104.04/102.74 YES 104.04/102.74 104.04/102.74 DP problem for innermost termination. 104.04/102.74 P = 104.04/102.74 f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 f17#(I0, I1, I2, I3, I4, I5, I6) -> f6#(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f5#(I14, I15, I16, I17, I18, I19, I20) -> f8#(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f7#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f7#(I28, I29, I30, I31, I32, I33, I34) -> f9#(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 f16#(I35, I36, I37, I38, I39, I40, I41) -> f15#(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15#(I56, I57, I58, I59, I60, I61, I62) -> f6#(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f12#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10#(I77, I78, I79, I80, I81, I82, I83) -> f12#(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f10#(I84, I85, I86, I87, I88, I89, I90) -> f5#(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 f13#(I91, I92, I93, I94, I95, I96, I97) -> f11#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13#(I98, I99, I100, I101, I102, I103, I104) -> f9#(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 f8#(I119, I120, I121, I122, I123, I124, I125) -> f4#(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 f8#(I128, I129, I130, I131, I132, I133, I134) -> f3#(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.74 f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 R = 104.04/102.74 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.74 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.74 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.74 104.04/102.74 The dependency graph for this problem is: 104.04/102.74 0 -> 1 104.04/102.74 1 -> 20 104.04/102.74 2 -> 22 104.04/102.74 3 -> 18, 19 104.04/102.74 4 -> 6, 7, 8 104.04/102.74 5 -> 17 104.04/102.74 6 -> 9 104.04/102.74 7 -> 10 104.04/102.74 8 -> 10 104.04/102.74 9 -> 20 104.04/102.74 10 -> 9 104.04/102.74 11 -> 14, 15 104.04/102.74 12 -> 11 104.04/102.74 13 -> 3 104.04/102.74 14 -> 16 104.04/102.74 15 -> 17 104.04/102.74 16 -> 11 104.04/102.74 17 -> 12, 13 104.04/102.74 18 -> 21 104.04/102.74 19 -> 2 104.04/102.74 20 -> 4, 5 104.04/102.74 21 -> 3 104.04/102.74 22 -> 2 104.04/102.74 Where: 104.04/102.74 0) f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 1) f17#(I0, I1, I2, I3, I4, I5, I6) -> f6#(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f8#(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 4) f7#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 5) f7#(I28, I29, I30, I31, I32, I33, I34) -> f9#(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 6) f16#(I35, I36, I37, I38, I39, I40, I41) -> f15#(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 8) f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 9) f15#(I56, I57, I58, I59, I60, I61, I62) -> f6#(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 10) f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 11) f12#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 12) f10#(I77, I78, I79, I80, I81, I82, I83) -> f12#(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 13) f10#(I84, I85, I86, I87, I88, I89, I90) -> f5#(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f11#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 15) f13#(I98, I99, I100, I101, I102, I103, I104) -> f9#(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 18) f8#(I119, I120, I121, I122, I123, I124, I125) -> f4#(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 19) f8#(I128, I129, I130, I131, I132, I133, I134) -> f3#(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.74 20) f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 22) f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 104.04/102.74 We have the following SCCs. 104.04/102.74 { 4, 6, 7, 8, 9, 10, 20 } 104.04/102.74 { 11, 12, 14, 15, 16, 17 } 104.04/102.74 { 3, 18, 21 } 104.04/102.74 { 2, 22 } 104.04/102.74 104.04/102.74 DP problem for innermost termination. 104.04/102.74 P = 104.04/102.74 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 R = 104.04/102.74 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.74 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.74 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.74 104.04/102.74 We use the reverse value criterion with the projection function NU: 104.04/102.74 NU[f1#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 104.04/102.74 NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 104.04/102.74 104.04/102.74 This gives the following inequalities: 104.04/102.74 ==> I10 + -1 * (1 + I8) >= I10 + -1 * (1 + I8) 104.04/102.74 1 + I157 <= I159 ==> I159 + -1 * (1 + I157) > I159 + -1 * (1 + (1 + I157)) with I159 + -1 * (1 + I157) >= 0 104.04/102.74 104.04/102.74 We remove all the strictly oriented dependency pairs. 104.04/102.74 104.04/102.74 DP problem for innermost termination. 104.04/102.74 P = 104.04/102.74 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 R = 104.04/102.74 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.74 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.74 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.74 104.04/102.74 The dependency graph for this problem is: 104.04/102.74 2 -> 104.04/102.74 Where: 104.04/102.74 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 104.04/102.74 We have the following SCCs. 104.04/102.74 104.04/102.74 104.04/102.74 DP problem for innermost termination. 104.04/102.74 P = 104.04/102.74 f5#(I14, I15, I16, I17, I18, I19, I20) -> f8#(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f8#(I119, I120, I121, I122, I123, I124, I125) -> f4#(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 R = 104.04/102.74 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.74 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.74 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.74 104.04/102.74 We use the extended value criterion with the projection function NU: 104.04/102.74 NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 104.04/102.74 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 104.04/102.74 NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 104.04/102.74 104.04/102.74 This gives the following inequalities: 104.04/102.74 ==> I14 - I15 - 1 >= I14 - I15 - 1 104.04/102.74 I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119 ==> I119 - I120 - 1 > I119 - I120 - 2 with I119 - I120 - 1 >= 0 104.04/102.74 ==> I149 - I150 - 2 >= I149 - (1 + I150) - 1 104.04/102.74 104.04/102.74 We remove all the strictly oriented dependency pairs. 104.04/102.74 104.04/102.74 DP problem for innermost termination. 