/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES DP problem for innermost termination. P = f14#(x1, x2, x3, x4, x5, x6) -> f13#(x1, x2, x3, x4, x5, x6) f13#(I0, I1, I2, I3, I4, I5) -> f8#(I0, I1, I2, I3, I4, I5) f13#(I6, I7, I8, I9, I10, I11) -> f3#(I6, I7, I8, I9, I10, I11) f13#(I12, I13, I14, I15, I16, I17) -> f2#(I12, I13, I14, I15, I16, I17) f13#(I24, I25, I26, I27, I28, I29) -> f11#(I24, I25, I26, I27, I28, I29) f13#(I30, I31, I32, I33, I34, I35) -> f10#(I30, I31, I32, I33, I34, I35) f13#(I36, I37, I38, I39, I40, I41) -> f9#(I36, I37, I38, I39, I40, I41) f13#(I48, I49, I50, I51, I52, I53) -> f7#(I48, I49, I50, I51, I52, I53) f13#(I54, I55, I56, I57, I58, I59) -> f5#(I54, I55, I56, I57, I58, I59) f13#(I60, I61, I62, I63, I64, I65) -> f4#(I60, I61, I62, I63, I64, I65) f13#(I66, I67, I68, I69, I70, I71) -> f1#(I66, I67, I68, I69, I70, I71) f8#(I72, I73, I74, I75, I76, I77) -> f11#(I76, I77, I74, I75, I76, I77) f3#(I78, I79, I80, I81, I82, I83) -> f4#(I82, I83, I80, I81, I82, -1 + I83) f11#(I100, I101, I102, I103, I104, I105) -> f10#(I104, I105, I102, I103, I104, I105) [1 <= I105] f11#(I106, I107, I108, I109, I110, I111) -> f9#(I110, I111, I108, I109, I110, I111) [I111 <= 0] f10#(I112, I113, I114, I115, I116, I117) -> f8#(I116, I117, I114, I115, I116, -1 + I117) f9#(I128, I129, I130, I131, I132, I133) -> f7#(I132, I133, I130, I131, I132, I133) [1 <= I132] f9#(I134, I135, I136, I137, I138, I139) -> f5#(I138, I139, I136, I137, I138, I139) [I138 <= 0] f7#(I140, I141, I142, I143, I144, I145) -> f8#(I144, I145, I142, I143, -1 + I144, I145) f4#(I166, I167, I168, I169, I170, I171) -> f1#(I170, I171, I168, I169, I170, I171) f1#(I172, I173, I174, I175, I176, I177) -> f3#(I176, I177, I174, I175, I176, I177) [1 <= I177 /\ 1 + I177 <= 0] f1#(I178, I179, I180, I181, I182, I183) -> f3#(I182, I183, I180, I181, I182, I183) [1 <= I183 /\ 1 <= I183] f1#(I184, I185, I186, I187, I188, I189) -> f2#(I188, I189, I186, I187, I188, I189) [0 <= I189 /\ I189 <= 0] f1#(I190, I191, I192, I193, I194, I195) -> f2#(I194, I195, I192, I193, I194, I195) [I195 <= 0] R = f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) f13(I0, I1, I2, I3, I4, I5) -> f8(I0, I1, I2, I3, I4, I5) f13(I6, I7, I8, I9, I10, I11) -> f3(I6, I7, I8, I9, I10, I11) f13(I12, I13, I14, I15, I16, I17) -> f2(I12, I13, I14, I15, I16, I17) f13(I18, I19, I20, I21, I22, I23) -> f12(I18, I19, I20, I21, I22, I23) f13(I24, I25, I26, I27, I28, I29) -> f11(I24, I25, I26, I27, I28, I29) f13(I30, I31, I32, I33, I34, I35) -> f10(I30, I31, I32, I33, I34, I35) f13(I36, I37, I38, I39, I40, I41) -> f9(I36, I37, I38, I39, I40, I41) f13(I42, I43, I44, I45, I46, I47) -> f6(I42, I43, I44, I45, I46, I47) f13(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, I50, I51, I52, I53) f13(I54, I55, I56, I57, I58, I59) -> f5(I54, I55, I56, I57, I58, I59) f13(I60, I61, I62, I63, I64, I65) -> f4(I60, I61, I62, I63, I64, I65) f13(I66, I67, I68, I69, I70, I71) -> f1(I66, I67, I68, I69, I70, I71) f8(I72, I73, I74, I75, I76, I77) -> f11(I76, I77, I74, I75, I76, I77) f3(I78, I79, I80, I81, I82, I83) -> f4(I82, I83, I80, I81, I82, -1 + I83) f3(I84, I85, I86, I87, I88, I89) -> f12(I88, I89, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] f2(I90, I91, I92, I93, I94, I95) -> f12(I94, I95, I96, I97, I98, I99) [I99 = I97 /\ I98 = I96 /\ I97 = I97 /\ I96 = I96] f11(I100, I101, I102, I103, I104, I105) -> f10(I104, I105, I102, I103, I104, I105) [1 <= I105] f11(I106, I107, I108, I109, I110, I111) -> f9(I110, I111, I108, I109, I110, I111) [I111 <= 0] f10(I112, I113, I114, I115, I116, I117) -> f8(I116, I117, I114, I115, I116, -1 + I117) f10(I118, I119, I120, I121, I122, I123) -> f6(I122, I123, I124, I125, I126, I127) [I127 = I125 /\ I126 = I124 /\ I125 = I125 /\ I124 = I124] f9(I128, I129, I130, I131, I132, I133) -> f7(I132, I133, I130, I131, I132, I133) [1 <= I132] f9(I134, I135, I136, I137, I138, I139) -> f5(I138, I139, I136, I137, I138, I139) [I138 <= 0] f7(I140, I141, I142, I143, I144, I145) -> f8(I144, I145, I142, I143, -1 + I144, I145) f7(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I153, I154, I155) [I155 = I153 /\ I154 = I152 /\ I153 = I153 /\ I152 = I152] f5(I156, I157, I158, I159, I160, I161) -> f6(I160, I161, I162, I163, I164, I165) [I165 = I163 /\ I164 = I162 /\ I163 = I163 /\ I162 = I162] f4(I166, I167, I168, I169, I170, I171) -> f1(I170, I171, I168, I169, I170, I171) f1(I172, I173, I174, I175, I176, I177) -> f3(I176, I177, I174, I175, I176, I177) [1 <= I177 /\ 1 + I177 <= 0] f1(I178, I179, I180, I181, I182, I183) -> f3(I182, I183, I180, I181, I182, I183) [1 <= I183 /\ 1 <= I183] f1(I184, I185, I186, I187, I188, I189) -> f2(I188, I189, I186, I187, I188, I189) [0 <= I189 /\ I189 <= 0] f1(I190, I191, I192, I193, I194, I195) -> f2(I194, I195, I192, I193, I194, I195) [I195 <= 0] The dependency graph for this problem is: 0 -> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1 -> 11 2 -> 12 3 -> 4 -> 13, 14 5 -> 15 6 -> 16, 17 7 -> 18 8 -> 9 -> 19 10 -> 21, 22, 23 11 -> 13, 14 12 -> 19 13 -> 15 14 -> 16, 17 15 -> 11 16 -> 18 17 -> 18 -> 11 19 -> 21, 22, 23 20 -> 21 -> 12 22 -> 23 -> Where: 0) f14#(x1, x2, x3, x4, x5, x6) -> f13#(x1, x2, x3, x4, x5, x6) 1) f13#(I0, I1, I2, I3, I4, I5) -> f8#(I0, I1, I2, I3, I4, I5) 2) f13#(I6, I7, I8, I9, I10, I11) -> f3#(I6, I7, I8, I9, I10, I11) 3) f13#(I12, I13, I14, I15, I16, I17) -> f2#(I12, I13, I14, I15, I16, I17) 4) f13#(I24, I25, I26, I27, I28, I29) -> f11#(I24, I25, I26, I27, I28, I29) 5) f13#(I30, I31, I32, I33, I34, I35) -> f10#(I30, I31, I32, I33, I34, I35) 6) f13#(I36, I37, I38, I39, I40, I41) -> f9#(I36, I37, I38, I39, I40, I41) 7) f13#(I48, I49, I50, I51, I52, I53) -> f7#(I48, I49, I50, I51, I52, I53) 8) f13#(I54, I55, I56, I57, I58, I59) -> f5#(I54, I55, I56, I57, I58, I59) 9) f13#(I60, I61, I62, I63, I64, I65) -> f4#(I60, I61, I62, I63, I64, I65) 10) f13#(I66, I67, I68, I69, I70, I71) -> f1#(I66, I67, I68, I69, I70, I71) 11) f8#(I72, I73, I74, I75, I76, I77) -> f11#(I76, I77, I74, I75, I76, I77) 12) f3#(I78, I79, I80, I81, I82, I83) -> f4#(I82, I83, I80, I81, I82, -1 + I83) 13) f11#(I100, I101, I102, I103, I104, I105) -> f10#(I104, I105, I102, I103, I104, I105) [1 <= I105] 14) f11#(I106, I107, I108, I109, I110, I111) -> f9#(I110, I111, I108, I109, I110, I111) [I111 <= 0] 15) f10#(I112, I113, I114, I115, I116, I117) -> f8#(I116, I117, I114, I115, I116, -1 + I117) 16) f9#(I128, I129, I130, I131, I132, I133) -> f7#(I132, I133, I130, I131, I132, I133) [1 <= I132] 17) f9#(I134, I135, I136, I137, I138, I139) -> f5#(I138, I139, I136, I137, I138, I139) [I138 <= 0] 18) f7#(I140, I141, I142, I143, I144, I145) -> f8#(I144, I145, I142, I143, -1 + I144, I145) 19) f4#(I166, I167, I168, I169, I170, I171) -> f1#(I170, I171, I168, I169, I170, I171) 20) f1#(I172, I173, I174, I175, I176, I177) -> f3#(I176, I177, I174, I175, I176, I177) [1 <= I177 /\ 1 + I177 <= 0] 21) f1#(I178, I179, I180, I181, I182, I183) -> f3#(I182, I183, I180, I181, I182, I183) [1 <= I183 /\ 1 <= I183] 