105.35/104.23 YES 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17#(I0, I1, I2, I3, I4, I5, I6) -> f6#(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5#(I14, I15, I16, I17, I18, I19, I20) -> f8#(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7#(I28, I29, I30, I31, I32, I33, I34) -> f11#(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16#(I35, I36, I37, I38, I39, I40, I41) -> f15#(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15#(I63, I64, I65, I66, I67, I68, I69) -> f6#(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12#(I84, I85, I86, I87, I88, I89, I90) -> f5#(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13#(I91, I92, I93, I94, I95, I96, I97) -> f9#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13#(I98, I99, I100, I101, I102, I103, I104) -> f11#(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8#(I119, I120, I121, I122, I123, I124, I125) -> f4#(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8#(I128, I129, I130, I131, I132, I133, I134) -> f3#(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 The dependency graph for this problem is: 105.35/104.23 0 -> 1 105.35/104.23 1 -> 20 105.35/104.23 2 -> 22 105.35/104.23 3 -> 18, 19 105.35/104.23 4 -> 6, 7, 8 105.35/104.23 5 -> 16 105.35/104.23 6 -> 10 105.35/104.23 7 -> 11 105.35/104.23 8 -> 11 105.35/104.23 9 -> 14, 15 105.35/104.23 10 -> 20 105.35/104.23 11 -> 10 105.35/104.23 12 -> 9 105.35/104.23 13 -> 3 105.35/104.23 14 -> 17 105.35/104.23 15 -> 16 105.35/104.23 16 -> 12, 13 105.35/104.23 17 -> 9 105.35/104.23 18 -> 21 105.35/104.23 19 -> 2 105.35/104.23 20 -> 4, 5 105.35/104.23 21 -> 3 105.35/104.23 22 -> 2 105.35/104.23 Where: 105.35/104.23 0) f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 1) f17#(I0, I1, I2, I3, I4, I5, I6) -> f6#(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f8#(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 4) f7#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 5) f7#(I28, I29, I30, I31, I32, I33, I34) -> f11#(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 6) f16#(I35, I36, I37, I38, I39, I40, I41) -> f15#(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 8) f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 9) f10#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 10) f15#(I63, I64, I65, I66, I67, I68, I69) -> f6#(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 11) f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 12) f12#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 13) f12#(I84, I85, I86, I87, I88, I89, I90) -> f5#(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f9#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 15) f13#(I98, I99, I100, I101, I102, I103, I104) -> f11#(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 18) f8#(I119, I120, I121, I122, I123, I124, I125) -> f4#(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 19) f8#(I128, I129, I130, I131, I132, I133, I134) -> f3#(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 20) f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 22) f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 105.35/104.23 We have the following SCCs. 105.35/104.23 { 4, 6, 7, 8, 10, 11, 20 } 105.35/104.23 { 9, 12, 14, 15, 16, 17 } 105.35/104.23 { 3, 18, 21 } 105.35/104.23 { 2, 22 } 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 We use the reverse value criterion with the projection function NU: 105.35/104.23 NU[f1#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 105.35/104.23 NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 105.35/104.23 105.35/104.23 This gives the following inequalities: 105.35/104.23 ==> I10 + -1 * (1 + I8) >= I10 + -1 * (1 + I8) 105.35/104.23 1 + I157 <= I159 ==> I159 + -1 * (1 + I157) > I159 + -1 * (1 + (1 + I157)) with I159 + -1 * (1 + I157) >= 0 105.35/104.23 105.35/104.23 We remove all the strictly oriented dependency pairs. 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 The dependency graph for this problem is: 105.35/104.23 2 -> 105.35/104.23 Where: 105.35/104.23 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 105.35/104.23 We have the following SCCs. 105.35/104.23 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f5#(I14, I15, I16, I17, I18, I19, I20) -> f8#(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f8#(I119, I120, I121, I122, I123, I124, I125) -> f4#(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 We use the extended value criterion with the projection function NU: 105.35/104.23 NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 105.35/104.23 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 105.35/104.23 NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 105.35/104.23 105.35/104.23 This gives the following inequalities: 105.35/104.23 ==> I14 - I15 - 1 >= I14 - I15 - 1 105.35/104.23 I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119 ==> I119 - I120 - 1 > I119 - I120 - 2 with I119 - I120 - 1 >= 0 105.35/104.23 ==> I149 - I150 - 2 >= I149 - (1 + I150) - 1 105.35/104.23 105.35/104.23 We remove all the strictly oriented dependency pairs. 