139.58/138.58 YES 139.58/138.58 139.58/138.58 DP problem for innermost termination. 139.58/138.58 P = 139.58/138.58 f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13#(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5#(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f5#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4#(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10#(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15#(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14#(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9#(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12#(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11#(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14#(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11#(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13#(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12#(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7#(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2#(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6#(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9#(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6#(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7#(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4#(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1#(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4#(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5#(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1#(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2#(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 R = 139.58/138.58 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f16(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) [I23 <= I21] 139.58/138.58 f5(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, I203, I204, I205, I206, I207, I208) 139.58/138.58 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 The dependency graph for this problem is: 139.58/138.58 0 -> 1 139.58/138.58 1 -> 7 139.58/138.58 2 -> 3 139.58/138.58 3 -> 2 139.58/138.58 4 -> 20, 21 139.58/138.58 5 -> 17, 18 139.58/138.58 6 -> 15, 16 139.58/138.58 7 -> 8, 9 139.58/138.58 8 -> 10, 11, 12 139.58/138.58 9 -> 6 139.58/138.58 10 -> 13 139.58/138.58 11 -> 14 139.58/138.58 12 -> 14 139.58/138.58 13 -> 7 139.58/138.58 14 -> 13 139.58/138.58 15 -> 5 139.58/138.58 16 -> 4 139.58/138.58 17 -> 19 139.58/138.58 18 -> 6 139.58/138.58 19 -> 5 139.58/138.58 20 -> 22 139.58/138.58 21 -> 3 139.58/138.58 22 -> 4 139.58/138.58 Where: 139.58/138.58 0) f18#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 1) f17#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13#(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 2) f16#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5#(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 3) f5#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 4) f2#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4#(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 5) f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 6) f9#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10#(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 7) f13#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15#(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 8) f15#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14#(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 9) f15#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9#(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 10) f14#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12#(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 11) f14#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11#(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 12) f14#(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11#(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 13) f12#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13#(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 14) f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12#(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 15) f10#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7#(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 16) f10#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2#(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 17) f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6#(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 18) f8#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9#(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 19) f6#(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7#(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 20) f4#(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1#(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 21) f4#(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5#(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 22) f1#(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2#(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 We have the following SCCs. 139.58/138.58 { 7, 8, 10, 11, 12, 13, 14 } 139.58/138.58 { 5, 6, 15, 17, 18, 19 } 139.58/138.58 { 4, 20, 22 } 139.58/138.58 { 2, 3 } 139.58/138.58 139.58/138.58 DP problem for innermost termination. 139.58/138.58 P = 139.58/138.58 f16#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5#(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f5#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 R = 139.58/138.58 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f16(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) [I23 <= I21] 139.58/138.58 f5(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, I203, I204, I205, I206, I207, I208) 139.58/138.58 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 We use the reverse value criterion with the projection function NU: 139.58/138.58 NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z6 + -1 * (1 + z4) 139.58/138.58 NU[f16#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z6 + -1 * (1 + z4) 139.58/138.58 139.58/138.58 This gives the following inequalities: 139.58/138.58 1 + I12 <= I14 ==> I14 + -1 * (1 + I12) > I14 + -1 * (1 + (1 + I12)) with I14 + -1 * (1 + I12) >= 0 139.58/138.58 ==> I32 + -1 * (1 + I30) >= I32 + -1 * (1 + I30) 139.58/138.58 139.58/138.58 We remove all the strictly oriented dependency pairs. 139.58/138.58 139.58/138.58 DP problem for innermost termination. 139.58/138.58 P = 139.58/138.58 f5#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 R = 139.58/138.58 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f16(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) [I23 <= I21] 139.58/138.58 f5(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, I203, I204, I205, I206, I207, I208) 139.58/138.58 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 The dependency graph for this problem is: 139.58/138.58 3 -> 139.58/138.58 Where: 139.58/138.58 3) f5#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 139.58/138.58 We have the following SCCs. 139.58/138.58 139.58/138.58 139.58/138.58 DP problem for innermost termination. 