85.79/84.68 YES 85.79/84.68 85.79/84.68 DP problem for innermost termination. 85.79/84.68 P = 85.79/84.68 f13#(x1, x2, x3, x4, x5, x6, x7, x8) -> f12#(x1, x2, x3, x4, x5, x6, x7, x8) 85.79/84.68 f12#(I0, I1, I2, I3, I4, I5, I6, I7) -> f1#(I0, I1, I2, 0, I4, I5, I6, rnd8) [rnd8 = rnd8] 85.79/84.68 f2#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 f2#(I16, I17, I18, I19, I20, I21, I22, I23) -> f3#(I17, I17, I18, I19, 0, I21, I22, I23) [I17 <= I19] 85.79/84.68 f4#(I24, I25, I26, I27, I28, I29, I30, I31) -> f8#(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 f4#(I32, I33, I34, I35, I36, I37, I38, I39) -> f7#(I32, I33, I34, I35, 0, I37, I38, I39) [-1 + I32 <= I36] 85.79/84.68 f7#(I40, I41, I42, I43, I44, I45, I46, I47) -> f5#(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 f9#(I48, I49, I50, I51, I52, I53, I54, I55) -> f11#(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9#(I56, I57, I58, I59, I60, I61, I62, I63) -> f3#(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11#(I64, I65, I66, I67, I68, I69, I70, I71) -> f10#(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11#(I72, I73, I74, I75, I76, I77, I78, I79) -> f10#(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8#(I88, I89, I90, I91, I92, I93, I94, I95) -> f9#(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f5#(I96, I97, I98, I99, I100, I101, I102, I103) -> f7#(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 f3#(I112, I113, I114, I115, I116, I117, I118, I119) -> f4#(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 f1#(I120, I121, I122, I123, I124, I125, I126, I127) -> f2#(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 R = 85.79/84.68 f13(x1, x2, x3, x4, x5, x6, x7, x8) -> f12(x1, x2, x3, x4, x5, x6, x7, x8) 85.79/84.68 f12(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, I5, I6, rnd8) [rnd8 = rnd8] 85.79/84.68 f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I17, I17, I18, I19, 0, I21, I22, I23) [I17 <= I19] 85.79/84.68 f4(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f7(I32, I33, I34, I35, 0, I37, I38, I39) [-1 + I32 <= I36] 85.79/84.68 f7(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 f9(I48, I49, I50, I51, I52, I53, I54, I55) -> f11(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f3(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11(I64, I65, I66, I67, I68, I69, I70, I71) -> f10(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11(I72, I73, I74, I75, I76, I77, I78, I79) -> f10(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8(I88, I89, I90, I91, I92, I93, I94, I95) -> f9(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f5(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 f5(I104, I105, I106, I107, I108, I109, I110, I111) -> f6(I104, I105, I106, I107, I108, I109, I110, I111) [-1 + I104 <= I108] 85.79/84.68 f3(I112, I113, I114, I115, I116, I117, I118, I119) -> f4(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 85.79/84.68 The dependency graph for this problem is: 85.79/84.68 0 -> 1 85.79/84.68 1 -> 15 85.79/84.68 2 -> 15 85.79/84.68 3 -> 14 85.79/84.68 4 -> 12 85.79/84.68 5 -> 6 85.79/84.68 6 -> 13 85.79/84.68 7 -> 9, 10 85.79/84.68 8 -> 14 85.79/84.68 9 -> 11 85.79/84.68 10 -> 11 85.79/84.68 11 -> 12 85.79/84.68 12 -> 7, 8 85.79/84.68 13 -> 6 85.79/84.68 14 -> 4, 5 85.79/84.68 15 -> 2, 3 85.79/84.68 Where: 85.79/84.68 0) f13#(x1, x2, x3, x4, x5, x6, x7, x8) -> f12#(x1, x2, x3, x4, x5, x6, x7, x8) 85.79/84.68 1) f12#(I0, I1, I2, I3, I4, I5, I6, I7) -> f1#(I0, I1, I2, 0, I4, I5, I6, rnd8) [rnd8 = rnd8] 85.79/84.68 2) f2#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 3) f2#(I16, I17, I18, I19, I20, I21, I22, I23) -> f3#(I17, I17, I18, I19, 0, I21, I22, I23) [I17 <= I19] 85.79/84.68 4) f4#(I24, I25, I26, I27, I28, I29, I30, I31) -> f8#(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 5) f4#(I32, I33, I34, I35, I36, I37, I38, I39) -> f7#(I32, I33, I34, I35, 0, I37, I38, I39) [-1 + I32 <= I36] 85.79/84.68 6) f7#(I40, I41, I42, I43, I44, I45, I46, I47) -> f5#(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 7) f9#(I48, I49, I50, I51, I52, I53, I54, I55) -> f11#(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 