86.55/85.11 YES 86.55/85.11 86.55/85.11 DP problem for innermost termination. 86.55/85.11 P = 86.55/85.11 f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17#(I0, I1, I2, I3, I4, I5, I6) -> f13#(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16#(I7, I8, I9, I10, I11, I12, I13) -> f5#(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f5#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2#(I28, I29, I30, I31, I32, I33, I34) -> f4#(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7#(I35, I36, I37, I38, I39, I40, I41) -> f8#(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9#(I42, I43, I44, I45, I46, I47, I48) -> f10#(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13#(I49, I50, I51, I52, I53, I54, I55) -> f15#(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14#(I77, I78, I79, I80, I81, I82, I83) -> f11#(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12#(I91, I92, I93, I94, I95, I96, I97) -> f13#(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11#(I98, I99, I100, I101, I102, I103, I104) -> f12#(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10#(I112, I113, I114, I115, I116, I117, I118) -> f2#(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8#(I119, I120, I121, I122, I123, I124, I125) -> f6#(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8#(I126, I127, I128, I129, I130, I131, I132) -> f9#(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6#(I133, I134, I135, I136, I137, I138, I139) -> f7#(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4#(I140, I141, I142, I143, I144, I145, I146) -> f1#(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 R = 86.55/85.11 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17(I0, I1, I2, I3, I4, I5, I6) -> f13(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16(I7, I8, I9, I10, I11, I12, I13) -> f5(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f16(I14, I15, I16, I17, I18, I19, I20) -> f3(I14, I15, I16, I17, I18, I19, I20) [I17 <= I15] 86.55/85.11 f5(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2(I28, I29, I30, I31, I32, I33, I34) -> f4(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7(I35, I36, I37, I38, I39, I40, I41) -> f8(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9(I42, I43, I44, I45, I46, I47, I48) -> f10(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14(I77, I78, I79, I80, I81, I82, I83) -> f11(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10(I112, I113, I114, I115, I116, I117, I118) -> f2(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8(I126, I127, I128, I129, I130, I131, I132) -> f9(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4(I140, I141, I142, I143, I144, I145, I146) -> f1(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, I157, I158, I159, I160, I161, I162) 86.55/85.11 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 The dependency graph for this problem is: 86.55/85.11 0 -> 1 86.55/85.11 1 -> 7 86.55/85.11 2 -> 3 86.55/85.11 3 -> 2 86.55/85.11 4 -> 20, 21 86.55/85.11 5 -> 17, 18 86.55/85.11 6 -> 15, 16 86.55/85.11 7 -> 8, 9 86.55/85.11 8 -> 10, 11, 12 86.55/85.11 9 -> 6 86.55/85.11 10 -> 13 86.55/85.11 11 -> 14 86.55/85.11 12 -> 14 86.55/85.11 13 -> 7 86.55/85.11 14 -> 13 86.55/85.11 15 -> 5 86.55/85.11 16 -> 4 86.55/85.11 17 -> 19 86.55/85.11 18 -> 6 86.55/85.11 19 -> 5 86.55/85.11 20 -> 22 86.55/85.11 21 -> 3 86.55/85.11 22 -> 4 86.55/85.11 Where: 86.55/85.11 0) f18#(x1, x2, x3, x4, x5, x6, x7) -> f17#(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 1) f17#(I0, I1, I2, I3, I4, I5, I6) -> f13#(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 2) f16#(I7, I8, I9, I10, I11, I12, I13) -> f5#(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 3) f5#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 4) f2#(I28, I29, I30, I31, I32, I33, I34) -> f4#(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 5) f7#(I35, I36, I37, I38, I39, I40, I41) -> f8#(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 6) f9#(I42, I43, I44, I45, I46, I47, I48) -> f10#(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 7) f13#(I49, I50, I51, I52, I53, I54, I55) -> f15#(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 8) f15#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 9) f15#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 