103.78/102.08 YES 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17#(I0, I1, I2, I3, I4, I5, I6) -> f1#(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2#(I21, I22, I23, I24, I25, I26, I27) -> f8#(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16#(I35, I36, I37, I38, I39, I40, I41) -> f14#(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7#(I56, I57, I58, I59, I60, I61, I62) -> f10#(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9#(I77, I78, I79, I80, I81, I82, I83) -> f7#(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10#(I112, I113, I114, I115, I116, I117, I118) -> f6#(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10#(I121, I122, I123, I124, I125, I126, I127) -> f5#(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8#(I128, I129, I130, I131, I132, I133, I134) -> f9#(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 The dependency graph for this problem is: 103.78/102.08 0 -> 1 103.78/102.08 1 -> 22 103.78/102.08 2 -> 21 103.78/102.08 3 -> 5, 6, 7 103.78/102.08 4 -> 19 103.78/102.08 5 -> 8 103.78/102.08 6 -> 10 103.78/102.08 7 -> 10 103.78/102.08 8 -> 22 103.78/102.08 9 -> 17, 18 103.78/102.08 10 -> 8 103.78/102.08 11 -> 15 103.78/102.08 12 -> 9 103.78/102.08 13 -> 16 103.78/102.08 14 -> 19 103.78/102.08 15 -> 13, 14 103.78/102.08 16 -> 15 103.78/102.08 17 -> 20 103.78/102.08 18 -> 2 103.78/102.08 19 -> 11, 12 103.78/102.08 20 -> 9 103.78/102.08 21 -> 2 103.78/102.08 22 -> 3, 4 103.78/102.08 Where: 103.78/102.08 0) f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 1) f17#(I0, I1, I2, I3, I4, I5, I6) -> f1#(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 2) f5#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 3) f2#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 4) f2#(I21, I22, I23, I24, I25, I26, I27) -> f8#(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 5) f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 6) f16#(I35, I36, I37, I38, I39, I40, I41) -> f14#(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 8) f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 9) f7#(I56, I57, I58, I59, I60, I61, I62) -> f10#(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 10) f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 11) f9#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 12) f9#(I77, I78, I79, I80, I81, I82, I83) -> f7#(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 13) f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 15) f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 17) f10#(I112, I113, I114, I115, I116, I117, I118) -> f6#(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 18) f10#(I121, I122, I123, I124, I125, I126, I127) -> f5#(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 19) f8#(I128, I129, I130, I131, I132, I133, I134) -> f9#(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 20) f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 21) f3#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 22) f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 We have the following SCCs. 103.78/102.08 { 3, 5, 6, 7, 8, 10, 22 } 103.78/102.08 { 11, 13, 14, 15, 16, 19 } 103.78/102.08 { 9, 17, 20 } 103.78/102.08 { 2, 21 } 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f5#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f3#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 We use the reverse value criterion with the projection function NU: 103.78/102.08 NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 103.78/102.08 NU[f5#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 103.78/102.08 103.78/102.08 This gives the following inequalities: 103.78/102.08 ==> I10 + -1 * (1 + I8) >= I10 + -1 * (1 + I8) 103.78/102.08 1 + I150 <= I152 ==> I152 + -1 * (1 + I150) > I152 + -1 * (1 + (1 + I150)) with I152 + -1 * (1 + I150) >= 0 103.78/102.08 103.78/102.08 We remove all the strictly oriented dependency pairs. 