8) f9#(I56, I57, I58, I59, I60, I61, I62, I63) -> f3#(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 9) f11#(I64, I65, I66, I67, I68, I69, I70, I71) -> f10#(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 10) f11#(I72, I73, I74, I75, I76, I77, I78, I79) -> f10#(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 11) f10#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 12) f8#(I88, I89, I90, I91, I92, I93, I94, I95) -> f9#(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 13) f5#(I96, I97, I98, I99, I100, I101, I102, I103) -> f7#(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 14) f3#(I112, I113, I114, I115, I116, I117, I118, I119) -> f4#(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 15) f1#(I120, I121, I122, I123, I124, I125, I126, I127) -> f2#(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 85.79/84.68 We have the following SCCs. 85.79/84.68 { 2, 15 } 85.79/84.68 { 4, 7, 8, 9, 10, 11, 12, 14 } 85.79/84.68 { 6, 13 } 85.79/84.68 85.79/84.68 DP problem for innermost termination. 85.79/84.68 P = 85.79/84.68 f7#(I40, I41, I42, I43, I44, I45, I46, I47) -> f5#(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 f5#(I96, I97, I98, I99, I100, I101, I102, I103) -> f7#(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 R = 85.79/84.68 f13(x1, x2, x3, x4, x5, x6, x7, x8) -> f12(x1, x2, x3, x4, x5, x6, x7, x8) 85.79/84.68 f12(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, I5, I6, rnd8) [rnd8 = rnd8] 85.79/84.68 f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I17, I17, I18, I19, 0, I21, I22, I23) [I17 <= I19] 85.79/84.68 f4(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f7(I32, I33, I34, I35, 0, I37, I38, I39) [-1 + I32 <= I36] 85.79/84.68 f7(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 f9(I48, I49, I50, I51, I52, I53, I54, I55) -> f11(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f3(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11(I64, I65, I66, I67, I68, I69, I70, I71) -> f10(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11(I72, I73, I74, I75, I76, I77, I78, I79) -> f10(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8(I88, I89, I90, I91, I92, I93, I94, I95) -> f9(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f5(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 f5(I104, I105, I106, I107, I108, I109, I110, I111) -> f6(I104, I105, I106, I107, I108, I109, I110, I111) [-1 + I104 <= I108] 85.79/84.68 f3(I112, I113, I114, I115, I116, I117, I118, I119) -> f4(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 85.79/84.68 We use the reverse value criterion with the projection function NU: 85.79/84.68 NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8)] = -1 + z1 + -1 * (1 + z5) 85.79/84.68 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8)] = -1 + z1 + -1 * (1 + z5) 85.79/84.68 85.79/84.68 This gives the following inequalities: 85.79/84.68 ==> -1 + I40 + -1 * (1 + I44) >= -1 + I40 + -1 * (1 + I44) 85.79/84.68 1 + I100 <= -1 + I96 ==> -1 + I96 + -1 * (1 + I100) > -1 + I96 + -1 * (1 + (1 + I100)) with -1 + I96 + -1 * (1 + I100) >= 0 85.79/84.68 85.79/84.68 We remove all the strictly oriented dependency pairs. 85.79/84.68 85.79/84.68 DP problem for innermost termination. 85.79/84.68 P = 85.79/84.68 f7#(I40, I41, I42, I43, I44, I45, I46, I47) -> f5#(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 R = 85.79/84.68 f13(x1, x2, x3, x4, x5, x6, x7, x8) -> f12(x1, x2, x3, x4, x5, x6, x7, x8) 85.79/84.68 f12(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, I5, I6, rnd8) [rnd8 = rnd8] 85.79/84.68 f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I17, I17, I18, I19, 0, I21, I22, I23) [I17 <= I19] 85.79/84.68 f4(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f7(I32, I33, I34, I35, 0, I37, I38, I39) [-1 + I32 <= I36] 85.79/84.68 f7(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 