104.04/102.74 P = 104.04/102.74 f5#(I14, I15, I16, I17, I18, I19, I20) -> f8#(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 R = 104.04/102.74 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.74 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.74 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.74 104.04/102.74 The dependency graph for this problem is: 104.04/102.74 3 -> 104.04/102.74 21 -> 3 104.04/102.74 Where: 104.04/102.74 3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f8#(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 104.04/102.74 We have the following SCCs. 104.04/102.74 104.04/102.74 104.04/102.74 DP problem for innermost termination. 104.04/102.74 P = 104.04/102.74 f12#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10#(I77, I78, I79, I80, I81, I82, I83) -> f12#(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f13#(I91, I92, I93, I94, I95, I96, I97) -> f11#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13#(I98, I99, I100, I101, I102, I103, I104) -> f9#(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 R = 104.04/102.74 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.74 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.74 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.74 104.04/102.74 We use the extended value criterion with the projection function NU: 104.04/102.74 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 104.04/102.74 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.04/102.74 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 104.04/102.74 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.04/102.74 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.04/102.74 104.04/102.74 This gives the following inequalities: 104.04/102.74 ==> -I71 + I73 - 2 >= -I71 + I73 - 2 104.04/102.74 1 + I78 <= I80 ==> -I78 + I80 - 1 > -I78 + I80 - 2 with -I78 + I80 - 1 >= 0 104.04/102.74 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91 ==> -I92 + I94 - 2 >= -I92 + I94 - 2 104.04/102.74 I98 <= I100 ==> -I99 + I101 - 2 >= -(1 + I99) + I101 - 1 104.04/102.74 ==> -I106 + I108 - 2 >= -I106 + I108 - 2 104.04/102.74 ==> -I113 + I115 - 1 >= -I113 + I115 - 1 104.04/102.74 104.04/102.74 We remove all the strictly oriented dependency pairs. 104.04/102.74 104.04/102.74 DP problem for innermost termination. 104.04/102.74 P = 104.04/102.74 f12#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f13#(I91, I92, I93, I94, I95, I96, I97) -> f11#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13#(I98, I99, I100, I101, I102, I103, I104) -> f9#(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 R = 104.04/102.74 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.74 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.74 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.74 104.04/102.74 The dependency graph for this problem is: 104.04/102.74 11 -> 14, 15 104.04/102.74 14 -> 16 104.04/102.74 15 -> 17 104.04/102.74 16 -> 11 104.04/102.74 17 -> 104.04/102.74 Where: 104.04/102.74 11) f12#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f11#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 15) f13#(I98, I99, I100, I101, I102, I103, I104) -> f9#(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 104.04/102.74 We have the following SCCs. 104.04/102.74 { 11, 14, 16 } 104.04/102.74 104.04/102.74 DP problem for innermost termination. 104.04/102.74 P = 104.04/102.74 f12#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f13#(I91, I92, I93, I94, I95, I96, I97) -> f11#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 R = 104.04/102.74 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.74 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.74 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.74 104.04/102.74 We use the extended value criterion with the projection function NU: 104.04/102.74 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2 104.04/102.74 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 104.04/102.74 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 104.04/102.74 104.04/102.74 This gives the following inequalities: 104.04/102.74 ==> I70 - I72 - 1 >= I70 - I72 - 1 104.04/102.74 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91 ==> I91 - I93 - 1 > I91 - I93 - 2 with I91 - I93 - 1 >= 0 104.04/102.74 ==> I105 - I107 - 2 >= I105 - (1 + I107) - 1 104.04/102.74 104.04/102.74 We remove all the strictly oriented dependency pairs. 104.04/102.74 104.04/102.74 DP problem for innermost termination. 104.04/102.74 P = 104.04/102.74 f12#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 R = 104.04/102.74 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.74 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.74 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.74 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.74 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.74 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.74 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.74 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.74 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.74 104.04/102.74 The dependency graph for this problem is: 104.04/102.74 11 -> 104.04/102.74 16 -> 11 104.04/102.74 Where: 104.04/102.74 11) f12#(I70, I71, I72, I73, I74, I75, I76) -> f13#(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.74 104.04/102.74 We have the following SCCs. 104.04/102.74 104.04/102.74 104.04/102.74 DP problem for innermost termination. 104.04/102.74 P = 104.04/102.74 f7#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f16#(I35, I36, I37, I38, I39, I40, I41) -> f15#(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15#(I56, I57, I58, I59, I60, I61, I62) -> f6#(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 104.04/102.74 R = 104.04/102.74 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.74 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.74 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.74 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.74 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.74 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.74 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.74 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.74 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.74 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.74 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.74 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.74 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.74 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.74 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.75 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.75 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.75 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.75 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.75 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.75 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.75 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.75 