10) f14#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 11) f14#(I77, I78, I79, I80, I81, I82, I83) -> f11#(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 12) f14#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 13) f12#(I91, I92, I93, I94, I95, I96, I97) -> f13#(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 14) f11#(I98, I99, I100, I101, I102, I103, I104) -> f12#(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 15) f10#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 16) f10#(I112, I113, I114, I115, I116, I117, I118) -> f2#(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 17) f8#(I119, I120, I121, I122, I123, I124, I125) -> f6#(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 18) f8#(I126, I127, I128, I129, I130, I131, I132) -> f9#(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 19) f6#(I133, I134, I135, I136, I137, I138, I139) -> f7#(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 20) f4#(I140, I141, I142, I143, I144, I145, I146) -> f1#(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 21) f4#(I149, I150, I151, I152, I153, I154, I155) -> f5#(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 22) f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 We have the following SCCs. 86.55/85.11 { 7, 8, 10, 11, 12, 13, 14 } 86.55/85.11 { 5, 6, 15, 17, 18, 19 } 86.55/85.11 { 4, 20, 22 } 86.55/85.11 { 2, 3 } 86.55/85.11 86.55/85.11 DP problem for innermost termination. 86.55/85.11 P = 86.55/85.11 f16#(I7, I8, I9, I10, I11, I12, I13) -> f5#(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f5#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 R = 86.55/85.11 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17(I0, I1, I2, I3, I4, I5, I6) -> f13(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16(I7, I8, I9, I10, I11, I12, I13) -> f5(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f16(I14, I15, I16, I17, I18, I19, I20) -> f3(I14, I15, I16, I17, I18, I19, I20) [I17 <= I15] 86.55/85.11 f5(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2(I28, I29, I30, I31, I32, I33, I34) -> f4(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7(I35, I36, I37, I38, I39, I40, I41) -> f8(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9(I42, I43, I44, I45, I46, I47, I48) -> f10(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14(I77, I78, I79, I80, I81, I82, I83) -> f11(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10(I112, I113, I114, I115, I116, I117, I118) -> f2(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8(I126, I127, I128, I129, I130, I131, I132) -> f9(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4(I140, I141, I142, I143, I144, I145, I146) -> f1(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, I157, I158, I159, I160, I161, I162) 86.55/85.11 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 We use the reverse value criterion with the projection function NU: 86.55/85.11 NU[f5#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 86.55/85.11 NU[f16#(z1,z2,z3,z4,z5,z6,z7)] = z4 + -1 * (1 + z2) 86.55/85.11 86.55/85.11 This gives the following inequalities: 86.55/85.11 1 + I8 <= I10 ==> I10 + -1 * (1 + I8) > I10 + -1 * (1 + (1 + I8)) with I10 + -1 * (1 + I8) >= 0 86.55/85.11 ==> I24 + -1 * (1 + I22) >= I24 + -1 * (1 + I22) 86.55/85.11 86.55/85.11 We remove all the strictly oriented dependency pairs. 86.55/85.11 86.55/85.11 DP problem for innermost termination. 86.55/85.11 P = 86.55/85.11 f5#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 R = 86.55/85.11 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17(I0, I1, I2, I3, I4, I5, I6) -> f13(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16(I7, I8, I9, I10, I11, I12, I13) -> f5(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f16(I14, I15, I16, I17, I18, I19, I20) -> f3(I14, I15, I16, I17, I18, I19, I20) [I17 <= I15] 86.55/85.11 