/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 = f16#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f15#(x1, x2, x3, x4, x5, x6, x7, x8, x9) f15#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f3#(1, I1, I2, I3, I4, I5, rnd7, -1, I8) [rnd7 = -1] f11#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f10#(I9, 1, 1, I12, I13, I14, I15, I16, I17) [I17 <= I14] f11#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4#(I18, I19, I20, I21, I22, I23, I24, I25, I26) [1 + I23 <= I26] f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14#(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13#(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f14#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] f13#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7#(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] f13#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12#(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] f12#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9#(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9#(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f2#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11#(I90, I91, I92, I93, I94, I95, I96, I97, I98) f9#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10#(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) f8#(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f6#(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I110 <= 0] f8#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f6#(I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 <= I119] f8#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2#(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] f7#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8#(I135, I136, I137, I138, I139, I140, I141, I142, I143) f6#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f4#(I144, I145, I146, I147, I148, I149, I150, I151, I152) f3#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1#(I162, I163, I164, I165, I166, I167, I168, I169, I170) f1#(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179) [I171 <= I175] f1#(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f2#(I180, I181, 0, I183, I184, I185, I186, I187, 1) [1 + I184 <= I180] R = f16(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9) f15(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f3(1, I1, I2, I3, I4, I5, rnd7, -1, I8) [rnd7 = -1] f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f10(I9, 1, 1, I12, I13, I14, I15, I16, I17) [I17 <= I14] f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) [1 + I23 <= I26] f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f14(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] f13(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] f12(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f2(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) f9(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) f8(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f6(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I110 <= 0] f8(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f6(I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 <= I119] f8(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] f7(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8(I135, I136, I137, I138, I139, I140, I141, I142, I143) f6(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152) f4(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f5(I153, I154, I155, I156, I157, I158, I159, I160, I161) f3(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1(I162, I163, I164, I165, I166, I167, I168, I169, I170) f1(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179) [I171 <= I175] f1(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f2(I180, I181, 0, I183, I184, I185, I186, I187, 1) [1 + I184 <= I180] The dependency graph for this problem is: 0 -> 1 1 -> 18 2 -> 4 3 -> 4 -> 5, 6 5 -> 7, 8 6 -> 16 7 -> 16 8 -> 9, 10 9 -> 12 10 -> 12 11 -> 2, 3 12 -> 4 13 -> 17 14 -> 17 15 -> 11 16 -> 13, 14, 15 17 -> 18 -> 19, 20 19 -> 18 20 -> 11 Where: 0) f16#(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f15#(x1, x2, x3, x4, x5, x6, x7, x8, x9) 1) f15#(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f3#(1, I1, I2, I3, I4, I5, rnd7, -1, I8) [rnd7 = -1] 2) f11#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f10#(I9, 1, 1, I12, I13, I14, I15, I16, I17) [I17 <= I14] 3) f11#(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4#(I18, I19, I20, I21, I22, I23, I24, I25, I26) [1 + I23 <= I26] 4) f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 5) f14#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13#(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] 6) f14#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] 7) f13#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7#(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] 8) f13#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12#(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] 9) f12#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9#(I72, I73, I74, I75, I76, I77, I78, I79, I80) 10) f12#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9#(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] 11) f2#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11#(I90, I91, I92, I93, I94, I95, I96, I97, I98) 12) f9#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10#(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) 13) f8#(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f6#(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I110 <= 0] 14) f8#(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f6#(I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 <= I119] 15) f8#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2#(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] 16) f7#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8#(I135, I136, I137, I138, I139, I140, I141, I142, I143) 17) f6#(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f4#(I144, I145, I146, I147, I148, I149, I150, I151, I152) 18) f3#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1#(I162, I163, I164, I165, I166, I167, I168, I169, I170) 19) f1#(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179) [I171 <= I175] 20) f1#(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f2#(I180, I181, 0, I183, I184, I185, I186, I187, 