80.00/78.78 YES 80.00/78.78 80.00/78.78 DP problem for innermost termination. 80.00/78.78 P = 80.00/78.78 f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17#(I0, I1, I2, I3, I4, I5, I6) -> f14#(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10#(I28, I29, I30, I31, I32, I33, I34) -> f11#(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14#(I35, I36, I37, I38, I39, I40, I41) -> f16#(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16#(I49, I50, I51, I52, I53, I54, I55) -> f10#(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15#(I63, I64, I65, I66, I67, I68, I69) -> f12#(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13#(I77, I78, I79, I80, I81, I82, I83) -> f14#(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12#(I84, I85, I86, I87, I88, I89, I90) -> f13#(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11#(I98, I99, I100, I101, I102, I103, I104) -> f5#(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6#(I135, I136, I137, I138, I139, I140, I141) -> f3#(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 R = 80.00/78.78 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17(I0, I1, I2, I3, I4, I5, I6) -> f14(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14(I35, I36, I37, I38, I39, I40, I41) -> f16(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16(I49, I50, I51, I52, I53, I54, I55) -> f10(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15(I63, I64, I65, I66, I67, I68, I69) -> f12(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13(I77, I78, I79, I80, I81, I82, I83) -> f14(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12(I84, I85, I86, I87, I88, I89, I90) -> f13(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 80.00/78.78 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 80.00/78.78 80.00/78.78 The dependency graph for this problem is: 80.00/78.78 0 -> 1 80.00/78.78 1 -> 6 80.00/78.78 2 -> 22 80.00/78.78 3 -> 19, 20 80.00/78.78 4 -> 16, 17 80.00/78.78 5 -> 14, 15 80.00/78.78 6 -> 7, 8 80.00/78.78 7 -> 9, 10, 11 80.00/78.78 8 -> 5 80.00/78.78 9 -> 12 80.00/78.78 10 -> 13 80.00/78.78 11 -> 13 80.00/78.78 12 -> 6 80.00/78.78 13 -> 12 80.00/78.78 14 -> 4 80.00/78.78 15 -> 3 80.00/78.78 16 -> 18 80.00/78.78 17 -> 5 80.00/78.78 18 -> 4 80.00/78.78 19 -> 21 80.00/78.78 20 -> 2 80.00/78.78 21 -> 3 80.00/78.78 22 -> 2 80.00/78.78 Where: 80.00/78.78 0) f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 1) f17#(I0, I1, I2, I3, I4, I5, I6) -> f14#(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 5) f10#(I28, I29, I30, I31, I32, I33, I34) -> f11#(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 6) f14#(I35, I36, I37, I38, I39, I40, I41) -> f16#(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 7) f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 8) f16#(I49, I50, I51, I52, I53, I54, I55) -> f10#(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 9) f15#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 10) f15#(I63, I64, I65, I66, I67, I68, I69) -> f12#(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 11) f15#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 12) f13#(I77, I78, I79, I80, I81, I82, I83) -> f14#(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 13) f12#(I84, I85, I86, I87, I88, I89, I90) -> f13#(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 14) f11#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 15) f11#(I98, I99, I100, I101, I102, I103, I104) -> f5#(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 16) f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 18) f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 19) f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 20) f6#(I135, I136, I137, I138, I139, I140, I141) -> f3#(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 22) f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 80.00/78.78 We have the following SCCs. 80.00/78.78 { 6, 7, 9, 10, 11, 12, 13 } 80.00/78.78 { 4, 5, 14, 16, 17, 18 } 80.00/78.78 { 3, 19, 21 } 80.00/78.78 { 2, 22 } 80.00/78.78 80.00/78.78 DP problem for innermost termination. 