f9(I48, I49, I50, I51, I52, I53, I54, I55) -> f11(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f3(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11(I64, I65, I66, I67, I68, I69, I70, I71) -> f10(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11(I72, I73, I74, I75, I76, I77, I78, I79) -> f10(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8(I88, I89, I90, I91, I92, I93, I94, I95) -> f9(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f5(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 f5(I104, I105, I106, I107, I108, I109, I110, I111) -> f6(I104, I105, I106, I107, I108, I109, I110, I111) [-1 + I104 <= I108] 85.79/84.68 f3(I112, I113, I114, I115, I116, I117, I118, I119) -> f4(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 85.79/84.68 The dependency graph for this problem is: 85.79/84.68 6 -> 85.79/84.68 Where: 85.79/84.68 6) f7#(I40, I41, I42, I43, I44, I45, I46, I47) -> f5#(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 85.79/84.68 We have the following SCCs. 85.79/84.68 85.79/84.68 85.79/84.68 DP problem for innermost termination. 85.79/84.68 P = 85.79/84.68 f4#(I24, I25, I26, I27, I28, I29, I30, I31) -> f8#(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 f9#(I48, I49, I50, I51, I52, I53, I54, I55) -> f11#(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9#(I56, I57, I58, I59, I60, I61, I62, I63) -> f3#(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11#(I64, I65, I66, I67, I68, I69, I70, I71) -> f10#(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11#(I72, I73, I74, I75, I76, I77, I78, I79) -> f10#(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8#(I88, I89, I90, I91, I92, I93, I94, I95) -> f9#(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f3#(I112, I113, I114, I115, I116, I117, I118, I119) -> f4#(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 R = 85.79/84.68 f13(x1, x2, x3, x4, x5, x6, x7, x8) -> f12(x1, x2, x3, x4, x5, x6, x7, x8) 85.79/84.68 f12(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, I5, I6, rnd8) [rnd8 = rnd8] 85.79/84.68 f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I17, I17, I18, I19, 0, I21, I22, I23) [I17 <= I19] 85.79/84.68 f4(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f7(I32, I33, I34, I35, 0, I37, I38, I39) [-1 + I32 <= I36] 85.79/84.68 f7(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 f9(I48, I49, I50, I51, I52, I53, I54, I55) -> f11(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f3(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11(I64, I65, I66, I67, I68, I69, I70, I71) -> f10(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11(I72, I73, I74, I75, I76, I77, I78, I79) -> f10(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8(I88, I89, I90, I91, I92, I93, I94, I95) -> f9(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f5(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 f5(I104, I105, I106, I107, I108, I109, I110, I111) -> f6(I104, I105, I106, I107, I108, I109, I110, I111) [-1 + I104 <= I108] 85.79/84.68 f3(I112, I113, I114, I115, I116, I117, I118, I119) -> f4(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 85.79/84.68 We use the extended value criterion with the projection function NU: 85.79/84.68 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x4 - 3 85.79/84.68 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x4 - 2 85.79/84.68 NU[f11#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x4 - 3 85.79/84.68 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x4 - 3 85.79/84.68 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x4 - 3 85.79/84.68 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x4 - 2 85.79/84.68 85.79/84.68 This gives the following inequalities: 85.79/84.68 1 + I28 <= -1 + I24 ==> I24 - I28 - 2 > I24 - I28 - 3 with I24 - I28 - 2 >= 0 85.79/84.68 1 + I50 <= I48 ==> I48 - I52 - 3 >= I48 - I52 - 3 85.79/84.68 rnd7 = rnd7 /\ I56 <= I58 ==> I56 - I60 - 3 >= I56 - (1 + I60) - 2 85.79/84.68 ==> I64 - I68 - 3 >= I64 - I68 - 3 85.79/84.68 ==> I72 - I76 - 3 >= I72 - I76 - 3 85.79/84.68 ==> I80 - I84 - 3 >= I80 - I84 - 3 85.79/84.68 ==> I88 - I92 - 3 >= I88 - I92 - 3 85.79/84.68 ==> I112 - I116 - 2 >= I112 - I116 - 2 85.79/84.68 85.79/84.68 We remove all the strictly oriented dependency pairs. 85.79/84.68 85.79/84.68 DP problem for innermost termination. 