143.04/140.99 YES 143.04/140.99 143.04/140.99 DP problem for innermost termination. 143.04/140.99 P = 143.04/140.99 f11#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f10#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 143.04/140.99 f10#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f4#(I0, I1, I2, I3, rnd5, rnd6, I2, 0, I0, I9, I1) [rnd5 = rnd6 /\ rnd6 = rnd6] 143.04/140.99 f6#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f8#(I11, I12, I13, rnd4, I15, I16, I17, I18, I19, 1, I21) [rnd4 = rnd4 /\ 1 + I18 <= I19] 143.04/140.99 f8#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 f7#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f8#(I44, I45, I46, I55, I48, I49, I50, I51, I52, 1 + I53, I54) [I55 = I55 /\ 1 + I53 <= I48] 143.04/140.99 f7#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) -> f5#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) [I60 <= I65] 143.04/140.99 f4#(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6#(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) 143.04/140.99 f5#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) -> f3#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) 143.04/140.99 f5#(I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f2#(I89, I90, I91, I92, -1 + I93, I94, I95, I96, I97, I98, I99) 143.04/140.99 f5#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f3#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) 143.04/140.99 f2#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f4#(I111, I112, I113, I114, I115, I116, I117, 1 + I118, I119, I120, I121) 143.04/140.99 f3#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f1#(I122, I123, I124, I125, 1 + I126, I127, I128, I129, I130, I131, I132) [1 + I126 <= I128] 143.04/140.99 f3#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f1#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I139 <= I137] 143.04/140.99 f1#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f2#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) 143.04/140.99 R = 143.04/140.99 f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 143.04/140.99 f10(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f4(I0, I1, I2, I3, rnd5, rnd6, I2, 0, I0, I9, I1) [rnd5 = rnd6 /\ rnd6 = rnd6] 143.04/140.99 f6(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f8(I11, I12, I13, rnd4, I15, I16, I17, I18, I19, 1, I21) [rnd4 = rnd4 /\ 1 + I18 <= I19] 143.04/140.99 f6(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f9(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [I30 <= I29] 143.04/140.99 f8(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f8(I44, I45, I46, I55, I48, I49, I50, I51, I52, 1 + I53, I54) [I55 = I55 /\ 1 + I53 <= I48] 143.04/140.99 f7(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) -> f5(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) [I60 <= I65] 143.04/140.99 f4(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) 143.04/140.99 f5(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) -> f3(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) 143.04/140.99 f5(I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f2(I89, I90, I91, I92, -1 + I93, I94, I95, I96, I97, I98, I99) 143.04/140.99 f5(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) 143.04/140.99 f2(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f4(I111, I112, I113, I114, I115, I116, I117, 1 + I118, I119, I120, I121) 143.04/140.99 f3(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f1(I122, I123, I124, I125, 1 + I126, I127, I128, I129, I130, I131, I132) [1 + I126 <= I128] 143.04/140.99 f3(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f1(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I139 <= I137] 143.04/140.99 f1(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) 143.04/140.99 143.04/140.99 The dependency graph for this problem is: 143.04/140.99 0 -> 1 143.04/140.99 1 -> 6 143.04/140.99 2 -> 3 143.04/140.99 3 -> 4, 5 143.04/140.99 4 -> 3 143.04/140.99 5 -> 7, 8, 9 143.04/140.99 6 -> 2 143.04/140.99 7 -> 11, 12 143.04/140.99 8 -> 10 143.04/140.99 9 -> 11, 12 143.04/140.99 10 -> 6 143.04/140.99 11 -> 13 143.04/140.99 12 -> 13 143.04/140.99 13 -> 10 143.04/140.99 Where: 143.04/140.99 0) f11#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f10#(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 143.04/140.99 1) f10#(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f4#(I0, I1, I2, I3, rnd5, rnd6, I2, 