18.32/18.07 YES 18.32/18.07 18.32/18.07 DP problem for innermost termination. 18.32/18.07 P = 18.32/18.07 f14#(x1, x2, x3, x4, x5, x6) -> f13#(x1, x2, x3, x4, x5, x6) 18.32/18.07 f13#(I0, I1, I2, I3, I4, I5) -> f12#(I0, I1, I2, I3, I4, I5) 18.32/18.07 f13#(I6, I7, I8, I9, I10, I11) -> f11#(I6, I7, I8, I9, I10, I11) 18.32/18.07 f13#(I12, I13, I14, I15, I16, I17) -> f10#(I12, I13, I14, I15, I16, I17) 18.32/18.07 f13#(I18, I19, I20, I21, I22, I23) -> f8#(I18, I19, I20, I21, I22, I23) 18.32/18.07 f13#(I30, I31, I32, I33, I34, I35) -> f7#(I30, I31, I32, I33, I34, I35) 18.32/18.07 f13#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 18.32/18.07 f13#(I42, I43, I44, I45, I46, I47) -> f5#(I42, I43, I44, I45, I46, I47) 18.32/18.07 f13#(I48, I49, I50, I51, I52, I53) -> f4#(I48, I49, I50, I51, I52, I53) 18.32/18.07 f13#(I54, I55, I56, I57, I58, I59) -> f3#(I54, I55, I56, I57, I58, I59) 18.32/18.07 f13#(I60, I61, I62, I63, I64, I65) -> f1#(I60, I61, I62, I63, I64, I65) 18.32/18.07 f13#(I72, I73, I74, I75, I76, I77) -> f7#(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] 18.32/18.07 f13#(I78, I79, I80, I81, I82, I83) -> f12#(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84] 18.32/18.07 f12#(I88, I89, I90, I91, I92, I93) -> f11#(I92, I93, I90, I91, 0, 0) 18.32/18.07 f11#(I94, I95, I96, I97, I98, I99) -> f10#(I98, I99, I96, I97, I98, I99) [I98 <= 63] 18.32/18.07 f11#(I100, I101, I102, I103, I104, I105) -> f8#(I104, I105, I102, I103, I104, I105) [64 <= I104] 18.32/18.07 f10#(I106, I107, I108, I109, I110, I111) -> f11#(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 f7#(I124, I125, I126, I127, I128, I129) -> f6#(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130] 18.32/18.07 f6#(I132, I133, I134, I135, I136, I137) -> f5#(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138] 18.32/18.07 f6#(I140, I141, I142, I143, I144, I145) -> f4#(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0] 18.32/18.07 f5#(I146, I147, I148, I149, I150, I151) -> f6#(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 f4#(I154, I155, I156, I157, I158, I159) -> f3#(I158, I159, I156, I157, I158, I159) [0 <= I159] 18.32/18.07 f4#(I160, I161, I162, I163, I164, I165) -> f1#(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0] 18.32/18.07 f3#(I166, I167, I168, I169, I170, I171) -> f4#(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 R = 18.32/18.07 f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 18.32/18.07 f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 18.32/18.07 f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 18.32/18.07 f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 18.32/18.07 f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 18.32/18.07 f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 18.32/18.07 f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 18.32/18.07 f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 18.32/18.07 f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 18.32/18.07 f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 18.32/18.07 f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 18.32/18.07 f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 18.32/18.07 f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 18.32/18.07 f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] 18.32/18.07 f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84] 18.32/18.07 f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 18.32/18.07 f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63] 18.32/18.07 f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104] 18.32/18.07 f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120] 18.32/18.07 f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130] 18.32/18.07 f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138] 18.32/18.07 f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0] 18.32/18.07 f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159] 18.32/18.07 f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0] 18.32/18.07 f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178] 18.32/18.07 18.32/18.07 The dependency graph for this problem is: 18.32/18.07 0 -> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 18.32/18.07 1 -> 13 18.32/18.07 2 -> 14, 15 18.32/18.07 3 -> 16 18.32/18.07 4 -> 18.32/18.07 5 -> 17 18.32/18.07 6 -> 18, 19 18.32/18.07 7 -> 20 18.32/18.07 8 -> 21, 22 18.32/18.07 9 -> 23 18.32/18.07 10 -> 18.32/18.07 11 -> 17 18.32/18.07 