105.65/104.17 YES 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17#(I0, I1, I2, I3, I4, I5, I6) -> f4#(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16#(I35, I36, I37, I38, I39, I40, I41) -> f14#(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7#(I49, I50, I51, I52, I53, I54, I55) -> f8#(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15#(I56, I57, I58, I59, I60, I61, I62) -> f4#(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10#(I77, I78, I79, I80, I81, I82, I83) -> f7#(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13#(I91, I92, I93, I94, I95, I96, I97) -> f9#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8#(I119, I120, I121, I122, I123, I124, I125) -> f6#(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8#(I128, I129, I130, I131, I132, I133, I134) -> f3#(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 The dependency graph for this problem is: 105.65/104.17 0 -> 1 105.65/104.17 1 -> 21 105.65/104.17 2 -> 22 105.65/104.17 3 -> 5, 6, 7 105.65/104.17 4 -> 17 105.65/104.17 5 -> 9 105.65/104.17 6 -> 10 105.65/104.17 7 -> 10 105.65/104.17 8 -> 18, 19 105.65/104.17 9 -> 21 105.65/104.17 10 -> 9 105.65/104.17 11 -> 15 105.65/104.17 12 -> 8 105.65/104.17 13 -> 16 105.65/104.17 14 -> 17 105.65/104.17 15 -> 13, 14 105.65/104.17 16 -> 15 105.65/104.17 17 -> 11, 12 105.65/104.17 18 -> 20 105.65/104.17 19 -> 2 105.65/104.17 20 -> 8 105.65/104.17 21 -> 3, 4 105.65/104.17 22 -> 2 105.65/104.17 Where: 105.65/104.17 0) f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 1) f17#(I0, I1, I2, I3, I4, I5, I6) -> f4#(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 4) f5#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 5) f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 6) f16#(I35, I36, I37, I38, I39, I40, I41) -> f14#(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 8) f7#(I49, I50, I51, I52, I53, I54, I55) -> f8#(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 9) f15#(I56, I57, I58, I59, I60, I61, I62) -> f4#(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 10) f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 11) f10#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 12) f10#(I77, I78, I79, I80, I81, I82, I83) -> f7#(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 13) f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f9#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 15) f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 18) f8#(I119, I120, I121, I122, I123, I124, I125) -> f6#(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 19) f8#(I128, I129, I130, I131, I132, I133, I134) -> f3#(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 20) f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 22) f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 105.65/104.17 We have the following SCCs. 105.65/104.17 { 3, 5, 6, 7, 9, 10, 21 } 105.65/104.17 { 11, 13, 14, 15, 16, 17 } 105.65/104.17 { 8, 18, 20 } 105.65/104.17 { 2, 22 } 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 We use the reverse value criterion with the projection function NU: 105.65/104.17 NU[f1#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 105.65/104.17 NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 105.65/104.17 105.65/104.17 This gives the following inequalities: 105.65/104.17 ==> I10 + -1 * (1 + I8) >= I10 + -1 * (1 + I8) 105.65/104.17 1 + I157 <= I159 ==> I159 + -1 * (1 + I157) > I159 + -1 * (1 + (1 + I157)) with I159 + -1 * (1 + I157) >= 0 105.65/104.17 105.65/104.17 We remove all the strictly oriented dependency pairs. 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 The dependency graph for this problem is: 105.65/104.17 2 -> 105.65/104.17 Where: 105.65/104.17 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 105.65/104.17 We have the following SCCs. 105.65/104.17 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f7#(I49, I50, I51, I52, I53, I54, I55) -> f8#(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f8#(I119, I120, I121, I122, I123, I124, I125) -> f6#(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 We use the extended value criterion with the projection function NU: 105.65/104.17 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 105.65/104.17 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 105.65/104.17 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 105.65/104.17 105.65/104.17 This gives the following inequalities: 105.65/104.17 ==> I49 - I50 - 1 >= I49 - I50 - 1 105.65/104.17 I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119 ==> I119 - I120 - 1 > I119 - I120 - 2 with I119 - I120 - 1 >= 0 105.65/104.17 ==> I142 - I143 - 2 >= I142 - (1 + I143) - 1 105.65/104.17 105.65/104.17 We remove all the strictly oriented dependency pairs. 