80.00/78.78 P = 80.00/78.78 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f1#(I156, I157, I158, I159, I160, I161, I162) -> f3#(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 R = 80.00/78.78 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17(I0, I1, I2, I3, I4, I5, I6) -> f14(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14(I35, I36, I37, I38, I39, I40, I41) -> f16(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16(I49, I50, I51, I52, I53, I54, I55) -> f10(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15(I63, I64, I65, I66, I67, I68, I69) -> f12(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13(I77, I78, I79, I80, I81, I82, I83) -> f14(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12(I84, I85, I86, I87, I88, I89, I90) -> f13(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 80.00/78.78 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 80.00/78.78 80.00/78.78 We use the reverse value criterion with the projection function NU: 80.00/78.78 NU[f1#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 80.00/78.78 NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 80.00/78.78 80.00/78.78 This gives the following inequalities: 80.00/78.78 ==> I10 + -1 * (1 + I8) >= I10 + -1 * (1 + I8) 80.00/78.78 1 + I157 <= I159 ==> I159 + -1 * (1 + I157) > I159 + -1 * (1 + (1 + I157)) with I159 + -1 * (1 + I157) >= 0 80.00/78.78 80.00/78.78 We remove all the strictly oriented dependency pairs. 80.00/78.78 80.00/78.78 DP problem for innermost termination. 80.00/78.78 P = 80.00/78.78 f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 R = 80.00/78.78 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17(I0, I1, I2, I3, I4, I5, I6) -> f14(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14(I35, I36, I37, I38, I39, I40, I41) -> f16(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16(I49, I50, I51, I52, I53, I54, I55) -> f10(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15(I63, I64, I65, I66, I67, I68, I69) -> f12(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13(I77, I78, I79, I80, I81, I82, I83) -> f14(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12(I84, I85, I86, I87, I88, I89, I90) -> f13(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 80.00/78.78 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 80.00/78.78 80.00/78.78 The dependency graph for this problem is: 80.00/78.78 2 -> 80.00/78.78 Where: 80.00/78.78 2) f3#(I7, I8, I9, I10, I11, I12, I13) -> f1#(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 80.00/78.78 We have the following SCCs. 80.00/78.78 80.00/78.78 80.00/78.78 DP problem for innermost termination. 80.00/78.78 P = 80.00/78.78 f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f6#(I126, I127, I128, I129, I130, I131, I132) -> f4#(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 R = 80.00/78.78 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17(I0, I1, I2, I3, I4, I5, I6) -> f14(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14(I35, I36, I37, I38, I39, I40, I41) -> f16(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16(I49, I50, I51, I52, I53, I54, I55) -> f10(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15(I63, I64, I65, I66, I67, I68, I69) -> f12(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13(I77, I78, I79, I80, I81, I82, I83) -> f14(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12(I84, I85, I86, I87, I88, I89, I90) -> f13(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 80.00/78.78 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 80.00/78.78 80.00/78.78 We use the extended value criterion with the projection function NU: 80.00/78.78 NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 80.00/78.78 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 80.00/78.78 NU[f5#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 80.00/78.78 80.00/78.78 This gives the following inequalities: 80.00/78.78 ==> I14 - I15 - 1 >= I14 - I15 - 1 80.00/78.78 I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126 ==> I126 - I127 - 1 > I126 - I127 - 2 with I126 - I127 - 1 >= 0 80.00/78.78 ==> I149 - I150 - 2 >= I149 - (1 + I150) - 1 80.00/78.78 80.00/78.78 We remove all the strictly oriented dependency pairs. 80.00/78.78 80.00/78.78 DP problem for innermost termination. 80.00/78.78 P = 80.00/78.78 f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 R = 80.00/78.78 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17(I0, I1, I2, I3, I4, I5, I6) -> f14(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14(I35, I36, I37, I38, I39, I40, I41) -> f16(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16(I49, I50, I51, I52, I53, I54, I55) -> f10(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15(I63, I64, I65, I66, I67, I68, I69) -> f12(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13(I77, I78, I79, I80, I81, I82, I83) -> f14(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12(I84, I85, I86, I87, I88, I89, I90) -> f13(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 80.00/78.78 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 80.00/78.78 80.00/78.78 The dependency graph for this problem is: 80.00/78.78 3 -> 80.00/78.78 21 -> 3 80.00/78.78 Where: 80.00/78.78 3) f5#(I14, I15, I16, I17, I18, I19, I20) -> f6#(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 80.00/78.78 We have the following SCCs. 80.00/78.78 80.00/78.78 80.00/78.78 DP problem for innermost termination. 