/export/starexec/sandbox/solver/bin/starexec_run_Transition /export/starexec/sandbox/benchmark/theBenchmark.smt2 /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE DP problem for innermost termination. P = f18#(x1, x2, x3, x4, x5, x6) -> f17#(x1, x2, x3, x4, x5, x6) f17#(I0, I1, I2, I3, I4, I5) -> f10#(4, 0, 0, I3, I4, I5) f3#(I6, I7, I8, I9, I10, I11) -> f16#(I6, I7, I8, I9, I10, I11) [1 <= I7 /\ I7 <= 1] f3#(I12, I13, I14, I15, I16, I17) -> f15#(I12, I13, I14, I15, I16, I17) [1 + I13 <= 1] f3#(I18, I19, I20, I21, I22, I23) -> f15#(I18, I19, I20, I21, I22, I23) [2 <= I19] f16#(I24, I25, I26, I27, I28, I29) -> f15#(-1 + I24, I25, 1, I27, I28, I29) [0 <= I26 /\ I26 <= 0] f16#(I30, I31, I32, I33, I34, I35) -> f15#(I30, I31, I32, I33, I34, I35) [1 + I32 <= 0] f16#(I36, I37, I38, I39, I40, I41) -> f15#(I36, I37, I38, I39, I40, I41) [1 <= I38] f15#(I42, I43, I44, I45, I46, I47) -> f14#(I42, 2, I44, I45, I46, I42 + I47) f14#(I48, I49, I50, I51, I52, I53) -> f7#(I48, I49, I50, I51, I52, I53) [256 <= I53] f14#(I54, I55, I56, I57, I58, I59) -> f10#(I54, I55, I56, I57, I58, I59) [I59 <= 255] f2#(I60, I61, I62, I63, I64, I65) -> f13#(I60, I61, I62, I63, I64, I65) [1 + I63 <= I64] f2#(I66, I67, I68, I69, I70, I71) -> f7#(I66, I67, I68, I69, I70, I71) [I70 <= I69] f13#(I72, I73, I74, I75, I76, I77) -> f12#(I72, I73, I74, I75, I76, I77) [2 <= I73 /\ I73 <= 2] f13#(I78, I79, I80, I81, I82, I83) -> f11#(I78, I79, I80, I81, I82, I83) [1 + I79 <= 2] f13#(I84, I85, I86, I87, I88, I89) -> f11#(I84, I85, I86, I87, I88, I89) [3 <= I85] f10#(I90, I91, I92, I93, I94, I95) -> f6#(I90, I91, I92, rnd4, I94, I95) [rnd4 = rnd4] f12#(I96, I97, I98, I99, I100, I101) -> f11#(-1 + I96, I97, 1, I99, I100, I101) [0 <= I98 /\ I98 <= 0] f12#(I102, I103, I104, I105, I106, I107) -> f11#(I102, I103, I104, I105, I106, I107) [1 + I104 <= 0] f12#(I108, I109, I110, I111, I112, I113) -> f11#(I108, I109, I110, I111, I112, I113) [1 <= I110] f11#(I114, I115, I116, I117, I118, I119) -> f9#(I114, 1, I116, I117, I118, -1 * I114 + I119) f9#(I120, I121, I122, I123, I124, I125) -> f7#(I120, I121, I122, I123, I124, I125) [1 + I125 <= 0] f9#(I126, I127, I128, I129, I130, I131) -> f10#(I126, I127, I128, I129, I130, I131) [0 <= I131] f6#(I138, I139, I140, I141, I142, I143) -> f7#(I138, I139, I140, I141, I142, I143) [1 <= I138 /\ I138 <= 1] f6#(I144, I145, I146, I147, I148, I149) -> f5#(I144, I145, I146, I147, I148, I149) [1 + I144 <= 1] f6#(I150, I151, I152, I153, I154, I155) -> f5#(I150, I151, I152, I153, I154, I155) [2 <= I150] f5#(I156, I157, I158, I159, I160, I161) -> f4#(I156, I157, I158, I159, I160, I161) [1 + I158 <= 0] f5#(I162, I163, I164, I165, I166, I167) -> f4#(I162, I163, I164, I165, I166, I167) [1 <= I164] f5#(I168, I169, I170, I171, I172, I173) -> f1#(I168, I169, I170, I171, I172, I173) [0 <= I170 /\ I170 <= 0] f4#(I174, I175, I176, I177, I178, I179) -> f1#(-1 + I174, I175, I176, I177, I178, I179) f1#(I180, I181, I182, I183, I184, I185) -> f3#(I180, I181, I182, I183, I184, I185) [1 + I184 <= I183] f1#(I186, I187, I188, I189, I190, I191) -> f2#(I186, I187, I188, I189, I190, I191) [I189 <= I190] R = f18(x1, x2, x3, x4, x5, x6) -> f17(x1, x2, x3, x4, x5, x6) f17(I0, I1, I2, I3, I4, I5) -> f10(4, 0, 0, I3, I4, I5) f3(I6, I7, I8, I9, I10, I11) -> f16(I6, I7, I8, I9, I10, I11) [1 <= I7 /\ I7 <= 1] f3(I12, I13, I14, I15, I16, I17) -> f15(I12, I13, I14, I15, I16, I17) [1 + I13 <= 1] f3(I18, I19, I20, I21, I22, I23) -> f15(I18, I19, I20, I21, I22, I23) [2 <= I19] f16(I24, I25, I26, I27, I28, I29) -> f15(-1 + I24, I25, 1, I27, I28, I29) [0 <= I26 /\ I26 <= 