161.56/159.61 MAYBE 161.56/159.61 161.56/159.61 DP problem for innermost termination. 161.56/159.61 P = 161.56/159.61 f15#(x1, x2, x3, x4, x5, x6, x7, x8) -> f1#(x1, x2, x3, x4, x5, x6, x7, x8) 161.56/159.61 f14#(I0, I1, I2, I3, I4, I5, I6, I7) -> f3#(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 f13#(I8, I9, I10, I11, I12, I13, I14, I15) -> f14#(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 f4#(I16, I17, I18, I19, I20, I21, I22, I23) -> f13#(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 f12#(I24, I25, I26, I27, I28, I29, I30, I31) -> f4#(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4#(I32, I33, I34, I35, I36, I37, I38, I39) -> f12#(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 f8#(I41, I42, I43, I44, I45, I46, I47, I48) -> f2#(I41, I42, I43, I44, I45, 1 + I46, I47, I48) [-1 * I47 + I48 <= 0] 161.56/159.61 f11#(I49, I50, I51, I52, I53, I54, I55, I56) -> f3#(I49, I50, I51, I52, I53, I54, 1 + I55, I56) 161.56/159.61 f10#(I57, I58, I59, I60, I61, I62, I63, I64) -> f11#(I57, I58, I59, I60, I61, I62, I63, I64) [I59 = I59] 161.56/159.61 f8#(I65, I66, I67, I68, I69, I70, I71, I72) -> f10#(I65, I66, I67, I68, I73, I70, I71, I72) [I73 = I73 /\ 0 <= -1 - I71 + I72] 161.56/159.61 f8#(I74, I75, I76, I77, I78, I79, I80, I81) -> f4#(I74, I75, I76, I77, I82, I79, I80, I81) [0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81] 161.56/159.61 f2#(I91, I92, I93, I94, I95, I96, I97, I98) -> f8#(I91, I92, I93, I94, I95, I96, I97, I98) [0 <= -1 - I96 + I97] 161.56/159.61 f3#(I99, I100, I101, I102, I103, I104, I105, I106) -> f2#(I99, I100, I101, I102, I103, 1 + I104, I105, I106) [-1 * I105 + I106 <= 0] 161.56/159.61 f7#(I107, I108, I109, I110, I111, I112, I113, I114) -> f3#(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 f6#(I115, I116, I117, I118, I119, I120, I121, I122) -> f7#(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 f5#(I123, I124, I125, I126, I127, I128, I129, I130) -> f6#(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 f3#(I131, I132, I133, I134, I135, I136, I137, I138) -> f5#(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 f3#(I140, I141, I142, I143, I144, I145, I146, I147) -> f4#(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 f1#(I149, I150, I151, I152, I153, I154, I155, I156) -> f2#(I149, I150, I151, I152, I153, I154, I155, I156) 161.56/159.61 R = 161.56/159.61 f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f1(x1, x2, x3, x4, x5, x6, x7, x8) 161.56/159.61 f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f3(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f14(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 f4(I16, I17, I18, I19, I20, I21, I22, I23) -> f13(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 f12(I24, I25, I26, I27, I28, I29, I30, I31) -> f4(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f12(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 f8(I41, I42, I43, I44, I45, I46, I47, I48) -> f2(I41, I42, I43, I44, I45, 1 + I46, I47, I48) [-1 * I47 + I48 <= 0] 161.56/159.61 f11(I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I49, I50, I51, I52, I53, I54, 1 + I55, I56) 161.56/159.61 f10(I57, I58, I59, I60, I61, I62, I63, I64) -> f11(I57, I58, I59, I60, I61, I62, I63, I64) [I59 = I59] 161.56/159.61 f8(I65, I66, I67, I68, I69, I70, I71, I72) -> f10(I65, I66, I67, I68, I73, I70, I71, I72) [I73 = I73 /\ 0 <= -1 - I71 + I72] 161.56/159.61 f8(I74, I75, I76, I77, I78, I79, I80, I81) -> f4(I74, I75, I76, I77, I82, I79, I80, I81) [0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81] 161.56/159.61 f2(I83, I84, I85, I86, I87, I88, I89, I90) -> f9(rnd1, I84, I85, I86, I87, I88, I89, I90) [rnd1 = rnd1 /\ -1 * I88 + I89 <= 0] 161.56/159.61 f2(I91, I92, I93, I94, I95, I96, I97, I98) -> f8(I91, I92, I93, I94, I95, I96, I97, I98) [0 <= -1 - I96 + I97] 161.56/159.61 f3(I99, I100, I101, I102, I103, I104, I105, I106) -> f2(I99, I100, I101, I102, I103, 1 + I104, I105, I106) [-1 * I105 + I106 <= 0] 161.56/159.61 f7(I107, I108, I109, I110, I111, I112, I113, I114) -> f3(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 