107.14/105.76 YES 107.14/105.76 107.14/105.76 DP problem for innermost termination. 107.14/105.76 P = 107.14/105.76 f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 107.14/105.76 f17#(I0, I1, I2, I3, I4, I5, I6) -> f7#(11, 0, I2, 5, 0, I5, I6) 107.14/105.76 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 107.14/105.76 f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 107.14/105.76 f10#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 107.14/105.76 f8#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.76 f8#(I35, I36, I37, I38, I39, I40, I41) -> f12#(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.76 f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.76 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.76 f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.76 f15#(I63, I64, I65, I66, I67, I68, I69) -> f7#(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.76 f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 107.14/105.76 f12#(I77, I78, I79, I80, I81, I82, I83) -> f13#(I77, I78, I79, I80, I81, I82, I83) 107.14/105.76 f13#(I84, I85, I86, I87, I88, I89, I90) -> f10#(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.76 f13#(I91, I92, I93, I94, I95, I96, I97) -> f5#(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.76 f11#(I98, I99, I100, I101, I102, I103, I104) -> f9#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.76 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.76 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.76 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, I121, I122, I123, I124, I125) 107.14/105.76 f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.76 f6#(I135, I136, I137, I138, I139, I140, I141) -> f3#(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.76 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.76 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.76 R = 107.14/105.76 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.76 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.76 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.76 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.76 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.76 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.76 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.76 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.76 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.76 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.76 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.76 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.76 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.76 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.76 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.76 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.76 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.76 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.76 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.76 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.76 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.76 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.76 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.76 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.76 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.76 107.14/105.76 The dependency graph for this problem is: 107.14/105.76 0 -> 1 107.14/105.76 1 -> 18 107.14/105.76 2 -> 22 107.14/105.76 3 -> 19, 20 107.14/105.76 4 -> 15, 16 107.14/105.76 5 -> 7, 8, 9 107.14/105.76 6 -> 12 107.14/105.76 7 -> 10 107.14/105.76 8 -> 11 107.14/105.76 9 -> 11 107.14/105.76 10 -> 18 107.14/105.76 11 -> 10 107.14/105.76 12 -> 13, 14 107.14/105.76 13 -> 4 107.14/105.76 14 -> 3 107.14/105.76 15 -> 17 107.14/105.76 16 -> 12 107.14/105.76 17 -> 4 107.14/105.76 18 -> 5, 6 107.14/105.76 19 -> 21 107.14/105.76 20 -> 2 107.14/105.76 21 -> 3 107.14/105.76 22 -> 2 107.14/105.76 Where: 107.14/105.76 0) f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 107.14/105.76 1) f17#(I0, I1, I2, I3, I4, I5, I6) -> f7#(11, 0, I2, 5, 0, I5, I6) 107.14/105.76 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 107.14/105.76 3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 107.14/105.76 4) f10#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 107.14/105.76 5) f8#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.76 6) f8#(I35, I36, I37, I38, I39, I40, I41) -> f12#(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.76 7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.76 8) f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.76 9) f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.76 10) f15#(I63, I64, I65, I66, I67, I68, I69) -> f7#(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.76 11) f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 107.14/105.76 12) f12#(I77, I78, I79, I80, I81, I82, I83) -> f13#(I77, I78, I79, I80, I81, I82, I83) 107.14/105.76 13) f13#(I84, I85, I86, I87, I88, I89, I90) -> f10#(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.76 14) f13#(I91, I92, I93, I94, I95, I96, I97) -> f5#(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.76 15) f11#(I98, I99, I100, I101, I102, I103, I104) -> f9#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.76 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.76 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.76 18) f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, I121, I122, I123, I124, I125) 107.14/105.76 19) f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.76 20) f6#(I135, I136, I137, I138, I139, I140, I141) -> f3#(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.76 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.76 22) f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.76 107.14/105.76 We have the following SCCs. 107.14/105.76 { 5, 7, 8, 9, 10, 11, 18 } 107.14/105.76 { 4, 12, 13, 15, 16, 17 } 107.14/105.76 { 3, 19, 21 } 107.14/105.76 { 2, 22 } 107.14/105.76 107.14/105.76 DP problem for innermost termination. 