85.79/84.68 P = 85.79/84.68 f9#(I48, I49, I50, I51, I52, I53, I54, I55) -> f11#(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9#(I56, I57, I58, I59, I60, I61, I62, I63) -> f3#(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11#(I64, I65, I66, I67, I68, I69, I70, I71) -> f10#(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11#(I72, I73, I74, I75, I76, I77, I78, I79) -> f10#(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8#(I88, I89, I90, I91, I92, I93, I94, I95) -> f9#(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f3#(I112, I113, I114, I115, I116, I117, I118, I119) -> f4#(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 R = 85.79/84.68 f13(x1, x2, x3, x4, x5, x6, x7, x8) -> f12(x1, x2, x3, x4, x5, x6, x7, x8) 85.79/84.68 f12(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, I5, I6, rnd8) [rnd8 = rnd8] 85.79/84.68 f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I17, I17, I18, I19, 0, I21, I22, I23) [I17 <= I19] 85.79/84.68 f4(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f7(I32, I33, I34, I35, 0, I37, I38, I39) [-1 + I32 <= I36] 85.79/84.68 f7(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 f9(I48, I49, I50, I51, I52, I53, I54, I55) -> f11(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f3(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11(I64, I65, I66, I67, I68, I69, I70, I71) -> f10(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11(I72, I73, I74, I75, I76, I77, I78, I79) -> f10(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8(I88, I89, I90, I91, I92, I93, I94, I95) -> f9(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f5(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 f5(I104, I105, I106, I107, I108, I109, I110, I111) -> f6(I104, I105, I106, I107, I108, I109, I110, I111) [-1 + I104 <= I108] 85.79/84.68 f3(I112, I113, I114, I115, I116, I117, I118, I119) -> f4(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 85.79/84.68 The dependency graph for this problem is: 85.79/84.68 7 -> 9, 10 85.79/84.68 8 -> 14 85.79/84.68 9 -> 11 85.79/84.68 10 -> 11 85.79/84.68 11 -> 12 85.79/84.68 12 -> 7, 8 85.79/84.68 14 -> 85.79/84.68 Where: 85.79/84.68 7) f9#(I48, I49, I50, I51, I52, I53, I54, I55) -> f11#(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 8) f9#(I56, I57, I58, I59, I60, I61, I62, I63) -> f3#(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 9) f11#(I64, I65, I66, I67, I68, I69, I70, I71) -> f10#(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 10) f11#(I72, I73, I74, I75, I76, I77, I78, I79) -> f10#(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 11) f10#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 12) f8#(I88, I89, I90, I91, I92, I93, I94, I95) -> f9#(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 14) f3#(I112, I113, I114, I115, I116, I117, I118, I119) -> f4#(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 85.79/84.68 We have the following SCCs. 85.79/84.68 { 7, 9, 10, 11, 12 } 85.79/84.68 85.79/84.68 DP problem for innermost termination. 85.79/84.68 P = 85.79/84.68 f9#(I48, I49, I50, I51, I52, I53, I54, I55) -> f11#(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f11#(I64, I65, I66, I67, I68, I69, I70, I71) -> f10#(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11#(I72, I73, I74, I75, I76, I77, I78, I79) -> f10#(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8#(I88, I89, I90, I91, I92, I93, I94, I95) -> f9#(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 R = 85.79/84.68 f13(x1, x2, x3, x4, x5, x6, x7, x8) -> f12(x1, x2, x3, x4, x5, x6, x7, x8) 85.79/84.68 f12(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, I5, I6, rnd8) [rnd8 = rnd8] 85.79/84.68 f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I17, I17, I18, I19, 0, I21, I22, I23) [I17 <= I19] 85.79/84.68 f4(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f7(I32, I33, I34, I35, 0, I37, I38, I39) [-1 + I32 <= I36] 85.79/84.68 f7(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 