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f5#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 The dependency graph for this problem is: 103.78/102.08 2 -> 103.78/102.08 Where: 103.78/102.08 2) f5#(I7, I8, I9, I10, I11, I12, I13) -> f3#(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 103.78/102.08 We have the following SCCs. 103.78/102.08 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f7#(I56, I57, I58, I59, I60, I61, I62) -> f10#(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f10#(I112, I113, I114, I115, I116, I117, I118) -> f6#(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 We use the extended value criterion with the projection function NU: 103.78/102.08 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 103.78/102.08 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 103.78/102.08 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 103.78/102.08 103.78/102.08 This gives the following inequalities: 103.78/102.08 ==> I56 - I57 - 1 >= I56 - I57 - 1 103.78/102.08 I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112 ==> I112 - I113 - 1 > I112 - I113 - 2 with I112 - I113 - 1 >= 0 103.78/102.08 ==> I142 - I143 - 2 >= I142 - (1 + I143) - 1 103.78/102.08 103.78/102.08 We remove all the strictly oriented dependency pairs. 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f7#(I56, I57, I58, I59, I60, I61, I62) -> f10#(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 The dependency graph for this problem is: 103.78/102.08 9 -> 103.78/102.08 20 -> 9 103.78/102.08 Where: 103.78/102.08 9) f7#(I56, I57, I58, I59, I60, I61, I62) -> f10#(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 20) f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 103.78/102.08 We have the following SCCs. 103.78/102.08 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f9#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f8#(I128, I129, I130, I131, I132, I133, I134) -> f9#(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 We use the extended value criterion with the projection function NU: 103.78/102.08 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 103.78/102.08 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 103.78/102.08 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 103.78/102.08 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 103.78/102.08 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 103.78/102.08 103.78/102.08 This gives the following inequalities: 103.78/102.08 1 + I71 <= I73 ==> -I71 + I73 - 1 > -I71 + I73 - 2 with -I71 + I73 - 1 >= 0 103.78/102.08 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84 ==> -I85 + I87 - 2 >= -I85 + I87 - 2 103.78/102.08 I91 <= I93 ==> -I92 + I94 - 2 >= -(1 + I92) + I94 - 1 103.78/102.08 ==> -I99 + I101 - 2 >= -I99 + I101 - 2 103.78/102.08 ==> -I106 + I108 - 2 >= -I106 + I108 - 2 103.78/102.08 ==> -I129 + I131 - 1 >= -I129 + I131 - 1 103.78/102.08 103.78/102.08 We remove all the strictly oriented dependency pairs. 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f8#(I128, I129, I130, I131, I132, I133, I134) -> f9#(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 The dependency graph for this problem is: 103.78/102.08 13 -> 16 103.78/102.08 14 -> 19 103.78/102.08 15 -> 13, 14 103.78/102.08 16 -> 15 103.78/102.08 19 -> 103.78/102.08 Where: 103.78/102.08 13) f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 15) f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 19) f8#(I128, I129, I130, I131, I132, I133, I134) -> f9#(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 103.78/102.08 We have the following SCCs. 103.78/102.08 { 13, 15, 16 } 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 We use the extended value criterion with the projection function NU: 103.78/102.08 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 103.78/102.08 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2 103.78/102.08 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 103.78/102.08 103.78/102.08 This gives the following inequalities: 103.78/102.08 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84 ==> I84 - I86 - 1 > I84 - I86 - 2 with I84 - I86 - 1 >= 0 103.78/102.08 ==> I98 - I100 - 1 >= I98 - I100 - 1 103.78/102.08 ==> I105 - I107 - 2 >= I105 - (1 + I107) - 1 103.78/102.08 103.78/102.08 We remove all the strictly oriented dependency pairs. 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 The dependency graph for this problem is: 103.78/102.08 15 -> 103.78/102.08 16 -> 15 103.78/102.08 Where: 103.78/102.08 15) f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 103.78/102.08 We have the following SCCs. 103.78/102.08 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f2#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16#(I35, I36, I37, I38, I39, I40, I41) -> f14#(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 We use the extended value criterion with the projection function NU: 103.78/102.08 NU[f1#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 103.78/102.08 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 103.78/102.08 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 103.78/102.08 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 