107.14/105.76 P = 107.14/105.76 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 107.14/105.76 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.76 R = 107.14/105.76 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.76 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.76 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.76 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.76 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.76 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.76 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.76 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.76 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.76 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.76 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.76 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.76 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.76 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.76 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.76 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.76 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.76 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.76 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.76 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.76 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.76 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.76 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.76 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.76 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.76 107.14/105.76 We use the reverse value criterion with the projection function NU: 107.14/105.76 NU[f1#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 107.14/105.76 NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 107.14/105.76 107.14/105.76 This gives the following inequalities: 107.14/105.76 ==> I10 + -1 * (1 + I8) >= I10 + -1 * (1 + I8) 107.14/105.76 1 + I157 <= I159 ==> I159 + -1 * (1 + I157) > I159 + -1 * (1 + (1 + I157)) with I159 + -1 * (1 + I157) >= 0 107.14/105.76 107.14/105.76 We remove all the strictly oriented dependency pairs. 107.14/105.76 107.14/105.76 DP problem for innermost termination. 107.14/105.76 P = 107.14/105.76 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 107.14/105.76 R = 107.14/105.76 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.76 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.76 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.76 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.76 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.76 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.77 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.77 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.77 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.77 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.77 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.77 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.77 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.77 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.77 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.77 107.14/105.77 The dependency graph for this problem is: 107.14/105.77 2 -> 107.14/105.77 Where: 107.14/105.77 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 107.14/105.77 107.14/105.77 We have the following SCCs. 107.14/105.77 107.14/105.77 107.14/105.77 DP problem for innermost termination. 107.14/105.77 P = 107.14/105.77 f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.77 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 R = 107.14/105.77 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.77 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.77 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.77 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.77 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.77 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.77 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.77 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.77 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.77 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.77 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.77 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.77 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.77 107.14/105.77 We use the extended value criterion with the projection function NU: 107.14/105.77 NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 107.14/105.77 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 107.14/105.77 NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 107.14/105.77 107.14/105.77 This gives the following inequalities: 107.14/105.77 ==> I14 - I15 - 1 >= I14 - I15 - 1 107.14/105.77 I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126 ==> I126 - I127 - 1 > I126 - I127 - 2 with I126 - I127 - 1 >= 0 107.14/105.77 ==> I149 - I150 - 2 >= I149 - (1 + I150) - 1 107.14/105.77 107.14/105.77 We remove all the strictly oriented dependency pairs. 107.14/105.77 107.14/105.77 DP problem for innermost termination. 107.14/105.77 P = 107.14/105.77 f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 R = 107.14/105.77 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.77 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.77 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.77 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.77 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.77 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.77 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.77 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.77 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.77 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.77 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.77 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.77 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.77 107.14/105.77 The dependency graph for this problem is: 107.14/105.77 3 -> 107.14/105.77 21 -> 3 107.14/105.77 Where: 107.14/105.77 3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 107.14/105.77 We have the following SCCs. 107.14/105.77 107.14/105.77 107.14/105.77 DP problem for innermost termination. 