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f7#(I49, I50, I51, I52, I53, I54, I55) -> f8#(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 The dependency graph for this problem is: 105.65/104.17 8 -> 105.65/104.17 20 -> 8 105.65/104.17 Where: 105.65/104.17 8) f7#(I49, I50, I51, I52, I53, I54, I55) -> f8#(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 20) f6#(I142, I143, I144, I145, I146, I147, I148) -> f7#(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 105.65/104.17 We have the following SCCs. 105.65/104.17 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f10#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13#(I91, I92, I93, I94, I95, I96, I97) -> f9#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 We use the extended value criterion with the projection function NU: 105.65/104.17 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 105.65/104.17 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.65/104.17 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.65/104.17 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.65/104.17 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 105.65/104.17 105.65/104.17 This gives the following inequalities: 105.65/104.17 1 + I71 <= I73 ==> -I71 + I73 - 1 > -I71 + I73 - 2 with -I71 + I73 - 1 >= 0 105.65/104.17 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84 ==> -I85 + I87 - 2 >= -I85 + I87 - 2 105.65/104.17 I91 <= I93 ==> -I92 + I94 - 2 >= -(1 + I92) + I94 - 1 105.65/104.17 ==> -I99 + I101 - 2 >= -I99 + I101 - 2 105.65/104.17 ==> -I106 + I108 - 2 >= -I106 + I108 - 2 105.65/104.17 ==> -I113 + I115 - 1 >= -I113 + I115 - 1 105.65/104.17 105.65/104.17 We remove all the strictly oriented dependency pairs. 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13#(I91, I92, I93, I94, I95, I96, I97) -> f9#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 The dependency graph for this problem is: 105.65/104.17 13 -> 16 105.65/104.17 14 -> 17 105.65/104.17 15 -> 13, 14 105.65/104.17 16 -> 15 105.65/104.17 17 -> 105.65/104.17 Where: 105.65/104.17 13) f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f9#(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 15) f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 105.65/104.17 We have the following SCCs. 105.65/104.17 { 13, 15, 16 } 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f13#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 We use the extended value criterion with the projection function NU: 105.65/104.17 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 105.65/104.17 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2 105.65/104.17 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 105.65/104.17 105.65/104.17 This gives the following inequalities: 105.65/104.17 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84 ==> I84 - I86 - 1 > I84 - I86 - 2 with I84 - I86 - 1 >= 0 105.65/104.17 ==> I98 - I100 - 1 >= I98 - I100 - 1 105.65/104.17 ==> I105 - I107 - 2 >= I105 - (1 + I107) - 1 105.65/104.17 105.65/104.17 We remove all the strictly oriented dependency pairs. 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 The dependency graph for this problem is: 105.65/104.17 15 -> 105.65/104.17 16 -> 15 105.65/104.17 Where: 105.65/104.17 15) f12#(I98, I99, I100, I101, I102, I103, I104) -> f13#(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 105.65/104.17 We have the following SCCs. 105.65/104.17 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f5#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f16#(I28, I29, I30, I31, I32, I33, I34) -> f15#(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16#(I35, I36, I37, I38, I39, I40, I41) -> f14#(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f15#(I56, I57, I58, I59, I60, I61, I62) -> f4#(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 We use the extended value criterion with the projection function NU: 105.65/104.17 NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 105.65/104.17 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 105.65/104.17 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 105.65/104.17 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 105.65/104.17 NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 105.65/104.17 105.65/104.17 This gives the following inequalities: 105.65/104.17 1 + I15 <= I17 ==> -I15 + I18 >= -I15 + I18 105.65/104.17 I32 <= I29 /\ I29 <= I32 ==> -I29 + I32 > -I29 + I32 - 1 with -I29 + I32 >= 0 105.65/104.17 1 + I36 <= I39 ==> -I36 + I39 > -I36 + I39 - 1 with -I36 + I39 >= 0 105.65/104.17 1 + I46 <= I43 ==> -I43 + I46 >= -I43 + I46 - 1 105.65/104.17 ==> -I57 + I60 - 1 >= -(1 + I57) + I60 105.65/104.17 ==> -I64 + I67 - 1 >= -I64 + I67 - 1 105.65/104.17 ==> -I150 + I153 >= -I150 + I153 105.65/104.17 105.65/104.17 We remove all the strictly oriented dependency pairs. 