f9(I48, I49, I50, I51, I52, I53, I54, I55) -> f11(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f3(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11(I64, I65, I66, I67, I68, I69, I70, I71) -> f10(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11(I72, I73, I74, I75, I76, I77, I78, I79) -> f10(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8(I88, I89, I90, I91, I92, I93, I94, I95) -> f9(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f5(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 f5(I104, I105, I106, I107, I108, I109, I110, I111) -> f6(I104, I105, I106, I107, I108, I109, I110, I111) [-1 + I104 <= I108] 85.79/84.68 f3(I112, I113, I114, I115, I116, I117, I118, I119) -> f4(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 85.79/84.68 We use the extended value criterion with the projection function NU: 85.79/84.68 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x2 - 1 85.79/84.68 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x2 - 2 85.79/84.68 NU[f11#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x2 - 2 85.79/84.68 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7)] = x0 - x2 - 1 85.79/84.68 85.79/84.68 This gives the following inequalities: 85.79/84.68 1 + I50 <= I48 ==> I48 - I50 - 1 > I48 - I50 - 2 with I48 - I50 - 1 >= 0 85.79/84.68 ==> I64 - I66 - 2 >= I64 - I66 - 2 85.79/84.68 ==> I72 - I74 - 2 >= I72 - I74 - 2 85.79/84.68 ==> I80 - I82 - 2 >= I80 - (1 + I82) - 1 85.79/84.68 ==> I88 - I90 - 1 >= I88 - I90 - 1 85.79/84.68 85.79/84.68 We remove all the strictly oriented dependency pairs. 85.79/84.68 85.79/84.68 DP problem for innermost termination. 85.79/84.68 P = 85.79/84.68 f11#(I64, I65, I66, I67, I68, I69, I70, I71) -> f10#(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11#(I72, I73, I74, I75, I76, I77, I78, I79) -> f10#(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8#(I88, I89, I90, I91, I92, I93, I94, I95) -> f9#(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 R = 85.79/84.68 f13(x1, x2, x3, x4, x5, x6, x7, x8) -> f12(x1, x2, x3, x4, x5, x6, x7, x8) 85.79/84.68 f12(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, I5, I6, rnd8) [rnd8 = rnd8] 85.79/84.68 f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I17, I17, I18, I19, 0, I21, I22, I23) [I17 <= I19] 85.79/84.68 f4(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f7(I32, I33, I34, I35, 0, I37, I38, I39) [-1 + I32 <= I36] 85.79/84.68 f7(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 f9(I48, I49, I50, I51, I52, I53, I54, I55) -> f11(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f3(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11(I64, I65, I66, I67, I68, I69, I70, I71) -> f10(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11(I72, I73, I74, I75, I76, I77, I78, I79) -> f10(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8(I88, I89, I90, I91, I92, I93, I94, I95) -> f9(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f5(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 f5(I104, I105, I106, I107, I108, I109, I110, I111) -> f6(I104, I105, I106, I107, I108, I109, I110, I111) [-1 + I104 <= I108] 85.79/84.68 f3(I112, I113, I114, I115, I116, I117, I118, I119) -> f4(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 85.79/84.68 The dependency graph for this problem is: 85.79/84.68 9 -> 11 85.79/84.68 10 -> 11 85.79/84.68 11 -> 12 85.79/84.68 12 -> 85.79/84.68 Where: 85.79/84.68 9) f11#(I64, I65, I66, I67, I68, I69, I70, I71) -> f10#(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 10) f11#(I72, I73, I74, I75, I76, I77, I78, I79) -> f10#(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 11) f10#(I80, I81, I82, I83, I84, I85, I86, I87) -> f8#(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 12) f8#(I88, I89, I90, I91, I92, I93, I94, I95) -> f9#(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 85.79/84.68 We have the following SCCs. 85.79/84.68 85.79/84.68 85.79/84.68 DP problem for innermost termination. 