0, I0, I9, I1) [rnd5 = rnd6 /\ rnd6 = rnd6] 143.04/140.99 2) f6#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f8#(I11, I12, I13, rnd4, I15, I16, I17, I18, I19, 1, I21) [rnd4 = rnd4 /\ 1 + I18 <= I19] 143.04/140.99 3) f8#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 4) f7#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f8#(I44, I45, I46, I55, I48, I49, I50, I51, I52, 1 + I53, I54) [I55 = I55 /\ 1 + I53 <= I48] 143.04/140.99 5) f7#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) -> f5#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) [I60 <= I65] 143.04/140.99 6) f4#(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6#(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) 143.04/140.99 7) f5#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) -> f3#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) 143.04/140.99 8) f5#(I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f2#(I89, I90, I91, I92, -1 + I93, I94, I95, I96, I97, I98, I99) 143.04/140.99 9) f5#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f3#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) 143.04/140.99 10) f2#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f4#(I111, I112, I113, I114, I115, I116, I117, 1 + I118, I119, I120, I121) 143.04/140.99 11) f3#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f1#(I122, I123, I124, I125, 1 + I126, I127, I128, I129, I130, I131, I132) [1 + I126 <= I128] 143.04/140.99 12) f3#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f1#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I139 <= I137] 143.04/140.99 13) f1#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f2#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) 143.04/140.99 143.04/140.99 We have the following SCCs. 143.04/140.99 { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 } 143.04/140.99 143.04/140.99 DP problem for innermost termination. 143.04/140.99 P = 143.04/140.99 f6#(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f8#(I11, I12, I13, rnd4, I15, I16, I17, I18, I19, 1, I21) [rnd4 = rnd4 /\ 1 + I18 <= I19] 143.04/140.99 f8#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 f7#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f8#(I44, I45, I46, I55, I48, I49, I50, I51, I52, 1 + I53, I54) [I55 = I55 /\ 1 + I53 <= I48] 143.04/140.99 f7#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) -> f5#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) [I60 <= I65] 143.04/140.99 f4#(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6#(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) 143.04/140.99 f5#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) -> f3#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) 143.04/140.99 f5#(I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f2#(I89, I90, I91, I92, -1 + I93, I94, I95, I96, I97, I98, I99) 143.04/140.99 f5#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f3#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) 143.04/140.99 f2#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f4#(I111, I112, I113, I114, I115, I116, I117, 1 + I118, I119, I120, I121) 143.04/140.99 f3#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f1#(I122, I123, I124, I125, 1 + I126, I127, I128, I129, I130, I131, I132) [1 + I126 <= I128] 143.04/140.99 f3#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f1#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I139 <= I137] 143.04/140.99 f1#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f2#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) 143.04/140.99 R = 143.04/140.99 f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 143.04/140.99 f10(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f4(I0, I1, I2, I3, rnd5, rnd6, I2, 0, I0, I9, I1) [rnd5 = rnd6 /\ rnd6 = rnd6] 143.04/140.99 f6(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f8(I11, I12, I13, rnd4, I15, I16, I17, I18, I19, 1, I21) [rnd4 = rnd4 /\ 1 + I18 <= I19] 143.04/140.99 f6(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f9(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [I30 <= I29] 143.04/140.99 f8(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f8(I44, I45, I46, I55, I48, I49, I50, I51, I52, 1 + I53, I54) [I55 = I55 /\ 1 + I53 <= I48] 143.04/140.99 f7(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) -> f5(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) [I60 <= I65] 143.04/140.99 f4(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) 143.04/140.99 f5(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) -> f3(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) 143.04/140.99 f5(I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f2(I89, I90, I91, I92, -1 + I93, I94, I95, I96, I97, I98, I99) 143.04/140.99 f5(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) 143.04/140.99 f2(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f4(I111, I112, I113, I114, I115, I116, I117, 1 + I118, I119, I120, I121) 143.04/140.99 f3(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f1(I122, I123, I124, I125, 1 + I126, I127, I128, I129, I130, I131, I132) [1 + I126 <= I128] 143.04/140.99 f3(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f1(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I139 <= I137] 143.04/140.99 f1(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) 143.04/140.99 143.04/140.99 We use the extended value criterion with the projection function NU: 143.04/140.99 NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x7 + x8 - 2 143.04/140.99 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x7 + x8 - 2 143.04/140.99 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x7 + x8 - 2 143.04/140.99 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x7 + x8 - 1 143.04/140.99 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x7 + x8 - 2 143.04/140.99 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x7 + x8 - 2 143.04/140.99 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x7 + x8 - 2 143.04/140.99 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)] = -x7 + x8 - 1 143.04/140.99 143.04/140.99 This gives the following inequalities: 143.04/140.99 rnd4 = rnd4 /\ 1 + I18 <= I19 ==> -I18 + I19 - 1 > -I18 + I19 - 2 with -I18 + I19 - 1 >= 0 143.04/140.99 ==> -I40 + I41 - 2 >= -I40 + I41 - 2 143.04/140.99 I55 = I55 /\ 1 + I53 <= I48 ==> -I51 + I52 - 2 >= -I51 + I52 - 2 143.04/140.99 I60 <= I65 ==> -I63 + I64 - 2 >= -I63 + I64 - 2 143.04/140.99 ==> -I74 + I75 - 1 >= -I74 + I75 - 1 143.04/140.99 ==> -I85 + I86 - 2 >= -I85 + I86 - 2 143.04/140.99 ==> -I96 + I97 - 2 >= -I96 + I97 - 2 143.04/140.99 ==> -I107 + I108 - 2 >= -I107 + I108 - 2 143.04/140.99 ==> -I118 + I119 - 2 >= -(1 + I118) + I119 - 1 143.04/140.99 1 + I126 <= I128 ==> -I129 + I130 - 2 >= -I129 + I130 - 2 143.04/140.99 I139 <= I137 ==> -I140 + I141 - 2 >= -I140 + I141 - 2 143.04/140.99 ==> -I151 + I152 - 2 >= -I151 + I152 - 2 143.04/140.99 143.04/140.99 We remove all the strictly oriented dependency pairs. 143.04/140.99 143.04/140.99 DP problem for innermost termination. 143.04/140.99 P = 143.04/140.99 f8#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 f7#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f8#(I44, I45, I46, I55, I48, I49, I50, I51, I52, 1 + I53, I54) [I55 = I55 /\ 1 + I53 <= I48] 143.04/140.99 f7#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) -> f5#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) [I60 <= I65] 143.04/140.99 f4#(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6#(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) 143.04/140.99 f5#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) -> f3#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) 143.04/140.99 f5#(I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f2#(I89, I90, I91, I92, -1 + I93, I94, I95, I96, I97, I98, I99) 143.04/140.99 f5#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f3#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) 143.04/140.99 f2#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f4#(I111, I112, I113, I114, I115, I116, I117, 1 + I118, I119, I120, I121) 143.04/140.99 f3#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f1#(I122, I123, I124, I125, 1 + I126, I127, I128, I129, I130, I131, I132) [1 + I126 <= I128] 143.04/140.99 f3#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f1#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I139 <= I137] 143.04/140.99 f1#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f2#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) 143.04/140.99 R = 143.04/140.99 f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 143.04/140.99 f10(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f4(I0, I1, I2, I3, rnd5, rnd6, I2, 0, I0, I9, I1) [rnd5 = rnd6 /\ rnd6 = rnd6] 143.04/140.99 