139.58/138.58 P = 139.58/138.58 f2#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4#(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f4#(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1#(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f1#(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2#(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 R = 139.58/138.58 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f16(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) [I23 <= I21] 139.58/138.58 f5(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, I203, I204, I205, I206, I207, I208) 139.58/138.58 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 We use the extended value criterion with the projection function NU: 139.58/138.58 NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x3 - 2 139.58/138.58 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x3 - 1 139.58/138.58 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x3 - 1 139.58/138.58 139.58/138.58 This gives the following inequalities: 139.58/138.58 ==> I38 - I39 - 1 >= I38 - I39 - 1 139.58/138.58 I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182 ==> I182 - I183 - 1 > I182 - I183 - 2 with I182 - I183 - 1 >= 0 139.58/138.58 ==> I211 - I212 - 2 >= I211 - (1 + I212) - 1 139.58/138.58 139.58/138.58 We remove all the strictly oriented dependency pairs. 139.58/138.58 139.58/138.58 DP problem for innermost termination. 139.58/138.58 P = 139.58/138.58 f2#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4#(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f1#(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2#(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 R = 139.58/138.58 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f16(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) [I23 <= I21] 139.58/138.58 f5(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, I203, I204, I205, I206, I207, I208) 139.58/138.58 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 The dependency graph for this problem is: 139.58/138.58 4 -> 139.58/138.58 22 -> 4 139.58/138.58 Where: 139.58/138.58 4) f2#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4#(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 22) f1#(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2#(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 We have the following SCCs. 139.58/138.58 139.58/138.58 139.58/138.58 DP problem for innermost termination. 139.58/138.58 P = 139.58/138.58 f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10#(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f10#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7#(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6#(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9#(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6#(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7#(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 R = 139.58/138.58 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f16(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) [I23 <= I21] 139.58/138.58 f5(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, I203, I204, I205, I206, I207, I208) 139.58/138.58 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 We use the extended value criterion with the projection function NU: 139.58/138.58 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 139.58/138.58 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 1 139.58/138.58 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 1 139.58/138.58 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 139.58/138.58 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 139.58/138.58 139.58/138.58 This gives the following inequalities: 139.58/138.58 ==> -I48 + I50 - 2 >= -I48 + I50 - 2 139.58/138.58 ==> -I57 + I59 - 1 >= -I57 + I59 - 1 139.58/138.58 1 + I138 <= I140 ==> -I138 + I140 - 1 > -I138 + I140 - 2 with -I138 + I140 - 1 >= 0 139.58/138.58 rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155 ==> -I156 + I158 - 2 >= -I156 + I158 - 2 139.58/138.58 I164 <= I166 ==> -I165 + I167 - 2 >= -(1 + I165) + I167 - 1 139.58/138.58 ==> -I174 + I176 - 2 >= -I174 + I176 - 2 139.58/138.58 139.58/138.58 We remove all the strictly oriented dependency pairs. 139.58/138.58 139.58/138.58 DP problem for innermost termination. 139.58/138.58 P = 139.58/138.58 f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10#(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6#(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9#(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6#(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7#(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 R = 139.58/138.58 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f16(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) [I23 <= I21] 139.58/138.58 f5(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, I203, I204, I205, I206, I207, I208) 139.58/138.58 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 The dependency graph for this problem is: 139.58/138.58 5 -> 17, 18 139.58/138.58 6 -> 139.58/138.58 17 -> 19 139.58/138.58 18 -> 6 139.58/138.58 19 -> 5 139.58/138.58 Where: 139.58/138.58 5) f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 6) f9#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10#(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 17) f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6#(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 18) f8#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9#(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 19) f6#(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7#(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 139.58/138.58 We have the following SCCs. 139.58/138.58 { 5, 17, 19 } 139.58/138.58 139.58/138.58 DP problem for innermost termination. 139.58/138.58 P = 139.58/138.58 f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f8#(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6#(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f6#(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7#(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 R = 139.58/138.58 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f16(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) [I23 <= I21] 139.58/138.58 f5(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, I203, I204, I205, I206, I207, I208) 139.58/138.58 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 We use the extended value criterion with the projection function NU: 139.58/138.58 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x4 - 2 139.58/138.58 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x4 - 1 139.58/138.58 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x2 - x4 - 1 139.58/138.58 139.58/138.58 This gives the following inequalities: 139.58/138.58 ==> I47 - I49 - 1 >= I47 - I49 - 1 139.58/138.58 rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155 ==> I155 - I157 - 1 > I155 - I157 - 2 with I155 - I157 - 1 >= 0 139.58/138.58 ==> I173 - I175 - 2 >= I173 - (1 + I175) - 1 139.58/138.58 139.58/138.58 We remove all the strictly oriented dependency pairs. 139.58/138.58 139.58/138.58 DP problem for innermost termination. 