12 -> 13 18.32/18.07 13 -> 14 18.32/18.07 14 -> 16 18.32/18.07 15 -> 18.32/18.07 16 -> 14, 15 18.32/18.07 17 -> 18 18.32/18.07 18 -> 20 18.32/18.07 19 -> 21 18.32/18.07 20 -> 18, 19 18.32/18.07 21 -> 23 18.32/18.07 22 -> 18.32/18.07 23 -> 21, 22 18.32/18.07 Where: 18.32/18.07 0) f14#(x1, x2, x3, x4, x5, x6) -> f13#(x1, x2, x3, x4, x5, x6) 18.32/18.07 1) f13#(I0, I1, I2, I3, I4, I5) -> f12#(I0, I1, I2, I3, I4, I5) 18.32/18.07 2) f13#(I6, I7, I8, I9, I10, I11) -> f11#(I6, I7, I8, I9, I10, I11) 18.32/18.07 3) f13#(I12, I13, I14, I15, I16, I17) -> f10#(I12, I13, I14, I15, I16, I17) 18.32/18.07 4) f13#(I18, I19, I20, I21, I22, I23) -> f8#(I18, I19, I20, I21, I22, I23) 18.32/18.07 5) f13#(I30, I31, I32, I33, I34, I35) -> f7#(I30, I31, I32, I33, I34, I35) 18.32/18.07 6) f13#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 18.32/18.07 7) f13#(I42, I43, I44, I45, I46, I47) -> f5#(I42, I43, I44, I45, I46, I47) 18.32/18.07 8) f13#(I48, I49, I50, I51, I52, I53) -> f4#(I48, I49, I50, I51, I52, I53) 18.32/18.07 9) f13#(I54, I55, I56, I57, I58, I59) -> f3#(I54, I55, I56, I57, I58, I59) 18.32/18.07 10) f13#(I60, I61, I62, I63, I64, I65) -> f1#(I60, I61, I62, I63, I64, I65) 18.32/18.07 11) f13#(I72, I73, I74, I75, I76, I77) -> f7#(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] 18.32/18.07 12) f13#(I78, I79, I80, I81, I82, I83) -> f12#(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84] 18.32/18.07 13) f12#(I88, I89, I90, I91, I92, I93) -> f11#(I92, I93, I90, I91, 0, 0) 18.32/18.07 14) f11#(I94, I95, I96, I97, I98, I99) -> f10#(I98, I99, I96, I97, I98, I99) [I98 <= 63] 18.32/18.07 15) f11#(I100, I101, I102, I103, I104, I105) -> f8#(I104, I105, I102, I103, I104, I105) [64 <= I104] 18.32/18.07 16) f10#(I106, I107, I108, I109, I110, I111) -> f11#(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 17) f7#(I124, I125, I126, I127, I128, I129) -> f6#(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130] 18.32/18.07 18) f6#(I132, I133, I134, I135, I136, I137) -> f5#(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138] 18.32/18.07 19) f6#(I140, I141, I142, I143, I144, I145) -> f4#(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0] 18.32/18.07 20) f5#(I146, I147, I148, I149, I150, I151) -> f6#(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 21) f4#(I154, I155, I156, I157, I158, I159) -> f3#(I158, I159, I156, I157, I158, I159) [0 <= I159] 18.32/18.07 22) f4#(I160, I161, I162, I163, I164, I165) -> f1#(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0] 18.32/18.07 23) f3#(I166, I167, I168, I169, I170, I171) -> f4#(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 18.32/18.07 We have the following SCCs. 18.32/18.07 { 14, 16 } 18.32/18.07 { 18, 20 } 18.32/18.07 { 21, 23 } 18.32/18.07 18.32/18.07 DP problem for innermost termination. 18.32/18.07 P = 18.32/18.07 f4#(I154, I155, I156, I157, I158, I159) -> f3#(I158, I159, I156, I157, I158, I159) [0 <= I159] 18.32/18.07 f3#(I166, I167, I168, I169, I170, I171) -> f4#(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 R = 18.32/18.07 f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 18.32/18.07 f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 18.32/18.07 f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 18.32/18.07 f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 18.32/18.07 f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 18.32/18.07 f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 18.32/18.07 f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 18.32/18.07 f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 18.32/18.07 f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 18.32/18.07 f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 18.32/18.07 f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 18.32/18.07 f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 18.32/18.07 f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 18.32/18.07 f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] 18.32/18.07 f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84] 18.32/18.07 f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 18.32/18.07 f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63] 18.32/18.07 f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104] 18.32/18.07 f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120] 18.32/18.07 f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130] 18.32/18.07 f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138] 