107.14/105.77 P = 107.14/105.77 f10#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f12#(I77, I78, I79, I80, I81, I82, I83) -> f13#(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f13#(I84, I85, I86, I87, I88, I89, I90) -> f10#(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.77 f11#(I98, I99, I100, I101, I102, I103, I104) -> f9#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 R = 107.14/105.77 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.77 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.77 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.77 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.77 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.77 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.77 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.77 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.77 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.77 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.77 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.77 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.77 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.77 107.14/105.77 We use the extended value criterion with the projection function NU: 107.14/105.77 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 107.14/105.77 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 107.14/105.77 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 107.14/105.77 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 107.14/105.77 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 107.14/105.77 107.14/105.77 This gives the following inequalities: 107.14/105.77 ==> -I22 + I24 - 2 >= -I22 + I24 - 2 107.14/105.77 ==> -I78 + I80 - 1 >= -I78 + I80 - 1 107.14/105.77 1 + I85 <= I87 ==> -I85 + I87 - 1 > -I85 + I87 - 2 with -I85 + I87 - 1 >= 0 107.14/105.77 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98 ==> -I99 + I101 - 2 >= -I99 + I101 - 2 107.14/105.77 I105 <= I107 ==> -I106 + I108 - 2 >= -(1 + I106) + I108 - 1 107.14/105.77 ==> -I113 + I115 - 2 >= -I113 + I115 - 2 107.14/105.77 107.14/105.77 We remove all the strictly oriented dependency pairs. 107.14/105.77 107.14/105.77 DP problem for innermost termination. 107.14/105.77 P = 107.14/105.77 f10#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f12#(I77, I78, I79, I80, I81, I82, I83) -> f13#(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f11#(I98, I99, I100, I101, I102, I103, I104) -> f9#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 R = 107.14/105.77 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.77 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.77 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.77 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.77 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.77 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.77 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.77 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.77 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.77 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.77 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.77 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.77 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.77 107.14/105.77 The dependency graph for this problem is: 107.14/105.77 4 -> 15, 16 107.14/105.77 12 -> 107.14/105.77 15 -> 17 107.14/105.77 16 -> 12 107.14/105.77 17 -> 4 107.14/105.77 Where: 107.14/105.77 4) f10#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 12) f12#(I77, I78, I79, I80, I81, I82, I83) -> f13#(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 15) f11#(I98, I99, I100, I101, I102, I103, I104) -> f9#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 16) f11#(I105, I106, I107, I108, I109, I110, I111) -> f12#(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 107.14/105.77 We have the following SCCs. 107.14/105.77 { 4, 15, 17 } 107.14/105.77 107.14/105.77 DP problem for innermost termination. 107.14/105.77 P = 107.14/105.77 f10#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f11#(I98, I99, I100, I101, I102, I103, I104) -> f9#(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 R = 107.14/105.77 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.77 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.77 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.77 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.77 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.77 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.77 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.77 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.77 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.77 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.77 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.77 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.77 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.77 107.14/105.77 We use the extended value criterion with the projection function NU: 107.14/105.77 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2 107.14/105.77 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 107.14/105.77 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 107.14/105.77 107.14/105.77 This gives the following inequalities: 107.14/105.77 ==> I21 - I23 - 1 >= I21 - I23 - 1 107.14/105.77 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98 ==> I98 - I100 - 1 > I98 - I100 - 2 with I98 - I100 - 1 >= 0 107.14/105.77 ==> I112 - I114 - 2 >= I112 - (1 + I114) - 1 107.14/105.77 107.14/105.77 We remove all the strictly oriented dependency pairs. 107.14/105.77 107.14/105.77 DP problem for innermost termination. 107.14/105.77 P = 107.14/105.77 f10#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 R = 107.14/105.77 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.77 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.77 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.77 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.77 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.77 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.77 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.77 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.77 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.77 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.77 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.77 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.77 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.77 107.14/105.77 The dependency graph for this problem is: 107.14/105.77 4 -> 107.14/105.77 17 -> 4 107.14/105.77 Where: 107.14/105.77 4) f10#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 107.14/105.77 We have the following SCCs. 107.14/105.77 107.14/105.77 107.14/105.77 DP problem for innermost termination. 