104.14/102.58 YES 104.14/102.58 104.14/102.58 DP problem for innermost termination. 104.14/102.58 P = 104.14/102.58 f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 104.14/102.58 f17#(I0, I1, I2, I3, I4, I5, I6) -> f9#(12, 0, I2, 5, 0, I5, I6) 104.14/102.58 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 104.14/102.58 f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 104.14/102.58 f8#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 104.14/102.58 f10#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.58 f10#(I35, I36, I37, I38, I39, I40, I41) -> f12#(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.58 f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.58 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.58 f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.58 f12#(I63, I64, I65, I66, I67, I68, I69) -> f13#(I63, I64, I65, I66, I67, I68, I69) 104.14/102.58 f15#(I70, I71, I72, I73, I74, I75, I76) -> f9#(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.58 f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 104.14/102.58 f13#(I84, I85, I86, I87, I88, I89, I90) -> f8#(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.58 f13#(I91, I92, I93, I94, I95, I96, I97) -> f5#(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.58 f11#(I98, I99, I100, I101, I102, I103, I104) -> f7#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.58 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.58 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 104.14/102.58 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.58 f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.58 f6#(I135, I136, I137, I138, I139, I140, I141) -> f3#(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.58 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.58 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.58 R = 104.14/102.58 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.58 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.58 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.58 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.58 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.58 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.58 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.58 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.58 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.58 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.58 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.58 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.58 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.58 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.58 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.58 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.58 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.58 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.58 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.58 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.58 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.58 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.58 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.58 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.58 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.58 104.14/102.58 The dependency graph for this problem is: 104.14/102.58 0 -> 1 104.14/102.58 1 -> 17 104.14/102.58 2 -> 22 104.14/102.58 3 -> 19, 20 104.14/102.58 4 -> 15, 16 104.14/102.58 5 -> 7, 8, 9 104.14/102.58 6 -> 10 104.14/102.58 7 -> 11 104.14/102.58 8 -> 12 104.14/102.58 9 -> 12 104.14/102.58 10 -> 13, 14 104.14/102.58 11 -> 17 104.14/102.58 12 -> 11 104.14/102.58 13 -> 4 104.14/102.58 14 -> 3 104.14/102.58 15 -> 18 104.14/102.58 16 -> 10 104.14/102.58 17 -> 5, 6 104.14/102.58 18 -> 4 104.14/102.58 19 -> 21 104.14/102.58 20 -> 2 104.14/102.58 21 -> 3 104.14/102.58 22 -> 2 104.14/102.58 Where: 104.14/102.58 0) f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 104.14/102.58 1) f17#(I0, I1, I2, I3, I4, I5, I6) -> f9#(12, 0, I2, 5, 0, I5, I6) 104.14/102.58 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 104.14/102.58 3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 104.14/102.58 4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 104.14/102.58 5) f10#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.58 6) f10#(I35, I36, I37, I38, I39, I40, I41) -> f12#(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.58 7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.58 8) f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.58 9) f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.58 10) f12#(I63, I64, I65, I66, I67, I68, I69) -> f13#(I63, I64, I65, I66, I67, I68, I69) 104.14/102.58 11) f15#(I70, I71, I72, I73, I74, I75, I76) -> f9#(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.58 12) f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 104.14/102.58 13) f13#(I84, I85, I86, I87, I88, I89, I90) -> f8#(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.58 14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f5#(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.58 15) f11#(I98, I99, I100, I101, I102, I103, I104) -> f7#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.58 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.58 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 104.14/102.58 18) f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.58 19) f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.58 20) f6#(I135, I136, I137, I138, I139, I140, I141) -> f3#(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.58 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.58 22) f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.58 104.14/102.58 We have the following SCCs. 104.14/102.58 { 5, 7, 8, 9, 11, 12, 17 } 104.14/102.58 { 4, 10, 13, 15, 16, 18 } 104.14/102.58 { 3, 19, 21 } 104.14/102.58 { 2, 22 } 104.14/102.58 104.14/102.58 DP problem for innermost termination. 104.14/102.58 P = 104.14/102.58 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 104.14/102.58 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.58 R = 104.14/102.58 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.58 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.58 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.58 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.58 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.58 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.58 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.58 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.58 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.58 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.58 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.58 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.58 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.58 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.58 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.58 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.58 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.58 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.58 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.58 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.58 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.58 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.58 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.58 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.58 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.58 104.14/102.58 We use the reverse value criterion with the projection function NU: 104.14/102.58 NU[f1#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 104.14/102.58 NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 104.14/102.58 104.14/102.58 This gives the following inequalities: 104.14/102.58 ==> I10 + -1 * (1 + I8) >= I10 + -1 * (1 + I8) 104.14/102.58 1 + I157 <= I159 ==> I159 + -1 * (1 + I157) > I159 + -1 * (1 + (1 + I157)) with I159 + -1 * (1 + I157) >= 0 104.14/102.58 104.14/102.58 We remove all the strictly oriented dependency pairs. 104.14/102.58 104.14/102.58 DP problem for innermost termination. 