80.00/78.78 P = 80.00/78.78 f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10#(I28, I29, I30, I31, I32, I33, I34) -> f11#(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f11#(I91, I92, I93, I94, I95, I96, I97) -> f8#(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 R = 80.00/78.78 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17(I0, I1, I2, I3, I4, I5, I6) -> f14(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14(I35, I36, I37, I38, I39, I40, I41) -> f16(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16(I49, I50, I51, I52, I53, I54, I55) -> f10(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15(I63, I64, I65, I66, I67, I68, I69) -> f12(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13(I77, I78, I79, I80, I81, I82, I83) -> f14(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12(I84, I85, I86, I87, I88, I89, I90) -> f13(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 80.00/78.78 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 80.00/78.78 80.00/78.78 We use the extended value criterion with the projection function NU: 80.00/78.78 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 80.00/78.78 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 80.00/78.78 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 80.00/78.78 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 80.00/78.78 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 80.00/78.78 80.00/78.78 This gives the following inequalities: 80.00/78.78 ==> -I22 + I24 - 2 >= -I22 + I24 - 2 80.00/78.78 ==> -I29 + I31 - 1 >= -I29 + I31 - 1 80.00/78.78 1 + I92 <= I94 ==> -I92 + I94 - 1 > -I92 + I94 - 2 with -I92 + I94 - 1 >= 0 80.00/78.78 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105 ==> -I106 + I108 - 2 >= -I106 + I108 - 2 80.00/78.78 I112 <= I114 ==> -I113 + I115 - 2 >= -(1 + I113) + I115 - 1 80.00/78.78 ==> -I120 + I122 - 2 >= -I120 + I122 - 2 80.00/78.78 80.00/78.78 We remove all the strictly oriented dependency pairs. 80.00/78.78 80.00/78.78 DP problem for innermost termination. 80.00/78.78 P = 80.00/78.78 f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10#(I28, I29, I30, I31, I32, I33, I34) -> f11#(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 R = 80.00/78.78 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17(I0, I1, I2, I3, I4, I5, I6) -> f14(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14(I35, I36, I37, I38, I39, I40, I41) -> f16(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16(I49, I50, I51, I52, I53, I54, I55) -> f10(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15(I63, I64, I65, I66, I67, I68, I69) -> f12(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13(I77, I78, I79, I80, I81, I82, I83) -> f14(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12(I84, I85, I86, I87, I88, I89, I90) -> f13(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 80.00/78.78 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 80.00/78.78 80.00/78.78 The dependency graph for this problem is: 80.00/78.78 4 -> 16, 17 80.00/78.78 5 -> 80.00/78.78 16 -> 18 80.00/78.78 17 -> 5 80.00/78.78 18 -> 4 80.00/78.78 Where: 80.00/78.78 4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 5) f10#(I28, I29, I30, I31, I32, I33, I34) -> f11#(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 16) f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 17) f9#(I112, I113, I114, I115, I116, I117, I118) -> f10#(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 18) f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 80.00/78.78 We have the following SCCs. 80.00/78.78 { 4, 16, 18 } 80.00/78.78 80.00/78.78 DP problem for innermost termination. 