140.19/138.86 YES 140.19/138.86 140.19/138.86 DP problem for innermost termination. 140.19/138.86 P = 140.19/138.86 f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.19/138.86 f17#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7#(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.19/138.86 f3#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.19/138.86 f5#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6#(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.19/138.86 f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.19/138.86 f8#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16#(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.19/138.86 f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12#(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.19/138.86 f16#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15#(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.19/138.86 f16#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14#(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.19/138.86 f16#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14#(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.19/138.86 f15#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7#(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.19/138.86 f14#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15#(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.19/138.86 f13#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10#(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.19/138.86 f13#(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5#(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.19/138.86 f12#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13#(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.19/138.86 f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9#(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.19/138.86 f11#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12#(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.19/138.86 f9#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10#(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.19/138.86 f7#(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.19/138.86 f6#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4#(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.19/138.86 f6#(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3#(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.19/138.86 f4#(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5#(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.19/138.86 f1#(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3#(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.19/138.86 R = 140.19/138.86 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.19/138.86 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.19/138.86 f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.19/138.86 f5(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.19/138.86 f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.19/138.86 f8(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.19/138.86 f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.19/138.86 f16(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.19/138.86 f16(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.19/138.86 f16(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.19/138.86 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.19/138.86 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.19/138.86 f13(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.19/138.86 f13(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.19/138.86 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.19/138.86 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.19/138.86 f11(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.19/138.86 f9(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.19/138.86 f7(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.19/138.86 f6(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.19/138.86 f6(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.19/138.86 f4(I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f2(I182, I183, I184, I185, I186, I187, I188, I189, I190) 140.19/138.86 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.19/138.86 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.19/138.86 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I214 <= I212] 140.19/138.86 140.19/138.86 The dependency graph for this problem is: 140.19/138.86 0 -> 1 140.19/138.86 1 -> 18 140.19/138.86 2 -> 22 140.19/138.86 3 -> 19, 20 140.19/138.86 4 -> 15, 16 140.19/138.86 5 -> 7, 8, 9 140.19/138.86 6 -> 14 140.19/138.86 7 -> 10 140.19/138.86 8 -> 11 140.19/138.86 9 -> 11 140.19/138.86 10 -> 18 140.19/138.86 11 -> 10 140.19/138.86 12 -> 4 140.19/138.86 13 -> 3 140.19/138.86 14 -> 12, 13 140.19/138.86 15 -> 17 140.19/138.86 16 -> 14 140.19/138.86 17 -> 4 140.19/138.86 18 -> 5, 6 140.19/138.86 19 -> 21 140.19/138.86 20 -> 2 140.19/138.86 21 -> 3 140.19/138.86 22 -> 2 140.19/138.86 Where: 140.19/138.86 0) f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.19/138.86 1) f17#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7#(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.19/138.86 2) f3#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.19/138.86 3) f5#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6#(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.19/138.86 4) f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.19/138.86 5) f8#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16#(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.19/138.86 6) f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12#(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.19/138.86 7) f16#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15#(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.19/138.86 8) f16#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14#(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.19/138.86 9) f16#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14#(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.19/138.86 10) f15#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7#(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.19/138.86 11) f14#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15#(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.19/138.86 12) f13#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10#(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.19/138.86 13) f13#(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5#(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.19/138.86 14) f12#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13#(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.19/138.86 15) f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9#(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.19/138.86 16) f11#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12#(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.19/138.86 17) f9#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10#(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.19/138.86 18) f7#(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.19/138.86 19) f6#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4#(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.19/138.86 20) f6#(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3#(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.19/138.86 21) f4#(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5#(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.19/138.86 22) f1#(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3#(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.19/138.86 140.19/138.86 We have the following SCCs. 140.19/138.86 { 5, 7, 8, 9, 10, 11, 18 } 140.19/138.86 { 4, 12, 14, 15, 16, 17 } 140.19/138.86 { 3, 19, 21 } 140.19/138.86 { 2, 22 } 140.19/138.86 140.19/138.86 DP problem for innermost termination. 