85.79/84.68 P = 85.79/84.68 f2#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 f1#(I120, I121, I122, I123, I124, I125, I126, I127) -> f2#(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 R = 85.79/84.68 f13(x1, x2, x3, x4, x5, x6, x7, x8) -> f12(x1, x2, x3, x4, x5, x6, x7, x8) 85.79/84.68 f12(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, I5, I6, rnd8) [rnd8 = rnd8] 85.79/84.68 f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I17, I17, I18, I19, 0, I21, I22, I23) [I17 <= I19] 85.79/84.68 f4(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f7(I32, I33, I34, I35, 0, I37, I38, I39) [-1 + I32 <= I36] 85.79/84.68 f7(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 f9(I48, I49, I50, I51, I52, I53, I54, I55) -> f11(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f3(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11(I64, I65, I66, I67, I68, I69, I70, I71) -> f10(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11(I72, I73, I74, I75, I76, I77, I78, I79) -> f10(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8(I88, I89, I90, I91, I92, I93, I94, I95) -> f9(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f5(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 f5(I104, I105, I106, I107, I108, I109, I110, I111) -> f6(I104, I105, I106, I107, I108, I109, I110, I111) [-1 + I104 <= I108] 85.79/84.68 f3(I112, I113, I114, I115, I116, I117, I118, I119) -> f4(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 85.79/84.68 We use the reverse value criterion with the projection function NU: 85.79/84.68 NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8)] = z2 + -1 * (1 + z4) 85.79/84.68 NU[f2#(z1,z2,z3,z4,z5,z6,z7,z8)] = z2 + -1 * (1 + z4) 85.79/84.68 85.79/84.68 This gives the following inequalities: 85.79/84.68 1 + I11 <= I9 ==> I9 + -1 * (1 + I11) > I9 + -1 * (1 + (1 + I11)) with I9 + -1 * (1 + I11) >= 0 85.79/84.68 ==> I121 + -1 * (1 + I123) >= I121 + -1 * (1 + I123) 85.79/84.68 85.79/84.68 We remove all the strictly oriented dependency pairs. 85.79/84.68 85.79/84.68 DP problem for innermost termination. 85.79/84.68 P = 85.79/84.68 f1#(I120, I121, I122, I123, I124, I125, I126, I127) -> f2#(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 R = 85.79/84.68 f13(x1, x2, x3, x4, x5, x6, x7, x8) -> f12(x1, x2, x3, x4, x5, x6, x7, x8) 85.79/84.68 f12(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, I4, I5, I6, rnd8) [rnd8 = rnd8] 85.79/84.68 f2(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, 1 + I11, I12, I13, I14, I15) [1 + I11 <= I9] 85.79/84.68 f2(I16, I17, I18, I19, I20, I21, I22, I23) -> f3(I17, I17, I18, I19, 0, I21, I22, I23) [I17 <= I19] 85.79/84.68 f4(I24, I25, I26, I27, I28, I29, I30, I31) -> f8(I24, I25, 1 + I28, I27, I28, I28, I30, I31) [1 + I28 <= -1 + I24] 85.79/84.68 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f7(I32, I33, I34, I35, 0, I37, I38, I39) [-1 + I32 <= I36] 85.79/84.68 f7(I40, I41, I42, I43, I44, I45, I46, I47) -> f5(I40, I41, I42, I43, I44, I45, I46, I47) 85.79/84.68 f9(I48, I49, I50, I51, I52, I53, I54, I55) -> f11(I48, I49, I50, I51, I52, I53, I54, I55) [1 + I50 <= I48] 85.79/84.68 f9(I56, I57, I58, I59, I60, I61, I62, I63) -> f3(I56, I57, I58, I59, 1 + I60, I61, rnd7, I63) [rnd7 = rnd7 /\ I56 <= I58] 85.79/84.68 f11(I64, I65, I66, I67, I68, I69, I70, I71) -> f10(I64, I65, I66, I67, I68, I69, I70, I71) 85.79/84.68 f11(I72, I73, I74, I75, I76, I77, I78, I79) -> f10(I72, I73, I74, I75, I76, I74, I78, I79) 85.79/84.68 f10(I80, I81, I82, I83, I84, I85, I86, I87) -> f8(I80, I81, 1 + I82, I83, I84, I85, I86, I87) 85.79/84.68 f8(I88, I89, I90, I91, I92, I93, I94, I95) -> f9(I88, I89, I90, I91, I92, I93, I94, I95) 85.79/84.68 f5(I96, I97, I98, I99, I100, I101, I102, I103) -> f7(I96, I97, I98, I99, 1 + I100, I101, I102, I103) [1 + I100 <= -1 + I96] 85.79/84.68 f5(I104, I105, I106, I107, I108, I109, I110, I111) -> f6(I104, I105, I106, I107, I108, I109, I110, I111) [-1 + I104 <= I108] 85.79/84.68 f3(I112, I113, I114, I115, I116, I117, I118, I119) -> f4(I112, I113, I114, I115, I116, I117, I118, I119) 85.79/84.68 f1(I120, I121, I122, I123, I124, I125, I126, I127) -> f2(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 85.79/84.68 The dependency graph for this problem is: 85.79/84.68 15 -> 85.79/84.68 Where: 85.79/84.68 15) f1#(I120, I121, I122, I123, I124, I125, I126, I127) -> f2#(I120, I121, I122, I123, I124, I125, I126, I127) 85.79/84.68 85.79/84.68 We have the following SCCs. 85.79/84.68 85.79/87.65 EOF