/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) -> f15#(x1, x2, x3, x4, x5, x6, x7) f15#(I0, I1, I2, I3, I4, I5, I6) -> f3#(1, I1, I2, I3, rnd5, -1, I6) [rnd5 = -1] f11#(I7, I8, I9, I10, I11, I12, I13) -> f10#(I7, 1, 1, I10, I11, I12, I13) [I13 <= 99] f11#(I14, I15, I16, I17, I18, I19, I20) -> f4#(I14, I15, I16, I17, I18, I19, I20) [100 <= I20] f10#(I21, I22, I23, I24, I25, I26, I27) -> f14#(I21, I22, I23, I24, I25, I26, I27) f14#(I28, I29, I30, I31, I32, I33, I34) -> f13#(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] f14#(I35, I36, I37, I38, I39, I40, I41) -> f7#(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] f13#(I42, I43, I44, I45, I46, I47, I48) -> f7#(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] f13#(I49, I50, I51, I52, I53, I54, I55) -> f12#(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12#(I56, I57, I58, I59, I60, I61, I62) -> f9#(I56, I57, I58, I59, I60, I61, I62) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f2#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, I71, I72, I73, I74, I75, I76) f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, 1 + I78, I79, I80, I81, I82, I83) f8#(I84, I85, I86, I87, I88, I89, I90) -> f6#(I84, I85, I86, I87, I88, I89, I90) [1 + I86 <= 0] f8#(I91, I92, I93, I94, I95, I96, I97) -> f6#(I91, I92, I93, I94, I95, I96, I97) [1 <= I93] f8#(I98, I99, I100, I101, I102, I103, I104) -> f2#(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] f7#(I105, I106, I107, I108, I109, I110, I111) -> f8#(I105, I106, I107, I108, I109, I110, I111) f6#(I112, I113, I114, I115, I116, I117, I118) -> f4#(I112, I113, I114, I115, I116, I117, I118) f3#(I126, I127, I128, I129, I130, I131, I132) -> f1#(I126, I127, I128, I129, I130, I131, I132) f1#(I133, I134, I135, I136, I137, I138, I139) -> f3#(1 + I133, I134, I135, I136, I137, I138, I139) [I133 <= 100] f1#(I140, I141, I142, I143, I144, I145, I146) -> f2#(I140, I141, 0, I143, I144, I145, 1) [101 <= I140] R = f16(x1, x2, x3, x4, x5, x6, x7) -> f15(x1, x2, x3, x4, x5, x6, x7) f15(I0, I1, I2, I3, I4, I5, I6) -> f3(1, I1, I2, I3, rnd5, -1, I6) [rnd5 = -1] f11(I7, I8, I9, I10, I11, I12, I13) -> f10(I7, 1, 1, I10, I11, I12, I13) [I13 <= 99] f11(I14, I15, I16, I17, I18, I19, I20) -> f4(I14, I15, I16, I17, I18, I19, I20) [100 <= I20] f10(I21, I22, I23, I24, I25, I26, I27) -> f14(I21, I22, I23, I24, I25, I26, I27) f14(I28, I29, I30, I31, I32, I33, I34) -> f13(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] f14(I35, I36, I37, I38, I39, I40, I41) -> f7(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] f13(I42, I43, I44, I45, I46, I47, I48) -> f7(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] f13(I49, I50, I51, I52, I53, I54, I55) -> f12(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12(I56, I57, I58, I59, I60, I61, I62) -> f9(I56, I57, I58, I59, I60, I61, I62) f12(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f2(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, I71, I72, I73, I74, I75, I76) f9(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, 1 + I78, I79, I80, I81, I82, I83) f8(I84, I85, I86, I87, I88, I89, I90) -> f6(I84, I85, I86, I87, I88, I89, I90) [1 + I86 <= 0] f8(I91, I92, I93, I94, I95, I96, I97) -> f6(I91, I92, I93, I94, I95, I96, I97) [1 <= I93] f8(I98, I99, I100, I101, I102, I103, I104) -> f2(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] f7(I105, I106, I107, I108, I109, I110, I111) -> f8(I105, I106, I107, I108, I109, I110, I111) f6(I112, I113, I114, I115, I116, I117, I118) -> f4(I112, I113, I114, I115, I116, I117, I118) f4(I119, I120, I121, I122, I123, I124, I125) -> f5(I119, I120, I121, I122, I123, I124, I125) f3(I126, I127, I128, I129, I130, I131, I132) -> f1(I126, I127, I128, I129, I130, I131, I132) f1(I133, I134, I135, I136, I137, I138, I139) -> f3(1 + I133, I134, I135, I136, I137, I138, I139) [I133 <= 100] f1(I140, I141, I142, I143, I144, I145, I146) -> f2(I140, I141, 0, I143, I144, I145, 1) [101 <= I140] 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) -> f15#(x1, x2, x3, x4, x5, x6, x7) 1) f15#(I0, I1, I2, I3, I4, I5, I6) -> f3#(1, I1, I2, I3, rnd5, -1, I6) [rnd5 = -1] 2) f11#(I7, I8, I9, I10, I11, I12, I13) -> f10#(I7, 1, 1, I10, I11, I12, I13) [I13 <= 99] 3) f11#(I14, I15, I16, I17, I18, I19, I20) -> f4#(I14, I15, I16, I17, I18, I19, I20) [100 <= I20] 4) f10#(I21, I22, I23, I24, I25, I26, I27) -> f14#(I21, I22, I23, I24, I25, I26, I27) 5) f14#(I28, I29, I30, I31, I32, I33, I34) -> f13#(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] 6) f14#(I35, I36, I37, I38, I39, I40, I41) -> f7#(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] 7) f13#(I42, I43, I44, I45, I46, I47, I48) -> f7#(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] 8) f13#(I49, I50, I51, I52, I53, I54, I55) -> f12#(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] 9) f12#(I56, I57, I58, I59, I60, I61, I62) -> f9#(I56, I57, I58, I59, I60, I61, I62) 10) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] 11) f2#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, I71, I72, I73, I74, I75, I76) 12) f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, 1 + I78, I79, I80, I81, I82, I83) 13) f8#(I84, I85, I86, I87, I88, I89, I90) -> f6#(I84, I85, I86, I87, I88, I89, I90) [1 + I86 <= 0] 14) f8#(I91, I92, I93, I94, I95, I96, I97) -> f6#(I91, I92, I93, I94, I95, I96, I97) [1 <= I93] 15) f8#(I98, I99, I100, I101, I102, I103, I104) -> f2#(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] 16) f7#(I105, I106, I107, I108, I109, I110, I111) -> f8#(I105, I106, I107, I108, I109, I110, I111) 17) f6#(I112, I113, I114, I115, I116, I117, I118) -> f4#(I112, I113, I114, I115, I116, I117, I118) 18) f3#(I126, I127, I128, I129, I130, I131, I132) -> f1#(I126, I127, I128, I129, I130, I131, I132) 19) f1#(I133, I134, I135, I136, I137, I138, I139) -> f3#(1 + I133, I134, I135, I136, I137, I138, I139) [I133 <= 100] 20) f1#(I140, I141, I142, I143, I144, I145, I146) -> f2#(I140, I141, 0, I143, I144, I145, 1) [101 <= I140] 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#(I7, I8, I9, I10, I11, I12, I13) -> f10#(I7, 1, 1, I10, I11, I12, I13) [I13 <= 99] f10#(I21, I22, I23, I24, I25, I26, I27) -> f14#(I21, I22, I23, I24, I25, I26, I27) f14#(I28, I29, I30, I31, I32, I33, I34) -> f13#(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] f14#(I35, I36, I37, I38, I39, I40, I41) -> f7#(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] f13#(I42, I43, I44, I45, I46, I47, I48) -> f7#(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] f13#(I49, I50, I51, I52, I53, I54, I55) -> f12#(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12#(I56, I57, I58, I59, I60, I61, I62) -> f9#(I56, I57, I58, I59, I60, I61, I62) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f2#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, I71, I72, I73, I74, I75, I76) f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, 1 + I78, I79, I80, I81, I82, I83) f8#(I98, I99, I100, I101, I102, I103, I104) -> f2#(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] f7#(I105, I106, I107, I108, I109, I110, I111) -> f8#(I105, I106, I107, I108, I109, I110, I111) R = f16(x1, x2, x3, x4, x5, x6, x7) -> f15(x1, x2, x3, x4, x5, x6, x7) f15(I0, I1, I2, I3, I4, I5, I6) -> f3(1, I1, I2, I3, rnd5, -1, I6) [rnd5 = -1] f11(I7, I8, I9, I10, I11, I12, I13) -> f10(I7, 1, 1, I10, I11, I12, I13) [I13 <= 99] f11(I14, I15, I16, I17, I18, I19, I20) -> f4(I14, I15, I16, I17, I18, I19, I20) [100 <= I20] f10(I21, I22, I23, I24, I25, I26, I27) -> f14(I21, I22, I23, I24, I25, I26, I27) f14(I28, I29, I30, I31, I32, I33, I34) -> f13(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] f14(I35, I36, I37, I38, I39, I40, I41) -> f7(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] f13(I42, I43, I44, I45, I46, I47, I48) -> f7(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] f13(I49, I50, I51, I52, I53, I54, I55) -> f12(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12(I56, I57, I58, I59, I60, I61, I62) -> f9(I56, I57, I58, I59, I60, I61, I62) f12(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f2(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, I71, I72, I73, I74, I75, I76) f9(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, 1 + I78, I79, I80, I81, I82, I83) f8(I84, I85, I86, I87, I88, I89, I90) -> f6(I84, I85, I86, I87, I88, I89, I90) [1 + I86 <= 0] f8(I91, I92, I93, I94, I95, I96, I97) -> f6(I91, I92, I93, I94, I95, I96, I97) [1 <= I93] f8(I98, I99, I100, I101, I102, I103, I104) -> f2(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] f7(I105, I106, I107, I108, I109, I110, I111) -> f8(I105, I106, I107, I108, I109, I110, I111) f6(I112, I113, I114, I115, I116, I117, I118) -> f4(I112, I113, I114, I115, I116, I117, I118) f4(I119, I120, I121, I122, I123, I124, I125) -> f5(I119, I120, I121, I122, I123, I124, I125) f3(I126, I127, I128, I129, I130, I131, I132) -> f1(I126, I127, I128, I129, I130, I131, I132) f1(I133, I134, I135, I136, I137, I138, I139) -> f3(1 + I133, I134, I135, I136, I137, I138, I139) [I133 <= 100] f1(I140, I141, I142, I143, I144, I145, I146) -> f2(I140, I141, 0, I143, I144, I145, 1) [101 <= I140] We use the extended value criterion with the projection function NU: NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = -x6 + 98 NU[f2#(x0,x1,x2,x3,x4,x5,x6)] = -x6 + 99 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x6 + 98 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x6 + 98 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x6 + 98 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x6 + 98 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x6 + 98 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x6 + 98 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x6 + 99 This gives the following inequalities: I13 <= 99 ==> -I13 + 99 > -I13 + 98 with -I13 + 99 >= 0 ==> -I27 + 98 >= -I27 + 98 I29 <= 99 ==> -I34 + 98 >= -I34 + 98 100 <= I36 ==> -I41 + 98 >= -I41 + 98 101 - I48 <= I43 ==> -I48 + 98 >= -I48 + 98 I50 <= 100 - I55 ==> -I55 + 98 >= -I55 + 98 ==> -I62 + 98 >= -I62 + 98 rnd4 = rnd4 ==> -I69 + 98 >= -I69 + 98 ==> -I76 + 99 >= -I76 + 99 ==> -I83 + 98 >= -I83 + 98 0 <= I100 /\ I100 <= 0 ==> -I104 + 98 >= -(1 + I104) + 99 ==> -I111 + 98 >= -I111 + 98 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f10#(I21, I22, I23, I24, I25, I26, I27) -> f14#(I21, I22, I23, I24, I25, I26, I27) f14#(I28, I29, I30, I31, I32, I33, I34) -> f13#(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] f14#(I35, I36, I37, I38, I39, I40, I41) -> f7#(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] f13#(I42, I43, I44, I45, I46, I47, I48) -> f7#(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] f13#(I49, I50, I51, I52, I53, I54, I55) -> f12#(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12#(I56, I57, I58, I59, I60, I61, I62) -> f9#(I56, I57, I58, I59, I60, I61, I62) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f2#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, I71, I72, I73, I74, I75, I76) f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, 1 + I78, I79, I80, I81, I82, I83) f8#(I98, I99, I100, I101, I102, I103, I104) -> f2#(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] f7#(I105, I106, I107, I108, I109, I110, I111) -> f8#(I105, I106, I107, I108, I109, I110, I111) R = f16(x1, x2, x3, x4, x5, x6, x7) -> f15(x1, x2, x3, x4, x5, x6, x7) f15(I0, I1, I2, I3, I4, I5, I6) -> f3(1, I1, I2, I3, rnd5, -1, I6) [rnd5 = -1] f11(I7, I8, I9, I10, I11, I12, I13) -> f10(I7, 1, 1, I10, I11, I12, I13) [I13 <= 99] f11(I14, I15, I16, I17, I18, I19, I20) -> f4(I14, I15, I16, I17, I18, I19, I20) [100 <= I20] f10(I21, I22, I23, I24, I25, I26, I27) -> f14(I21, I22, I23, I24, I25, I26, I27) f14(I28, I29, I30, I31, I32, I33, I34) -> f13(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] f14(I35, I36, I37, I38, I39, I40, I41) -> f7(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] f13(I42, I43, I44, I45, I46, I47, I48) -> f7(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] f13(I49, I50, I51, I52, I53, I54, I55) -> f12(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12(I56, I57, I58, I59, I60, I61, I62) -> f9(I56, I57, I58, I59, I60, I61, I62) f12(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f2(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, I71, I72, I73, I74, I75, I76) f9(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, 1 + I78, I79, I80, I81, I82, I83) f8(I84, I85, I86, I87, I88, I89, I90) -> f6(I84, I85, I86, I87, I88, I89, I90) [1 + I86 <= 0] f8(I91, I92, I93, I94, I95, I96, I97) -> f6(I91, I92, I93, I94, I95, I96, I97) [1 <= I93] f8(I98, I99, I100, I101, I102, I103, I104) -> f2(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] f7(I105, I106, I107, I108, I109, I110, I111) -> f8(I105, I106, I107, I108, I109, I110, I111) f6(I112, I113, I114, I115, I116, I117, I118) -> f4(I112, I113, I114, I115, I116, I117, I118) f4(I119, I120, I121, I122, I123, I124, I125) -> f5(I119, I120, I121, I122, I123, I124, I125) f3(I126, I127, I128, I129, I130, I131, I132) -> f1(I126, I127, I128, I129, I130, I131, I132) f1(I133, I134, I135, I136, I137, I138, I139) -> f3(1 + I133, I134, I135, I136, I137, I138, I139) [I133 <= 100] f1(I140, I141, I142, I143, I144, I145, I146) -> f2(I140, I141, 0, I143, I144, I145, 1) [101 <= I140] 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#(I21, I22, I23, I24, I25, I26, I27) -> f14#(I21, I22, I23, I24, I25, I26, I27) 5) f14#(I28, I29, I30, I31, I32, I33, I34) -> f13#(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] 6) f14#(I35, I36, I37, I38, I39, I40, I41) -> f7#(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] 7) f13#(I42, I43, I44, I45, I46, I47, I48) -> f7#(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] 8) f13#(I49, I50, I51, I52, I53, I54, I55) -> f12#(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] 9) f12#(I56, I57, I58, I59, I60, I61, I62) -> f9#(I56, I57, I58, I59, I60, I61, I62) 10) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] 11) f2#(I70, I71, I72, I73, I74, I75, I76) -> f11#(I70, I71, I72, I73, I74, I75, I76) 12) f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, 1 + I78, I79, I80, I81, I82, I83) 15) f8#(I98, I99, I100, I101, I102, I103, I104) -> f2#(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] 16) f7#(I105, I106, I107, I108, I109, I110, I111) -> f8#(I105, I106, I107, I108, I109, I110, I111) We have the following SCCs. { 4, 5, 8, 9, 10, 12 } DP problem for innermost termination. P = f10#(I21, I22, I23, I24, I25, I26, I27) -> f14#(I21, I22, I23, I24, I25, I26, I27) f14#(I28, I29, I30, I31, I32, I33, I34) -> f13#(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] f13#(I49, I50, I51, I52, I53, I54, I55) -> f12#(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12#(I56, I57, I58, I59, I60, I61, I62) -> f9#(I56, I57, I58, I59, I60, I61, I62) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, 1 + I78, I79, I80, I81, I82, I83) R = f16(x1, x2, x3, x4, x5, x6, x7) -> f15(x1, x2, x3, x4, x5, x6, x7) f15(I0, I1, I2, I3, I4, I5, I6) -> f3(1, I1, I2, I3, rnd5, -1, I6) [rnd5 = -1] f11(I7, I8, I9, I10, I11, I12, I13) -> f10(I7, 1, 1, I10, I11, I12, I13) [I13 <= 