18.32/18.07 f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0] 18.32/18.07 f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159] 18.32/18.07 f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0] 18.32/18.07 f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178] 18.32/18.07 18.32/18.07 We use the reverse value criterion with the projection function NU: 18.32/18.07 NU[f3#(z1,z2,z3,z4,z5,z6)] = -1 + z6 + -1 * 0 18.32/18.07 NU[f4#(z1,z2,z3,z4,z5,z6)] = z6 18.32/18.07 18.32/18.07 This gives the following inequalities: 18.32/18.07 0 <= I159 ==> I159 > -1 + I159 + -1 * 0 with I159 >= 0 18.32/18.07 ==> -1 + I171 + -1 * 0 >= -1 + I171 18.32/18.07 18.32/18.07 We remove all the strictly oriented dependency pairs. 18.32/18.07 18.32/18.07 DP problem for innermost termination. 18.32/18.07 P = 18.32/18.07 f3#(I166, I167, I168, I169, I170, I171) -> f4#(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 R = 18.32/18.07 f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 18.32/18.07 f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 18.32/18.07 f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 18.32/18.07 f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 18.32/18.07 f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 18.32/18.07 f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 18.32/18.07 f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 18.32/18.07 f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 18.32/18.07 f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 18.32/18.07 f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 18.32/18.07 f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 18.32/18.07 f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 18.32/18.07 f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 18.32/18.07 f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] 18.32/18.07 f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84] 18.32/18.07 f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 18.32/18.07 f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63] 18.32/18.07 f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104] 18.32/18.07 f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120] 18.32/18.07 f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130] 18.32/18.07 f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138] 18.32/18.07 f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0] 18.32/18.07 f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159] 18.32/18.07 f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0] 18.32/18.07 f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178] 18.32/18.07 18.32/18.07 The dependency graph for this problem is: 18.32/18.07 23 -> 18.32/18.07 Where: 18.32/18.07 23) f3#(I166, I167, I168, I169, I170, I171) -> f4#(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 18.32/18.07 We have the following SCCs. 18.32/18.07 18.32/18.07 18.32/18.07 DP problem for innermost termination. 18.32/18.07 P = 18.32/18.07 f6#(I132, I133, I134, I135, I136, I137) -> f5#(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138] 18.32/18.07 f5#(I146, I147, I148, I149, I150, I151) -> f6#(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 R = 18.32/18.07 f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 18.32/18.07 f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 18.32/18.07 f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 18.32/18.07 f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 18.32/18.07 f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 18.32/18.07 f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 18.32/18.07 f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 18.32/18.07 f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 18.32/18.07 f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 18.32/18.07 f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 18.32/18.07 f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 18.32/18.07 f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 18.32/18.07 f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 18.32/18.07 f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] 18.32/18.07 f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84] 18.32/18.07 f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 18.32/18.07 f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63] 18.32/18.07 f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104] 18.32/18.07 