107.14/105.77 P = 107.14/105.77 f8#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.77 f16#(I49, I50, I51, I52, I53, I54, I55) -> f14#(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.77 f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15#(I63, I64, I65, I66, I67, I68, I69) -> f7#(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 R = 107.14/105.77 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.77 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.77 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.77 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.77 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.77 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.77 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.77 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.77 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.77 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.77 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.77 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.77 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.77 107.14/105.77 We use the extended value criterion with the projection function NU: 107.14/105.77 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 107.14/105.77 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 107.14/105.77 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 - 1 107.14/105.77 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 107.14/105.77 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x4 107.14/105.77 107.14/105.77 This gives the following inequalities: 107.14/105.77 1 + I29 <= I31 ==> -I29 + I32 >= -I29 + I32 107.14/105.77 I46 <= I43 /\ I43 <= I46 ==> -I43 + I46 > -I43 + I46 - 1 with -I43 + I46 >= 0 107.14/105.77 1 + I50 <= I53 ==> -I50 + I53 > -I50 + I53 - 1 with -I50 + I53 >= 0 107.14/105.77 1 + I60 <= I57 ==> -I57 + I60 >= -I57 + I60 - 1 107.14/105.77 ==> -I64 + I67 - 1 >= -(1 + I64) + I67 107.14/105.77 ==> -I71 + I74 - 1 >= -I71 + I74 - 1 107.14/105.77 ==> -I120 + I123 >= -I120 + I123 107.14/105.77 107.14/105.77 We remove all the strictly oriented dependency pairs. 107.14/105.77 107.14/105.77 DP problem for innermost termination. 107.14/105.77 P = 107.14/105.77 f8#(I28, I29, I30, I31, I32, I33, I34) -> f16#(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15#(I63, I64, I65, I66, I67, I68, I69) -> f7#(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 R = 107.14/105.77 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.77 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.77 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.77 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.77 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.77 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.77 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.77 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.77 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.77 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.77 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.77 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.77 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.77 107.14/105.77 We use the extended value criterion with the projection function NU: 107.14/105.77 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 107.14/105.77 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 107.14/105.77 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 107.14/105.77 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 107.14/105.77 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 107.14/105.77 107.14/105.77 This gives the following inequalities: 107.14/105.77 1 + I29 <= I31 ==> -I29 + I31 - 1 > -I29 + I31 - 2 with -I29 + I31 - 1 >= 0 107.14/105.77 1 + I60 <= I57 ==> -I57 + I59 - 2 >= -I57 + I59 - 2 107.14/105.77 ==> -I64 + I66 - 2 >= -(1 + I64) + I66 - 1 107.14/105.77 ==> -I71 + I73 - 2 >= -I71 + I73 - 2 107.14/105.77 ==> -I120 + I122 - 1 >= -I120 + I122 - 1 107.14/105.77 107.14/105.77 We remove all the strictly oriented dependency pairs. 107.14/105.77 107.14/105.77 DP problem for innermost termination. 107.14/105.77 P = 107.14/105.77 f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15#(I63, I64, I65, I66, I67, I68, I69) -> f7#(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 R = 107.14/105.77 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 107.14/105.77 f17(I0, I1, I2, I3, I4, I5, I6) -> f7(11, 0, I2, 5, 0, I5, I6) 107.14/105.77 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 107.14/105.77 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 107.14/105.77 f10(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, I25, I26, I27) 107.14/105.77 f8(I28, I29, I30, I31, I32, I33, I34) -> f16(I28, I29, I30, I31, I32, I33, I34) [1 + I29 <= I31] 107.14/105.77 f8(I35, I36, I37, I38, I39, I40, I41) -> f12(I35, 0, I37, I38, I39, I40, I41) [I38 <= I36] 107.14/105.77 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [I46 <= I43 /\ I43 <= I46] 107.14/105.77 f16(I49, I50, I51, I52, I53, I54, I55) -> f14(I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I53] 107.14/105.77 f16(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 f15(I63, I64, I65, I66, I67, I68, I69) -> f7(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 f14(I70, I71, I72, I73, I74, I75, I76) -> f15(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 f12(I77, I78, I79, I80, I81, I82, I83) -> f13(I77, I78, I79, I80, I81, I82, I83) 107.14/105.77 f13(I84, I85, I86, I87, I88, I89, I90) -> f10(I84, I85, 0, I87, I88, I89, I90) [1 + I85 <= I87] 107.14/105.77 f13(I91, I92, I93, I94, I95, I96, I97) -> f5(I91, 0, I93, I94, I95, I96, I97) [I94 <= I92] 107.14/105.77 f11(I98, I99, I100, I101, I102, I103, I104) -> f9(I98, I99, I100, I101, I102, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I100 <= I98] 107.14/105.77 f11(I105, I106, I107, I108, I109, I110, I111) -> f12(I105, 1 + I106, I107, I108, I109, I110, I111) [I105 <= I107] 107.14/105.77 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, I113, 1 + I114, I115, I116, I117, I118) 107.14/105.77 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 107.14/105.77 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 107.14/105.77 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 107.14/105.77 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 107.14/105.77 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 107.14/105.77 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 107.14/105.77 107.14/105.77 The dependency graph for this problem is: 107.14/105.77 9 -> 11 107.14/105.77 10 -> 18 107.14/105.77 11 -> 10 107.14/105.77 18 -> 107.14/105.77 Where: 107.14/105.77 9) f16#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I60 <= I57] 107.14/105.77 10) f15#(I63, I64, I65, I66, I67, I68, I69) -> f7#(I63, 1 + I64, I65, I66, I67, I68, I69) 107.14/105.77 11) f14#(I70, I71, I72, I73, I74, I75, I76) -> f15#(I70, I71, I72, I73, I74, I75, I76) 107.14/105.77 18) f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, I121, I122, I123, I124, I125) 107.14/105.77 107.14/105.77 We have the following SCCs. 107.14/105.77 107.14/108.74 EOF