0] f16(I30, I31, I32, I33, I34, I35) -> f15(I30, I31, I32, I33, I34, I35) [1 + I32 <= 0] f16(I36, I37, I38, I39, I40, I41) -> f15(I36, I37, I38, I39, I40, I41) [1 <= I38] f15(I42, I43, I44, I45, I46, I47) -> f14(I42, 2, I44, I45, I46, I42 + I47) f14(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, I50, I51, I52, I53) [256 <= I53] f14(I54, I55, I56, I57, I58, I59) -> f10(I54, I55, I56, I57, I58, I59) [I59 <= 255] f2(I60, I61, I62, I63, I64, I65) -> f13(I60, I61, I62, I63, I64, I65) [1 + I63 <= I64] f2(I66, I67, I68, I69, I70, I71) -> f7(I66, I67, I68, I69, I70, I71) [I70 <= I69] f13(I72, I73, I74, I75, I76, I77) -> f12(I72, I73, I74, I75, I76, I77) [2 <= I73 /\ I73 <= 2] f13(I78, I79, I80, I81, I82, I83) -> f11(I78, I79, I80, I81, I82, I83) [1 + I79 <= 2] f13(I84, I85, I86, I87, I88, I89) -> f11(I84, I85, I86, I87, I88, I89) [3 <= I85] f10(I90, I91, I92, I93, I94, I95) -> f6(I90, I91, I92, rnd4, I94, I95) [rnd4 = rnd4] f12(I96, I97, I98, I99, I100, I101) -> f11(-1 + I96, I97, 1, I99, I100, I101) [0 <= I98 /\ I98 <= 0] f12(I102, I103, I104, I105, I106, I107) -> f11(I102, I103, I104, I105, I106, I107) [1 + I104 <= 0] f12(I108, I109, I110, I111, I112, I113) -> f11(I108, I109, I110, I111, I112, I113) [1 <= I110] f11(I114, I115, I116, I117, I118, I119) -> f9(I114, 1, I116, I117, I118, -1 * I114 + I119) f9(I120, I121, I122, I123, I124, I125) -> f7(I120, I121, I122, I123, I124, I125) [1 + I125 <= 0] f9(I126, I127, I128, I129, I130, I131) -> f10(I126, I127, I128, I129, I130, I131) [0 <= I131] f7(I132, I133, I134, I135, I136, I137) -> f8(I132, I133, I134, I135, I136, I137) f6(I138, I139, I140, I141, I142, I143) -> f7(I138, I139, I140, I141, I142, I143) [1 <= I138 /\ I138 <= 1] f6(I144, I145, I146, I147, I148, I149) -> f5(I144, I145, I146, I147, I148, I149) [1 + I144 <= 1] f6(I150, I151, I152, I153, I154, I155) -> f5(I150, I151, I152, I153, I154, I155) [2 <= I150] f5(I156, I157, I158, I159, I160, I161) -> f4(I156, I157, I158, I159, I160, I161) [1 + I158 <= 0] f5(I162, I163, I164, I165, I166, I167) -> f4(I162, I163, I164, I165, I166, I167) [1 <= I164] f5(I168, I169, I170, I171, I172, I173) -> f1(I168, I169, I170, I171, I172, I173) [0 <= I170 /\ I170 <= 0] f4(I174, I175, I176, I177, I178, I179) -> f1(-1 + I174, I175, I176, I177, I178, I179) f1(I180, I181, I182, I183, I184, I185) -> f3(I180, I181, I182, I183, I184, I185) [1 + I184 <= I183] f1(I186, I187, I188, I189, I190, I191) -> f2(I186, I187, I188, I189, I190, I191) [I189 <= I190] The dependency graph for this problem is: 0 -> 1 1 -> 16 2 -> 5, 6, 7 3 -> 8 4 -> 8 5 -> 8 6 -> 8 7 -> 8 8 -> 9, 10 9 -> 10 -> 16 11 -> 13, 14, 15 12 -> 13 -> 17, 18, 19 14 -> 20 15 -> 20 16 -> 23, 24, 25 17 -> 20 18 -> 20 19 -> 20 20 -> 21, 22 21 -> 22 -> 16 23 -> 24 -> 26, 27, 28 25 -> 26, 27, 28 26 -> 29 27 -> 29 28 -> 30, 31 29 -> 30, 31 30 -> 2, 3, 4 31 -> 11, 12 Where: 0) f18#(x1, x2, x3, x4, x5, x6) -> f17#(x1, x2, x3, x4, x5, x6) 1) f17#(I0, I1, I2, I3, I4, I5) -> f10#(4, 0, 0, I3, I4, I5) 2) f3#(I6, I7, I8, I9, I10, I11) -> f16#(I6, I7, I8, I9, I10, I11) [1 <= I7 /\ I7 <= 1] 3) f3#(I12, I13, I14, I15, I16, I17) -> f15#(I12, I13, I14, I15, I16, I17) [1 + I13 <= 1] 4) f3#(I18, I19, I20, I21, I22, I23) -> f15#(I18, I19, I20, I21, I22, I23) [2 <= I19] 5) f16#(I24, I25, I26, I27, I28, I29) -> f15#(-1 + I24, I25, 1, I27, I28, I29) [0 <= I26 /\ I26 <= 0] 6) f16#(I30, I31, I32, I33, I34, I35) -> f15#(I30, I31, I32, I33, I34, I35) [1 + I32 <= 0] 7) f16#(I36, I37, I38, I39, I40, I41) -> f15#(I36, I37, I38, I39, I40, I41) [1 <= I38] 8) f15#(I42, I43, I44, I45, I46, I47) -> f14#(I42, 2, I44, I45, I46, I42 + I47) 