140.19/138.86 P = 140.19/138.86 f3#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.19/138.86 f1#(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3#(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.19/138.86 R = 140.19/138.86 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.19/138.86 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.19/138.86 f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.19/138.86 f5(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.19/138.86 f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.19/138.86 f8(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.19/138.86 f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.23/138.86 f16(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f13(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.23/138.86 f13(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.23/138.86 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 f7(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 f6(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.23/138.86 f6(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.23/138.86 f4(I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f2(I182, I183, I184, I185, I186, I187, I188, I189, I190) 140.23/138.86 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.23/138.86 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I214 <= I212] 140.23/138.86 140.23/138.86 We use the reverse value criterion with the projection function NU: 140.23/138.86 NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z6 + -1 * (1 + z4) 140.23/138.86 NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z6 + -1 * (1 + z4) 140.23/138.86 140.23/138.86 This gives the following inequalities: 140.23/138.86 ==> I14 + -1 * (1 + I12) >= I14 + -1 * (1 + I12) 140.23/138.86 1 + I203 <= I205 ==> I205 + -1 * (1 + I203) > I205 + -1 * (1 + (1 + I203)) with I205 + -1 * (1 + I203) >= 0 140.23/138.86 140.23/138.86 We remove all the strictly oriented dependency pairs. 140.23/138.86 140.23/138.86 DP problem for innermost termination. 140.23/138.86 P = 140.23/138.86 f3#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.23/138.86 R = 140.23/138.86 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.23/138.86 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.23/138.86 f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.23/138.86 f5(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f8(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.23/138.86 f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.23/138.86 f16(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f13(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.23/138.86 f13(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.23/138.86 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 f7(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 f6(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.23/138.86 f6(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.23/138.86 f4(I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f2(I182, I183, I184, I185, I186, I187, I188, I189, I190) 140.23/138.86 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.23/138.86 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I214 <= I212] 140.23/138.86 140.23/138.86 The dependency graph for this problem is: 140.23/138.86 2 -> 140.23/138.86 Where: 140.23/138.86 2) f3#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1#(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.23/138.86 140.23/138.86 We have the following SCCs. 140.23/138.86 140.23/138.86 140.23/138.86 DP problem for innermost termination. 140.23/138.86 P = 140.23/138.86 f5#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6#(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 f6#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4#(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.23/138.86 f4#(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5#(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 R = 140.23/138.86 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.23/138.86 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.23/138.86 f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.23/138.86 f5(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f8(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.23/138.86 f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.23/138.86 f16(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f13(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.23/138.86 f13(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.23/138.86 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 f7(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 f6(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.23/138.86 f6(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.23/138.86 f4(I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f2(I182, I183, I184, I185, I186, I187, I188, I189, I190) 140.23/138.86 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.23/138.86 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I214 <= I212] 140.23/138.86 140.23/138.86 We use the extended value criterion with the projection function NU: 140.23/138.86 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x3 - 2 140.23/138.86 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x3 - 1 140.23/138.86 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x3 - 1 140.23/138.86 140.23/138.86 This gives the following inequalities: 140.23/138.86 ==> I20 - I21 - 1 >= I20 - I21 - 1 140.23/138.86 I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164 ==> I164 - I165 - 1 > I164 - I165 - 2 with I164 - I165 - 1 >= 0 140.23/138.86 ==> I193 - I194 - 2 >= I193 - (1 + I194) - 1 140.23/138.86 140.23/138.86 We remove all the strictly oriented dependency pairs. 140.23/138.86 140.23/138.86 DP problem for innermost termination. 140.23/138.86 P = 140.23/138.86 f5#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6#(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 f4#(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5#(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 R = 140.23/138.86 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.23/138.86 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.23/138.86 f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.23/138.86 f5(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f8(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.23/138.86 f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.23/138.86 f16(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f13(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.23/138.86 f13(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.23/138.86 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 f7(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 f6(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.23/138.86 f6(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.23/138.86 f4(I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f2(I182, I183, I184, I185, I186, I187, I188, I189, I190) 140.23/138.86 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.23/138.86 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I214 <= I212] 140.23/138.86 140.23/138.86 The dependency graph for this problem is: 140.23/138.86 3 -> 140.23/138.86 21 -> 3 140.23/138.86 Where: 140.23/138.86 3) f5#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6#(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 21) f4#(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5#(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 140.23/138.86 We have the following SCCs. 140.23/138.86 140.23/138.86 140.23/138.86 DP problem for innermost termination. 