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f5#(I14, I15, I16, I17, I18, I19, I20) -> f16#(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f15#(I56, I57, I58, I59, I60, I61, I62) -> f4#(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 We use the extended value criterion with the projection function NU: 105.65/104.17 NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 105.65/104.17 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.65/104.17 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.65/104.17 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 105.65/104.17 NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 105.65/104.17 105.65/104.17 This gives the following inequalities: 105.65/104.17 1 + I15 <= I17 ==> -I15 + I17 - 1 > -I15 + I17 - 2 with -I15 + I17 - 1 >= 0 105.65/104.17 1 + I46 <= I43 ==> -I43 + I45 - 2 >= -I43 + I45 - 2 105.65/104.17 ==> -I57 + I59 - 2 >= -(1 + I57) + I59 - 1 105.65/104.17 ==> -I64 + I66 - 2 >= -I64 + I66 - 2 105.65/104.17 ==> -I150 + I152 - 1 >= -I150 + I152 - 1 105.65/104.17 105.65/104.17 We remove all the strictly oriented dependency pairs. 105.65/104.17 105.65/104.17 DP problem for innermost termination. 105.65/104.17 P = 105.65/104.17 f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f15#(I56, I57, I58, I59, I60, I61, I62) -> f4#(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 R = 105.65/104.17 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 105.65/104.17 f17(I0, I1, I2, I3, I4, I5, I6) -> f4(6, 0, I2, 5, 0, I5, I6) 105.65/104.17 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 105.65/104.17 f5(I14, I15, I16, I17, I18, I19, I20) -> f16(I14, I15, I16, I17, I18, I19, I20) [1 + I15 <= I17] 105.65/104.17 f5(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, 0, I23, I24, I25, I26, I27) [I24 <= I22] 105.65/104.17 f16(I28, I29, I30, I31, I32, I33, I34) -> f15(I28, I29, I30, I31, I32, I33, I34) [I32 <= I29 /\ I29 <= I32] 105.65/104.17 f16(I35, I36, I37, I38, I39, I40, I41) -> f14(I35, I36, I37, I38, I39, I40, I41) [1 + I36 <= I39] 105.65/104.17 f16(I42, I43, I44, I45, I46, I47, I48) -> f14(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 f7(I49, I50, I51, I52, I53, I54, I55) -> f8(I49, I50, I51, I52, I53, I54, I55) 105.65/104.17 f15(I56, I57, I58, I59, I60, I61, I62) -> f4(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 f14(I63, I64, I65, I66, I67, I68, I69) -> f15(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 f10(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, 0, I73, I74, I75, I76) [1 + I71 <= I73] 105.65/104.17 f10(I77, I78, I79, I80, I81, I82, I83) -> f7(I77, 0, I79, I80, I81, I82, I83) [I80 <= I78] 105.65/104.17 f13(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I86 <= I84] 105.65/104.17 f13(I91, I92, I93, I94, I95, I96, I97) -> f9(I91, 1 + I92, I93, I94, I95, I96, I97) [I91 <= I93] 105.65/104.17 f12(I98, I99, I100, I101, I102, I103, I104) -> f13(I98, I99, I100, I101, I102, I103, I104) 105.65/104.17 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, I106, 1 + I107, I108, I109, I110, I111) 105.65/104.17 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, I114, I115, I116, I117, I118) 105.65/104.17 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, I126, I127) [I127 = I127 /\ I126 = I126 /\ 1 + I120 <= I119] 105.65/104.17 f8(I128, I129, I130, I131, I132, I133, I134) -> f3(I128, 0, I130, I131, I132, I133, I134) [I128 <= I129] 105.65/104.17 f6(I135, I136, I137, I138, I139, I140, I141) -> f2(I135, I136, I137, I138, I139, I140, I141) 105.65/104.17 f6(I142, I143, I144, I145, I146, I147, I148) -> f7(I142, 1 + I143, I144, I145, I146, I147, I148) 105.65/104.17 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 105.65/104.17 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 105.65/104.17 105.65/104.17 The dependency graph for this problem is: 105.65/104.17 7 -> 10 105.65/104.17 9 -> 21 105.65/104.17 10 -> 9 105.65/104.17 21 -> 105.65/104.17 Where: 105.65/104.17 7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f14#(I42, I43, I44, I45, I46, I47, I48) [1 + I46 <= I43] 105.65/104.17 9) f15#(I56, I57, I58, I59, I60, I61, I62) -> f4#(I56, 1 + I57, I58, I59, I60, I61, I62) 105.65/104.17 10) f14#(I63, I64, I65, I66, I67, I68, I69) -> f15#(I63, I64, I65, I66, I67, I68, I69) 105.65/104.17 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, I150, I151, I152, I153, I154, I155) 105.65/104.17 105.65/104.17 We have the following SCCs. 105.65/104.17 105.65/107.14 EOF