103.78/102.08 NU[f2#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 103.78/102.08 103.78/102.08 This gives the following inequalities: 103.78/102.08 1 + I15 <= I17 ==> -I15 + I18 >= -I15 + I18 103.78/102.08 I32 <= I29 /\ I29 <= I32 ==> -I29 + I32 > -I29 + I32 - 1 with -I29 + I32 >= 0 103.78/102.08 1 + I36 <= I39 ==> -I36 + I39 > -I36 + I39 - 1 with -I36 + I39 >= 0 103.78/102.08 1 + I46 <= I43 ==> -I43 + I46 >= -I43 + I46 - 1 103.78/102.08 ==> -I50 + I53 - 1 >= -(1 + I50) + I53 103.78/102.08 ==> -I64 + I67 - 1 >= -I64 + I67 - 1 103.78/102.08 ==> -I164 + I167 >= -I164 + I167 103.78/102.08 103.78/102.08 We remove all the strictly oriented dependency pairs. 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f2#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 We use the extended value criterion with the projection function NU: 103.78/102.08 NU[f1#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 103.78/102.08 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 103.78/102.08 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 103.78/102.08 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 103.78/102.08 NU[f2#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 103.78/102.08 103.78/102.08 This gives the following inequalities: 103.78/102.08 1 + I15 <= I17 ==> -I15 + I17 - 1 > -I15 + I17 - 2 with -I15 + I17 - 1 >= 0 103.78/102.08 1 + I46 <= I43 ==> -I43 + I45 - 2 >= -I43 + I45 - 2 103.78/102.08 ==> -I50 + I52 - 2 >= -(1 + I50) + I52 - 1 103.78/102.08 ==> -I64 + I66 - 2 >= -I64 + I66 - 2 103.78/102.08 ==> -I164 + I166 - 1 >= -I164 + I166 - 1 103.78/102.08 103.78/102.08 We remove all the strictly oriented dependency pairs. 103.78/102.08 103.78/102.08 DP problem for innermost termination. 103.78/102.08 P = 103.78/102.08 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 R = 103.78/102.08 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 103.78/102.08 f17(I0, I1, I2, I3, I4, I5, I6) -> f1(5, 0, I2, 5, 0, I5, I6) 103.78/102.08 f5(I7, I8, I9, I10, I11, I12, I13) -> f3(I7, I8, I9, I10, I11, I12, I13) 103.78/102.08 f2(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 103.78/102.08 f2(I21, I22, I23, I24, I25, I26, I27) -> f8(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 103.78/102.08 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 103.78/102.08 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 103.78/102.08 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 f15(I49, I50, I51, I52, I53, I54, I55) -> f1(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 f7(I56, I57, I58, I59, I60, I61, I62) -> f10(I56, I57, I58, I59, I60, I61, I62) 103.78/102.08 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 f9(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 103.78/102.08 f9(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 103.78/102.08 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 103.78/102.08 f13(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 103.78/102.08 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 103.78/102.08 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 103.78/102.08 f10(I112, I113, I114, I115, I116, I117, I118) -> f6(I112, I113, I114, I115, I116, I119, I120) [I120 = I120 /\ I119 = I119 /\ 1 + I113 <= I112] 103.78/102.08 f10(I121, I122, I123, I124, I125, I126, I127) -> f5(I121, 0, I123, I124, I125, I126, I127) [I121 <= I122] 103.78/102.08 f8(I128, I129, I130, I131, I132, I133, I134) -> f9(I128, I129, I130, I131, I132, I133, I134) 103.78/102.08 f6(I135, I136, I137, I138, I139, I140, I141) -> f4(I135, I136, I137, I138, I139, I140, I141) 103.78/102.08 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 103.78/102.08 f3(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) [1 + I150 <= I152] 103.78/102.08 f3(I156, I157, I158, I159, I160, I161, I162) -> f4(I156, I157, I158, I159, I160, I161, I162) [I159 <= I157] 103.78/102.08 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 The dependency graph for this problem is: 103.78/102.08 7 -> 10 103.78/102.08 8 -> 22 103.78/102.08 10 -> 8 103.78/102.08 22 -> 103.78/102.08 Where: 103.78/102.08 7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 103.78/102.08 8) f15#(I49, I50, I51, I52, I53, I54, I55) -> f1#(I49, 1 + I50, I51, I52, I53, I54, I55) 103.78/102.08 10) f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 103.78/102.08 22) f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, I164, I165, I166, I167, I168, I169) 103.78/102.08 103.78/102.08 We have the following SCCs. 103.78/102.08 103.78/105.05 EOF