f5(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2(I28, I29, I30, I31, I32, I33, I34) -> f4(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7(I35, I36, I37, I38, I39, I40, I41) -> f8(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9(I42, I43, I44, I45, I46, I47, I48) -> f10(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14(I77, I78, I79, I80, I81, I82, I83) -> f11(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10(I112, I113, I114, I115, I116, I117, I118) -> f2(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8(I126, I127, I128, I129, I130, I131, I132) -> f9(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4(I140, I141, I142, I143, I144, I145, I146) -> f1(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, I157, I158, I159, I160, I161, I162) 86.55/85.11 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 The dependency graph for this problem is: 86.55/85.11 3 -> 86.55/85.11 Where: 86.55/85.11 3) f5#(I21, I22, I23, I24, I25, I26, I27) -> f16#(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 86.55/85.11 We have the following SCCs. 86.55/85.11 86.55/85.11 86.55/85.11 DP problem for innermost termination. 86.55/85.11 P = 86.55/85.11 f2#(I28, I29, I30, I31, I32, I33, I34) -> f4#(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f4#(I140, I141, I142, I143, I144, I145, I146) -> f1#(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 R = 86.55/85.11 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17(I0, I1, I2, I3, I4, I5, I6) -> f13(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16(I7, I8, I9, I10, I11, I12, I13) -> f5(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f16(I14, I15, I16, I17, I18, I19, I20) -> f3(I14, I15, I16, I17, I18, I19, I20) [I17 <= I15] 86.55/85.11 f5(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2(I28, I29, I30, I31, I32, I33, I34) -> f4(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7(I35, I36, I37, I38, I39, I40, I41) -> f8(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9(I42, I43, I44, I45, I46, I47, I48) -> f10(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14(I77, I78, I79, I80, I81, I82, I83) -> f11(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10(I112, I113, I114, I115, I116, I117, I118) -> f2(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8(I126, I127, I128, I129, I130, I131, I132) -> f9(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4(I140, I141, I142, I143, I144, I145, I146) -> f1(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, I157, I158, I159, I160, I161, I162) 86.55/85.11 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 We use the extended value criterion with the projection function NU: 86.55/85.11 NU[f1#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 2 86.55/85.11 NU[f4#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 86.55/85.11 NU[f2#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x1 - 1 86.55/85.11 86.55/85.11 This gives the following inequalities: 86.55/85.11 ==> I28 - I29 - 1 >= I28 - I29 - 1 86.55/85.11 I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140 ==> I140 - I141 - 1 > I140 - I141 - 2 with I140 - I141 - 1 >= 0 86.55/85.11 ==> I163 - I164 - 2 >= I163 - (1 + I164) - 1 86.55/85.11 86.55/85.11 We remove all the strictly oriented dependency pairs. 86.55/85.11 86.55/85.11 DP problem for innermost termination. 86.55/85.11 P = 86.55/85.11 f2#(I28, I29, I30, I31, I32, I33, I34) -> f4#(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 R = 86.55/85.11 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17(I0, I1, I2, I3, I4, I5, I6) -> f13(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16(I7, I8, I9, I10, I11, I12, I13) -> f5(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f16(I14, I15, I16, I17, I18, I19, I20) -> f3(I14, I15, I16, I17, I18, I19, I20) [I17 <= I15] 86.55/85.11 f5(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2(I28, I29, I30, I31, I32, I33, I34) -> f4(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7(I35, I36, I37, I38, I39, I40, I41) -> f8(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9(I42, I43, I44, I45, I46, I47, I48) -> f10(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14(I77, I78, I79, I80, I81, I82, I83) -> f11(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10(I112, I113, I114, I115, I116, I117, I118) -> f2(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8(I126, I127, I128, I129, I130, I131, I132) -> f9(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4(I140, I141, I142, I143, I144, I145, I146) -> f1(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, I157, I158, I159, I160, I161, I162) 86.55/85.11 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 The dependency graph for this problem is: 86.55/85.11 4 -> 86.55/85.11 22 -> 4 86.55/85.11 Where: 86.55/85.11 4) f2#(I28, I29, I30, I31, I32, I33, I34) -> f4#(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 22) f1#(I163, I164, I165, I166, I167, I168, I169) -> f2#(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 We have the following SCCs. 86.55/85.11 86.55/85.11 86.55/85.11 DP problem for innermost termination. 