22) f1#(I184, I185, I186, I187, I188, I189) -> f2#(I188, I189, I186, I187, I188, I189) [0 <= I189 /\ I189 <= 0] 23) f1#(I190, I191, I192, I193, I194, I195) -> f2#(I194, I195, I192, I193, I194, I195) [I195 <= 0] We have the following SCCs. { 11, 13, 14, 15, 16, 18 } { 12, 19, 21 } DP problem for innermost termination. P = f3#(I78, I79, I80, I81, I82, I83) -> f4#(I82, I83, I80, I81, I82, -1 + I83) f4#(I166, I167, I168, I169, I170, I171) -> f1#(I170, I171, I168, I169, I170, I171) f1#(I178, I179, I180, I181, I182, I183) -> f3#(I182, I183, I180, I181, I182, I183) [1 <= I183 /\ 1 <= I183] R = f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) f13(I0, I1, I2, I3, I4, I5) -> f8(I0, I1, I2, I3, I4, I5) f13(I6, I7, I8, I9, I10, I11) -> f3(I6, I7, I8, I9, I10, I11) f13(I12, I13, I14, I15, I16, I17) -> f2(I12, I13, I14, I15, I16, I17) f13(I18, I19, I20, I21, I22, I23) -> f12(I18, I19, I20, I21, I22, I23) f13(I24, I25, I26, I27, I28, I29) -> f11(I24, I25, I26, I27, I28, I29) f13(I30, I31, I32, I33, I34, I35) -> f10(I30, I31, I32, I33, I34, I35) f13(I36, I37, I38, I39, I40, I41) -> f9(I36, I37, I38, I39, I40, I41) f13(I42, I43, I44, I45, I46, I47) -> f6(I42, I43, I44, I45, I46, I47) f13(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, I50, I51, I52, I53) f13(I54, I55, I56, I57, I58, I59) -> f5(I54, I55, I56, I57, I58, I59) f13(I60, I61, I62, I63, I64, I65) -> f4(I60, I61, I62, I63, I64, I65) f13(I66, I67, I68, I69, I70, I71) -> f1(I66, I67, I68, I69, I70, I71) f8(I72, I73, I74, I75, I76, I77) -> f11(I76, I77, I74, I75, I76, I77) f3(I78, I79, I80, I81, I82, I83) -> f4(I82, I83, I80, I81, I82, -1 + I83) f3(I84, I85, I86, I87, I88, I89) -> f12(I88, I89, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] f2(I90, I91, I92, I93, I94, I95) -> f12(I94, I95, I96, I97, I98, I99) [I99 = I97 /\ I98 = I96 /\ I97 = I97 /\ I96 = I96] f11(I100, I101, I102, I103, I104, I105) -> f10(I104, I105, I102, I103, I104, I105) [1 <= I105] f11(I106, I107, I108, I109, I110, I111) -> f9(I110, I111, I108, I109, I110, I111) [I111 <= 0] f10(I112, I113, I114, I115, I116, I117) -> f8(I116, I117, I114, I115, I116, -1 + I117) f10(I118, I119, I120, I121, I122, I123) -> f6(I122, I123, I124, I125, I126, I127) [I127 = I125 /\ I126 = I124 /\ I125 = I125 /\ I124 = I124] f9(I128, I129, I130, I131, I132, I133) -> f7(I132, I133, I130, I131, I132, I133) [1 <= I132] f9(I134, I135, I136, I137, I138, I139) -> f5(I138, I139, I136, I137, I138, I139) [I138 <= 0] f7(I140, I141, I142, I143, I144, I145) -> f8(I144, I145, I142, I143, -1 + I144, I145) f7(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I153, I154, I155) [I155 = I153 /\ I154 = I152 /\ I153 = I153 /\ I152 = I152] f5(I156, I157, I158, I159, I160, I161) -> f6(I160, I161, I162, I163, I164, I165) [I165 = I163 /\ I164 = I162 /\ I163 = I163 /\ I162 = I162] f4(I166, I167, I168, I169, I170, I171) -> f1(I170, I171, I168, I169, I170, I171) f1(I172, I173, I174, I175, I176, I177) -> f3(I176, I177, I174, I175, I176, I177) [1 <= I177 /\ 1 + I177 <= 0] f1(I178, I179, I180, I181, I182, I183) -> f3(I182, I183, I180, I181, I182, I183) [1 <= I183 /\ 1 <= I183] f1(I184, I185, I186, I187, I188, I189) -> f2(I188, I189, I186, I187, I188, I189) [0 <= I189 /\ I189 <= 0] f1(I190, I191, I192, I193, I194, I195) -> f2(I194, I195, I192, I193, I194, I195) [I195 <= 0] We use the extended value criterion with the projection function NU: NU[f1#(x0,x1,x2,x3,x4,x5)] = x5 - 1 NU[f4#(x0,x1,x2,x3,x4,x5)] = x5 - 1 NU[f3#(x0,x1,x2,x3,x4,x5)] = x5 - 2 This gives the following inequalities: ==> I83 - 2 >= (-1 + I83) - 1 ==> I171 - 1 >= I171 - 1 1 <= I183 /\ 1 <= I183 ==> I183 - 1 > I183 - 2 with I183 - 1 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f3#(I78, I79, I80, I81, I82, I83) -> f4#(I82, I83, I80, I81, I82, -1 + I83) f4#(I166, I167, I168, I169, I170, I171) -> f1#(I170, I171, I168, I169, I170, I171) R = f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) f13(I0, I1, I2, I3, I4, I5) -> f8(I0, I1, I2, I3, I4, I5) f13(I6, I7, I8, I9, I10, I11) -> f3(I6, I7, I8, I9, I10, I11) f13(I12, I13, I14, I15, I16, I17) -> f2(I12, I13, I14, I15, I16, I17) f13(I18, I19, I20, I21, I22, I23) -> f12(I18, I19, I20, I21, I22, I23) f13(I24, I25, I26, I27, I28, I29) -> f11(I24, I25, I26, I27, I28, I29) f13(I30, I31, I32, I33, I34, I35) -> f10(I30, I31, I32, I33, I34, I35) f13(I36, I37, I38, I39, I40, I41) -> f9(I36, I37, I38, I39, I40, I41) f13(I42, I43, I44, I45, I46, I47) -> f6(I42, I43, I44, I45, I46, I47) f13(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, I50, I51, I52, I53) f13(I54, I55, I56, I57, I58, I59) -> f5(I54, I55, I56, I57, I58, I59) f13(I60, I61, I62, I63, I64, I65) -> f4(I60, I61, I62, I63, I64, I65) f13(I66, I67, I68, I69, I70, I71) -> f1(I66, I67, I68, I69, I70, I71) f8(I72, I73, I74, I75, I76, I77) -> f11(I76, I77, I74, I75, I76, I77) f3(I78, I79, I80, I81, I82, I83) -> f4(I82, I83, I80, I81, I82, -1 + I83) f3(I84, I85, I86, I87, I88, I89) -> f12(I88, I89, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] f2(I90, I91, I92, I93, I94, I95) -> f12(I94, I95, I96, I97, I98, I99) [I99 = I97 /\ I98 = I96 /\ I97 = I97 /\ I96 = I96] f11(I100, I101, I102, I103, I104, I105) -> f10(I104, I105, I102, I103, I104, I105) [1 <= I105] f11(I106, I107, I108, I109, I110, I111) -> f9(I110, I111, I108, I109, I110, I111) [I111 <= 0] f10(I112, I113, I114, I115, I116, I117) -> f8(I116, I117, I114, I115, I116, -1 + I117) f10(I118, I119, I120, I121, I122, I123) -> f6(I122, I123, I124, I125, I126, I127) [I127 = I125 /\ I126 = I124 /\ I125 = I125 /\ I124 = I124] f9(I128, I129, I130, I131, I132, I133) -> f7(I132, I133, I130, I131, I132, I133) [1 <= I132] f9(I134, I135, I136, I137, I138, I139) -> f5(I138, I139, I136, I137, I138, I139) [I138 <= 0] f7(I140, I141, I142, I143, I144, I145) -> f8(I144, I145, I142, I143, -1 + I144, I145) f7(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I153, I154, I155) [I155 = I153 /\ I154 = I152 /\ I153 = I153 /\ I152 = I152] f5(I156, I157, I158, I159, I160, I161) -> f6(I160, I161, I162, I163, I164, I165) [I165 = I163 /\ I164 = I162 /\ I163 = I163 /\ I162 = I162] f4(I166, I167, I168, I169, I170, I171) -> f1(I170, I171, I168, I169, I170, I171) f1(I172, I173, I174, I175, I176, I177) -> f3(I176, I177, I174, I175, I176, I177) [1 <= I177 /\ 1 + I177 <= 0] f1(I178, I179, I180, I181, I182, I183) -> f3(I182, I183, I180, I181, I182, I183) [1 <= I183 /\ 1 <= I183] f1(I184, I185, I186, I187, I188, I189) -> f2(I188, I189, I186, I187, I188, I189) [0 <= I189 /\ I189 <= 0] f1(I190, I191, I192, I193, I194, I195) -> f2(I194, I195, I192, I193, I194, I195) [I195 <= 0] The dependency graph for this problem is: 12 -> 19 19 -> Where: 12) f3#(I78, I79, I80, I81, I82, I83) -> f4#(I82, I83, I80, I81, I82, -1 + I83) 19) f4#(I166, I167, I168, I169, I170, I171) -> f1#(I170, I171, I168, I169, I170, I171) We have the following SCCs. DP problem for innermost termination. P = f8#(I72, I73, I74, I75, I76, I77) -> f11#(I76, I77, I74, I75, I76, I77) f11#(I100, I101, I102, I103, I104, I105) -> f10#(I104, I105, I102, I103, I104, I105) [1 <= I105] f11#(I106, I107, I108, I109, I110, I111) -> f9#(I110, I111, I108, I109, I110, I111) [I111 <= 0] f10#(I112, I113, I114, I115, I116, I117) -> f8#(I116, I117, I114, I115, I116, -1 + I117) f9#(I128, I129, I130, I131, I132, I133) -> f7#(I132, I133, I130, I131, I132, I133) [1 <= I132] f7#(I140, I141, I142, I143, I144, I145) -> f8#(I144, I145, I142, I143, -1 + I144, I145) R = f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) f13(I0, I1, I2, I3, I4, I5) -> f8(I0, I1, I2, I3, I4, I5) f13(I6, I7, I8, I9, I10, I11) -> f3(I6, I7, I8, I9, I10, I11) f13(I12, I13, I14, I15, I16, I17) -> f2(I12, I13, I14, I15, I16, I17) f13(I18, I19, I20, I21, I22, I23) -> f12(I18, I19, I20, I21, I22, I23) f13(I24, I25, I26, I27, I28, I29) -> f11(I24, I25, I26, I27, I28, I29) f13(I30, I31, I32, I33, I34, I35) -> f10(I30, I31, I32, I33, I34, I35) f13(I36, I37, I38, I39, I40, I41) -> f9(I36, I37, I38, I39, I40, I41) f13(I42, I43, I44, I45, I46, I47) -> f6(I42, I43, I44, I45, I46, I47) f13(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, I50, I51, I52, I53) f13(I54, I55, I56, I57, I58, I59) -> f5(I54, I55, I56, I57, I58, I59) f13(I60, I61, I62, I63, I64, I65) -> f4(I60, I61, I62, I63, I64, I65) f13(I66, I67, I68, I69, I70, I71) -> f1(I66, I67, I68, I69, I70, I71) f8(I72, I73, I74, I75, I76, I77) -> f11(I76, I77, I74, I75, I76, I77) f3(I78, I79, I80, I81, I82, I83) -> f4(I82, I83, I80, I81, I82, -1 + I83) f3(I84, I85, I86, I87, I88, I89) -> f12(I88, I89, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] f2(I90, I91, I92, I93, I94, I95) -> f12(I94, I95, I96, I97, I98, I99) [I99 = I97 /\ I98 = I96 /\ I97 = I97 /\ I96 = I96] f11(I100, I101, I102, I103, I104, I105) -> f10(I104, I105, I102, I103, I104, I105) [1 <= I105] f11(I106, I107, I108, I109, I110, I111) -> f9(I110, I111, I108, I109, I110, I111) [I111 <= 0] f10(I112, I113, I114, I115, I116, I117) -> f8(I116, I117, I114, I115, I116, -1 + I117) f10(I118, I119, I120, I121, I122, I123) -> f6(I122, I123, I124, I125, I126, I127) [I127 = I125 /\ I126 = I124 /\ I125 = I125 /\ I124 = I124] f9(I128, I129, I130, I131, I132, I133) -> f7(I132, I133, I130, I131, I132, I133) [1 <= I132] f9(I134, I135, I136, I137, I138, I139) -> f5(I138, I139, I136, I137, I138, I139) [I138 <= 0] f7(I140, I141, I142, I143, I144, I145) -> f8(I144, I145, I142, I143, -1 + I144, I145) f7(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I153, I154, I155) [I155 = I153 /\ I154 = I152 /\ I153 = I153 /\ I152 = I152] f5(I156, I157, I158, I159, I160, I161) -> f6(I160, I161, I162, I163, I164, I165) [I165 = I163 /\ I164 = I162 /\ I163 = I163 /\ I162 = I162] f4(I166, I167, I168, I169, I170, I171) -> f1(I170, I171, I168, I169, I170, I171) f1(I172, I173, I174, I175, I176, I177) -> f3(I176, I177, I174, I175, I176, I177) [1 <= I177 /\ 1 + I177 <= 0] f1(I178, I179, I180, I181, I182, I183) -> f3(I182, I183, I180, I181, I182, I183) [1 <= I183 /\ 1 <= I183] f1(I184, I185, I186, I187, I188, I189) -> f2(I188, I189, I186, I187, I188, I189) [0 <= I189 /\ I189 <= 0] f1(I190, I191, I192, I193, I194, I195) -> f2(I194, I195, I192, I193, I194, I195) [I195 <= 0] We use the extended value criterion with the projection function NU: NU[f7#(x0,x1,x2,x3,x4,x5)] = x4 - 2 NU[f9#(x0,x1,x2,x3,x4,x5)] = x4 - 1 NU[f10#(x0,x1,x2,x3,x4,x5)] = x4 - 1 NU[f11#(x0,x1,x2,x3,x4,x5)] = x4 - 1 NU[f8#(x0,x1,x2,x3,x4,x5)] = x4 - 1 This gives the following inequalities: ==> I76 - 1 >= I76 - 1 1 <= I105 ==> I104 - 1 >= I104 - 1 I111 <= 0 ==> I110 - 1 >= I110 - 1 ==> I116 - 1 >= I116 - 1 1 <= I132 ==> I132 - 1 > I132 - 2 with I132 - 1 >= 0 ==> I144 - 2 >= (-1 + I144) - 1 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f8#(I72, I73, I74, I75, I76, I77) -> f11#(I76, I77, I74, I75, I76, I77) f11#(I100, I101, I102, I103, I104, I105) -> f10#(I104, I105, I102, I103, I104, I105) [1 <= I105] f11#(I106, I107, I108, I109, I110, I111) -> f9#(I110, I111, I108, I109, I110, I111) [I111 <= 0] f10#(I112, I113, I114, I115, I116, I117) -> f8#(I116, I117, I114, I115, I116, -1 + I117) f7#(I140, I141, I142, I143, I144, I145) -> f8#(I144, I145, I142, I143, -1 + I144, I145) R = f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) f13(I0, I1, I2, I3, I4, I5) -> f8(I0, I1, I2, I3, I4, I5) f13(I6, I7, I8, I9, I10, I11) -> f3(I6, I7, I8, I9, I10, I11) f13(I12, I13, I14, I15, I16, I17) -> f2(I12, I13, I14, I15, I16, I17) f13(I18, I19, I20, I21, I22, I23) -> f12(I18, I19, I20, I21, I22, I23) f13(I24, I25, I26, I27, I28, I29) -> f11(I24, I25, I26, I27, I28, I29) f13(I30, I31, I32, I33, I34, I35) -> f10(I30, I31, I32, I33, I34, I35) f13(I36, I37, I38, I39, I40, I41) -> f9(I36, I37, I38, I39, I40, I41) f13(I42, I43, I44, I45, I46, I47) -> f6(I42, I43, I44, I45, I46, I47) f13(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, I50, I51, I52, I53) f13(I54, I55, I56, I57, I58, I59) -> f5(I54, I55, I56, I57, I58, I59) f13(I60, I61, I62, I63, I64, I65) -> f4(I60, I61, I62, I63, I64, I65) f13(I66, I67, I68, I69, I70, I71) -> f1(I66, I67, I68, I69, I70, I71) f8(I72, I73, I74, I75, I76, I77) -> f11(I76, I77, I74, I75, I76, I77) f3(I78, I79, I80, I81, I82, I83) -> f4(I82, I83, I80, I81, I82, -1 + I83) f3(I84, I85, I86, I87, I88, I89) -> f12(I88, I89, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] f2(I90, I91, I92, I93, I94, I95) -> f12(I94, I95, I96, I97, I98, I99) [I99 = I97 /\ I98 = I96 /\ I97 = I97 /\ I96 = I96] f11(I100, I101, I102, I103, I104, I105) -> f10(I104, I105, I102, I103, I104, I105) [1 <= I105] f11(I106, I107, I108, I109, I110, I111) -> f9(I110, I111, I108, I109, I110, I111) [I111 <= 0] f10(I112, I113, I114, I115, I116, I117) -> f8(I116, I117, I114, I115, I116, -1 + I117) f10(I118, I119, I120, I121, I122, I123) -> f6(I122, I123, I124, I125, I126, I127) [I127 = I125 /\ I126 = I124 /\ I125 = I125 /\ I124 = I124] f9(I128, I129, I130, I131, I132, I133) -> f7(I132, I133, I130, I131, I132, I133) [1 <= I132] f9(I134, I135, I136, I137, I138, I139) -> f5(I138, I139, I136, I137, I138, I139) [I138 <= 0] f7(I140, I141, I142, I143, I144, I145) -> f8(I144, I145, I142, I143, -1 + I144, I145) f7(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I153, I154, I155) [I155 = I153 /\ I154 = I152 /\ I153 = I153 /\ I152 = I152] f5(I156, I157, I158, I159, I160, I161) -> f6(I160, I161, I162, I163, I164, I165) [I165 = I163 /\ I164 = I162 /\ I163 = I163 /\ I162 = I162] f4(I166, I167, I168, I169, I170, I171) -> f1(I170, I171, I168, I169, I170, I171) f1(I172, I173, I174, I175, I176, I177) -> f3(I176, I177, I174, I175, I176, I177) [1 <= I177 /\ 1 + I177 <= 0] f1(I178, I179, I180, I181, I182, I183) -> f3(I182, I183, I180, I181, I182, I183) [1 <= I183 /\ 1 <= I183] f1(I184, I185, I186, I187, I188, I189) -> f2(I188, I189, I186, I187, I188, I189) [0 <= I189 /\ I189 <= 0] f1(I190, I191, I192, I193, I194, I195) -> f2(I194, I195, I192, I193, I194, I195) [I195 <= 0] The dependency graph for this problem is: 11 -> 13, 14 13 -> 15 14 -> 15 -> 11 18 -> 11 Where: 11) f8#(I72, I73, I74, I75, I76, I77) -> f11#(I76, I77, I74, I75, I76, I77) 