9) f14#(I48, I49, I50, I51, I52, I53) -> f7#(I48, I49, I50, I51, I52, I53) [256 <= I53] 10) f14#(I54, I55, I56, I57, I58, I59) -> f10#(I54, I55, I56, I57, I58, I59) [I59 <= 255] 11) f2#(I60, I61, I62, I63, I64, I65) -> f13#(I60, I61, I62, I63, I64, I65) [1 + I63 <= I64] 12) f2#(I66, I67, I68, I69, I70, I71) -> f7#(I66, I67, I68, I69, I70, I71) [I70 <= I69] 13) f13#(I72, I73, I74, I75, I76, I77) -> f12#(I72, I73, I74, I75, I76, I77) [2 <= I73 /\ I73 <= 2] 14) f13#(I78, I79, I80, I81, I82, I83) -> f11#(I78, I79, I80, I81, I82, I83) [1 + I79 <= 2] 15) f13#(I84, I85, I86, I87, I88, I89) -> f11#(I84, I85, I86, I87, I88, I89) [3 <= I85] 16) f10#(I90, I91, I92, I93, I94, I95) -> f6#(I90, I91, I92, rnd4, I94, I95) [rnd4 = rnd4] 17) f12#(I96, I97, I98, I99, I100, I101) -> f11#(-1 + I96, I97, 1, I99, I100, I101) [0 <= I98 /\ I98 <= 0] 18) f12#(I102, I103, I104, I105, I106, I107) -> f11#(I102, I103, I104, I105, I106, I107) [1 + I104 <= 0] 19) f12#(I108, I109, I110, I111, I112, I113) -> f11#(I108, I109, I110, I111, I112, I113) [1 <= I110] 20) f11#(I114, I115, I116, I117, I118, I119) -> f9#(I114, 1, I116, I117, I118, -1 * I114 + I119) 21) f9#(I120, I121, I122, I123, I124, I125) -> f7#(I120, I121, I122, I123, I124, I125) [1 + I125 <= 0] 22) f9#(I126, I127, I128, I129, I130, I131) -> f10#(I126, I127, I128, I129, I130, I131) [0 <= I131] 23) f6#(I138, I139, I140, I141, I142, I143) -> f7#(I138, I139, I140, I141, I142, I143) [1 <= I138 /\ I138 <= 1] 24) f6#(I144, I145, I146, I147, I148, I149) -> f5#(I144, I145, I146, I147, I148, I149) [1 + I144 <= 1] 25) f6#(I150, I151, I152, I153, I154, I155) -> f5#(I150, I151, I152, I153, I154, I155) [2 <= I150] 26) f5#(I156, I157, I158, I159, I160, I161) -> f4#(I156, I157, I158, I159, I160, I161) [1 + I158 <= 0] 27) f5#(I162, I163, I164, I165, I166, I167) -> f4#(I162, I163, I164, I165, I166, I167) [1 <= I164] 28) f5#(I168, I169, I170, I171, I172, I173) -> f1#(I168, I169, I170, I171, I172, I173) [0 <= I170 /\ I170 <= 0] 29) f4#(I174, I175, I176, I177, I178, I179) -> f1#(-1 + I174, I175, I176, I177, I178, I179) 30) f1#(I180, I181, I182, I183, I184, I185) -> f3#(I180, I181, I182, I183, I184, I185) [1 + I184 <= I183] 31) f1#(I186, I187, I188, I189, I190, I191) -> f2#(I186, I187, I188, I189, I190, I191) [I189 <= I190] We have the following SCCs. { 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31 } DP problem for innermost termination. P = f3#(I6, I7, I8, I9, I10, I11) -> f16#(I6, I7, I8, I9, I10, I11) [1 <= I7 /\ I7 <= 1] f3#(I12, I13, I14, I15, I16, I17) -> f15#(I12, I13, I14, I15, I16, I17) [1 + I13 <= 1] f3#(I18, I19, I20, I21, I22, I23) -> f15#(I18, I19, I20, I21, I22, I23) [2 <= I19] f16#(I24, I25, I26, I27, I28, I29) -> f15#(-1 + I24, I25, 1, I27, I28, I29) [0 <= I26 /\ I26 <= 0] f16#(I30, I31, I32, I33, I34, I35) -> f15#(I30, I31, I32, I33, I34, I35) [1 + I32 <= 0] f16#(I36, I37, I38, I39, I40, I41) -> f15#(I36, I37, I38, I39, I40, I41) [1 <= I38] f15#(I42, I43, I44, I45, I46, I47) -> f14#(I42, 2, I44, I45, I46, I42 + I47) f14#(I54, I55, I56, I57, I58, I59) -> f10#(I54, I55, I56, I57, I58, I59) [I59 <= 255] f2#(I60, I61, I62, I63, I64, I65) -> f13#(I60, I61, I62, I63, I64, I65) [1 + I63 <= I64] f13#(I72, I73, I74, I75, I76, I77) -> f12#(I72, I73, I74, I75, I76, I77) [2 <= I73 /\ I73 <= 2] f13#(I78, I79, I80, I81, I82, I83) -> f11#(I78, I79, I80, I81, I82, I83) [1 + I79 <= 2] f13#(I84, I85, I86, I87, I88, I89) -> f11#(I84, I85, I86, I87, I88, I89) [3 <= I85] f10#(I90, I91, I92, I93, I94, I95) -> f6#(I90, I91, I92, rnd4, I94, I95) [rnd4 = rnd4] f12#(I96, I97, I98, I99, I100, I101) -> f11#(-1 + I96, I97, 1, I99, I100, I101) [0 <= I98 /\ I98 <= 0] f12#(I102, I103, I104, I105, I106, I107) -> f11#(I102, I103, I104, I105, I106, I107) [1 + I104 <= 0] f12#(I108, I109, I110, I111, I112, I113) -> f11#(I108, I109, I110, I111, I112, I113) [1 <= I110] f11#(I114, I115, I116, I117, I118, I119) -> f9#(I114, 1, I116, I117, I118, -1 * I114 + I119) f9#(I126, I127, I128, I129, I130, I131) -> f10#(I126, I127, I128, I129, I130, I131) [0 <= I131] f6#(I144, I145, I146, I147, I148, I149) -> f5#(I144, I145, I146, I147, I148, I149) [1 + I144 <= 1] f6#(I150, I151, I152, I153, I154, I155) -> f5#(I150, I151, I152, I153, I154, I155) [2 <= I150] f5#(I156, I157, I158, I159, I160, I161) -> f4#(I156, I157, I158, I159, I160, I161) [1 + I158 <= 0] f5#(I162, I163, I164, I165, I166, I167) -> f4#(I162, I163, I164, I165, I166, I167) [1 <= I164] f5#(I168, I169, I170, I171, I172, I173) -> f1#(I168, I169, I170, I171, I172, I173) [0 <= I170 /\ I170 <= 0] f4#(I174, I175, I176, I177, I178, I179) -> f1#(-1 + I174, I175, I176, I177, I178, I179) f1#(I180, I181, I182, I183, I184, I185) -> f3#(I180, I181, I182, I183, I184, I185) [1 + I184 <= I183] f1#(I186, I187, I188, I189, I190, I191) -> f2#(I186, I187, I188, I189, I190, I191) [I189 <= I190] R = f18(x1, x2, x3, x4, x5, x6) -> f17(x1, x2, x3, x4, x5, x6) f17(I0, I1, I2, I3, I4, I5) -> f10(4, 0, 0, I3, I4, I5) f3(I6, I7, I8, I9, I10, I11) -> f16(I6, I7, I8, I9, I10, I11) [1 <= I7 /\ I7 <= 1] f3(I12, I13, I14, I15, I16, I17) -> f15(I12, I13, I14, I15, I16, I17) [1 + I13 <= 1] f3(I18, I19, I20, I21, I22, I23) -> f15(I18, I19, I20, I21, I22, I23) [2 <= I19] f16(I24, I25, I26, I27, I28, I29) -> f15(-1 + I24, I25, 1, I27, I28, I29) [0 <= I26 /\ I26 <= 0] f16(I30, I31, I32, I33, I34, I35) -> f15(I30, I31, I32, I33, I34, I35) [1 + I32 <= 0] f16(I36, I37, I38, I39, I40, I41) -> f15(I36, I37, I38, I39, I40, I41) [1 <= I38] f15(I42, I43, I44, I45, I46, I47) -> f14(I42, 2, I44, I45, I46, I42 + I47) f14(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, I50, I51, I52, I53) [256 <= I53] f14(I54, I55, I56, I57, I58, I59) -> f10(I54, I55, I56, I57, I58, I59) [I59 <= 255] f2(I60, I61, I62, I63, I64, I65) -> f13(I60, I61, I62, I63, I64, I65) [1 + I63 <= I64] f2(I66, I67, I68, I69, I70, I71) -> f7(I66, I67, I68, I69, I70, I71) [I70 <= I69] f13(I72, I73, I74, I75, I76, I77) -> f12(I72, I73, I74, I75, I76, I77) [2 <= I73 /\ I73 <= 2] f13(I78, I79, I80, I81, I82, I83) -> f11(I78, I79, I80, I81, I82, I83) [1 + I79 <= 2] f13(I84, I85, I86, I87, I88, I89) -> f11(I84, I85, I86, I87, I88, I89) [3 <= I85] f10(I90, I91, I92, I93, I94, I95) -> f6(I90, I91, I92, rnd4, I94, I95) [rnd4 = rnd4] f12(I96, I97, I98, I99, I100, I101) -> f11(-1 + I96, I97, 1, I99, I100, I101) [0 <= I98 /\ I98 <= 0] f12(I102, I103, I104, I105, I106, I107) -> f11(I102, I103, I104, I105, I106, I107) [1 + I104 <= 0] f12(I108, I109, I110, I111, I112, I113) -> f11(I108, I109, I110, I111, I112, I113) [1 <= I110] f11(I114, I115, I116, I117, I118, I119) -> f9(I114, 1, I116, I117, I118, -1 * I114 + I119) f9(I120, I121, I122, I123, I124, I125) -> f7(I120, I121, I122, I123, I124, I125) [1 + I125 <= 0] f9(I126, I127, I128, I129, I130, I131) -> f10(I126, I127, I128, I129, I130, I131) [0 <= I131] f7(I132, I133, I134, I135, I136, I137) -> f8(I132, I133, I134, I135, I136, I137) f6(I138, I139, I140, I141, I142, I143) -> f7(I138, I139, I140, I141, I142, I143) [1 <= I138 /\ I138 <= 1] f6(I144, I145, I146, I147, I148, I149) -> f5(I144, I145, I146, I147, I148, I149) [1 + I144 <= 1] f6(I150, I151, I152, I153, I154, I155) -> f5(I150, I151, I152, I153, I154, I155) [2 <= I150] f5(I156, I157, I158, I159, I160, I161) -> f4(I156, I157, I158, I159, I160, I161) [1 + I158 <= 0] f5(I162, I163, I164, I165, I166, I167) -> f4(I162, I163, I164, I165, I166, I167) [1 <= I164] f5(I168, I169, I170, I171, I172, I173) -> f1(I168, I169, I170, I171, I172, I173) [0 <= I170 /\ I170 <= 0] f4(I174, I175, I176, I177, I178, I179) -> f1(-1 + I174, I175, I176, I177, I178, I179) f1(I180, I181, I182, I183, I184, I185) -> f3(I180, I181, I182, I183, I184, I185) [1 + I184 <= I183] f1(I186, I187, I188, I189, I190, I191) -> f2(I186, I187, I188, I189, I190, I191) [I189 <= I190] We use the extended value criterion with the projection function NU: NU[f1#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f4#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f5#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f9#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f6#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f11#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f12#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f13#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f2#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f10#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f14#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f15#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f16#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f3#(x0,x1,x2,x3,x4,x5)] = -x2 This gives the following inequalities: 1 <= I7 /\ I7 <= 1 ==> -I8 >= -I8 1 + I13 <= 1 ==> -I14 >= -I14 2 <= I19 ==> -I20 >= -I20 0 <= I26 /\ I26 <= 0 ==> -I26 > -1 with -I26 >= 0 1 + I32 <= 0 ==> -I32 >= -I32 1 <= I38 ==> -I38 >= -I38 ==> -I44 >= -I44 I59 <= 255 ==> -I56 >= -I56 1 + I63 <= I64 ==> -I62 >= -I62 2 <= I73 /\ I73 <= 2 ==> -I74 >= -I74 1 + I79 <= 2 ==> -I80 >= -I80 3 <= I85 ==> -I86 >= -I86 rnd4 = rnd4 ==> -I92 >= -I92 0 <= I98 /\ I98 <= 0 ==> -I98 >= -1 1 + I104 <= 0 ==> -I104 >= -I104 1 <= I110 ==> -I110 >= -I110 ==> -I116 >= -I116 0 <= I131 ==> -I128 >= -I128 1 + I144 <= 1 ==> -I146 >= -I146 2 <= I150 ==> -I152 >= -I152 1 + I158 <= 0 ==> -I158 >= -I158 1 <= I164 ==> -I164 >= -I164 0 <= I170 /\ I170 <= 0 ==> -I170 >= -I170 ==> -I176 >= -I176 1 + I184 <= I183 ==> -I182 >= -I182 I189 <= I190 ==> -I188 >= -I188 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f3#(I6, I7, I8, I9, I10, I11) -> f16#(I6, I7, I8, I9, I10, I11) [1 <= I7 /\ I7 <= 1] f3#(I12, I13, I14, I15, I16, I17) -> f15#(I12, I13, I14, I15, I16, I17) [1 + I13 <= 1] f3#(I18, I19, I20, I21, I22, I23) -> f15#(I18, I19, I20, I21, I22, I23) [2 <= I19] f16#(I30, I31, I32, I33, I34, I35) -> f15#(I30, I31, I32, I33, I34, I35) [1 + I32 <= 0] f16#(I36, I37, I38, I39, I40, I41) -> f15#(I36, I37, I38, I39, I40, I41) [1 <= I38] f15#(I42, I43, I44, I45, I46, I47) -> f14#(I42, 2, I44, I45, I46, I42 + I47) f14#(I54, I55, I56, I57, I58, I59) -> f10#(I54, I55, I56, I57, I58, I59) [I59 <= 255] f2#(I60, I61, I62, I63, I64, I65) -> f13#(I60, I61, I62, I63, I64, I65) [1 + I63 <= I64] f13#(I72, I73, I74, I75, I76, I77) -> f12#(I72, I73, I74, I75, I76, I77) [2 <= I73 /\ I73 <= 2] f13#(I78, I79, I80, I81, I82, I83) -> f11#(I78, I79, I80, I81, I82, I83) [1 + I79 <= 2] f13#(I84, I85, I86, I87, I88, I89) -> f11#(I84, I85, I86, I87, I88, I89) [3 <= I85] f10#(I90, I91, I92, I93, I94, I95) -> f6#(I90, I91, I92, rnd4, I94, I95) [rnd4 = rnd4] f12#(I96, I97, I98, I99, I100, I101) -> f11#(-1 + I96, I97, 1, I99, I100, I101) [0 <= I98 /\ I98 <= 0] f12#(I102, I103, I104, I105, I106, I107) -> f11#(I102, I103, I104, I105, I106, I107) [1 + I104 <= 0] f12#(I108, I109, I110, I111, I112, I113) -> f11#(I108, I109, I110, I111, I112, I113) [1 <= I110] f11#(I114, I115, I116, I117, I118, I119) -> f9#(I114, 1, I116, I117, I118, -1 * I114 + I119) f9#(I126, I127, I128, I129, I130, I131) -> f10#(I126, I127, I128, I129, I130, I131) [0 <= I131] f6#(I144, I145, I146, I147, I148, I149) -> f5#(I144, I145, I146, I147, I148, I149) [1 + I144 <= 1] f6#(I150, I151, I152, I153, I154, I155) -> f5#(I150, I151, I152, I153, I154, I155) [2 <= I150] f5#(I156, I157, I158, I159, I160, I161) -> f4#(I156, I157, I158, I159, I160, I161) [1 + I158 <= 0] f5#(I162, I163, I164, I165, I166, I167) -> f4#(I162, I163, I164, I165, I166, I167) [1 <= I164] f5#(I168, I169, I170, I171, I172, I173) -> f1#(I168, I169, I170, I171, I172, I173) [0 <= I170 /\ I170 <= 0] f4#(I174, I175, I176, I177, I178, I179) -> f1#(-1 + I174, I175, I176, I177, I178, I179) f1#(I180, I181, I182, I183, I184, I185) -> f3#(I180, I181, I182, I183, I184, I185) [1 + I184 <= I183] f1#(I186, I187, I188, I189, I190, I191) -> f2#(I186, I187, I188, I189, I190, I191) [I189 <= I190] R = f18(x1, x2, x3, x4, x5, x6) -> f17(x1, x2, x3, x4, x5, x6) f17(I0, I1, I2, I3, I4, I5) -> f10(4, 0, 0, I3, I4, I5) f3(I6, I7, I8, I9, I10, I11) -> f16(I6, I7, I8, I9, I10, I11) [1 <= I7 /\ I7 <= 1] f3(I12, I13, I14, I15, I16, I17) -> f15(I12, I13, I14, I15, I16, I17) [1 + I13 <= 1] f3(I18, I19, I20, I21, I22, I23) -> f15(I18, I19, I20, I21, I22, I23) [2 <= I19] f16(I24, I25, I26, I27, I28, I29) -> f15(-1 + I24, I25, 1, I27, I28, I29) [0 <= I26 /\ I26 <= 0] f16(I30, I31, I32, I33, I34, I35) -> f15(I30, I31, I32, I33, I34, I35) [1 + I32 <= 0] f16(I36, I37, I38, I39, I40, I41) -> f15(I36, I37, I38, I39, I40, I41) [1 <= I38] f15(I42, I43, I44, I45, I46, I47) -> f14(I42, 2, I44, I45, I46, I42 + I47) f14(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, I50, I51, I52, I53) [256 <= I53] f14(I54, I55, I56, I57, I58, I59) -> f10(I54, I55, I56, I57, I58, I59) [I59 <= 255] f2(I60, I61, I62, I63, I64, I65) -> f13(I60, I61, I62, I63, I64, I65) [1 + I63 <= I64] f2(I66, I67, I68, I69, I70, I71) -> f7(I66, I67, I68, I69, I70, I71) [I70 <= I69] f13(I72, I73, I74, I75, I76, I77) -> f12(I72, I73, I74, I75, I76, I77) [2 <= I73 /\ I73 <= 2] f13(I78, I79, I80, I81, I82, I83) -> f11(I78, I79, I80, I81, I82, I83) [1 + I79 <= 2] f13(I84, I85, I86, I87, I88, I89) -> f11(I84, I85, I86, I87, I88, I89) [3 <= I85] f10(I90, I91, I92, I93, I94, I95) -> f6(I90, I91, I92, rnd4, I94, I95) [rnd4 = rnd4] f12(I96, I97, I98, I99, I100, I101) -> f11(-1 + I96, I97, 1, I99, I100, I101) [0 <= I98 /\ I98 <= 0] f12(I102, I103, I104, I105, I106, I107) -> f11(I102, I103, I104, I105, I106, I107) [1 + I104 <= 0] f12(I108, I109, I110, I111, I112, I113) -> f11(I108, I109, I110, I111, I112, I113) [1 <= I110] f11(I114, I115, I116, I117, I118, I119) -> f9(I114, 1, I116, I117, I118, -1 * I114 + I119) f9(I120, I121, I122, I123, I124, I125) -> f7(I120, I121, I122, I123, I124, I125) [1 + I125 <= 0] f9(I126, I127, I128, I129, I130, I131) -> f10(I126, I127, I128, I129, I130, I131) [0 <= I131] f7(I132, I133, I134, I135, I136, I137) -> f8(I132, I133, I134, I135, I136, I137) f6(I138, I139, I140, I141, I142, I143) -> f7(I138, I139, I140, I141, I142, I143) [1 <= I138 /\ I138 <= 1] f6(I144, I145, I146, I147, I148, I149) -> f5(I144, I145, I146, I147, I148, I149) [1 + I144 <= 1] f6(I150, I151, I152, I153, I154, I155) -> f5(I150, I151, I152, I153, I154, I155) [2 <= I150] f5(I156, I157, I158, I159, I160, I161) -> f4(I156, I157, I158, I159, I160, I161) [1 + I158 <= 0] f5(I162, I163, I164, I165, I166, I167) -> f4(I162, I163, I164, I165, I166, I167) [1 <= I164] f5(I168, I169, I170, I171, I172, I173) -> f1(I168, I169, I170, I171, I172, I173) [0 <= I170 /\ I170 <= 0] f4(I174, I175, I176, I177, I178, I179) -> f1(-1 + I174, I175, I176, I177, I178, I179) f1(I180, I181, I182, I183, I184, I185) -> f3(I180, I181, I182, I183, I184, I185) [1 + I184 <= I183] f1(I186, I187, I188, I189, I190, I191) -> f2(I186, I187, I188, I189, I190, I191) [I189 <= I190] We use the extended value criterion with the projection function NU: NU[f1#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f4#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f5#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f9#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f6#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f11#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f12#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f13#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f2#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f10#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f14#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f15#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f16#(x0,x1,x2,x3,x4,x5)] = -x2 NU[f3#(x0,x1,x2,x3,x4,x5)] = -x2 This gives the following inequalities: 1 <= I7 /\ I7 <= 1 ==> -I8 >= -I8 1 + I13 <= 1 ==> -I14 >= -I14 2 <= I19 ==> -I20 >= -I20 1 + I32 <= 0 ==> -I32 >= -I32 1 <= I38 ==> -I38 >= -I38 ==> -I44 >= -I44 I59 <= 255 ==> -I56 >= -I56 1 + I63 <= I64 ==> -I62 >= -I62 2 <= I73 /\ I73 <= 2 ==> -I74 >= -I74 1 + I79 <= 2 ==> -I80 >= -I80 3 <= I85 ==> -I86 >= -I86 rnd4 = rnd4 ==> -I92 >= -I92 0 <= I98 /\ I98 <= 0 ==> -I98 > -1 with -I98 >= 0 1 + I104 <= 0 ==> -I104 >= -I104 1 <= I110 ==> -I110 >= -I110 ==> -I116 >= -I116 0 <= I131 ==> -I128 >= -I128 1 + I144 <= 1 ==> -I146 >= -I146 2 <= I150 ==> -I152 >= -I152 1 + I158 <= 0 ==> -I158 >= -I158 1 <= I164 ==> -I164 >= -I164 0 <= I170 /\ I170 <= 0 ==> -I170 >= -I170 ==> -I176 >= -I176 1 + I184 <= I183 ==> -I182 >= -I182 I189 <= I190 ==> -I188 >= -I188 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f3#(I6, I7, I8, I9, I10, I11) -> f16#(I6, I7, I8, I9, I10, I11) [1 <= I7 /\ I7 <= 1] f3#(I12, I13, I14, I15, I16, I17) -> f15#(I12, I13, I14, I15, I16, I17) [1 + I13 <= 1] f3#(I18, I19, I20, I21, I22, I23) -> f15#(I18, I19, I20, I21, I22, I23) [2 <= I19] f16#(I30, I31, I32, I33, I34, I35) -> f15#(I30, I31, I32, I33, I34, I35) [1 + I32 <= 0] f16#(I36, I37, I38, I39, I40, I41) -> f15#(I36, I37, I38, I39, I40, I41) [1 <= I38] f15#(I42, I43, I44, I45, I46, I47) -> f14#(I42, 2, I44, I45, I46, I42 + I47) f14#(I54, I55, I56, I57, I58, I59) -> f10#(I54, I55, I56, I57, I58, I59) [I59 <= 255] f2#(I60, I61, I62, I63, I64, I65) -> f13#(I60, I61, I62, I63, I64, I65) [1 + I63 <= I64] f13#(I72, I73, I74, I75, I76, I77) -> f12#(I72, I73, I74, I75, I76, I77) [2 <= I73 /\ I73 <= 2] f13#(I78, I79, I80, I81, I82, I83) -> f11#(I78, I79, I80, I81, I82, I83) [1 + I79 <= 2] f13#(I84, I85, I86, I87, I88, I89) -> f11#(I84, I85, I86, I87, I88, I89) [3 <= I85] f10#(I90, I91, I92, I93, I94, I95) -> f6#(I90, I91, I92, rnd4, I94, I95) [rnd4 = rnd4] f12#(I102, I103, I104, I105, I106, I107) -> f11#(I102, I103, I104, I105, I106, I107) [1 + I104 <= 0] f12#(I108, I109, I110, I111, I112, I113) -> f11#(I108, I109, I110, I111, I112, I113) [1 <= I110] f11#(I114, I115, I116, I117, I118, I119) -> f9#(I114, 1, I116, I117, I118, -1 * I114 + I119) f9#(I126, I127, I128, I129, I130, I131) -> f10#(I126, I127, I128, I129, I130, I131) [0 <= I131] f6#(I144, I145, I146, I147, I148, I149) -> f5#(I144, I145, I146, I147, I148, I149) [1 + I144 <= 