99] f11(I14, I15, I16, I17, I18, I19, I20) -> f4(I14, I15, I16, I17, I18, I19, I20) [100 <= I20] f10(I21, I22, I23, I24, I25, I26, I27) -> f14(I21, I22, I23, I24, I25, I26, I27) f14(I28, I29, I30, I31, I32, I33, I34) -> f13(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] f14(I35, I36, I37, I38, I39, I40, I41) -> f7(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] f13(I42, I43, I44, I45, I46, I47, I48) -> f7(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] f13(I49, I50, I51, I52, I53, I54, I55) -> f12(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12(I56, I57, I58, I59, I60, I61, I62) -> f9(I56, I57, I58, I59, I60, I61, I62) f12(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f2(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, I71, I72, I73, I74, I75, I76) f9(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, 1 + I78, I79, I80, I81, I82, I83) f8(I84, I85, I86, I87, I88, I89, I90) -> f6(I84, I85, I86, I87, I88, I89, I90) [1 + I86 <= 0] f8(I91, I92, I93, I94, I95, I96, I97) -> f6(I91, I92, I93, I94, I95, I96, I97) [1 <= I93] f8(I98, I99, I100, I101, I102, I103, I104) -> f2(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] f7(I105, I106, I107, I108, I109, I110, I111) -> f8(I105, I106, I107, I108, I109, I110, I111) f6(I112, I113, I114, I115, I116, I117, I118) -> f4(I112, I113, I114, I115, I116, I117, I118) f4(I119, I120, I121, I122, I123, I124, I125) -> f5(I119, I120, I121, I122, I123, I124, I125) f3(I126, I127, I128, I129, I130, I131, I132) -> f1(I126, I127, I128, I129, I130, I131, I132) f1(I133, I134, I135, I136, I137, I138, I139) -> f3(1 + I133, I134, I135, I136, I137, I138, I139) [I133 <= 100] f1(I140, I141, I142, I143, I144, I145, I146) -> f2(I140, I141, 0, I143, I144, I145, 1) [101 <= I140] We use the extended value criterion with the projection function NU: NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + 100 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + 100 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + 100 NU[f14#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + 101 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x1 + 101 This gives the following inequalities: ==> -I22 + 101 >= -I22 + 101 I29 <= 99 ==> -I29 + 101 > -I29 + 100 with -I29 + 101 >= 0 I50 <= 100 - I55 ==> -I50 + 100 >= -I50 + 100 ==> -I57 + 100 >= -I57 + 100 rnd4 = rnd4 ==> -I64 + 100 >= -I64 + 100 ==> -I78 + 100 >= -(1 + I78) + 101 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f10#(I21, I22, I23, I24, I25, I26, I27) -> f14#(I21, I22, I23, I24, I25, I26, I27) f13#(I49, I50, I51, I52, I53, I54, I55) -> f12#(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12#(I56, I57, I58, I59, I60, I61, I62) -> f9#(I56, I57, I58, I59, I60, I61, I62) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, 1 + I78, I79, I80, I81, I82, I83) R = f16(x1, x2, x3, x4, x5, x6, x7) -> f15(x1, x2, x3, x4, x5, x6, x7) f15(I0, I1, I2, I3, I4, I5, I6) -> f3(1, I1, I2, I3, rnd5, -1, I6) [rnd5 = -1] f11(I7, I8, I9, I10, I11, I12, I13) -> f10(I7, 1, 1, I10, I11, I12, I13) [I13 <= 99] f11(I14, I15, I16, I17, I18, I19, I20) -> f4(I14, I15, I16, I17, I18, I19, I20) [100 <= I20] f10(I21, I22, I23, I24, I25, I26, I27) -> f14(I21, I22, I23, I24, I25, I26, I27) f14(I28, I29, I30, I31, I32, I33, I34) -> f13(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] f14(I35, I36, I37, I38, I39, I40, I41) -> f7(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] f13(I42, I43, I44, I45, I46, I47, I48) -> f7(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] f13(I49, I50, I51, I52, I53, I54, I55) -> f12(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12(I56, I57, I58, I59, I60, I61, I62) -> f9(I56, I57, I58, I59, I60, I61, I62) f12(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f2(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, I71, I72, I73, I74, I75, I76) f9(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, 