13) f11#(I100, I101, I102, I103, I104, I105) -> f10#(I104, I105, I102, I103, I104, I105) [1 <= I105] 14) f11#(I106, I107, I108, I109, I110, I111) -> f9#(I110, I111, I108, I109, I110, I111) [I111 <= 0] 15) f10#(I112, I113, I114, I115, I116, I117) -> f8#(I116, I117, I114, I115, I116, -1 + I117) 18) f7#(I140, I141, I142, I143, I144, I145) -> f8#(I144, I145, I142, I143, -1 + I144, I145) We have the following SCCs. { 11, 13, 15 } DP problem for innermost termination. P = f8#(I72, I73, I74, I75, I76, I77) -> f11#(I76, I77, I74, I75, I76, I77) f11#(I100, I101, I102, I103, I104, I105) -> f10#(I104, I105, I102, I103, I104, I105) [1 <= I105] f10#(I112, I113, I114, I115, I116, I117) -> f8#(I116, I117, I114, I115, I116, -1 + I117) R = f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) f13(I0, I1, I2, I3, I4, I5) -> f8(I0, I1, I2, I3, I4, I5) f13(I6, I7, I8, I9, I10, I11) -> f3(I6, I7, I8, I9, I10, I11) f13(I12, I13, I14, I15, I16, I17) -> f2(I12, I13, I14, I15, I16, I17) f13(I18, I19, I20, I21, I22, I23) -> f12(I18, I19, I20, I21, I22, I23) f13(I24, I25, I26, I27, I28, I29) -> f11(I24, I25, I26, I27, I28, I29) f13(I30, I31, I32, I33, I34, I35) -> f10(I30, I31, I32, I33, I34, I35) f13(I36, I37, I38, I39, I40, I41) -> f9(I36, I37, I38, I39, I40, I41) f13(I42, I43, I44, I45, I46, I47) -> f6(I42, I43, I44, I45, I46, I47) f13(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, I50, I51, I52, I53) f13(I54, I55, I56, I57, I58, I59) -> f5(I54, I55, I56, I57, I58, I59) f13(I60, I61, I62, I63, I64, I65) -> f4(I60, I61, I62, I63, I64, I65) f13(I66, I67, I68, I69, I70, I71) -> f1(I66, I67, I68, I69, I70, I71) f8(I72, I73, I74, I75, I76, I77) -> f11(I76, I77, I74, I75, I76, I77) f3(I78, I79, I80, I81, I82, I83) -> f4(I82, I83, I80, I81, I82, -1 + I83) f3(I84, I85, I86, I87, I88, I89) -> f12(I88, I89, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] f2(I90, I91, I92, I93, I94, I95) -> f12(I94, I95, I96, I97, I98, I99) [I99 = I97 /\ I98 = I96 /\ I97 = I97 /\ I96 = I96] f11(I100, I101, I102, I103, I104, I105) -> f10(I104, I105, I102, I103, I104, I105) [1 <= I105] f11(I106, I107, I108, I109, I110, I111) -> f9(I110, I111, I108, I109, I110, I111) [I111 <= 0] f10(I112, I113, I114, I115, I116, I117) -> f8(I116, I117, I114, I115, I116, -1 + I117) f10(I118, I119, I120, I121, I122, I123) -> f6(I122, I123, I124, I125, I126, I127) [I127 = I125 /\ I126 = I124 /\ I125 = I125 /\ I124 = I124] f9(I128, I129, I130, I131, I132, I133) -> f7(I132, I133, I130, I131, I132, I133) [1 <= I132] f9(I134, I135, I136, I137, I138, I139) -> f5(I138, I139, I136, I137, I138, I139) [I138 <= 0] f7(I140, I141, I142, I143, I144, I145) -> f8(I144, I145, I142, I143, -1 + I144, I145) f7(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I153, I154, I155) [I155 = I153 /\ I154 = I152 /\ I153 = I153 /\ I152 = I152] f5(I156, I157, I158, I159, I160, I161) -> f6(I160, I161, I162, I163, I164, I165) [I165 = I163 /\ I164 = I162 /\ I163 = I163 /\ I162 = I162] f4(I166, I167, I168, I169, I170, I171) -> f1(I170, I171, I168, I169, I170, I171) f1(I172, I173, I174, I175, I176, I177) -> f3(I176, I177, I174, I175, I176, I177) [1 <= I177 /\ 1 + I177 <= 0] f1(I178, I179, I180, I181, I182, I183) -> f3(I182, I183, I180, I181, I182, I183) [1 <= I183 /\ 1 <= I183] f1(I184, I185, I186, I187, I188, I189) -> f2(I188, I189, I186, I187, I188, I189) [0 <= I189 /\ I189 <= 0] f1(I190, I191, I192, I193, I194, I195) -> f2(I194, I195, I192, I193, I194, I195) [I195 <= 0] We use the extended value criterion with the