104.14/102.58 P = 104.14/102.58 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 104.14/102.58 R = 104.14/102.58 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.58 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.58 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.58 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.58 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.58 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.58 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.58 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.58 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.58 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.58 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.58 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.58 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.58 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.58 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.58 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.58 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.58 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.58 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.58 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.58 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.58 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.58 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.58 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.58 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.58 104.14/102.58 The dependency graph for this problem is: 104.14/102.58 2 -> 104.14/102.58 Where: 104.14/102.58 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 104.14/102.58 104.14/102.58 We have the following SCCs. 104.14/102.58 104.14/102.58 104.14/102.58 DP problem for innermost termination. 104.14/102.58 P = 104.14/102.58 f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 104.14/102.58 f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.58 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.58 R = 104.14/102.58 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.58 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.58 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.58 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.58 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.58 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.58 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.58 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.58 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.58 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.58 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.58 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.58 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.58 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.58 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.58 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.58 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.58 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.58 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.58 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.58 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.58 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.58 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.58 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.58 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.58 104.14/102.58 We use the extended value criterion with the projection function NU: 104.14/102.58 NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 104.14/102.58 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 104.14/102.58 NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 104.14/102.58 104.14/102.58 This gives the following inequalities: 104.14/102.58 ==> I14 - I15 - 1 >= I14 - I15 - 1 104.14/102.58 I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126 ==> I126 - I127 - 1 > I126 - I127 - 2 with I126 - I127 - 1 >= 0 104.14/102.58 ==> I149 - I150 - 2 >= I149 - (1 + I150) - 1 104.14/102.58 104.14/102.58 We remove all the strictly oriented dependency pairs. 104.14/102.58 104.14/102.58 DP problem for innermost termination. 104.14/102.58 P = 104.14/102.58 f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 104.14/102.58 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.58 R = 104.14/102.58 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.58 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.58 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.58 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.58 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.58 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.58 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.58 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.58 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.58 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.58 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.58 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.58 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.58 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.58 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.58 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.58 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.58 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.58 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.58 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.58 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.58 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.58 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.58 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.58 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.58 104.14/102.58 The dependency graph for this problem is: 104.14/102.58 3 -> 104.14/102.58 21 -> 3 104.14/102.58 Where: 104.14/102.58 3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 104.14/102.58 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.58 104.14/102.58 We have the following SCCs. 104.14/102.58 104.14/102.58 104.14/102.58 DP problem for innermost termination. 104.14/102.58 P = 104.14/102.58 f8#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 104.14/102.58 f12#(I63, I64, I65, I66, I67, I68, I69) -> f13#(I63, I64, I65, I66, I67, I68, I69) 104.14/102.58 f13#(I84, I85, I86, I87, I88, I89, I90) -> f8#(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.58 f11#(I98, I99, I100, I101, I102, I103, I104) -> f7#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.58 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.58 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.58 R = 104.14/102.58 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.58 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.58 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.58 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.58 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.58 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.58 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.58 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.58 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.58 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.58 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.58 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.59 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.59 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.59 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.59 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.59 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.59 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.59 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.59 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.59 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.59 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.59 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.59 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.59 104.14/102.59 We use the extended value criterion with the projection function NU: 104.14/102.59 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.14/102.59 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 104.14/102.59 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 104.14/102.59 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.14/102.59 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.14/102.59 104.14/102.59 This gives the following inequalities: 104.14/102.59 ==> -I22 + I24 - 2 >= -I22 + I24 - 2 104.14/102.59 ==> -I64 + I66 - 1 >= -I64 + I66 - 1 104.14/102.59 1 + I85 <= I87 ==> -I85 + I87 - 1 > -I85 + I87 - 2 with -I85 + I87 - 1 >= 0 104.14/102.59 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98 ==> -I99 + I101 - 2 >= -I99 + I101 - 2 104.14/102.59 I105 <= I107 ==> -I106 + I108 - 2 >= -(1 + I106) + I108 - 1 104.14/102.59 ==> -I120 + I122 - 2 >= -I120 + I122 - 2 104.14/102.59 104.14/102.59 We remove all the strictly oriented dependency pairs. 