86.55/85.11 P = 86.55/85.11 f7#(I35, I36, I37, I38, I39, I40, I41) -> f8#(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9#(I42, I43, I44, I45, I46, I47, I48) -> f10#(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f10#(I105, I106, I107, I108, I109, I110, I111) -> f7#(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f8#(I119, I120, I121, I122, I123, I124, I125) -> f6#(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8#(I126, I127, I128, I129, I130, I131, I132) -> f9#(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6#(I133, I134, I135, I136, I137, I138, I139) -> f7#(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 R = 86.55/85.11 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17(I0, I1, I2, I3, I4, I5, I6) -> f13(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16(I7, I8, I9, I10, I11, I12, I13) -> f5(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f16(I14, I15, I16, I17, I18, I19, I20) -> f3(I14, I15, I16, I17, I18, I19, I20) [I17 <= I15] 86.55/85.11 f5(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2(I28, I29, I30, I31, I32, I33, I34) -> f4(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7(I35, I36, I37, I38, I39, I40, I41) -> f8(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9(I42, I43, I44, I45, I46, I47, I48) -> f10(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14(I77, I78, I79, I80, I81, I82, I83) -> f11(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10(I112, I113, I114, I115, I116, I117, I118) -> f2(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8(I126, I127, I128, I129, I130, I131, I132) -> f9(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4(I140, I141, I142, I143, I144, I145, I146) -> f1(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, I157, I158, I159, I160, I161, I162) 86.55/85.11 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 We use the extended value criterion with the projection function NU: 86.55/85.11 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 86.55/85.11 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 86.55/85.11 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 86.55/85.11 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 86.55/85.11 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 86.55/85.11 86.55/85.11 This gives the following inequalities: 86.55/85.11 ==> -I36 + I38 - 2 >= -I36 + I38 - 2 86.55/85.11 ==> -I43 + I45 - 1 >= -I43 + I45 - 1 86.55/85.11 1 + I106 <= I108 ==> -I106 + I108 - 1 > -I106 + I108 - 2 with -I106 + I108 - 1 >= 0 86.55/85.11 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119 ==> -I120 + I122 - 2 >= -I120 + I122 - 2 86.55/85.11 I126 <= I128 ==> -I127 + I129 - 2 >= -(1 + I127) + I129 - 1 86.55/85.11 ==> -I134 + I136 - 2 >= -I134 + I136 - 2 86.55/85.11 86.55/85.11 We remove all the strictly oriented dependency pairs. 86.55/85.11 86.55/85.11 DP problem for innermost termination. 86.55/85.11 P = 86.55/85.11 f7#(I35, I36, I37, I38, I39, I40, I41) -> f8#(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9#(I42, I43, I44, I45, I46, I47, I48) -> f10#(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f8#(I119, I120, I121, I122, I123, I124, I125) -> f6#(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8#(I126, I127, I128, I129, I130, I131, I132) -> f9#(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6#(I133, I134, I135, I136, I137, I138, I139) -> f7#(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 R = 86.55/85.11 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17(I0, I1, I2, I3, I4, I5, I6) -> f13(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16(I7, I8, I9, I10, I11, I12, I13) -> f5(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f16(I14, I15, I16, I17, I18, I19, I20) -> f3(I14, I15, I16, I17, I18, I19, I20) [I17 <= I15] 86.55/85.11 