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f5#(I14, I15, I16, I17, I18, I19, I20) -> f8#(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 The dependency graph for this problem is: 105.35/104.23 3 -> 105.35/104.23 21 -> 3 105.35/104.23 Where: 105.35/104.23 3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f8#(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 105.35/104.23 We have the following SCCs. 105.35/104.23 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f10#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f12#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f13#(I91, I92, I93, I94, I95, I96, I97) -> f9#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13#(I98, I99, I100, I101, I102, I103, I104) -> f11#(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 We use the extended value criterion with the projection function NU: 105.35/104.23 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 105.35/104.23 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.35/104.23 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 105.35/104.23 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.35/104.23 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.35/104.23 105.35/104.23 This gives the following inequalities: 105.35/104.23 ==> -I57 + I59 - 2 >= -I57 + I59 - 2 105.35/104.23 1 + I78 <= I80 ==> -I78 + I80 - 1 > -I78 + I80 - 2 with -I78 + I80 - 1 >= 0 105.35/104.23 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91 ==> -I92 + I94 - 2 >= -I92 + I94 - 2 105.35/104.23 I98 <= I100 ==> -I99 + I101 - 2 >= -(1 + I99) + I101 - 1 105.35/104.23 ==> -I106 + I108 - 1 >= -I106 + I108 - 1 105.35/104.23 ==> -I113 + I115 - 2 >= -I113 + I115 - 2 105.35/104.23 105.35/104.23 We remove all the strictly oriented dependency pairs. 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f10#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f13#(I91, I92, I93, I94, I95, I96, I97) -> f9#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13#(I98, I99, I100, I101, I102, I103, I104) -> f11#(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 The dependency graph for this problem is: 105.35/104.23 9 -> 14, 15 105.35/104.23 14 -> 17 105.35/104.23 15 -> 16 105.35/104.23 16 -> 105.35/104.23 17 -> 9 105.35/104.23 Where: 105.35/104.23 9) f10#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f9#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 15) f13#(I98, I99, I100, I101, I102, I103, I104) -> f11#(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 105.35/104.23 We have the following SCCs. 105.35/104.23 { 9, 14, 17 } 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f10#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f13#(I91, I92, I93, I94, I95, I96, I97) -> f9#(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 We use the extended value criterion with the projection function NU: 105.35/104.23 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2 105.35/104.23 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 105.35/104.23 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 105.35/104.23 105.35/104.23 This gives the following inequalities: 105.35/104.23 ==> I56 - I58 - 1 >= I56 - I58 - 1 105.35/104.23 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91 ==> I91 - I93 - 1 > I91 - I93 - 2 with I91 - I93 - 1 >= 0 105.35/104.23 ==> I112 - I114 - 2 >= I112 - (1 + I114) - 1 105.35/104.23 105.35/104.23 We remove all the strictly oriented dependency pairs. 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f10#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 The dependency graph for this problem is: 105.35/104.23 9 -> 105.35/104.23 17 -> 9 105.35/104.23 Where: 105.35/104.23 9) f10#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 105.35/104.23 We have the following SCCs. 105.35/104.23 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f7#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f16#(I35, I36, I37, I38, I39, I40, I41) -> f15#(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f15#(I63, I64, I65, I66, I67, I68, I69) -> f6#(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 We use the extended value criterion with the projection function NU: 105.35/104.23 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 105.35/104.23 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 105.35/104.23 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 105.35/104.23 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 105.35/104.23 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 105.35/104.23 105.35/104.23 This gives the following inequalities: 105.35/104.23 1 + I22 <= I24 ==> -I22 + I25 >= -I22 + I25 105.35/104.23 I39 <= I36 /\ I36 <= I39 ==> -I36 + I39 > -I36 + I39 - 1 with -I36 + I39 >= 0 105.35/104.23 1 + I43 <= I46 ==> -I43 + I46 > -I43 + I46 - 1 with -I43 + I46 >= 0 105.35/104.23 1 + I53 <= I50 ==> -I50 + I53 >= -I50 + I53 - 1 105.35/104.23 ==> -I64 + I67 - 1 >= -(1 + I64) + I67 105.35/104.23 ==> -I71 + I74 - 1 >= -I71 + I74 - 1 105.35/104.23 ==> -I136 + I139 >= -I136 + I139 105.35/104.23 105.35/104.23 We remove all the strictly oriented dependency pairs. 