f6(I115, I116, I117, I118, I119, I120, I121, I122) -> f7(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 f5(I123, I124, I125, I126, I127, I128, I129, I130) -> f6(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 f3(I140, I141, I142, I143, I144, I145, I146, I147) -> f4(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 f1(I149, I150, I151, I152, I153, I154, I155, I156) -> f2(I149, I150, I151, I152, I153, I154, I155, I156) 161.56/159.61 161.56/159.61 The dependency graph for this problem is: 161.56/159.61 0 -> 18 161.56/159.61 1 -> 12, 16, 17 161.56/159.61 2 -> 1 161.56/159.61 3 -> 2 161.56/159.61 4 -> 3, 5 161.56/159.61 5 -> 4 161.56/159.61 6 -> 11 161.56/159.61 7 -> 12, 16, 17 161.56/159.61 8 -> 7 161.56/159.61 9 -> 8 161.56/159.61 10 -> 3, 5 161.56/159.61 11 -> 6, 9, 10 161.56/159.61 12 -> 11 161.56/159.61 13 -> 12, 16, 17 161.56/159.61 14 -> 13 161.56/159.61 15 -> 14 161.56/159.61 16 -> 15 161.56/159.61 17 -> 3, 5 161.56/159.61 18 -> 11 161.56/159.61 Where: 161.56/159.61 0) f15#(x1, x2, x3, x4, x5, x6, x7, x8) -> f1#(x1, x2, x3, x4, x5, x6, x7, x8) 161.56/159.61 1) f14#(I0, I1, I2, I3, I4, I5, I6, I7) -> f3#(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 2) f13#(I8, I9, I10, I11, I12, I13, I14, I15) -> f14#(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 3) f4#(I16, I17, I18, I19, I20, I21, I22, I23) -> f13#(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 4) f12#(I24, I25, I26, I27, I28, I29, I30, I31) -> f4#(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 5) f4#(I32, I33, I34, I35, I36, I37, I38, I39) -> f12#(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 6) f8#(I41, I42, I43, I44, I45, I46, I47, I48) -> f2#(I41, I42, I43, I44, I45, 1 + I46, I47, I48) [-1 * I47 + I48 <= 0] 161.56/159.61 7) f11#(I49, I50, I51, I52, I53, I54, I55, I56) -> f3#(I49, I50, I51, I52, I53, I54, 1 + I55, I56) 161.56/159.61 8) f10#(I57, I58, I59, I60, I61, I62, I63, I64) -> f11#(I57, I58, I59, I60, I61, I62, I63, I64) [I59 = I59] 161.56/159.61 9) f8#(I65, I66, I67, I68, I69, I70, I71, I72) -> f10#(I65, I66, I67, I68, I73, I70, I71, I72) [I73 = I73 /\ 0 <= -1 - I71 + I72] 161.56/159.61 10) f8#(I74, I75, I76, I77, I78, I79, I80, I81) -> f4#(I74, I75, I76, I77, I82, I79, I80, I81) [0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81] 161.56/159.61 11) f2#(I91, I92, I93, I94, I95, I96, I97, I98) -> f8#(I91, I92, I93, I94, I95, I96, I97, I98) [0 <= -1 - I96 + I97] 161.56/159.61 12) f3#(I99, I100, I101, I102, I103, I104, I105, I106) -> f2#(I99, I100, I101, I102, I103, 1 + I104, I105, I106) [-1 * I105 + I106 <= 0] 161.56/159.61 13) f7#(I107, I108, I109, I110, I111, I112, I113, I114) -> f3#(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 14) f6#(I115, I116, I117, I118, I119, I120, I121, I122) -> f7#(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 15) f5#(I123, I124, I125, I126, I127, I128, I129, I130) -> f6#(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 16) f3#(I131, I132, I133, I134, I135, I136, I137, I138) -> f5#(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 17) f3#(I140, I141, I142, I143, I144, I145, I146, I147) -> f4#(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 18) f1#(I149, I150, I151, I152, I153, I154, I155, I156) -> f2#(I149, I150, I151, I152, I153, I154, I155, I156) 161.56/159.61 161.56/159.61 We have the following SCCs. 161.56/159.61 { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 } 161.56/159.61 161.56/159.61 DP problem for innermost termination. 161.56/159.61 P = 161.56/159.61 f14#(I0, I1, I2, I3, I4, I5, I6, I7) -> f3#(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 f13#(I8, I9, I10, I11, I12, I13, I14, I15) -> f14#(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 f4#(I16, I17, I18, I19, I20, I21, I22, I23) -> f13#(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 f12#(I24, I25, I26, I27, I28, I29, I30, I31) -> f4#(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4#(I32, I33, I34, I35, I36, I37, I38, I39) -> f12#(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 f8#(I41, I42, I43, I44, I45, I46, I47, I48) -> f2#(I41, I42, I43, I44, I45, 1 + I46, I47, I48) [-1 * I47 + I48 <= 0] 161.56/159.61 