144 /\ I143 = I143] 32.90/32.45 f9(I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f8(I155, I156, I157, I158, I159, I154, I155, I160, I161) [I161 = I159 /\ I160 = I158 /\ I155 <= 0 /\ I159 = I159 /\ I158 = I158] 32.90/32.45 f9(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f5(I168, I169, I170, I171, I172, I167, I168, I173, I174) [I174 = I172 /\ I173 = I171 /\ 1 <= I168 /\ I172 = I172 /\ I171 = I171] 32.90/32.45 f8(I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f6(I181, I182, I183, I184, I185, I186, I187, I188, I189) [I189 = I186 /\ I188 = I185 /\ I187 = I184 /\ I186 = I186 /\ I185 = I185 /\ I184 = I184] 32.90/32.45 f5(I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f7(I196, I197, I198, I199, I200, I195, -1 + I196, I201, I202) [I202 = I200 /\ I201 = I199 /\ I200 = I200 /\ I199 = I199] 32.90/32.45 f5(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f6(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I217 = I214 /\ I216 = I213 /\ I215 = I212 /\ I214 = I214 /\ I213 = I213 /\ I212 = I212] 32.90/32.45 f4(I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(I224, I225, I226, I221, I222, I223, I224, 0, I224) 32.90/32.45 f2(I227, I228, I229, I230, I231, I232, I233, I234, I235) -> f1(I233, I234, I235, I230, I231, I232, I233, I234, I235) [0 <= I235] 32.90/32.45 f2(I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f3(I242, I243, I244, I239, I240, I241, I242, I243, I244) [1 + I244 <= 0] 32.90/32.45 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253) -> f2(I251, I252, I253, I254, I249, I250, I251, I255, -1 + I253) [I255 = I252 + I254 /\ I254 = I254] 32.90/32.45 32.90/32.45 We use the extended value criterion with the projection function NU: 32.90/32.45 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x6 - 2 32.90/32.45 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x6 - 1 32.90/32.45 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x6 - 1 32.90/32.45 32.90/32.45 This gives the following inequalities: 32.90/32.45 I133 = I131 /\ I132 = I130 /\ I131 = I131 /\ I130 = I130 ==> I127 - 1 >= I127 - 1 32.90/32.45 I174 = I172 /\ I173 = I171 /\ 1 <= I168 /\ I172 = I172 /\ I171 = I171 ==> I168 - 1 > I168 - 2 with I168 - 1 >= 0 32.90/32.45 I202 = I200 /\ I201 = I199 /\ I200 = I200 /\ I199 = I199 ==> I196 - 2 >= (-1 + I196) - 1 32.90/32.45 32.90/32.45 We remove all the strictly oriented dependency pairs. 32.90/32.45 32.90/32.45 DP problem for innermost termination. 32.90/32.45 P = 32.90/32.45 f7#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f9#(I127, I128, I129, I130, I131, I126, I127, I132, I133) [I133 = I131 /\ I132 = I130 /\ I131 = I131 /\ I130 = I130] 32.90/32.45 f5#(I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f7#(I196, I197, I198, I199, I200, I195, -1 + I196, I201, I202) [I202 = I200 /\ I201 = I199 /\ I200 = I200 /\ I199 = I199] 32.90/32.45 R = 32.90/32.45 f13(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f11(x1, x2, x3, x4, x5, x6, x7, x8, x9) 32.90/32.45 f11(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I2, I3, I4, I5, I6, I7, I8) 32.90/32.45 f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) 32.90/32.45 f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f10(I18, I19, I20, I21, I22, I23, I24, I25, I26) 32.90/32.45 f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f12(I27, I28, I29, I30, I31, I32, I33, I34, I35) 32.90/32.45 f11(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f9(I36, I37, I38, I39, I40, I41, I42, I43, I44) 32.90/32.45 f11(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 32.90/32.45 