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f7#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f15#(I63, I64, I65, I66, I67, I68, I69) -> f6#(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 We use the extended value criterion with the projection function NU: 105.35/104.23 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 105.35/104.23 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.35/104.23 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.35/104.23 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.35/104.23 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 105.35/104.23 105.35/104.23 This gives the following inequalities: 105.35/104.23 1 + I22 <= I24 ==> -I22 + I24 - 1 > -I22 + I24 - 2 with -I22 + I24 - 1 >= 0 105.35/104.23 1 + I53 <= I50 ==> -I50 + I52 - 2 >= -I50 + I52 - 2 105.35/104.23 ==> -I64 + I66 - 2 >= -(1 + I64) + I66 - 1 105.35/104.23 ==> -I71 + I73 - 2 >= -I71 + I73 - 2 105.35/104.23 ==> -I136 + I138 - 1 >= -I136 + I138 - 1 105.35/104.23 105.35/104.23 We remove all the strictly oriented dependency pairs. 105.35/104.23 105.35/104.23 DP problem for innermost termination. 105.35/104.23 P = 105.35/104.23 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f15#(I63, I64, I65, I66, I67, I68, I69) -> f6#(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 R = 105.35/104.23 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.35/104.23 f17(I0, I1, I2, I3, I4, I5, I6) -> f6(9, 0, I2, 5, 0, I5, I6) 105.35/104.23 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.35/104.23 f5(I14, I15, I16, I17, I18, I19, I20) -> f8(I14, I15, I16, I17, I18, I19, I20) 105.35/104.23 f7(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) [1 + I22 <= I24] 105.35/104.23 f7(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, 0, I30, I31, I32, I33, I34) [I31 <= I29] 105.35/104.23 f16(I35, I36, I37, I38, I39, I40, I41) -> f15(I35, I36, I37, I38, I39, I40, I41) [I39 <= I36 /\ I36 <= I39] 105.35/104.23 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I46] 105.35/104.23 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 f10(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) 105.35/104.23 f15(I63, I64, I65, I66, I67, I68, I69) -> f6(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 f12(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, I78, 0, I80, I81, I82, I83) [1 + I78 <= I80] 105.35/104.23 f12(I84, I85, I86, I87, I88, I89, I90) -> f5(I84, 0, I86, I87, I88, I89, I90) [I87 <= I85] 105.35/104.23 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, I92, I93, I94, I95, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I93 <= I91] 105.35/104.23 f13(I98, I99, I100, I101, I102, I103, I104) -> f11(I98, 1 + I99, I100, I101, I102, I103, I104) [I98 <= I100] 105.35/104.23 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, I107, I108, I109, I110, I111) 105.35/104.23 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 105.35/104.23 f8(I119, I120, I121, I122, I123, I124, I125) -> f4(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.35/104.23 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.35/104.23 f6(I135, I136, I137, I138, I139, I140, I141) -> f7(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 105.35/104.23 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 105.35/104.23 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.35/104.23 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.35/104.23 105.35/104.23 The dependency graph for this problem is: 105.35/104.23 8 -> 11 105.35/104.23 10 -> 20 105.35/104.23 11 -> 10 105.35/104.23 20 -> 105.35/104.23 Where: 105.35/104.23 8) f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I53 <= I50] 105.35/104.23 10) f15#(I63, I64, I65, I66, I67, I68, I69) -> f6#(I63, 1 + I64, I65, I66, I67, I68, I69) 105.35/104.23 11) f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 105.35/104.23 20) f6#(I135, I136, I137, I138, I139, I140, I141) -> f7#(I135, I136, I137, I138, I139, I140, I141) 105.35/104.23 105.35/104.23 We have the following SCCs. 105.35/104.23 105.35/107.20 EOF