f6(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f8(I11, I12, I13, rnd4, I15, I16, I17, I18, I19, 1, I21) [rnd4 = rnd4 /\ 1 + I18 <= I19] 143.04/140.99 f6(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f9(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [I30 <= I29] 143.04/140.99 f8(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f8(I44, I45, I46, I55, I48, I49, I50, I51, I52, 1 + I53, I54) [I55 = I55 /\ 1 + I53 <= I48] 143.04/140.99 f7(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) -> f5(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) [I60 <= I65] 143.04/140.99 f4(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) 143.04/140.99 f5(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) -> f3(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) 143.04/140.99 f5(I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f2(I89, I90, I91, I92, -1 + I93, I94, I95, I96, I97, I98, I99) 143.04/140.99 f5(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) 143.04/140.99 f2(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f4(I111, I112, I113, I114, I115, I116, I117, 1 + I118, I119, I120, I121) 143.04/140.99 f3(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f1(I122, I123, I124, I125, 1 + I126, I127, I128, I129, I130, I131, I132) [1 + I126 <= I128] 143.04/140.99 f3(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f1(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I139 <= I137] 143.04/140.99 f1(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) 143.04/140.99 143.04/140.99 The dependency graph for this problem is: 143.04/140.99 3 -> 4, 5 143.04/140.99 4 -> 3 143.04/140.99 5 -> 7, 8, 9 143.04/140.99 6 -> 143.04/140.99 7 -> 11, 12 143.04/140.99 8 -> 10 143.04/140.99 9 -> 11, 12 143.04/140.99 10 -> 6 143.04/140.99 11 -> 13 143.04/140.99 12 -> 13 143.04/140.99 13 -> 10 143.04/140.99 Where: 143.04/140.99 3) f8#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 4) f7#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f8#(I44, I45, I46, I55, I48, I49, I50, I51, I52, 1 + I53, I54) [I55 = I55 /\ 1 + I53 <= I48] 143.04/140.99 5) f7#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) -> f5#(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) [I60 <= I65] 143.04/140.99 6) f4#(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6#(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) 143.04/140.99 7) f5#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) -> f3#(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) 143.04/140.99 8) f5#(I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f2#(I89, I90, I91, I92, -1 + I93, I94, I95, I96, I97, I98, I99) 143.04/140.99 9) f5#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f3#(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) 143.04/140.99 10) f2#(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f4#(I111, I112, I113, I114, I115, I116, I117, 1 + I118, I119, I120, I121) 143.04/140.99 11) f3#(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f1#(I122, I123, I124, I125, 1 + I126, I127, I128, I129, I130, I131, I132) [1 + I126 <= I128] 143.04/140.99 12) f3#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f1#(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I139 <= I137] 143.04/140.99 13) f1#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f2#(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) 143.04/140.99 143.04/140.99 We have the following SCCs. 143.04/140.99 { 3, 4 } 143.04/140.99 143.04/140.99 DP problem for innermost termination. 143.04/140.99 P = 143.04/140.99 f8#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 f7#(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f8#(I44, I45, I46, I55, I48, I49, I50, I51, I52, 1 + I53, I54) [I55 = I55 /\ 1 + I53 <= I48] 143.04/140.99 R = 143.04/140.99 f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 143.04/140.99 f10(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f4(I0, I1, I2, I3, rnd5, rnd6, I2, 0, I0, I9, I1) [rnd5 = rnd6 /\ rnd6 = rnd6] 143.04/140.99 f6(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f8(I11, I12, I13, rnd4, I15, I16, I17, I18, I19, 1, I21) [rnd4 = rnd4 /\ 1 + I18 <= I19] 143.04/140.99 f6(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f9(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [I30 <= I29] 143.04/140.99 f8(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f8(I44, I45, I46, I55, I48, I49, I50, I51, I52, 