f11#(I49, I50, I51, I52, I53, I54, I55, I56) -> f3#(I49, I50, I51, I52, I53, I54, 1 + I55, I56) 161.56/159.61 f10#(I57, I58, I59, I60, I61, I62, I63, I64) -> f11#(I57, I58, I59, I60, I61, I62, I63, I64) [I59 = I59] 161.56/159.61 f8#(I65, I66, I67, I68, I69, I70, I71, I72) -> f10#(I65, I66, I67, I68, I73, I70, I71, I72) [I73 = I73 /\ 0 <= -1 - I71 + I72] 161.56/159.61 f8#(I74, I75, I76, I77, I78, I79, I80, I81) -> f4#(I74, I75, I76, I77, I82, I79, I80, I81) [0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81] 161.56/159.61 f2#(I91, I92, I93, I94, I95, I96, I97, I98) -> f8#(I91, I92, I93, I94, I95, I96, I97, I98) [0 <= -1 - I96 + I97] 161.56/159.61 f3#(I99, I100, I101, I102, I103, I104, I105, I106) -> f2#(I99, I100, I101, I102, I103, 1 + I104, I105, I106) [-1 * I105 + I106 <= 0] 161.56/159.61 f7#(I107, I108, I109, I110, I111, I112, I113, I114) -> f3#(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 f6#(I115, I116, I117, I118, I119, I120, I121, I122) -> f7#(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 f5#(I123, I124, I125, I126, I127, I128, I129, I130) -> f6#(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 f3#(I131, I132, I133, I134, I135, I136, I137, I138) -> f5#(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 f3#(I140, I141, I142, I143, I144, I145, I146, I147) -> f4#(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 R = 161.56/159.61 f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f1(x1, x2, x3, x4, x5, x6, x7, x8) 161.56/159.61 f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f3(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f14(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 f4(I16, I17, I18, I19, I20, I21, I22, I23) -> f13(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 f12(I24, I25, I26, I27, I28, I29, I30, I31) -> f4(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f12(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 f8(I41, I42, I43, I44, I45, I46, I47, I48) -> f2(I41, I42, I43, I44, I45, 1 + I46, I47, I48) [-1 * I47 + I48 <= 0] 161.56/159.61 f11(I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I49, I50, I51, I52, I53, I54, 1 + I55, I56) 161.56/159.61 f10(I57, I58, I59, I60, I61, I62, I63, I64) -> f11(I57, I58, I59, I60, I61, I62, I63, I64) [I59 = I59] 161.56/159.61 f8(I65, I66, I67, I68, I69, I70, I71, I72) -> f10(I65, I66, I67, I68, I73, I70, I71, I72) [I73 = I73 /\ 0 <= -1 - I71 + I72] 161.56/159.61 f8(I74, I75, I76, I77, I78, I79, I80, I81) -> f4(I74, I75, I76, I77, I82, I79, I80, I81) [0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81] 161.56/159.61 f2(I83, I84, I85, I86, I87, I88, I89, I90) -> f9(rnd1, I84, I85, I86, I87, I88, I89, I90) [rnd1 = rnd1 /\ -1 * I88 + I89 <= 0] 161.56/159.61 f2(I91, I92, I93, I94, I95, I96, I97, I98) -> f8(I91, I92, I93, I94, I95, I96, I97, I98) [0 <= -1 - I96 + I97] 161.56/159.61 f3(I99, I100, I101, I102, I103, I104, I105, I106) -> f2(I99, I100, I101, I102, I103, 1 + I104, I105, I106) [-1 * I105 + I106 <= 0] 161.56/159.61 f7(I107, I108, I109, I110, I111, I112, I113, I114) -> f3(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 f6(I115, I116, I117, I118, I119, I120, I121, I122) -> f7(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 f5(I123, I124, I125, I126, I127, I128, I129, I130) -> f6(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 f3(I140, I141, I142, I143, I144, I145, I146, I147) -> f4(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 f1(I149, I150, I151, I152, I153, I154, I155, I156) -> f2(I149, I150, I151, I152, I153, I154, I155, I156) 161.56/159.61 161.56/159.61 We use the extended value criterion with the projection function NU: 161.56/159.61 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7)] = 0 161.56/159.61 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7)] = 0 161.56/159.61 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7)] = 0 161.56/159.61 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7)] = 0 161.56/159.61 NU[f11#(x0,x1,x2,x3,x4,x5,x6,x7)] = 0 161.56/159.61 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x6 + x7 - 1 161.56/159.61 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x6 + x7 - 