f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120] 18.32/18.07 f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130] 18.32/18.07 f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138] 18.32/18.07 f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0] 18.32/18.07 f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159] 18.32/18.07 f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0] 18.32/18.07 f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178] 18.32/18.07 18.32/18.07 We use the reverse value criterion with the projection function NU: 18.32/18.07 NU[f5#(z1,z2,z3,z4,z5,z6)] = -1 + z5 + -1 * 0 18.32/18.07 NU[f6#(z1,z2,z3,z4,z5,z6)] = z5 18.32/18.07 18.32/18.07 This gives the following inequalities: 18.32/18.07 I139 = I138 /\ 0 <= I136 /\ I138 = I138 ==> I136 > -1 + I136 + -1 * 0 with I136 >= 0 18.32/18.07 I153 = I152 /\ I152 = I152 ==> -1 + I150 + -1 * 0 >= -1 + I150 18.32/18.07 18.32/18.07 We remove all the strictly oriented dependency pairs. 18.32/18.07 18.32/18.07 DP problem for innermost termination. 18.32/18.07 P = 18.32/18.07 f5#(I146, I147, I148, I149, I150, I151) -> f6#(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 R = 18.32/18.07 f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 18.32/18.07 f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 18.32/18.07 f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 18.32/18.07 f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 18.32/18.07 f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 18.32/18.07 f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 18.32/18.07 f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 18.32/18.07 f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 18.32/18.07 f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 18.32/18.07 f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 18.32/18.07 f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 18.32/18.07 f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 18.32/18.07 f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 18.32/18.07 f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] 18.32/18.07 f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84] 18.32/18.07 f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 18.32/18.07 f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63] 18.32/18.07 f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104] 18.32/18.07 f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120] 18.32/18.07 f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130] 18.32/18.07 f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138] 18.32/18.07 f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0] 18.32/18.07 f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159] 18.32/18.07 f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0] 18.32/18.07 f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178] 18.32/18.07 18.32/18.07 The dependency graph for this problem is: 18.32/18.07 20 -> 18.32/18.07 Where: 18.32/18.07 20) f5#(I146, I147, I148, I149, I150, I151) -> f6#(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 18.32/18.07 We have the following SCCs. 18.32/18.07 18.32/18.07 18.32/18.07 DP problem for innermost termination. 18.32/18.07 P = 18.32/18.07 f11#(I94, I95, I96, I97, I98, I99) -> f10#(I98, I99, I96, I97, I98, I99) [I98 <= 63] 18.32/18.07 f10#(I106, I107, I108, I109, I110, I111) -> f11#(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 R = 18.32/18.07 f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 18.32/18.07 f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 18.32/18.07 f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 18.32/18.07 f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 18.32/18.07 f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 18.32/18.07 f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 18.32/18.07 f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 18.32/18.07 f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 18.32/18.07 f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 18.32/18.07 f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 18.32/18.07 f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 18.32/18.07 f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 18.32/18.07 f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 18.32/18.07 f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] 18.32/18.07 f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84] 