140.23/138.86 P = 140.23/138.86 f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f13#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10#(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.23/138.86 f12#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13#(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9#(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12#(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10#(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 R = 140.23/138.86 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.23/138.86 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.23/138.86 f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.23/138.86 f5(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f8(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.23/138.86 f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.23/138.86 f16(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f13(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.23/138.86 f13(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.23/138.86 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 f7(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 f6(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.23/138.86 f6(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.23/138.86 f4(I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f2(I182, I183, I184, I185, I186, I187, I188, I189, I190) 140.23/138.86 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.23/138.86 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I214 <= I212] 140.23/138.86 140.23/138.86 We use the extended value criterion with the projection function NU: 140.23/138.86 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 140.23/138.86 NU[f12#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 1 140.23/138.86 NU[f13#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 1 140.23/138.86 NU[f11#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 140.23/138.86 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 140.23/138.86 140.23/138.86 This gives the following inequalities: 140.23/138.86 ==> -I30 + I32 - 2 >= -I30 + I32 - 2 140.23/138.86 1 + I102 <= I104 ==> -I102 + I104 - 1 > -I102 + I104 - 2 with -I102 + I104 - 1 >= 0 140.23/138.86 ==> -I120 + I122 - 1 >= -I120 + I122 - 1 140.23/138.86 rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128 ==> -I129 + I131 - 2 >= -I129 + I131 - 2 140.23/138.86 I137 <= I139 ==> -I138 + I140 - 2 >= -(1 + I138) + I140 - 1 140.23/138.86 ==> -I147 + I149 - 2 >= -I147 + I149 - 2 140.23/138.86 140.23/138.86 We remove all the strictly oriented dependency pairs. 140.23/138.86 140.23/138.86 DP problem for innermost termination. 140.23/138.86 P = 140.23/138.86 f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f12#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13#(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9#(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12#(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10#(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 R = 140.23/138.86 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.23/138.86 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.23/138.86 f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.23/138.86 f5(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f8(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.23/138.86 f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.23/138.86 f16(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f13(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.23/138.86 f13(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.23/138.86 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 f7(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 f6(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.23/138.86 f6(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.23/138.86 f4(I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f2(I182, I183, I184, I185, I186, I187, I188, I189, I190) 140.23/138.86 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.23/138.86 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I214 <= I212] 140.23/138.86 140.23/138.86 The dependency graph for this problem is: 140.23/138.86 4 -> 15, 16 140.23/138.86 14 -> 140.23/138.86 15 -> 17 140.23/138.86 16 -> 14 140.23/138.86 17 -> 4 140.23/138.86 Where: 140.23/138.86 4) f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 14) f12#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13#(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 15) f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9#(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 16) f11#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12#(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 17) f9#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10#(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 140.23/138.86 We have the following SCCs. 140.23/138.86 { 4, 15, 17 } 140.23/138.86 140.23/138.86 DP problem for innermost termination. 140.23/138.86 P = 140.23/138.86 f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9#(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f9#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10#(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 R = 140.23/138.86 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.23/138.86 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.23/138.86 f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.23/138.86 f5(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f8(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.23/138.86 f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.23/138.86 f16(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f13(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.23/138.86 f13(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.23/138.86 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 f7(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 f6(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.23/138.86 f6(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.23/138.86 f4(I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f2(I182, I183, I184, I185, I186, I187, I188, I189, I190) 140.23/138.86 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.23/138.86 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I214 <= I212] 140.23/138.86 140.23/138.86 We use the extended value criterion with the projection function NU: 140.23/138.86 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x4 - 2 140.23/138.86 NU[f11#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x4 - 1 140.23/138.86 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x4 - 1 140.23/138.86 140.23/138.86 This gives the following inequalities: 140.23/138.86 ==> I29 - I31 - 1 >= I29 - I31 - 1 140.23/138.86 rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128 ==> I128 - I130 - 1 > I128 - I130 - 2 with I128 - I130 - 1 >= 0 140.23/138.86 ==> I146 - I148 - 2 >= I146 - (1 + I148) - 1 140.23/138.86 140.23/138.86 We remove all the strictly oriented dependency pairs. 140.23/138.86 140.23/138.86 DP problem for innermost termination. 