1 161.56/159.61 NU[f12#(x0,x1,x2,x3,x4,x5,x6,x7)] = 0 161.56/159.61 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7)] = 0 161.56/159.61 NU[f13#(x0,x1,x2,x3,x4,x5,x6,x7)] = 0 161.56/159.61 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7)] = 0 161.56/159.61 NU[f14#(x0,x1,x2,x3,x4,x5,x6,x7)] = 0 161.56/159.61 161.56/159.61 This gives the following inequalities: 161.56/159.61 ==> 0 >= 0 161.56/159.61 I11 = I11 ==> 0 >= 0 161.56/159.61 rnd5 = rnd5 /\ 0 <= -1 - I22 + I23 ==> 0 >= 0 161.56/159.61 ==> 0 >= 0 161.56/159.61 0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39 ==> 0 >= 0 161.56/159.61 -1 * I47 + I48 <= 0 ==> -I47 + I48 - 1 >= -I47 + I48 - 1 161.56/159.61 ==> 0 >= 0 161.56/159.61 I59 = I59 ==> 0 >= 0 161.56/159.61 I73 = I73 /\ 0 <= -1 - I71 + I72 ==> -I71 + I72 - 1 >= 0 161.56/159.61 0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81 ==> -I80 + I81 - 1 >= 0 161.56/159.61 0 <= -1 - I96 + I97 ==> -I97 + I98 - 1 >= -I97 + I98 - 1 161.56/159.61 -1 * I105 + I106 <= 0 ==> 0 > -I105 + I106 - 1 with 0 >= 0 161.56/159.61 ==> 0 >= 0 161.56/159.61 ==> 0 >= 0 161.56/159.61 I124 = I124 ==> 0 >= 0 161.56/159.61 I139 = I139 /\ 0 <= -1 - I137 + I138 ==> 0 >= 0 161.56/159.61 0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147 ==> 0 >= 0 161.56/159.61 161.56/159.61 We remove all the strictly oriented dependency pairs. 161.56/159.61 161.56/159.61 DP problem for innermost termination. 161.56/159.61 P = 161.56/159.61 f14#(I0, I1, I2, I3, I4, I5, I6, I7) -> f3#(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 f13#(I8, I9, I10, I11, I12, I13, I14, I15) -> f14#(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 f4#(I16, I17, I18, I19, I20, I21, I22, I23) -> f13#(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 f12#(I24, I25, I26, I27, I28, I29, I30, I31) -> f4#(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4#(I32, I33, I34, I35, I36, I37, I38, I39) -> f12#(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 f8#(I41, I42, I43, I44, I45, I46, I47, I48) -> f2#(I41, I42, I43, I44, I45, 1 + I46, I47, I48) [-1 * I47 + I48 <= 0] 161.56/159.61 f11#(I49, I50, I51, I52, I53, I54, I55, I56) -> f3#(I49, I50, I51, I52, I53, I54, 1 + I55, I56) 161.56/159.61 f10#(I57, I58, I59, I60, I61, I62, I63, I64) -> f11#(I57, I58, I59, I60, I61, I62, I63, I64) [I59 = I59] 161.56/159.61 f8#(I65, I66, I67, I68, I69, I70, I71, I72) -> f10#(I65, I66, I67, I68, I73, I70, I71, I72) [I73 = I73 /\ 0 <= -1 - I71 + I72] 161.56/159.61 f8#(I74, I75, I76, I77, I78, I79, I80, I81) -> f4#(I74, I75, I76, I77, I82, I79, I80, I81) [0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81] 161.56/159.61 f2#(I91, I92, I93, I94, I95, I96, I97, I98) -> f8#(I91, I92, I93, I94, I95, I96, I97, I98) [0 <= -1 - I96 + I97] 161.56/159.61 f7#(I107, I108, I109, I110, I111, I112, I113, I114) -> f3#(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 f6#(I115, I116, I117, I118, I119, I120, I121, I122) -> f7#(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 f5#(I123, I124, I125, I126, I127, I128, I129, I130) -> f6#(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 f3#(I131, I132, I133, I134, I135, I136, I137, I138) -> f5#(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 f3#(I140, I141, I142, I143, I144, I145, I146, I147) -> f4#(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 R = 161.56/159.61 f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f1(x1, x2, x3, x4, x5, x6, x7, x8) 161.56/159.61 f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f3(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f14(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 f4(I16, I17, I18, I19, I20, I21, I22, I23) -> f13(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 f12(I24, I25, I26, I27, I28, I29, I30, I31) -> f4(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f12(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 f8(I41, I42, I43, I44, I45, I46, I47, I48) -> f2(I41, I42, I43, I44, I45, 1 + I46, I47, I48) [-1 * I47 + I48 <= 0] 161.56/159.61 f11(I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I49, I50, I51, I52, I53, I54, 1 + I55, I56) 161.56/159.61 