1) [1 + I184 <= I180] We have the following SCCs. { 18, 19 } { 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16 } DP problem for innermost termination. P = f11#(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f10#(I9, 1, 1, I12, I13, I14, I15, I16, I17) [I17 <= I14] f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14#(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13#(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f14#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] f13#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7#(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] f13#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12#(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] f12#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9#(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9#(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f2#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11#(I90, I91, I92, I93, I94, I95, I96, I97, I98) f9#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10#(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) f8#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2#(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] f7#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8#(I135, I136, I137, I138, I139, I140, I141, I142, I143) R = f16(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9) f15(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f3(1, I1, I2, I3, I4, I5, rnd7, -1, I8) [rnd7 = -1] f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f10(I9, 1, 1, I12, I13, I14, I15, I16, I17) [I17 <= I14] f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) [1 + I23 <= I26] f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f14(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] f13(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] f12(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f2(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) f9(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) f8(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f6(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I110 <= 0] f8(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f6(I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 <= I119] f8(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] f7(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8(I135, I136, I137, I138, I139, I140, I141, I142, I143) f6(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152) f4(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f5(I153, I154, I155, I156, I157, I158, I159, I160, I161) f3(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1(I162, I163, I164, I165, I166, I167, I168, I169, I170) f1(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179) [I171 <= I175] f1(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f2(I180, I181, 0, I183, I184, I185, I186, I187, 1) [1 + I184 <= I180] We use the extended value criterion with the projection function NU: NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x5 - x8 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x5 - x8 + 1 NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x5 - x8 NU[f12#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x5 - x8 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x5 - x8 NU[f13#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x5 - x8 NU[f14#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x5 - x8 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x5 - x8 NU[f11#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = x5 - x8 + 1 This gives the following inequalities: I17 <= I14 ==> I14 - I17 + 1 > I14 - I17 with I14 - I17 + 1 >= 0 ==> I32 - I35 >= I32 - I35 I37 <= I41 ==> I41 - I44 >= I41 - I44 1 + I50 <= I46 ==> I50 - I53 >= I50 - I53 1 + I58 - I62 <= I55 ==> I59 - I62 >= I59 - I62 I64 <= I67 - I71 ==> I68 - I71 >= I68 - I71 ==> I77 - I80 >= I77 - I80 rnd4 = rnd4 ==> I86 - I89 >= I86 - I89 ==> I95 - I98 + 1 >= I95 - I98 + 1 ==> I104 - I107 >= I104 - I107 0 <= I128 /\ I128 <= 0 ==> I131 - I134 >= I131 - (1 + I134) + 1 ==> I140 - I143 >= I140 - I143 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14#(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13#(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f14#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] f13#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7#(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] f13#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12#(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] f12#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9#(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9#(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f2#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11#(I90, I91, I92, I93, I94, I95, I96, I97, I98) f9#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10#(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) f8#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2#(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] f7#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8#(I135, I136, I137, I138, I139, I140, I141, I142, I143) R = f16(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9) f15(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f3(1, I1, I2, I3, I4, I5, rnd7, -1, I8) [rnd7 = -1] f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f10(I9, 1, 1, I12, I13, I14, I15, I16, I17) [I17 <= I14] f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) [1 + I23 <= I26] f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f14(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] f13(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] f12(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f2(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) f9(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) f8(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f6(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I110 <= 0] f8(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f6(I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 <= I119] f8(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] f7(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8(I135, I136, I137, I138, I139, I140, I141, I142, I143) f6(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152) f4(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f5(I153, I154, I155, I156, I157, I158, I159, I160, I161) f3(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1(I162, I163, I164, I165, I166, I167, I168, I169, I170) f1(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179) [I171 <= I175] f1(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f2(I180, I181, 0, I183, I184, I185, I186, I187, 1) [1 + I184 <= I180] The dependency graph for this problem is: 4 -> 5, 6 5 -> 7, 8 6 -> 16 7 -> 16 8 -> 9, 10 9 -> 12 10 -> 12 11 -> 12 -> 4 15 -> 11 16 -> 15 Where: 4) f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 5) f14#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13#(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] 6) f14#(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7#(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] 7) f13#(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7#(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] 8) f13#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12#(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] 9) f12#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9#(I72, I73, I74, I75, I76, I77, I78, I79, I80) 10) f12#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9#(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] 11) f2#(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11#(I90, I91, I92, I93, I94, I95, I96, I97, I98) 12) f9#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10#(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) 15) f8#(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2#(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] 16) f7#(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8#(I135, I136, I137, I138, I139, I140, I141, I142, I143) We have the following SCCs. { 4, 5, 8, 9, 10, 12 } DP problem for innermost termination. P = f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14#(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13#(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f13#(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12#(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] f12#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9#(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9#(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f9#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10#(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) R = f16(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9) f15(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f3(1, I1, I2, I3, I4, I5, rnd7, -1, I8) [rnd7 = -1] f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f10(I9, 1, 1, I12, I13, I14, I15, I16, I17) [I17 <= I14] f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) [1 + I23 <= I26] f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f14(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] f13(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] f12(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f2(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) f9(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) f8(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f6(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I110 <= 0] f8(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f6(I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 <= I119] f8(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] f7(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8(I135, I136, I137, I138, I139, I140, I141, I142, I143) f6(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152) f4(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f5(I153, I154, I155, I156, I157, I158, I159, I160, I161) f3(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1(I162, I163, I164, I165, I166, I167, I168, I169, I170) f1(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179) [I171 <= I175] f1(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f2(I180, I181, 0, I183, I184, I185, I186, I187, 1) [1 + I184 <= I180] We use the extended value criterion with the projection function NU: NU[f9#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x1 + x4 - x8 - 1 NU[f12#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x1 + x4 - x8 - 1 NU[f13#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x1 + x4 - x8 NU[f14#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x1 + x4 - x8 NU[f10#(x0,x1,x2,x3,x4,x5,x6,x7,x8)] = -x1 + x4 - x8 This gives the following inequalities: ==> -I28 + I31 - I35 >= -I28 + I31 - I35 I37 <= I41 ==> -I37 + I40 - I44 >= -I37 + I40 - I44 I64 <= I67 - I71 ==> -I64 + I67 - I71 > -I64 + I67 - I71 - 1 with -I64 + I67 - I71 >= 0 ==> -I73 + I76 - I80 - 1 >= -I73 + I76 - I80 - 1 rnd4 = rnd4 ==> -I82 + I85 - I89 - 1 >= -I82 + I85 - I89 - 1 ==> -I100 + I103 - I107 - 1 >= -(1 + I100) + I103 - I107 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14#(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13#(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f12#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9#(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9#(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f9#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10#(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) R = f16(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9) f15(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f3(1, I1, I2, I3, I4, I5, rnd7, -1, I8) [rnd7 = -1] f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f10(I9, 1, 1, I12, I13, I14, I15, I16, I17) [I17 <= I14] f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) [1 + I23 <= I26] f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f14(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] f13(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] f12(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f2(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) f9(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) f8(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f6(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I110 <= 0] f8(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f6(I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 <= I119] f8(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] f7(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8(I135, I136, I137, I138, I139, I140, I141, I142, I143) f6(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152) f4(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f5(I153, I154, I155, I156, I157, I158, I159, I160, I161) f3(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1(I162, I163, I164, I165, I166, I167, I168, I169, I170) f1(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179) [I171 <= I175] f1(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f2(I180, I181, 0, I183, I184, I185, I186, I187, 1) [1 + I184 <= I180] The dependency graph for this problem is: 4 -> 5 5 -> 9 -> 12 10 -> 12 12 -> 4 Where: 4) f10#(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14#(I27, I28, I29, I30, I31, I32, I33, I34, I35) 5) f14#(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13#(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] 9) f12#(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9#(I72, I73, I74, I75, I76, I77, I78, I79, I80) 10) f12#(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9#(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] 12) f9#(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10#(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) We have the following SCCs. DP problem for innermost termination. P = f3#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1#(I162, I163, I164, I165, I166, I167, I168, I169, I170) f1#(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3#(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179) [I171 <= I175] R = f16(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9) f15(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f3(1, I1, I2, I3, I4, I5, rnd7, -1, I8) [rnd7 = -1] f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f10(I9, 1, 1, I12, I13, I14, I15, I16, I17) [I17 <= I14] f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) [1 + I23 <= I26] f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f14(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] f13(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] f12(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f2(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) f9(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) f8(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f6(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I110 <= 0] f8(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f6(I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 <= I119] f8(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] f7(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8(I135, I136, I137, I138, I139, I140, I141, I142, I143) f6(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152) f4(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f5(I153, I154, I155, I156, I157, I158, I159, I160, I161) f3(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1(I162, I163, I164, I165, I166, I167, I168, I169, I170) f1(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179) [I171 <= I175] f1(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f2(I180, I181, 0, I183, I184, I185, I186, I187, 1) [1 + I184 <= I180] We use the reverse value criterion with the projection function NU: NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z5 + -1 * z1 NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8,z9)] = z5 + -1 * z1 This gives the following inequalities: ==> I166 + -1 * I162 >= I166 + -1 * I162 I171 <= I175 ==> I175 + -1 * I171 > I175 + -1 * (1 + I171) with I175 + -1 * I171 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f3#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1#(I162, I163, I164, I165, I166, I167, I168, I169, I170) R = f16(x1, x2, x3, x4, x5, x6, x7, x8, x9) -> f15(x1, x2, x3, x4, x5, x6, x7, x8, x9) f15(I0, I1, I2, I3, I4, I5, I6, I7, I8) -> f3(1, I1, I2, I3, I4, I5, rnd7, -1, I8) [rnd7 = -1] f11(I9, I10, I11, I12, I13, I14, I15, I16, I17) -> f10(I9, 1, 1, I12, I13, I14, I15, I16, I17) [I17 <= I14] f11(I18, I19, I20, I21, I22, I23, I24, I25, I26) -> f4(I18, I19, I20, I21, I22, I23, I24, I25, I26) [1 + I23 <= I26] f10(I27, I28, I29, I30, I31, I32, I33, I34, I35) -> f14(I27, I28, I29, I30, I31, I32, I33, I34, I35) f14(I36, I37, I38, I39, I40, I41, I42, I43, I44) -> f13(I36, I37, I38, I39, I40, I41, I42, I43, I44) [I37 <= I41] f14(I45, I46, I47, I48, I49, I50, I51, I52, I53) -> f7(I45, I46, I47, I48, I49, I50, I51, I52, I53) [1 + I50 <= I46] f13(I54, I55, I56, I57, I58, I59, I60, I61, I62) -> f7(I54, I55, I56, I57, I58, I59, I60, I61, I62) [1 + I58 - I62 <= I55] f13(I63, I64, I65, I66, I67, I68, I69, I70, I71) -> f12(I63, I64, I65, I66, I67, I68, I69, I70, I71) [I64 <= I67 - I71] f12(I72, I73, I74, I75, I76, I77, I78, I79, I80) -> f9(I72, I73, I74, I75, I76, I77, I78, I79, I80) f12(I81, I82, I83, I84, I85, I86, I87, I88, I89) -> f9(I81, I82, 0, rnd4, I85, I86, I87, I88, I89) [rnd4 = rnd4] f2(I90, I91, I92, I93, I94, I95, I96, I97, I98) -> f11(I90, I91, I92, I93, I94, I95, I96, I97, I98) f9(I99, I100, I101, I102, I103, I104, I105, I106, I107) -> f10(I99, 1 + I100, I101, I102, I103, I104, I105, I106, I107) f8(I108, I109, I110, I111, I112, I113, I114, I115, I116) -> f6(I108, I109, I110, I111, I112, I113, I114, I115, I116) [1 + I110 <= 0] f8(I117, I118, I119, I120, I121, I122, I123, I124, I125) -> f6(I117, I118, I119, I120, I121, I122, I123, I124, I125) [1 <= I119] f8(I126, I127, I128, I129, I130, I131, I132, I133, I134) -> f2(I126, I127, I128, I129, I130, I131, I132, I133, 1 + I134) [0 <= I128 /\ I128 <= 0] f7(I135, I136, I137, I138, I139, I140, I141, I142, I143) -> f8(I135, I136, I137, I138, I139, I140, I141, I142, I143) f6(I144, I145, I146, I147, I148, I149, I150, I151, I152) -> f4(I144, I145, I146, I147, I148, I149, I150, I151, I152) f4(I153, I154, I155, I156, I157, I158, I159, I160, I161) -> f5(I153, I154, I155, I156, I157, I158, I159, I160, I161) f3(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1(I162, I163, I164, I165, I166, I167, I168, I169, I170) f1(I171, I172, I173, I174, I175, I176, I177, I178, I179) -> f3(1 + I171, I172, I173, I174, I175, I176, I177, I178, I179) [I171 <= I175] f1(I180, I181, I182, I183, I184, I185, I186, I187, I188) -> f2(I180, I181, 0, I183, I184, I185, I186, I187, 1) [1 + I184 <= I180] The dependency graph for this problem is: 18 -> Where: 18) f3#(I162, I163, I164, I165, I166, I167, I168, I169, I170) -> f1#(I162, I163, I164, I165, I166, I167, I168, I169, I170) We have the following SCCs.