f11(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f5(I54, I55, I56, I57, I58, I59, I60, I61, I62) 32.90/32.45 f11(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f6(I63, I64, I65, I66, I67, I68, I69, I70, I71) 32.90/32.45 f11(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f4(I72, I73, I74, I75, I76, I77, I78, I79, I80) 32.90/32.45 f11(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f2(I81, I82, I83, I84, I85, I86, I87, I88, I89) 32.90/32.45 f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f1(I90, I91, I92, I93, I94, I95, I96, I97, I98) 32.90/32.45 f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f4(I105, I106, I107, rnd4, rnd5, I104, I105, rnd8, rnd9) [rnd9 = rnd5 /\ rnd8 = rnd4 /\ rnd5 = rnd5 /\ rnd4 = rnd4] 32.90/32.45 f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f12(I114, I115, I116, I117, I118, rnd6, rnd7, I119, I120) [I120 = rnd6 /\ I119 = I118 /\ rnd7 = I117 /\ rnd6 = rnd6 /\ I118 = I118 /\ I117 = I117] 32.90/32.45 f7(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f9(I127, I128, I129, I130, I131, I126, I127, I132, I133) [I133 = I131 /\ I132 = I130 /\ I131 = I131 /\ I130 = I130] 32.90/32.45 f3(I134, I135, I136, I137, I138, I139, I140, I141, I142) -> f10(I140, I141, I142, I143, I144, I145, I146, I147, I148) [I148 = I145 /\ I147 = I144 /\ I146 = I143 /\ I145 = I145 /\ I144 = I144 /\ I143 = I143] 32.90/32.45 f9(I149, I150, I151, I152, I153, I154, I155, I156, I157) -> f8(I155, I156, I157, I158, I159, I154, I155, I160, I161) [I161 = I159 /\ I160 = I158 /\ I155 <= 0 /\ I159 = I159 /\ I158 = I158] 32.90/32.45 f9(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f5(I168, I169, I170, I171, I172, I167, I168, I173, I174) [I174 = I172 /\ I173 = I171 /\ 1 <= I168 /\ I172 = I172 /\ I171 = I171] 32.90/32.45 f8(I175, I176, I177, I178, I179, I180, I181, I182, I183) -> f6(I181, I182, I183, I184, I185, I186, I187, I188, I189) [I189 = I186 /\ I188 = I185 /\ I187 = I184 /\ I186 = I186 /\ I185 = I185 /\ I184 = I184] 32.90/32.45 f5(I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f7(I196, I197, I198, I199, I200, I195, -1 + I196, I201, I202) [I202 = I200 /\ I201 = I199 /\ I200 = I200 /\ I199 = I199] 32.90/32.45 f5(I203, I204, I205, I206, I207, I208, I209, I210, I211) -> f6(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I217 = I214 /\ I216 = I213 /\ I215 = I212 /\ I214 = I214 /\ I213 = I213 /\ I212 = I212] 32.90/32.45 f4(I218, I219, I220, I221, I222, I223, I224, I225, I226) -> f2(I224, I225, I226, I221, I222, I223, I224, 0, I224) 32.90/32.45 f2(I227, I228, I229, I230, I231, I232, I233, I234, I235) -> f1(I233, I234, I235, I230, I231, I232, I233, I234, I235) [0 <= I235] 32.90/32.45 f2(I236, I237, I238, I239, I240, I241, I242, I243, I244) -> f3(I242, I243, I244, I239, I240, I241, I242, I243, I244) [1 + I244 <= 0] 32.90/32.45 f1(I245, I246, I247, I248, I249, I250, I251, I252, I253) -> f2(I251, I252, I253, I254, I249, I250, I251, I255, -1 + I253) [I255 = I252 + I254 /\ I254 = I254] 32.90/32.45 32.90/32.45 The dependency graph for this problem is: 32.90/32.45 10 -> 32.90/32.45 13 -> 10 32.90/32.45 Where: 32.90/32.45 10) f7#(I121, I122, I123, I124, I125, I126, I127, I128, I129) -> f9#(I127, I128, I129, I130, I131, I126, I127, I132, I133) [I133 = I131 /\ I132 = I130 /\ I131 = I131 /\ I130 = I130] 32.90/32.45 13) f5#(I190, I191, I192, I193, I194, I195, I196, I197, I198) -> f7#(I196, I197, I198, I199, I200, I195, -1 + I196, I201, I202) [I202 = I200 /\ I201 = I199 /\ I200 = I200 /\ I199 = I199] 32.90/32.45 32.90/32.45 We have the following SCCs. 32.90/32.45 32.90/35.42 EOF