projection function NU: NU[f10#(x0,x1,x2,x3,x4,x5)] = x5 NU[f11#(x0,x1,x2,x3,x4,x5)] = x5 + 1 NU[f8#(x0,x1,x2,x3,x4,x5)] = x5 + 1 This gives the following inequalities: ==> I77 + 1 >= I77 + 1 1 <= I105 ==> I105 + 1 > I105 with I105 + 1 >= 0 ==> I117 >= (-1 + I117) + 1 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f8#(I72, I73, I74, I75, I76, I77) -> f11#(I76, I77, I74, I75, I76, I77) f10#(I112, I113, I114, I115, I116, I117) -> f8#(I116, I117, I114, I115, I116, -1 + I117) R = f14(x1, x2, x3, x4, x5, x6) -> f13(x1, x2, x3, x4, x5, x6) f13(I0, I1, I2, I3, I4, I5) -> f8(I0, I1, I2, I3, I4, I5) f13(I6, I7, I8, I9, I10, I11) -> f3(I6, I7, I8, I9, I10, I11) f13(I12, I13, I14, I15, I16, I17) -> f2(I12, I13, I14, I15, I16, I17) f13(I18, I19, I20, I21, I22, I23) -> f12(I18, I19, I20, I21, I22, I23) f13(I24, I25, I26, I27, I28, I29) -> f11(I24, I25, I26, I27, I28, I29) f13(I30, I31, I32, I33, I34, I35) -> f10(I30, I31, I32, I33, I34, I35) f13(I36, I37, I38, I39, I40, I41) -> f9(I36, I37, I38, I39, I40, I41) f13(I42, I43, I44, I45, I46, I47) -> f6(I42, I43, I44, I45, I46, I47) f13(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, I50, I51, I52, I53) f13(I54, I55, I56, I57, I58, I59) -> f5(I54, I55, I56, I57, I58, I59) f13(I60, I61, I62, I63, I64, I65) -> f4(I60, I61, I62, I63, I64, I65) f13(I66, I67, I68, I69, I70, I71) -> f1(I66, I67, I68, I69, I70, I71) f8(I72, I73, I74, I75, I76, I77) -> f11(I76, I77, I74, I75, I76, I77) f3(I78, I79, I80, I81, I82, I83) -> f4(I82, I83, I80, I81, I82, -1 + I83) f3(I84, I85, I86, I87, I88, I89) -> f12(I88, I89, rnd3, rnd4, rnd5, rnd6) [rnd6 = rnd4 /\ rnd5 = rnd3 /\ rnd4 = rnd4 /\ rnd3 = rnd3] f2(I90, I91, I92, I93, I94, I95) -> f12(I94, I95, I96, I97, I98, I99) [I99 = I97 /\ I98 = I96 /\ I97 = I97 /\ I96 = I96] f11(I100, I101, I102, I103, I104, I105) -> f10(I104, I105, I102, I103, I104, I105) [1 <= I105] f11(I106, I107, I108, I109, I110, I111) -> f9(I110, I111, I108, I109, I110, I111) [I111 <= 0] f10(I112, I113, I114, I115, I116, I117) -> f8(I116, I117, I114, I115, I116, -1 + I117) f10(I118, I119, I120, I121, I122, I123) -> f6(I122, I123, I124, I125, I126, I127) [I127 = I125 /\ I126 = I124 /\ I125 = I125 /\ I124 = I124] f9(I128, I129, I130, I131, I132, I133) -> f7(I132, I133, I130, I131, I132, I133) [1 <= I132] f9(I134, I135, I136, I137, I138, I139) -> f5(I138, I139, I136, I137, I138, I139) [I138 <= 0] f7(I140, I141, I142, I143, I144, I145) -> f8(I144, I145, I142, I143, -1 + I144, I145) f7(I146, I147, I148, I149, I150, I151) -> f6(I150, I151, I152, I153, I154, I155) [I155 = I153 /\ I154 = I152 /\ I153 = I153 /\ I152 = I152] f5(I156, I157, I158, I159, I160, I161) -> f6(I160, I161, I162, I163, I164, I165) [I165 = I163 /\ I164 = I162 /\ I163 = I163 /\ I162 = I162] f4(I166, I167, I168, I169, I170, I171) -> f1(I170, I171, I168, I169, I170, I171) f1(I172, I173, I174, I175, I176, I177) -> f3(I176, I177, I174, I175, I176, I177) [1 <= I177 /\ 1 + I177 <= 0] f1(I178, I179, I180, I181, I182, I183) -> f3(I182, I183, I180, I181, I182, I183) [1 <= I183 /\ 1 <= I183] f1(I184, I185, I186, I187, I188, I189) -> f2(I188, I189, I186, I187, I188, I189) [0 <= I189 /\ I189 <= 0] f1(I190, I191, I192, I193, I194, I195) -> f2(I194, I195, I192, I193, I194, I195) [I195 <= 0] The dependency graph for this problem is: 11 -> 15 -> 11 Where: 11) f8#(I72, I73, I74, I75, I76, I77) -> f11#(I76, I77, I74, I75, I76, I77) 15) f10#(I112, I113, I114, I115, I116, I117) -> f8#(I116, I117, I114, I115, I116, -1 + I117) We have the following SCCs.