f10(I57, I58, I59, I60, I61, I62, I63, I64) -> f11(I57, I58, I59, I60, I61, I62, I63, I64) [I59 = I59] 161.56/159.61 f8(I65, I66, I67, I68, I69, I70, I71, I72) -> f10(I65, I66, I67, I68, I73, I70, I71, I72) [I73 = I73 /\ 0 <= -1 - I71 + I72] 161.56/159.61 f8(I74, I75, I76, I77, I78, I79, I80, I81) -> f4(I74, I75, I76, I77, I82, I79, I80, I81) [0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81] 161.56/159.61 f2(I83, I84, I85, I86, I87, I88, I89, I90) -> f9(rnd1, I84, I85, I86, I87, I88, I89, I90) [rnd1 = rnd1 /\ -1 * I88 + I89 <= 0] 161.56/159.61 f2(I91, I92, I93, I94, I95, I96, I97, I98) -> f8(I91, I92, I93, I94, I95, I96, I97, I98) [0 <= -1 - I96 + I97] 161.56/159.61 f3(I99, I100, I101, I102, I103, I104, I105, I106) -> f2(I99, I100, I101, I102, I103, 1 + I104, I105, I106) [-1 * I105 + I106 <= 0] 161.56/159.61 f7(I107, I108, I109, I110, I111, I112, I113, I114) -> f3(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 f6(I115, I116, I117, I118, I119, I120, I121, I122) -> f7(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 f5(I123, I124, I125, I126, I127, I128, I129, I130) -> f6(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 f3(I140, I141, I142, I143, I144, I145, I146, I147) -> f4(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 f1(I149, I150, I151, I152, I153, I154, I155, I156) -> f2(I149, I150, I151, I152, I153, I154, I155, I156) 161.56/159.61 161.56/159.61 The dependency graph for this problem is: 161.56/159.61 1 -> 16, 17 161.56/159.61 2 -> 1 161.56/159.61 3 -> 2 161.56/159.61 4 -> 3, 5 161.56/159.61 5 -> 4 161.56/159.61 6 -> 11 161.56/159.61 7 -> 16, 17 161.56/159.61 8 -> 7 161.56/159.61 9 -> 8 161.56/159.61 10 -> 3, 5 161.56/159.61 11 -> 6, 9, 10 161.56/159.61 13 -> 16, 17 161.56/159.61 14 -> 13 161.56/159.61 15 -> 14 161.56/159.61 16 -> 15 161.56/159.61 17 -> 3, 5 161.56/159.61 Where: 161.56/159.61 1) f14#(I0, I1, I2, I3, I4, I5, I6, I7) -> f3#(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 2) f13#(I8, I9, I10, I11, I12, I13, I14, I15) -> f14#(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 3) f4#(I16, I17, I18, I19, I20, I21, I22, I23) -> f13#(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 4) f12#(I24, I25, I26, I27, I28, I29, I30, I31) -> f4#(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 5) f4#(I32, I33, I34, I35, I36, I37, I38, I39) -> f12#(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 6) f8#(I41, I42, I43, I44, I45, I46, I47, I48) -> f2#(I41, I42, I43, I44, I45, 1 + I46, I47, I48) [-1 * I47 + I48 <= 0] 161.56/159.61 7) f11#(I49, I50, I51, I52, I53, I54, I55, I56) -> f3#(I49, I50, I51, I52, I53, I54, 1 + I55, I56) 161.56/159.61 8) f10#(I57, I58, I59, I60, I61, I62, I63, I64) -> f11#(I57, I58, I59, I60, I61, I62, I63, I64) [I59 = I59] 161.56/159.61 9) f8#(I65, I66, I67, I68, I69, I70, I71, I72) -> f10#(I65, I66, I67, I68, I73, I70, I71, I72) [I73 = I73 /\ 0 <= -1 - I71 + I72] 161.56/159.61 10) f8#(I74, I75, I76, I77, I78, I79, I80, I81) -> f4#(I74, I75, I76, I77, I82, I79, I80, I81) [0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81] 161.56/159.61 11) f2#(I91, I92, I93, I94, I95, I96, I97, I98) -> f8#(I91, I92, I93, I94, I95, I96, I97, I98) [0 <= -1 - I96 + I97] 161.56/159.61 13) f7#(I107, I108, I109, I110, I111, I112, I113, I114) -> f3#(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 14) f6#(I115, I116, I117, I118, I119, I120, I121, I122) -> f7#(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 15) f5#(I123, I124, I125, I126, I127, I128, I129, I130) -> f6#(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 16) f3#(I131, I132, I133, I134, I135, I136, I137, I138) -> f5#(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 17) f3#(I140, I141, I142, I143, I144, I145, I146, I147) -> f4#(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 161.56/159.61 We have the following SCCs. 161.56/159.61 { 6, 11 } 161.56/159.61 { 1, 2, 3, 4, 5, 13, 14, 15, 16, 17 } 161.56/159.61 161.56/159.61 DP problem for innermost termination. 