f5(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2(I28, I29, I30, I31, I32, I33, I34) -> f4(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7(I35, I36, I37, I38, I39, I40, I41) -> f8(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9(I42, I43, I44, I45, I46, I47, I48) -> f10(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14(I77, I78, I79, I80, I81, I82, I83) -> f11(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10(I112, I113, I114, I115, I116, I117, I118) -> f2(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8(I126, I127, I128, I129, I130, I131, I132) -> f9(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4(I140, I141, I142, I143, I144, I145, I146) -> f1(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, I157, I158, I159, I160, I161, I162) 86.55/85.11 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 The dependency graph for this problem is: 86.55/85.11 5 -> 17, 18 86.55/85.11 6 -> 86.55/85.11 17 -> 19 86.55/85.11 18 -> 6 86.55/85.11 19 -> 5 86.55/85.11 Where: 86.55/85.11 5) f7#(I35, I36, I37, I38, I39, I40, I41) -> f8#(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 6) f9#(I42, I43, I44, I45, I46, I47, I48) -> f10#(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 17) f8#(I119, I120, I121, I122, I123, I124, I125) -> f6#(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 18) f8#(I126, I127, I128, I129, I130, I131, I132) -> f9#(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 19) f6#(I133, I134, I135, I136, I137, I138, I139) -> f7#(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 86.55/85.11 We have the following SCCs. 86.55/85.11 { 5, 17, 19 } 86.55/85.11 86.55/85.11 DP problem for innermost termination. 86.55/85.11 P = 86.55/85.11 f7#(I35, I36, I37, I38, I39, I40, I41) -> f8#(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f8#(I119, I120, I121, I122, I123, I124, I125) -> f6#(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f6#(I133, I134, I135, I136, I137, I138, I139) -> f7#(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 R = 86.55/85.11 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17(I0, I1, I2, I3, I4, I5, I6) -> f13(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16(I7, I8, I9, I10, I11, I12, I13) -> f5(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f16(I14, I15, I16, I17, I18, I19, I20) -> f3(I14, I15, I16, I17, I18, I19, I20) [I17 <= I15] 86.55/85.11 f5(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2(I28, I29, I30, I31, I32, I33, I34) -> f4(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7(I35, I36, I37, I38, I39, I40, I41) -> f8(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9(I42, I43, I44, I45, I46, I47, I48) -> f10(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14(I77, I78, I79, I80, I81, I82, I83) -> f11(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10(I112, I113, I114, I115, I116, I117, I118) -> f2(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8(I126, I127, I128, I129, I130, I131, I132) -> f9(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4(I140, I141, I142, I143, I144, I145, I146) -> f1(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, I157, I158, I159, I160, I161, I162) 86.55/85.11 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 We use the extended value criterion with the projection function NU: 86.55/85.11 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 2 86.55/85.11 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 86.55/85.11 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = x0 - x2 - 1 86.55/85.11 86.55/85.11 This gives the following inequalities: 86.55/85.11 ==> I35 - I37 - 1 >= I35 - I37 - 1 86.55/85.11 rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119 ==> I119 - I121 - 1 > I119 - I121 - 2 with I119 - I121 - 1 >= 0 86.55/85.11 ==> I133 - I135 - 2 >= I133 - (1 + I135) - 1 86.55/85.11 86.55/85.11 We remove all the strictly oriented dependency pairs. 86.55/85.11 86.55/85.11 DP problem for innermost termination. 