139.58/138.58 P = 139.58/138.58 f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f6#(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7#(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 R = 139.58/138.58 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f16(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) [I23 <= I21] 139.58/138.58 f5(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, I203, I204, I205, I206, I207, I208) 139.58/138.58 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 The dependency graph for this problem is: 139.58/138.58 5 -> 139.58/138.58 19 -> 5 139.58/138.58 Where: 139.58/138.58 5) f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8#(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 19) f6#(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7#(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 139.58/138.58 We have the following SCCs. 139.58/138.58 139.58/138.58 139.58/138.58 DP problem for innermost termination. 139.58/138.58 P = 139.58/138.58 f13#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15#(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14#(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f14#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12#(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11#(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14#(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11#(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13#(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12#(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 R = 139.58/138.58 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f16(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) [I23 <= I21] 139.58/138.58 f5(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, I203, I204, I205, I206, I207, I208) 139.58/138.58 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 We use the extended value criterion with the projection function NU: 139.58/138.58 NU[f11#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 139.58/138.58 NU[f12#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 139.58/138.58 NU[f14#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 2 139.58/138.58 NU[f15#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 1 139.58/138.58 NU[f13#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x3 + x5 - 1 139.58/138.58 139.58/138.58 This gives the following inequalities: 139.58/138.58 ==> -I66 + I68 - 1 >= -I66 + I68 - 1 139.58/138.58 1 + I75 <= I77 ==> -I75 + I77 - 1 > -I75 + I77 - 2 with -I75 + I77 - 1 >= 0 139.58/138.58 I96 <= I93 /\ I93 <= I96 ==> -I93 + I95 - 2 >= -I93 + I95 - 2 139.58/138.58 1 + I102 <= I105 ==> -I102 + I104 - 2 >= -I102 + I104 - 2 139.58/138.58 1 + I114 <= I111 ==> -I111 + I113 - 2 >= -I111 + I113 - 2 139.58/138.58 ==> -I120 + I122 - 2 >= -(1 + I120) + I122 - 1 139.58/138.58 ==> -I129 + I131 - 2 >= -I129 + I131 - 2 139.58/138.58 139.58/138.58 We remove all the strictly oriented dependency pairs. 139.58/138.58 139.58/138.58 DP problem for innermost termination. 139.58/138.58 P = 139.58/138.58 f13#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15#(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f14#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12#(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11#(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14#(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11#(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13#(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12#(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 R = 139.58/138.58 f18(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f17(x1, x2, x3, x4, x5, x6, x7, x8, x9) 139.58/138.58 f17(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f13(I0, I1, I0, 0, I4, I1, 0, I7, I8) 139.58/138.58 f16(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f5(I9, I10, I11, 1 + I12, I13, I14, I15, I16, I17) [1 + I12 <= I14] 139.58/138.58 f16(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f3(I18, I19, I20, I21, I22, I23, I24, I25, I26) [I23 <= I21] 139.58/138.58 f5(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f16(I27, I28, I29, I30, I31, I32, I33, I34, I35) 139.58/138.58 f2(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f4(I36, I37, I38, I39, I40, I41, I42, I43, I44) 139.58/138.58 f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f8(I45, I46, I47, I48, I49, I50, I51, I52, I53) 139.58/138.58 f9(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f10(I54, I55, I56, I57, I58, I59, I60, I61, I62) 139.58/138.58 f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 f15(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f14(I72, I73, I74, I75, I76, I77, I78, I79, I80) [1 + I75 <= I77] 139.58/138.58 f15(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, I83, 0, I85, I86, I87, I88, I89) [I86 <= I84] 139.58/138.58 f14(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 f14(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 f14(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 f12(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 f11(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 f10(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f7(I135, I136, I137, I138, 0, I140, I141, I142, I143) [1 + I138 <= I140] 139.58/138.58 f10(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f2(I144, I145, I146, 0, I148, I149, I150, I151, I152) [I149 <= I147] 139.58/138.58 f8(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f6(I153, I154, I155, I156, I157, I158, I159, rnd8, rnd9) [rnd9 = rnd9 /\ rnd8 = rnd8 /\ 1 + I157 <= I155] 139.58/138.58 f8(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f9(I162, I163, I164, 1 + I165, I166, I167, I168, I169, I170) [I164 <= I166] 139.58/138.58 f6(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f7(I171, I172, I173, I174, 1 + I175, I176, I177, I178, I179) 139.58/138.58 f4(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f1(I180, I181, I182, I183, I184, I185, I186, I189, I190) [I190 = I190 /\ I189 = I189 /\ 1 + I183 <= I182] 139.58/138.58 f4(I191, I192, I193, I194, I195, I196, I197, I198, I199) -> f5(I191, I192, I193, 0, I195, I196, I197, I198, I199) [I193 <= I194] 139.58/138.58 f1(I200, I201, I202, I203, I204, I205, I206, I207, I208) -> f3(I200, I201, I202, I203, I204, I205, I206, I207, I208) 139.58/138.58 f1(I209, I210, I211, I212, I213, I214, I215, I216, I217) -> f2(I209, I210, I211, 1 + I212, I213, I214, I215, I216, I217) 139.58/138.58 139.58/138.58 The dependency graph for this problem is: 139.58/138.58 7 -> 139.58/138.58 10 -> 13 139.58/138.58 11 -> 14 139.58/138.58 12 -> 14 139.58/138.58 13 -> 7 139.58/138.58 14 -> 13 139.58/138.58 Where: 139.58/138.58 7) f13#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f15#(I63, I64, I65, I66, I67, I68, I69, I70, I71) 139.58/138.58 10) f14#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f12#(I90, I91, I92, I93, I94, I95, I96, I97, I98) [I96 <= I93 /\ I93 <= I96] 139.58/138.58 11) f14#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f11#(I99, I100, I101, I102, I103, I104, I105, I106, I107) [1 + I102 <= I105] 139.58/138.58 12) f14#(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f11#(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I114 <= I111] 139.58/138.58 13) f12#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f13#(I117, I118, I119, 1 + I120, I121, I122, I123, I124, I125) 139.58/138.58 14) f11#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f12#(I126, I127, I128, I129, I130, I131, I132, I133, I134) 139.58/138.58 139.58/138.58 We have the following SCCs. 139.58/138.58 139.58/141.55 EOF