18.32/18.07 f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 18.32/18.07 f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63] 18.32/18.07 f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104] 18.32/18.07 f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120] 18.32/18.07 f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130] 18.32/18.07 f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138] 18.32/18.07 f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0] 18.32/18.07 f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159] 18.32/18.07 f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0] 18.32/18.07 f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178] 18.32/18.07 18.32/18.07 We use the reverse value criterion with the projection function NU: 18.32/18.07 NU[f10#(z1,z2,z3,z4,z5,z6)] = 63 + -1 * (1 + z5) 18.32/18.07 NU[f11#(z1,z2,z3,z4,z5,z6)] = 63 + -1 * z5 18.32/18.07 18.32/18.07 This gives the following inequalities: 18.32/18.07 I98 <= 63 ==> 63 + -1 * I98 > 63 + -1 * (1 + I98) with 63 + -1 * I98 >= 0 18.32/18.07 I113 = I112 /\ I112 = I112 ==> 63 + -1 * (1 + I110) >= 63 + -1 * (1 + I110) 18.32/18.07 18.32/18.07 We remove all the strictly oriented dependency pairs. 18.32/18.07 18.32/18.07 DP problem for innermost termination. 18.32/18.07 P = 18.32/18.07 f10#(I106, I107, I108, I109, I110, I111) -> f11#(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 R = 18.32/18.07 f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) 18.32/18.07 f13(I0, I1, I2, I3, I4, I5) -> f12(I0, I1, I2, I3, I4, I5) 18.32/18.07 f13(I6, I7, I8, I9, I10, I11) -> f11(I6, I7, I8, I9, I10, I11) 18.32/18.07 f13(I12, I13, I14, I15, I16, I17) -> f10(I12, I13, I14, I15, I16, I17) 18.32/18.07 f13(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) 18.32/18.07 f13(I24, I25, I26, I27, I28, I29) -> f9(I24, I25, I26, I27, I28, I29) 18.32/18.07 f13(I30, I31, I32, I33, I34, I35) -> f7(I30, I31, I32, I33, I34, I35) 18.32/18.07 f13(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 18.32/18.07 f13(I42, I43, I44, I45, I46, I47) -> f5(I42, I43, I44, I45, I46, I47) 18.32/18.07 f13(I48, I49, I50, I51, I52, I53) -> f4(I48, I49, I50, I51, I52, I53) 18.32/18.07 f13(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) 18.32/18.07 f13(I60, I61, I62, I63, I64, I65) -> f1(I60, I61, I62, I63, I64, I65) 18.32/18.07 f13(I66, I67, I68, I69, I70, I71) -> f2(I66, I67, I68, I69, I70, I71) 18.32/18.07 f13(I72, I73, I74, I75, I76, I77) -> f7(I76, I77, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] 18.32/18.07 f13(I78, I79, I80, I81, I82, I83) -> f12(I82, I83, I84, I85, I86, I87) [I87 = I85 /\ I86 = I84 /\ I85 = I85 /\ I84 = I84] 18.32/18.07 f12(I88, I89, I90, I91, I92, I93) -> f11(I92, I93, I90, I91, 0, 0) 18.32/18.07 f11(I94, I95, I96, I97, I98, I99) -> f10(I98, I99, I96, I97, I98, I99) [I98 <= 63] 18.32/18.07 f11(I100, I101, I102, I103, I104, I105) -> f8(I104, I105, I102, I103, I104, I105) [64 <= I104] 18.32/18.07 f10(I106, I107, I108, I109, I110, I111) -> f11(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 f8(I114, I115, I116, I117, I118, I119) -> f9(I118, I119, I120, I121, I122, I123) [I123 = I121 /\ I122 = I120 /\ I121 = I121 /\ I120 = I120] 18.32/18.07 f7(I124, I125, I126, I127, I128, I129) -> f6(I128, I129, I130, I127, 7, I131) [I131 = I130 /\ I130 = I130] 18.32/18.07 f6(I132, I133, I134, I135, I136, I137) -> f5(I136, I137, I138, I135, I136, I139) [I139 = I138 /\ 0 <= I136 /\ I138 = I138] 18.32/18.07 f6(I140, I141, I142, I143, I144, I145) -> f4(I144, I145, I142, I143, I144, 7) [1 + I144 <= 0] 18.32/18.07 f5(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I149, -1 + I150, I153) [I153 = I152 /\ I152 = I152] 18.32/18.07 f4(I154, I155, I156, I157, I158, I159) -> f3(I158, I159, I156, I157, I158, I159) [0 <= I159] 18.32/18.07 f4(I160, I161, I162, I163, I164, I165) -> f1(I164, I165, I162, I163, I164, I165) [1 + I165 <= 0] 18.32/18.07 f3(I166, I167, I168, I169, I170, I171) -> f4(I170, I171, I168, I169, I170, -1 + I171) 18.32/18.07 f1(I172, I173, I174, I175, I176, I177) -> f2(I176, I177, I178, I179, I180, I181) [I181 = I179 /\ I180 = I178 /\ I179 = I179 /\ I178 = I178] 18.32/18.07 18.32/18.07 The dependency graph for this problem is: 18.32/18.07 16 -> 18.32/18.07 Where: 18.32/18.07 16) f10#(I106, I107, I108, I109, I110, I111) -> f11#(I110, I111, I112, I109, 1 + I110, I113) [I113 = I112 /\ I112 = I112] 18.32/18.07 18.32/18.07 We have the following SCCs. 18.32/18.07 18.32/21.05 EOF