86.55/85.11 P = 86.55/85.11 f7#(I35, I36, I37, I38, I39, I40, I41) -> f8#(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f6#(I133, I134, I135, I136, I137, I138, I139) -> f7#(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 R = 86.55/85.11 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17(I0, I1, I2, I3, I4, I5, I6) -> f13(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16(I7, I8, I9, I10, I11, I12, I13) -> f5(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f16(I14, I15, I16, I17, I18, I19, I20) -> f3(I14, I15, I16, I17, I18, I19, I20) [I17 <= I15] 86.55/85.11 f5(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2(I28, I29, I30, I31, I32, I33, I34) -> f4(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7(I35, I36, I37, I38, I39, I40, I41) -> f8(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9(I42, I43, I44, I45, I46, I47, I48) -> f10(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14(I77, I78, I79, I80, I81, I82, I83) -> f11(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10(I112, I113, I114, I115, I116, I117, I118) -> f2(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8(I126, I127, I128, I129, I130, I131, I132) -> f9(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4(I140, I141, I142, I143, I144, I145, I146) -> f1(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, I157, I158, I159, I160, I161, I162) 86.55/85.11 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 The dependency graph for this problem is: 86.55/85.11 5 -> 86.55/85.11 19 -> 5 86.55/85.11 Where: 86.55/85.11 5) f7#(I35, I36, I37, I38, I39, I40, I41) -> f8#(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 19) f6#(I133, I134, I135, I136, I137, I138, I139) -> f7#(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 86.55/85.11 We have the following SCCs. 86.55/85.11 86.55/85.11 86.55/85.11 DP problem for innermost termination. 86.55/85.11 P = 86.55/85.11 f13#(I49, I50, I51, I52, I53, I54, I55) -> f15#(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15#(I56, I57, I58, I59, I60, I61, I62) -> f14#(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f14#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14#(I77, I78, I79, I80, I81, I82, I83) -> f11#(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12#(I91, I92, I93, I94, I95, I96, I97) -> f13#(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11#(I98, I99, I100, I101, I102, I103, I104) -> f12#(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 R = 86.55/85.11 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17(I0, I1, I2, I3, I4, I5, I6) -> f13(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16(I7, I8, I9, I10, I11, I12, I13) -> f5(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f16(I14, I15, I16, I17, I18, I19, I20) -> f3(I14, I15, I16, I17, I18, I19, I20) [I17 <= I15] 86.55/85.11 f5(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2(I28, I29, I30, I31, I32, I33, I34) -> f4(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7(I35, I36, I37, I38, I39, I40, I41) -> f8(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9(I42, I43, I44, I45, I46, I47, I48) -> f10(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14(I77, I78, I79, I80, I81, I82, I83) -> f11(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10(I112, I113, I114, I115, I116, I117, I118) -> f2(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8(I126, I127, I128, I129, I130, I131, I132) -> f9(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4(I140, I141, I142, I143, I144, I145, I146) -> f1(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, I157, I158, I159, I160, I161, I162) 86.55/85.11 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 We use the extended value criterion with the projection function NU: 86.55/85.11 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 86.55/85.11 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 86.55/85.11 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 2 86.55/85.11 NU[f15#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 86.55/85.11 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + x3 - 1 86.55/85.11 86.55/85.11 This gives the following inequalities: 86.55/85.11 ==> -I50 + I52 - 1 >= -I50 + I52 - 1 86.55/85.11 1 + I57 <= I59 ==> -I57 + I59 - 1 > -I57 + I59 - 2 with -I57 + I59 - 1 >= 0 86.55/85.11 I74 <= I71 /\ I71 <= I74 ==> -I71 + I73 - 2 >= -I71 + I73 - 2 86.55/85.11 1 + I78 <= I81 ==> -I78 + I80 - 2 >= -I78 + I80 - 2 86.55/85.11 1 + I88 <= I85 ==> -I85 + I87 - 2 >= -I85 + I87 - 2 86.55/85.11 ==> -I92 + I94 - 2 >= -(1 + I92) + I94 - 1 86.55/85.11 ==> -I99 + I101 - 2 >= -I99 + I101 - 2 86.55/85.11 86.55/85.11 We remove all the strictly oriented dependency pairs. 