80.00/78.78 P = 80.00/78.78 f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f9#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 R = 80.00/78.78 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17(I0, I1, I2, I3, I4, I5, I6) -> f14(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14(I35, I36, I37, I38, I39, I40, I41) -> f16(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16(I49, I50, I51, I52, I53, I54, I55) -> f10(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15(I63, I64, I65, I66, I67, I68, I69) -> f12(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13(I77, I78, I79, I80, I81, I82, I83) -> f14(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12(I84, I85, I86, I87, I88, I89, I90) -> f13(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 80.00/78.78 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 80.00/78.78 80.00/78.78 We use the extended value criterion with the projection function NU: 80.00/78.78 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2 80.00/78.78 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 80.00/78.78 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 80.00/78.78 80.00/78.78 This gives the following inequalities: 80.00/78.78 ==> I21 - I23 - 1 >= I21 - I23 - 1 80.00/78.78 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105 ==> I105 - I107 - 1 > I105 - I107 - 2 with I105 - I107 - 1 >= 0 80.00/78.78 ==> I119 - I121 - 2 >= I119 - (1 + I121) - 1 80.00/78.78 80.00/78.78 We remove all the strictly oriented dependency pairs. 80.00/78.78 80.00/78.78 DP problem for innermost termination. 80.00/78.78 P = 80.00/78.78 f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 R = 80.00/78.78 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17(I0, I1, I2, I3, I4, I5, I6) -> f14(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14(I35, I36, I37, I38, I39, I40, I41) -> f16(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16(I49, I50, I51, I52, I53, I54, I55) -> f10(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15(I63, I64, I65, I66, I67, I68, I69) -> f12(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13(I77, I78, I79, I80, I81, I82, I83) -> f14(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12(I84, I85, I86, I87, I88, I89, I90) -> f13(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 80.00/78.78 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 80.00/78.78 80.00/78.78 The dependency graph for this problem is: 80.00/78.78 4 -> 80.00/78.78 18 -> 4 80.00/78.78 Where: 80.00/78.78 4) f8#(I21, I22, I23, I24, I25, I26, I27) -> f9#(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 18) f7#(I119, I120, I121, I122, I123, I124, I125) -> f8#(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 80.00/78.78 We have the following SCCs. 80.00/78.78 80.00/78.78 80.00/78.78 DP problem for innermost termination. 80.00/78.78 P = 80.00/78.78 f14#(I35, I36, I37, I38, I39, I40, I41) -> f16#(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16#(I42, I43, I44, I45, I46, I47, I48) -> f15#(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f15#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15#(I63, I64, I65, I66, I67, I68, I69) -> f12#(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13#(I77, I78, I79, I80, I81, I82, I83) -> f14#(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12#(I84, I85, I86, I87, I88, I89, I90) -> f13#(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 R = 80.00/78.78 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17(I0, I1, I2, I3, I4, I5, I6) -> f14(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14(I35, I36, I37, I38, I39, I40, I41) -> f16(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16(I49, I50, I51, I52, I53, I54, I55) -> f10(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15(I63, I64, I65, I66, I67, I68, I69) -> f12(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13(I77, I78, I79, I80, I81, I82, I83) -> f14(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12(I84, I85, I86, I87, I88, I89, I90) -> f13(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 80.00/78.78 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 80.00/78.78 80.00/78.78 We use the extended value criterion with the projection function NU: 80.00/78.78 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 80.00/78.78 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 80.00/78.78 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 80.00/78.78 NU[f16#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 80.00/78.78 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 80.00/78.78 80.00/78.78 This gives the following inequalities: 80.00/78.78 ==> -I36 + I38 - 1 >= -I36 + I38 - 1 80.00/78.78 1 + I43 <= I45 ==> -I43 + I45 - 1 > -I43 + I45 - 2 with -I43 + I45 - 1 >= 0 80.00/78.78 I60 <= I57 /\ I57 <= I60 ==> -I57 + I59 - 2 >= -I57 + I59 - 2 80.00/78.78 1 + I64 <= I67 ==> -I64 + I66 - 2 >= -I64 + I66 - 2 80.00/78.78 1 + I74 <= I71 ==> -I71 + I73 - 2 >= -I71 + I73 - 2 80.00/78.78 ==> -I78 + I80 - 2 >= -(1 + I78) + I80 - 1 80.00/78.78 ==> -I85 + I87 - 2 >= -I85 + I87 - 2 80.00/78.78 80.00/78.78 We remove all the strictly oriented dependency pairs. 