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.75 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.75 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.75 104.04/102.75 We use the extended value criterion with the projection function NU: 104.04/102.75 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 104.04/102.75 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 104.04/102.75 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 104.04/102.75 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 104.04/102.75 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 104.04/102.75 104.04/102.75 This gives the following inequalities: 104.04/102.75 1 + I22 <= I24 ==> -I22 + I25 >= -I22 + I25 104.04/102.75 I39 <= I36 /\ I36 <= I39 ==> -I36 + I39 > -I36 + I39 - 1 with -I36 + I39 >= 0 104.04/102.75 1 + I43 <= I46 ==> -I43 + I46 > -I43 + I46 - 1 with -I43 + I46 >= 0 104.04/102.75 1 + I53 <= I50 ==> -I50 + I53 >= -I50 + I53 - 1 104.04/102.75 ==> -I57 + I60 - 1 >= -(1 + I57) + I60 104.04/102.75 ==> -I64 + I67 - 1 >= -I64 + I67 - 1 104.04/102.75 ==> -I136 + I139 >= -I136 + I139 104.04/102.75 104.04/102.75 We remove all the strictly oriented dependency pairs. 104.04/102.75 104.04/102.75 DP problem for innermost termination. 104.04/102.75 P = 104.04/102.75 f7#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.75 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.75 f15#(I56, I57, I58, I59, I60, I61, I62) -> f6#(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.75 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 104.04/102.75 f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 104.04/102.75 R = 104.04/102.75 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.75 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.75 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.75 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.75 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.75 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.75 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.75 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.75 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.75 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.75 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.75 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.75 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.75 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.75 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.75 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.75 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.75 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.75 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.75 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.75 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.75 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.75 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.75 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.75 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.75 104.04/102.75 We use the extended value criterion with the projection function NU: 104.04/102.75 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 104.04/102.75 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.04/102.75 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.04/102.75 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.04/102.75 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 104.04/102.75 104.04/102.75 This gives the following inequalities: 104.04/102.75 1 + I22 <= I24 ==> -I22 + I24 - 1 > -I22 + I24 - 2 with -I22 + I24 - 1 >= 0 104.04/102.75 1 + I53 <= I50 ==> -I50 + I52 - 2 >= -I50 + I52 - 2 104.04/102.75 ==> -I57 + I59 - 2 >= -(1 + I57) + I59 - 1 104.04/102.75 ==> -I64 + I66 - 2 >= -I64 + I66 - 2 104.04/102.75 ==> -I136 + I138 - 1 >= -I136 + I138 - 1 104.04/102.75 104.04/102.75 We remove all the strictly oriented dependency pairs. 104.04/102.75 104.04/102.75 DP problem for innermost termination. 104.04/102.75 P = 104.04/102.75 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.75 f15#(I56, I57, I58, I59, I60, I61, I62) -> f6#(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.75 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 104.04/102.75 f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 104.04/102.75 R = 104.04/102.75 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.04/102.75 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(8, 0, I2, 5, 0, I5, I6) 104.04/102.75 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.04/102.75 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 104.04/102.75 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 104.04/102.75 f7(I28, I29, I30, I31, I32, I33, I34) -> f9(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 104.04/102.75 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 104.04/102.75 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 104.04/102.75 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.75 f15(I56, I57, I58, I59, I60, I61, I62) -> f6(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.75 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 104.04/102.75 f12(I70, I71, I72, I73, I74, I75, I76) -> f13(I70, I71, I72, I73, I74, I75, I76) 104.04/102.75 f10(I77, I78, I79, I80, I81, I82, I83) -> f12(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 104.04/102.75 f10(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 104.04/102.75 f13(I91, I92, I93, I94, I95, I96, I97) -> f11(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 104.04/102.75 f13(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 104.04/102.75 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 104.04/102.75 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.04/102.75 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 104.04/102.75 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 104.04/102.75 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 104.04/102.75 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.04/102.75 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.04/102.75 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.04/102.75 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.04/102.75 104.04/102.75 The dependency graph for this problem is: 104.04/102.75 8 -> 10 104.04/102.75 9 -> 20 104.04/102.75 10 -> 9 104.04/102.75 20 -> 104.04/102.75 Where: 104.04/102.75 8) f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 104.04/102.75 9) f15#(I56, I57, I58, I59, I60, I61, I62) -> f6#(I56, 1 + I57, I58, I59, I60, I61, I62) 104.04/102.75 10) f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 104.04/102.75 20) f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 104.04/102.75 104.04/102.75 We have the following SCCs. 104.04/102.75 104.04/105.71 EOF