140.23/138.86 P = 140.23/138.86 f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f9#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10#(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 R = 140.23/138.86 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.23/138.86 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.23/138.86 f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.23/138.86 f5(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f8(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.23/138.86 f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.23/138.86 f16(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f13(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.23/138.86 f13(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.23/138.86 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 f7(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 f6(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.23/138.86 f6(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.23/138.86 f4(I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f2(I182, I183, I184, I185, I186, I187, I188, I189, I190) 140.23/138.86 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.23/138.86 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I214 <= I212] 140.23/138.86 140.23/138.86 The dependency graph for this problem is: 140.23/138.86 4 -> 140.23/138.86 17 -> 4 140.23/138.86 Where: 140.23/138.86 4) f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 17) f9#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10#(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 140.23/138.86 We have the following SCCs. 140.23/138.86 140.23/138.86 140.23/138.86 DP problem for innermost termination. 140.23/138.86 P = 140.23/138.86 f8#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16#(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.23/138.86 f16#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15#(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14#(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14#(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7#(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15#(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f7#(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 R = 140.23/138.86 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.23/138.86 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.23/138.86 f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.23/138.86 f5(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f8(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.23/138.86 f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.23/138.86 f16(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f13(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.23/138.86 f13(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.23/138.86 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 f7(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 f6(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.23/138.86 f6(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.23/138.86 f4(I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f2(I182, I183, I184, I185, I186, I187, I188, I189, I190) 140.23/138.86 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.23/138.86 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I214 <= I212] 140.23/138.86 140.23/138.86 We use the extended value criterion with the projection function NU: 140.23/138.86 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 1 140.23/138.86 NU[f14#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 140.23/138.86 NU[f15#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 140.23/138.86 NU[f16#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 140.23/138.86 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 1 140.23/138.86 140.23/138.86 This gives the following inequalities: 140.23/138.86 1 + I39 <= I41 ==> -I39 + I41 - 1 > -I39 + I41 - 2 with -I39 + I41 - 1 >= 0 140.23/138.86 I60 <= I57 /\ I57 <= I60 ==> -I57 + I59 - 2 >= -I57 + I59 - 2 140.23/138.86 1 + I66 <= I69 ==> -I66 + I68 - 2 >= -I66 + I68 - 2 140.23/138.86 1 + I78 <= I75 ==> -I75 + I77 - 2 >= -I75 + I77 - 2 140.23/138.86 ==> -I84 + I86 - 2 >= -(1 + I84) + I86 - 1 140.23/138.86 ==> -I93 + I95 - 2 >= -I93 + I95 - 2 140.23/138.86 ==> -I156 + I158 - 1 >= -I156 + I158 - 1 140.23/138.86 140.23/138.86 We remove all the strictly oriented dependency pairs. 140.23/138.86 140.23/138.86 DP problem for innermost termination. 140.23/138.86 P = 140.23/138.86 f16#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15#(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14#(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14#(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7#(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15#(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f7#(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 R = 140.23/138.86 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 140.23/138.86 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f7(I0, I1, I0, 0, I4, I1, 0, I7, I8) 140.23/138.86 f3(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f1(I9, I10, I11, I12, I13, I14, I15, I16, I17) 140.23/138.86 f5(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f6(I18, I19, I20, I21, I22, I23, I24, I25, I26) 140.23/138.86 f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f11(I27, I28, I29, I30, I31, I32, I33, I34, I35) 140.23/138.86 f8(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f16(I36, I37, I38, I39, I40, I41, I42, I43, I44) [1 + I39 <= I41] 140.23/138.86 f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f12(I45, I46, I47, 0, I49, I50, I51, I52, I53) [I50 <= I48] 140.23/138.86 f16(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 f16(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 f16(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 f13(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, I100, I101, I102, 0, I104, I105, I106, I107) [1 + I102 <= I104] 140.23/138.86 f13(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f5(I108, I109, I110, 0, I112, I113, I114, I115, I116) [I113 <= I111] 140.23/138.86 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, I120, I121, I122, I123, I124, I125) 140.23/138.86 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f9(I126, I127, I128, I129, I130, I131, I132, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I130 <= I128] 140.23/138.86 f11(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f12(I135, I136, I137, 1 + I138, I139, I140, I141, I142, I143) [I137 <= I139] 140.23/138.86 f9(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f10(I144, I145, I146, I147, 1 + I148, I149, I150, I151, I152) 140.23/138.86 f7(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 f6(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f4(I162, I163, I164, I165, I166, I167, I168, I171, I172) [I172 = I172 /\ I171 = I171 /\ 1 + I165 <= I164] 140.23/138.86 f6(I173, I174, I175, I176, I177, I178, I179, I180, I181) -> f3(I173, I174, I175, 0, I177, I178, I179, I180, I181) [I175 <= I176] 140.23/138.86 f4(I182, I183, I184, I185, I186, I187, I188, I189, I190) -> f2(I182, I183, I184, I185, I186, I187, I188, I189, I190) 140.23/138.86 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 1 + I194, I195, I196, I197, I198, I199) 140.23/138.86 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, 1 + I203, I204, I205, I206, I207, I208) [1 + I203 <= I205] 140.23/138.86 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, I212, I213, I214, I215, I216, I217) [I214 <= I212] 140.23/138.86 140.23/138.86 The dependency graph for this problem is: 140.23/138.86 7 -> 10 140.23/138.86 8 -> 11 140.23/138.86 9 -> 11 140.23/138.86 10 -> 18 140.23/138.86 11 -> 10 140.23/138.86 18 -> 140.23/138.86 Where: 140.23/138.86 7) f16#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f15#(I54, I55, I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 140.23/138.86 8) f16#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f14#(I63, I64, I65, I66, I67, I68, I69, I70, I71) [1 + I66 <= I69] 140.23/138.86 9) f16#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14#(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I78 <= I75] 140.23/138.86 10) f15#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f7#(I81, I82, I83, 1 + I84, I85, I86, I87, I88, I89) 140.23/138.86 11) f14#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f15#(I90, I91, I92, I93, I94, I95, I96, I97, I98) 140.23/138.86 18) f7#(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161) 140.23/138.86 140.23/138.86 We have the following SCCs. 140.23/138.86 140.23/141.82 EOF