161.56/159.61 P = 161.56/159.61 f14#(I0, I1, I2, I3, I4, I5, I6, I7) -> f3#(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 f13#(I8, I9, I10, I11, I12, I13, I14, I15) -> f14#(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 f4#(I16, I17, I18, I19, I20, I21, I22, I23) -> f13#(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 f12#(I24, I25, I26, I27, I28, I29, I30, I31) -> f4#(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4#(I32, I33, I34, I35, I36, I37, I38, I39) -> f12#(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 f7#(I107, I108, I109, I110, I111, I112, I113, I114) -> f3#(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 f6#(I115, I116, I117, I118, I119, I120, I121, I122) -> f7#(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 f5#(I123, I124, I125, I126, I127, I128, I129, I130) -> f6#(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 f3#(I131, I132, I133, I134, I135, I136, I137, I138) -> f5#(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 f3#(I140, I141, I142, I143, I144, I145, I146, I147) -> f4#(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 R = 161.56/159.61 f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f1(x1, x2, x3, x4, x5, x6, x7, x8) 161.56/159.61 f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f3(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f14(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 f4(I16, I17, I18, I19, I20, I21, I22, I23) -> f13(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 f12(I24, I25, I26, I27, I28, I29, I30, I31) -> f4(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f12(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 f8(I41, I42, I43, I44, I45, I46, I47, I48) -> f2(I41, I42, I43, I44, I45, 1 + I46, I47, I48) [-1 * I47 + I48 <= 0] 161.56/159.61 f11(I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I49, I50, I51, I52, I53, I54, 1 + I55, I56) 161.56/159.61 f10(I57, I58, I59, I60, I61, I62, I63, I64) -> f11(I57, I58, I59, I60, I61, I62, I63, I64) [I59 = I59] 161.56/159.61 f8(I65, I66, I67, I68, I69, I70, I71, I72) -> f10(I65, I66, I67, I68, I73, I70, I71, I72) [I73 = I73 /\ 0 <= -1 - I71 + I72] 161.56/159.61 f8(I74, I75, I76, I77, I78, I79, I80, I81) -> f4(I74, I75, I76, I77, I82, I79, I80, I81) [0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81] 161.56/159.61 f2(I83, I84, I85, I86, I87, I88, I89, I90) -> f9(rnd1, I84, I85, I86, I87, I88, I89, I90) [rnd1 = rnd1 /\ -1 * I88 + I89 <= 0] 161.56/159.61 f2(I91, I92, I93, I94, I95, I96, I97, I98) -> f8(I91, I92, I93, I94, I95, I96, I97, I98) [0 <= -1 - I96 + I97] 161.56/159.61 f3(I99, I100, I101, I102, I103, I104, I105, I106) -> f2(I99, I100, I101, I102, I103, 1 + I104, I105, I106) [-1 * I105 + I106 <= 0] 161.56/159.61 f7(I107, I108, I109, I110, I111, I112, I113, I114) -> f3(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 f6(I115, I116, I117, I118, I119, I120, I121, I122) -> f7(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 f5(I123, I124, I125, I126, I127, I128, I129, I130) -> f6(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 f3(I140, I141, I142, I143, I144, I145, I146, I147) -> f4(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 f1(I149, I150, I151, I152, I153, I154, I155, I156) -> f2(I149, I150, I151, I152, I153, I154, I155, I156) 161.56/159.61 161.56/159.61 We use the extended value criterion with the projection function NU: 161.56/159.61 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x6 + x7 - 1 161.56/159.61 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x6 + x7 - 1 161.56/159.61 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x6 + x7 161.56/159.61 NU[f12#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x6 + x7 - 1 161.56/159.61 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x6 + x7 - 1 161.56/159.61 NU[f13#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x6 + x7 - 2 161.56/159.61 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x6 + x7 - 1 161.56/159.61 NU[f14#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x6 + x7 - 2 161.56/159.61 161.56/159.61 This gives the following inequalities: 161.56/159.61 ==> -I6 + I7 - 2 >= -(1 + I6) + I7 - 1 161.56/159.61 I11 = I11 ==> -I14 + I15 - 2 >= -I14 + I15 - 2 161.56/159.61 rnd5 = rnd5 /\ 0 <= -1 - I22 + I23 ==> -I22 + I23 - 1 > -I22 + I23 - 2 with -I22 + I23 - 1 >= 0 161.56/159.61 ==> -I30 + I31 - 1 >= -I30 + I31 - 1 161.56/159.61 0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39 ==> -I38 + I39 - 1 >= -I38 + I39 - 1 161.56/159.61 ==> -I113 + I114 >= -I113 + I114 - 1 161.56/159.61 ==> -I121 + I122 - 1 >= -(1 + I121) + I122 161.56/159.61 I124 = I124 ==> -I129 + I130 - 1 >= -I129 + I130 - 1 161.56/159.61 I139 = I139 /\ 0 <= -1 - I137 + I138 ==> -I137 + I138 - 1 >= -I137 + I138 - 1 161.56/159.61 0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147 ==> -I146 + I147 - 1 >= -I146 + I147 - 1 161.56/159.61 161.56/159.61 We remove all the strictly oriented dependency pairs. 161.56/159.61 161.56/159.61 DP problem for innermost termination. 161.56/159.61 P = 161.56/159.61 f14#(I0, I1, I2, I3, I4, I5, I6, I7) -> f3#(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 f13#(I8, I9, I10, I11, I12, I13, I14, I15) -> f14#(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 f12#(I24, I25, I26, I27, I28, I29, I30, I31) -> f4#(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4#(I32, I33, I34, I35, I36, I37, I38, I39) -> f12#(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 f7#(I107, I108, I109, I110, I111, I112, I113, I114) -> f3#(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 f6#(I115, I116, I117, I118, I119, I120, I121, I122) -> f7#(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 f5#(I123, I124, I125, I126, I127, I128, I129, I130) -> f6#(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 f3#(I131, I132, I133, I134, I135, I136, I137, I138) -> f5#(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 f3#(I140, I141, I142, I143, I144, I145, I146, I147) -> f4#(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 R = 161.56/159.61 f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f1(x1, x2, x3, x4, x5, x6, x7, x8) 161.56/159.61 f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f3(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f14(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 f4(I16, I17, I18, I19, I20, I21, I22, I23) -> f13(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 f12(I24, I25, I26, I27, I28, I29, I30, I31) -> f4(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f12(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 f8(I41, I42, I43, I44, I45, I46, I47, I48) -> f2(I41, I42, I43, I44, I45, 1 + I46, I47, I48) [-1 * I47 + I48 <= 0] 161.56/159.61 f11(I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I49, I50, I51, I52, I53, I54, 1 + I55, I56) 161.56/159.61 f10(I57, I58, I59, I60, I61, I62, I63, I64) -> f11(I57, I58, I59, I60, I61, I62, I63, I64) [I59 = I59] 161.56/159.61 f8(I65, I66, I67, I68, I69, I70, I71, I72) -> f10(I65, I66, I67, I68, I73, I70, I71, I72) [I73 = I73 /\ 0 <= -1 - I71 + I72] 161.56/159.61 f8(I74, I75, I76, I77, I78, I79, I80, I81) -> f4(I74, I75, I76, I77, I82, I79, I80, I81) [0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81] 161.56/159.61 f2(I83, I84, I85, I86, I87, I88, I89, I90) -> f9(rnd1, I84, I85, I86, I87, I88, I89, I90) [rnd1 = rnd1 /\ -1 * I88 + I89 <= 0] 161.56/159.61 f2(I91, I92, I93, I94, I95, I96, I97, I98) -> f8(I91, I92, I93, I94, I95, I96, I97, I98) [0 <= -1 - I96 + I97] 161.56/159.61 f3(I99, I100, I101, I102, I103, I104, I105, I106) -> f2(I99, I100, I101, I102, I103, 1 + I104, I105, I106) [-1 * I105 + I106 <= 0] 161.56/159.61 f7(I107, I108, I109, I110, I111, I112, I113, I114) -> f3(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 f6(I115, I116, I117, I118, I119, I120, I121, I122) -> f7(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 f5(I123, I124, I125, I126, I127, I128, I129, I130) -> f6(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 f3(I140, I141, I142, I143, I144, I145, I146, I147) -> f4(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 f1(I149, I150, I151, I152, I153, I154, I155, I156) -> f2(I149, I150, I151, I152, I153, I154, I155, I156) 161.56/159.61 161.56/159.61 The dependency graph for this problem is: 161.56/159.61 1 -> 16, 17 161.56/159.61 2 -> 1 161.56/159.61 4 -> 5 161.56/159.61 5 -> 4 161.56/159.61 13 -> 16, 17 161.56/159.61 14 -> 13 161.56/159.61 15 -> 14 