104.14/102.59 104.14/102.59 DP problem for innermost termination. 104.14/102.59 P = 104.14/102.59 f8#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 104.14/102.59 f12#(I63, I64, I65, I66, I67, I68, I69) -> f13#(I63, I64, I65, I66, I67, I68, I69) 104.14/102.59 f11#(I98, I99, I100, I101, I102, I103, I104) -> f7#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.59 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.59 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 R = 104.14/102.59 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.59 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.59 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.59 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.59 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.59 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.59 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.59 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.59 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.59 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.59 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.59 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.59 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.59 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.59 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.59 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.59 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.59 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.59 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.59 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.59 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.59 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.59 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.59 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.59 104.14/102.59 The dependency graph for this problem is: 104.14/102.59 4 -> 15, 16 104.14/102.59 10 -> 104.14/102.59 15 -> 18 104.14/102.59 16 -> 10 104.14/102.59 18 -> 4 104.14/102.59 Where: 104.14/102.59 4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 104.14/102.59 10) f12#(I63, I64, I65, I66, I67, I68, I69) -> f13#(I63, I64, I65, I66, I67, I68, I69) 104.14/102.59 15) f11#(I98, I99, I100, I101, I102, I103, I104) -> f7#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.59 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.59 18) f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 104.14/102.59 We have the following SCCs. 104.14/102.59 { 4, 15, 18 } 104.14/102.59 104.14/102.59 DP problem for innermost termination. 104.14/102.59 P = 104.14/102.59 f8#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 104.14/102.59 f11#(I98, I99, I100, I101, I102, I103, I104) -> f7#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.59 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 R = 104.14/102.59 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.59 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.59 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.59 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.59 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.59 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.59 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.59 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.59 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.59 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.59 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.59 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.59 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.59 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.59 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.59 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.59 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.59 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.59 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.59 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.59 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.59 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.59 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.59 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.59 104.14/102.59 We use the extended value criterion with the projection function NU: 104.14/102.59 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2 104.14/102.59 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 104.14/102.59 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 104.14/102.59 104.14/102.59 This gives the following inequalities: 104.14/102.59 ==> I21 - I23 - 1 >= I21 - I23 - 1 104.14/102.59 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98 ==> I98 - I100 - 1 > I98 - I100 - 2 with I98 - I100 - 1 >= 0 104.14/102.59 ==> I119 - I121 - 2 >= I119 - (1 + I121) - 1 104.14/102.59 104.14/102.59 We remove all the strictly oriented dependency pairs. 104.14/102.59 104.14/102.59 DP problem for innermost termination. 104.14/102.59 P = 104.14/102.59 f8#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 104.14/102.59 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 R = 104.14/102.59 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.59 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.59 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.59 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.59 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.59 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.59 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.59 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.59 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.59 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.59 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.59 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.59 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.59 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.59 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.59 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.59 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.59 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.59 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.59 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.59 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.59 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.59 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.59 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.59 104.14/102.59 The dependency graph for this problem is: 104.14/102.59 4 -> 104.14/102.59 18 -> 4 104.14/102.59 Where: 104.14/102.59 4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 104.14/102.59 18) f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 104.14/102.59 We have the following SCCs. 104.14/102.59 104.14/102.59 104.14/102.59 DP problem for innermost termination. 