1] f6#(I150, I151, I152, I153, I154, I155) -> f5#(I150, I151, I152, I153, I154, I155) [2 <= I150] f5#(I156, I157, I158, I159, I160, I161) -> f4#(I156, I157, I158, I159, I160, I161) [1 + I158 <= 0] f5#(I162, I163, I164, I165, I166, I167) -> f4#(I162, I163, I164, I165, I166, I167) [1 <= I164] f5#(I168, I169, I170, I171, I172, I173) -> f1#(I168, I169, I170, I171, I172, I173) [0 <= I170 /\ I170 <= 0] f4#(I174, I175, I176, I177, I178, I179) -> f1#(-1 + I174, I175, I176, I177, I178, I179) f1#(I180, I181, I182, I183, I184, I185) -> f3#(I180, I181, I182, I183, I184, I185) [1 + I184 <= I183] f1#(I186, I187, I188, I189, I190, I191) -> f2#(I186, I187, I188, I189, I190, I191) [I189 <= I190] R = f18(x1, x2, x3, x4, x5, x6) -> f17(x1, x2, x3, x4, x5, x6) f17(I0, I1, I2, I3, I4, I5) -> f10(4, 0, 0, I3, I4, I5) f3(I6, I7, I8, I9, I10, I11) -> f16(I6, I7, I8, I9, I10, I11) [1 <= I7 /\ I7 <= 1] f3(I12, I13, I14, I15, I16, I17) -> f15(I12, I13, I14, I15, I16, I17) [1 + I13 <= 1] f3(I18, I19, I20, I21, I22, I23) -> f15(I18, I19, I20, I21, I22, I23) [2 <= I19] f16(I24, I25, I26, I27, I28, I29) -> f15(-1 + I24, I25, 1, I27, I28, I29) [0 <= I26 /\ I26 <= 0] f16(I30, I31, I32, I33, I34, I35) -> f15(I30, I31, I32, I33, I34, I35) [1 + I32 <= 0] f16(I36, I37, I38, I39, I40, I41) -> f15(I36, I37, I38, I39, I40, I41) [1 <= I38] f15(I42, I43, I44, I45, I46, I47) -> f14(I42, 2, I44, I45, I46, I42 + I47) f14(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, I50, I51, I52, I53) [256 <= I53] f14(I54, I55, I56, I57, I58, I59) -> f10(I54, I55, I56, I57, I58, I59) [I59 <= 255] f2(I60, I61, I62, I63, I64, I65) -> f13(I60, I61, I62, I63, I64, I65) [1 + I63 <= I64] f2(I66, I67, I68, I69, I70, I71) -> f7(I66, I67, I68, I69, I70, I71) [I70 <= I69] f13(I72, I73, I74, I75, I76, I77) -> f12(I72, I73, I74, I75, I76, I77) [2 <= I73 /\ I73 <= 2] f13(I78, I79, I80, I81, I82, I83) -> f11(I78, I79, I80, I81, I82, I83) [1 + I79 <= 2] f13(I84, I85, I86, I87, I88, I89) -> f11(I84, I85, I86, I87, I88, I89) [3 <= I85] f10(I90, I91, I92, I93, I94, I95) -> f6(I90, I91, I92, rnd4, I94, I95) [rnd4 = rnd4] f12(I96, I97, I98, I99, I100, I101) -> f11(-1 + I96, I97, 1, I99, I100, I101) [0 <= I98 /\ I98 <= 0] f12(I102, I103, I104, I105, I106, I107) -> f11(I102, I103, I104, I105, I106, I107) [1 + I104 <= 0] f12(I108, I109, I110, I111, I112, I113) -> f11(I108, I109, I110, I111, I112, I113) [1 <= I110] f11(I114, I115, I116, I117, I118, I119) -> f9(I114, 1, I116, I117, I118, -1 * I114 + I119) f9(I120, I121, I122, I123, I124, I125) -> f7(I120, I121, I122, I123, I124, I125) [1 + I125 <= 0] f9(I126, I127, I128, I129, I130, I131) -> f10(I126, I127, I128, I129, I130, I131) [0 <= I131] f7(I132, I133, I134, I135, I136, I137) -> f8(I132, I133, I134, I135, I136, I137) f6(I138, I139, I140, I141, I142, I143) -> f7(I138, I139, I140, I141, I142, I143) [1 <= I138 /\ I138 <= 1] f6(I144, I145, I146, I147, I148, I149) -> f5(I144, I145, I146, I147, I148, I149) [1 + I144 <= 1] f6(I150, I151, I152, I153, I154, I155) -> f5(I150, I151, I152, I153, I154, I155) [2 <= I150] f5(I156, I157, I158, I159, I160, I161) -> f4(I156, I157, I158, I159, I160, I161) [1 + I158 <= 0] f5(I162, I163, I164, I165, I166, I167) -> f4(I162, I163, I164, I165, I166, I167) [1 <= I164] f5(I168, I169, I170, I171, I172, I173) -> f1(I168, I169, I170, I171, I172, I173) [0 <= I170 /\ I170 <= 0] f4(I174, I175, I176, I177, I178, I179) -> f1(-1 + I174, I175, I176, I177, I178, I179) f1(I180, I181, I182, I183, I184, I185) -> f3(I180, I181, I182, I183, I184, I185) [1 + I184 <= I183] f1(I186, I187, I188, I189, I190, I191) -> f2(I186, I187, I188, I189, I190, I191) [I189 <= I190]