80.00/78.78 80.00/78.78 DP problem for innermost termination. 80.00/78.78 P = 80.00/78.78 f14#(I35, I36, I37, I38, I39, I40, I41) -> f16#(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f15#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15#(I63, I64, I65, I66, I67, I68, I69) -> f12#(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13#(I77, I78, I79, I80, I81, I82, I83) -> f14#(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12#(I84, I85, I86, I87, I88, I89, I90) -> f13#(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 R = 80.00/78.78 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 80.00/78.78 f17(I0, I1, I2, I3, I4, I5, I6) -> f14(17, 0, I2, 5, 0, I5, I6) 80.00/78.78 f3(I7, I8, I9, I10, I11, I12, I13) -> f1(I7, I8, I9, I10, I11, I12, I13) 80.00/78.78 f5(I14, I15, I16, I17, I18, I19, I20) -> f6(I14, I15, I16, I17, I18, I19, I20) 80.00/78.78 f8(I21, I22, I23, I24, I25, I26, I27) -> f9(I21, I22, I23, I24, I25, I26, I27) 80.00/78.78 f10(I28, I29, I30, I31, I32, I33, I34) -> f11(I28, I29, I30, I31, I32, I33, I34) 80.00/78.78 f14(I35, I36, I37, I38, I39, I40, I41) -> f16(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 f16(I42, I43, I44, I45, I46, I47, I48) -> f15(I42, I43, I44, I45, I46, I47, I48) [1 + I43 <= I45] 80.00/78.78 f16(I49, I50, I51, I52, I53, I54, I55) -> f10(I49, 0, I51, I52, I53, I54, I55) [I52 <= I50] 80.00/78.78 f15(I56, I57, I58, I59, I60, I61, I62) -> f13(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 f15(I63, I64, I65, I66, I67, I68, I69) -> f12(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 f15(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 f13(I77, I78, I79, I80, I81, I82, I83) -> f14(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 f12(I84, I85, I86, I87, I88, I89, I90) -> f13(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 f11(I91, I92, I93, I94, I95, I96, I97) -> f8(I91, I92, 0, I94, I95, I96, I97) [1 + I92 <= I94] 80.00/78.78 f11(I98, I99, I100, I101, I102, I103, I104) -> f5(I98, 0, I100, I101, I102, I103, I104) [I101 <= I99] 80.00/78.78 f9(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, I107, I108, I109, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I107 <= I105] 80.00/78.78 f9(I112, I113, I114, I115, I116, I117, I118) -> f10(I112, 1 + I113, I114, I115, I116, I117, I118) [I112 <= I114] 80.00/78.78 f7(I119, I120, I121, I122, I123, I124, I125) -> f8(I119, I120, 1 + I121, I122, I123, I124, I125) 80.00/78.78 f6(I126, I127, I128, I129, I130, I131, I132) -> f4(I126, I127, I128, I129, I130, I133, I134) [I134 = I134 /\ I133 = I133 /\ 1 + I127 <= I126] 80.00/78.78 f6(I135, I136, I137, I138, I139, I140, I141) -> f3(I135, 0, I137, I138, I139, I140, I141) [I135 <= I136] 80.00/78.78 f4(I142, I143, I144, I145, I146, I147, I148) -> f2(I142, I143, I144, I145, I146, I147, I148) 80.00/78.78 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 1 + I150, I151, I152, I153, I154, I155) 80.00/78.78 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, 1 + I157, I158, I159, I160, I161, I162) [1 + I157 <= I159] 80.00/78.78 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, I164, I165, I166, I167, I168, I169) [I166 <= I164] 80.00/78.78 80.00/78.78 The dependency graph for this problem is: 80.00/78.78 6 -> 80.00/78.78 9 -> 12 80.00/78.78 10 -> 13 80.00/78.78 11 -> 13 80.00/78.78 12 -> 6 80.00/78.78 13 -> 12 80.00/78.78 Where: 80.00/78.78 6) f14#(I35, I36, I37, I38, I39, I40, I41) -> f16#(I35, I36, I37, I38, I39, I40, I41) 80.00/78.78 9) f15#(I56, I57, I58, I59, I60, I61, I62) -> f13#(I56, I57, I58, I59, I60, I61, I62) [I60 <= I57 /\ I57 <= I60] 80.00/78.78 10) f15#(I63, I64, I65, I66, I67, I68, I69) -> f12#(I63, I64, I65, I66, I67, I68, I69) [1 + I64 <= I67] 80.00/78.78 11) f15#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, I72, I73, I74, I75, I76) [1 + I74 <= I71] 80.00/78.78 12) f13#(I77, I78, I79, I80, I81, I82, I83) -> f14#(I77, 1 + I78, I79, I80, I81, I82, I83) 80.00/78.78 13) f12#(I84, I85, I86, I87, I88, I89, I90) -> f13#(I84, I85, I86, I87, I88, I89, I90) 80.00/78.78 80.00/78.78 We have the following SCCs. 80.00/78.78 80.00/81.75 EOF