104.14/102.59 P = 104.14/102.59 f10#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.59 f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.59 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.59 f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.59 f15#(I70, I71, I72, I73, I74, I75, I76) -> f9#(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.59 f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 104.14/102.59 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 104.14/102.59 R = 104.14/102.59 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.59 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.59 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.59 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.59 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.59 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.59 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.59 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.59 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.59 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.59 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.59 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.59 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.59 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.59 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.59 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.59 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.59 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.59 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.59 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.59 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.59 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.59 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.59 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.59 104.14/102.59 We use the extended value criterion with the projection function NU: 104.14/102.59 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 104.14/102.59 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 104.14/102.59 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 104.14/102.59 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 104.14/102.59 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 104.14/102.59 104.14/102.59 This gives the following inequalities: 104.14/102.59 1 + I29 <= I31 ==> -I29 + I32 >= -I29 + I32 104.14/102.59 I46 <= I43 /\ I43 <= I46 ==> -I43 + I46 > -I43 + I46 - 1 with -I43 + I46 >= 0 104.14/102.59 1 + I50 <= I53 ==> -I50 + I53 > -I50 + I53 - 1 with -I50 + I53 >= 0 104.14/102.59 1 + I60 <= I57 ==> -I57 + I60 >= -I57 + I60 - 1 104.14/102.59 ==> -I71 + I74 - 1 >= -(1 + I71) + I74 104.14/102.59 ==> -I78 + I81 - 1 >= -I78 + I81 - 1 104.14/102.59 ==> -I113 + I116 >= -I113 + I116 104.14/102.59 104.14/102.59 We remove all the strictly oriented dependency pairs. 104.14/102.59 104.14/102.59 DP problem for innermost termination. 104.14/102.59 P = 104.14/102.59 f10#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.59 f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.59 f15#(I70, I71, I72, I73, I74, I75, I76) -> f9#(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.59 f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 104.14/102.59 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 104.14/102.59 R = 104.14/102.59 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.59 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.59 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.59 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.59 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.59 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.59 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.59 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.59 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.59 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.59 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.59 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.59 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.59 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.59 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.59 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.59 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.59 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.59 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.59 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.59 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.59 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.59 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.59 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.59 104.14/102.59 We use the extended value criterion with the projection function NU: 104.14/102.59 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 104.14/102.59 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.14/102.59 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.14/102.59 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 104.14/102.59 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 104.14/102.59 104.14/102.59 This gives the following inequalities: 104.14/102.59 1 + I29 <= I31 ==> -I29 + I31 - 1 > -I29 + I31 - 2 with -I29 + I31 - 1 >= 0 104.14/102.59 1 + I60 <= I57 ==> -I57 + I59 - 2 >= -I57 + I59 - 2 104.14/102.59 ==> -I71 + I73 - 2 >= -(1 + I71) + I73 - 1 104.14/102.59 ==> -I78 + I80 - 2 >= -I78 + I80 - 2 104.14/102.59 ==> -I113 + I115 - 1 >= -I113 + I115 - 1 104.14/102.59 104.14/102.59 We remove all the strictly oriented dependency pairs. 104.14/102.59 104.14/102.59 DP problem for innermost termination. 104.14/102.59 P = 104.14/102.59 f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.59 f15#(I70, I71, I72, I73, I74, I75, I76) -> f9#(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.59 f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 104.14/102.59 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 104.14/102.59 R = 104.14/102.59 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 104.14/102.59 f17(I0, I1, I2, I3, I4, I5, I6) -> f9(12, 0, I2, 5, 0, I5, I6) 104.14/102.59 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 104.14/102.59 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 104.14/102.59 f8(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 104.14/102.59 f10(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 104.14/102.59 f10(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 104.14/102.59 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 104.14/102.59 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 104.14/102.59 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.59 f12(I63, I64, I65, I66, I67, I68, I69) -> f13(I63, I64, I65, I66, I67, I68, I69) 104.14/102.59 f15(I70, I71, I72, I73, I74, I75, I76) -> f9(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.59 f14(I77, I78, I79, I80, I81, I82, I83) -> f15(I77, I78, I79, I80, I81, I82, I83) 104.14/102.59 f13(I84, I85, I86, I87, I88, I89, I90) -> f8(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 104.14/102.59 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 104.14/102.59 f11(I98, I99, I100, I101, I102, I103, I104) -> f7(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 104.14/102.59 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 104.14/102.59 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 104.14/102.59 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 104.14/102.59 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 104.14/102.59 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 104.14/102.59 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 104.14/102.59 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 104.14/102.59 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 104.14/102.59 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 104.14/102.59 104.14/102.59 The dependency graph for this problem is: 104.14/102.59 9 -> 12 104.14/102.59 11 -> 17 104.14/102.59 12 -> 11 104.14/102.59 17 -> 104.14/102.59 Where: 104.14/102.59 9) f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 104.14/102.59 11) f15#(I70, I71, I72, I73, I74, I75, I76) -> f9#(I70, 1 + I71, I72, I73, I74, I75, I76) 104.14/102.59 12) f14#(I77, I78, I79, I80, I81, I82, I83) -> f15#(I77, I78, I79, I80, I81, I82, I83) 104.14/102.59 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 104.14/102.59 104.14/102.59 We have the following SCCs. 104.14/102.59 104.14/102.59 EOF