1 + I53, I54) [I55 = I55 /\ 1 + I53 <= I48] 143.04/140.99 f7(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) -> f5(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) [I60 <= I65] 143.04/140.99 f4(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) 143.04/140.99 f5(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) -> f3(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) 143.04/140.99 f5(I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f2(I89, I90, I91, I92, -1 + I93, I94, I95, I96, I97, I98, I99) 143.04/140.99 f5(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) 143.04/140.99 f2(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f4(I111, I112, I113, I114, I115, I116, I117, 1 + I118, I119, I120, I121) 143.04/140.99 f3(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f1(I122, I123, I124, I125, 1 + I126, I127, I128, I129, I130, I131, I132) [1 + I126 <= I128] 143.04/140.99 f3(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f1(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I139 <= I137] 143.04/140.99 f1(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) 143.04/140.99 143.04/140.99 We use the reverse value criterion with the projection function NU: 143.04/140.99 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11)] = z5 + -1 * (1 + z10) 143.04/140.99 NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11)] = z5 + -1 * (1 + z10) 143.04/140.99 143.04/140.99 This gives the following inequalities: 143.04/140.99 ==> I37 + -1 * (1 + I42) >= I37 + -1 * (1 + I42) 143.04/140.99 I55 = I55 /\ 1 + I53 <= I48 ==> I48 + -1 * (1 + I53) > I48 + -1 * (1 + (1 + I53)) with I48 + -1 * (1 + I53) >= 0 143.04/140.99 143.04/140.99 We remove all the strictly oriented dependency pairs. 143.04/140.99 143.04/140.99 DP problem for innermost termination. 143.04/140.99 P = 143.04/140.99 f8#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 R = 143.04/140.99 f11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> f10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) 143.04/140.99 f10(I0, I1, I2, I3, I4, I5, I6, I7, I8, I9, I10) -> f4(I0, I1, I2, I3, rnd5, rnd6, I2, 0, I0, I9, I1) [rnd5 = rnd6 /\ rnd6 = rnd6] 143.04/140.99 f6(I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21) -> f8(I11, I12, I13, rnd4, I15, I16, I17, I18, I19, 1, I21) [rnd4 = rnd4 /\ 1 + I18 <= I19] 143.04/140.99 f6(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) -> f9(I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32) [I30 <= I29] 143.04/140.99 f8(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 f7(I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54) -> f8(I44, I45, I46, I55, I48, I49, I50, I51, I52, 1 + I53, I54) [I55 = I55 /\ 1 + I53 <= I48] 143.04/140.99 f7(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) -> f5(I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66) [I60 <= I65] 143.04/140.99 f4(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) -> f6(I67, I68, I69, I70, I71, I72, I73, I74, I75, I76, I77) 143.04/140.99 f5(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) -> f3(I78, I79, I80, I81, I82, I83, I84, I85, I86, I87, I88) 143.04/140.99 f5(I89, I90, I91, I92, I93, I94, I95, I96, I97, I98, I99) -> f2(I89, I90, I91, I92, -1 + I93, I94, I95, I96, I97, I98, I99) 143.04/140.99 f5(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) -> f3(I100, I101, I102, I103, I104, I105, I106, I107, I108, I109, I110) 143.04/140.99 f2(I111, I112, I113, I114, I115, I116, I117, I118, I119, I120, I121) -> f4(I111, I112, I113, I114, I115, I116, I117, 1 + I118, I119, I120, I121) 143.04/140.99 f3(I122, I123, I124, I125, I126, I127, I128, I129, I130, I131, I132) -> f1(I122, I123, I124, I125, 1 + I126, I127, I128, I129, I130, I131, I132) [1 + I126 <= I128] 143.04/140.99 f3(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f1(I133, I134, I135, I136, I137, I138, I139, I140, I141, I142, I143) [I139 <= I137] 143.04/140.99 f1(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) -> f2(I144, I145, I146, I147, I148, I149, I150, I151, I152, I153, I154) 143.04/140.99 143.04/140.99 The dependency graph for this problem is: 143.04/140.99 3 -> 143.04/140.99 Where: 143.04/140.99 3) f8#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) -> f7#(I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43) 143.04/140.99 143.04/140.99 We have the following SCCs. 143.04/140.99 143.04/143.95 EOF