161.56/159.61 16 -> 15 161.56/159.61 17 -> 5 161.56/159.61 Where: 161.56/159.61 1) f14#(I0, I1, I2, I3, I4, I5, I6, I7) -> f3#(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 2) f13#(I8, I9, I10, I11, I12, I13, I14, I15) -> f14#(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 4) f12#(I24, I25, I26, I27, I28, I29, I30, I31) -> f4#(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 5) f4#(I32, I33, I34, I35, I36, I37, I38, I39) -> f12#(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 13) f7#(I107, I108, I109, I110, I111, I112, I113, I114) -> f3#(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 14) f6#(I115, I116, I117, I118, I119, I120, I121, I122) -> f7#(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 15) f5#(I123, I124, I125, I126, I127, I128, I129, I130) -> f6#(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 16) f3#(I131, I132, I133, I134, I135, I136, I137, I138) -> f5#(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 17) f3#(I140, I141, I142, I143, I144, I145, I146, I147) -> f4#(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 161.56/159.61 We have the following SCCs. 161.56/159.61 { 13, 14, 15, 16 } 161.56/159.61 { 4, 5 } 161.56/159.61 161.56/159.61 DP problem for innermost termination. 161.56/159.61 P = 161.56/159.61 f12#(I24, I25, I26, I27, I28, I29, I30, I31) -> f4#(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4#(I32, I33, I34, I35, I36, I37, I38, I39) -> f12#(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 R = 161.56/159.61 f15(x1, x2, x3, x4, x5, x6, x7, x8) -> f1(x1, x2, x3, x4, x5, x6, x7, x8) 161.56/159.61 f14(I0, I1, I2, I3, I4, I5, I6, I7) -> f3(I0, I1, I2, I3, I4, I5, 1 + I6, I7) 161.56/159.61 f13(I8, I9, I10, I11, I12, I13, I14, I15) -> f14(I8, I9, I10, I11, I12, I13, I14, I15) [I11 = I11] 161.56/159.61 f4(I16, I17, I18, I19, I20, I21, I22, I23) -> f13(I16, I17, I18, I19, rnd5, I21, I22, I23) [rnd5 = rnd5 /\ 0 <= -1 - I22 + I23] 161.56/159.61 f12(I24, I25, I26, I27, I28, I29, I30, I31) -> f4(I24, I25, I26, I27, I28, I29, I30, I31) 161.56/159.61 f4(I32, I33, I34, I35, I36, I37, I38, I39) -> f12(I32, I33, I34, I35, I40, I37, I38, I39) [0 <= I40 /\ I40 <= 0 /\ I40 = I40 /\ 0 <= -1 - I38 + I39] 161.56/159.61 f8(I41, I42, I43, I44, I45, I46, I47, I48) -> f2(I41, I42, I43, I44, I45, 1 + I46, I47, I48) [-1 * I47 + I48 <= 0] 161.56/159.61 f11(I49, I50, I51, I52, I53, I54, I55, I56) -> f3(I49, I50, I51, I52, I53, I54, 1 + I55, I56) 161.56/159.61 f10(I57, I58, I59, I60, I61, I62, I63, I64) -> f11(I57, I58, I59, I60, I61, I62, I63, I64) [I59 = I59] 161.56/159.61 f8(I65, I66, I67, I68, I69, I70, I71, I72) -> f10(I65, I66, I67, I68, I73, I70, I71, I72) [I73 = I73 /\ 0 <= -1 - I71 + I72] 161.56/159.61 f8(I74, I75, I76, I77, I78, I79, I80, I81) -> f4(I74, I75, I76, I77, I82, I79, I80, I81) [0 <= I82 /\ I82 <= 0 /\ I82 = I82 /\ 0 <= -1 - I80 + I81] 161.56/159.61 f2(I83, I84, I85, I86, I87, I88, I89, I90) -> f9(rnd1, I84, I85, I86, I87, I88, I89, I90) [rnd1 = rnd1 /\ -1 * I88 + I89 <= 0] 161.56/159.61 f2(I91, I92, I93, I94, I95, I96, I97, I98) -> f8(I91, I92, I93, I94, I95, I96, I97, I98) [0 <= -1 - I96 + I97] 161.56/159.61 f3(I99, I100, I101, I102, I103, I104, I105, I106) -> f2(I99, I100, I101, I102, I103, 1 + I104, I105, I106) [-1 * I105 + I106 <= 0] 161.56/159.61 f7(I107, I108, I109, I110, I111, I112, I113, I114) -> f3(I107, I108, I109, I110, I111, I112, I113, I114) 161.56/159.61 f6(I115, I116, I117, I118, I119, I120, I121, I122) -> f7(I115, I116, I117, I118, I119, I120, 1 + I121, I122) 161.56/159.61 f5(I123, I124, I125, I126, I127, I128, I129, I130) -> f6(I123, I124, I125, I126, I127, I128, I129, I130) [I124 = I124] 161.56/159.61 f3(I131, I132, I133, I134, I135, I136, I137, I138) -> f5(I131, I132, I133, I134, I139, I136, I137, I138) [I139 = I139 /\ 0 <= -1 - I137 + I138] 161.56/159.61 f3(I140, I141, I142, I143, I144, I145, I146, I147) -> f4(I140, I141, I142, I143, I148, I145, I146, I147) [0 <= I148 /\ I148 <= 0 /\ I148 = I148 /\ 0 <= -1 - I146 + I147] 161.56/159.61 f1(I149, I150, I151, I152, I153, I154, I155, I156) -> f2(I149, I150, I151, I152, I153, I154, I155, I156) 161.56/159.61 161.56/162.59 EOF