86.55/85.11 86.55/85.11 DP problem for innermost termination. 86.55/85.11 P = 86.55/85.11 f13#(I49, I50, I51, I52, I53, I54, I55) -> f15#(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f14#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14#(I77, I78, I79, I80, I81, I82, I83) -> f11#(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12#(I91, I92, I93, I94, I95, I96, I97) -> f13#(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11#(I98, I99, I100, I101, I102, I103, I104) -> f12#(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 R = 86.55/85.11 f18(x1, x2, x3, x4, x5, x6, x7) -> f17(x1, x2, x3, x4, x5, x6, x7) 86.55/85.11 f17(I0, I1, I2, I3, I4, I5, I6) -> f13(20, 0, I2, 5, 0, I5, I6) 86.55/85.11 f16(I7, I8, I9, I10, I11, I12, I13) -> f5(I7, 1 + I8, I9, I10, I11, I12, I13) [1 + I8 <= I10] 86.55/85.11 f16(I14, I15, I16, I17, I18, I19, I20) -> f3(I14, I15, I16, I17, I18, I19, I20) [I17 <= I15] 86.55/85.11 f5(I21, I22, I23, I24, I25, I26, I27) -> f16(I21, I22, I23, I24, I25, I26, I27) 86.55/85.11 f2(I28, I29, I30, I31, I32, I33, I34) -> f4(I28, I29, I30, I31, I32, I33, I34) 86.55/85.11 f7(I35, I36, I37, I38, I39, I40, I41) -> f8(I35, I36, I37, I38, I39, I40, I41) 86.55/85.11 f9(I42, I43, I44, I45, I46, I47, I48) -> f10(I42, I43, I44, I45, I46, I47, I48) 86.55/85.11 f13(I49, I50, I51, I52, I53, I54, I55) -> f15(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 f15(I56, I57, I58, I59, I60, I61, I62) -> f14(I56, I57, I58, I59, I60, I61, I62) [1 + I57 <= I59] 86.55/85.11 f15(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, 0, I65, I66, I67, I68, I69) [I66 <= I64] 86.55/85.11 f14(I70, I71, I72, I73, I74, I75, I76) -> f12(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 f14(I77, I78, I79, I80, I81, I82, I83) -> f11(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 f14(I84, I85, I86, I87, I88, I89, I90) -> f11(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 f12(I91, I92, I93, I94, I95, I96, I97) -> f13(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 f11(I98, I99, I100, I101, I102, I103, I104) -> f12(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 f10(I105, I106, I107, I108, I109, I110, I111) -> f7(I105, I106, 0, I108, I109, I110, I111) [1 + I106 <= I108] 86.55/85.11 f10(I112, I113, I114, I115, I116, I117, I118) -> f2(I112, 0, I114, I115, I116, I117, I118) [I115 <= I113] 86.55/85.11 f8(I119, I120, I121, I122, I123, I124, I125) -> f6(I119, I120, I121, I122, I123, rnd6, rnd7) [rnd7 = rnd7 /\ rnd6 = rnd6 /\ 1 + I121 <= I119] 86.55/85.11 f8(I126, I127, I128, I129, I130, I131, I132) -> f9(I126, 1 + I127, I128, I129, I130, I131, I132) [I126 <= I128] 86.55/85.11 f6(I133, I134, I135, I136, I137, I138, I139) -> f7(I133, I134, 1 + I135, I136, I137, I138, I139) 86.55/85.11 f4(I140, I141, I142, I143, I144, I145, I146) -> f1(I140, I141, I142, I143, I144, I147, I148) [I148 = I148 /\ I147 = I147 /\ 1 + I141 <= I140] 86.55/85.11 f4(I149, I150, I151, I152, I153, I154, I155) -> f5(I149, 0, I151, I152, I153, I154, I155) [I149 <= I150] 86.55/85.11 f1(I156, I157, I158, I159, I160, I161, I162) -> f3(I156, I157, I158, I159, I160, I161, I162) 86.55/85.11 f1(I163, I164, I165, I166, I167, I168, I169) -> f2(I163, 1 + I164, I165, I166, I167, I168, I169) 86.55/85.11 86.55/85.11 The dependency graph for this problem is: 86.55/85.11 7 -> 86.55/85.11 10 -> 13 86.55/85.11 11 -> 14 86.55/85.11 12 -> 14 86.55/85.11 13 -> 7 86.55/85.11 14 -> 13 86.55/85.11 Where: 86.55/85.11 7) f13#(I49, I50, I51, I52, I53, I54, I55) -> f15#(I49, I50, I51, I52, I53, I54, I55) 86.55/85.11 10) f14#(I70, I71, I72, I73, I74, I75, I76) -> f12#(I70, I71, I72, I73, I74, I75, I76) [I74 <= I71 /\ I71 <= I74] 86.55/85.11 11) f14#(I77, I78, I79, I80, I81, I82, I83) -> f11#(I77, I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 86.55/85.11 12) f14#(I84, I85, I86, I87, I88, I89, I90) -> f11#(I84, I85, I86, I87, I88, I89, I90) [1 + I88 <= I85] 86.55/85.11 13) f12#(I91, I92, I93, I94, I95, I96, I97) -> f13#(I91, 1 + I92, I93, I94, I95, I96, I97) 86.55/85.11 14) f11#(I98, I99, I100, I101, I102, I103, I104) -> f12#(I98, I99, I100, I101, I102, I103, I104) 86.55/85.11 86.55/85.11 We have the following SCCs. 86.55/85.11 86.55/88.08 EOF