1 + I78, I79, I80, I81, I82, I83) f8(I84, I85, I86, I87, I88, I89, I90) -> f6(I84, I85, I86, I87, I88, I89, I90) [1 + I86 <= 0] f8(I91, I92, I93, I94, I95, I96, I97) -> f6(I91, I92, I93, I94, I95, I96, I97) [1 <= I93] f8(I98, I99, I100, I101, I102, I103, I104) -> f2(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] f7(I105, I106, I107, I108, I109, I110, I111) -> f8(I105, I106, I107, I108, I109, I110, I111) f6(I112, I113, I114, I115, I116, I117, I118) -> f4(I112, I113, I114, I115, I116, I117, I118) f4(I119, I120, I121, I122, I123, I124, I125) -> f5(I119, I120, I121, I122, I123, I124, I125) f3(I126, I127, I128, I129, I130, I131, I132) -> f1(I126, I127, I128, I129, I130, I131, I132) f1(I133, I134, I135, I136, I137, I138, I139) -> f3(1 + I133, I134, I135, I136, I137, I138, I139) [I133 <= 100] f1(I140, I141, I142, I143, I144, I145, I146) -> f2(I140, I141, 0, I143, I144, I145, 1) [101 <= I140] The dependency graph for this problem is: 4 -> 8 -> 9, 10 9 -> 12 10 -> 12 12 -> 4 Where: 4) f10#(I21, I22, I23, I24, I25, I26, I27) -> f14#(I21, I22, I23, I24, I25, I26, I27) 8) f13#(I49, I50, I51, I52, I53, I54, I55) -> f12#(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] 9) f12#(I56, I57, I58, I59, I60, I61, I62) -> f9#(I56, I57, I58, I59, I60, I61, I62) 10) f12#(I63, I64, I65, I66, I67, I68, I69) -> f9#(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] 12) f9#(I77, I78, I79, I80, I81, I82, I83) -> f10#(I77, 1 + I78, I79, I80, I81, I82, I83) We have the following SCCs. DP problem for innermost termination. P = f3#(I126, I127, I128, I129, I130, I131, I132) -> f1#(I126, I127, I128, I129, I130, I131, I132) f1#(I133, I134, I135, I136, I137, I138, I139) -> f3#(1 + I133, I134, I135, I136, I137, I138, I139) [I133 <= 100] R = f16(x1, x2, x3, x4, x5, x6, x7) -> f15(x1, x2, x3, x4, x5, x6, x7) f15(I0, I1, I2, I3, I4, I5, I6) -> f3(1, I1, I2, I3, rnd5, -1, I6) [rnd5 = -1] f11(I7, I8, I9, I10, I11, I12, I13) -> f10(I7, 1, 1, I10, I11, I12, I13) [I13 <= 99] f11(I14, I15, I16, I17, I18, I19, I20) -> f4(I14, I15, I16, I17, I18, I19, I20) [100 <= I20] f10(I21, I22, I23, I24, I25, I26, I27) -> f14(I21, I22, I23, I24, I25, I26, I27) f14(I28, I29, I30, I31, I32, I33, I34) -> f13(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] f14(I35, I36, I37, I38, I39, I40, I41) -> f7(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] f13(I42, I43, I44, I45, I46, I47, I48) -> f7(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] f13(I49, I50, I51, I52, I53, I54, I55) -> f12(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12(I56, I57, I58, I59, I60, I61, I62) -> f9(I56, I57, I58, I59, I60, I61, I62) f12(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f2(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, I71, I72, I73, I74, I75, I76) f9(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, 1 + I78, I79, I80, I81, I82, I83) f8(I84, I85, I86, I87, I88, I89, I90) -> f6(I84, I85, I86, I87, I88, I89, I90) [1 + I86 <= 0] f8(I91, I92, I93, I94, I95, I96, I97) -> f6(I91, I92, I93, I94, I95, I96, I97) [1 <= I93] f8(I98, I99, I100, I101, I102, I103, I104) -> f2(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] f7(I105, I106, I107, I108, I109, I110, I111) -> f8(I105, I106, I107, I108, I109, I110, I111) f6(I112, I113, I114, I115, I116, I117, I118) -> f4(I112, I113, I114, I115, I116, I117, I118) f4(I119, I120, I121, I122, I123, I124, I125) -> f5(I119, I120, I121, I122, I123, I124, I125) f3(I126, I127, I128, I129, I130, I131, I132) -> f1(I126, I127, I128, I129, I130, I131, I132) f1(I133, I134, I135, I136, I137, I138, I139) -> f3(1 + I133, I134, I135, I136, I137, I138, I139) [I133 <= 100] f1(I140, I141, I142, I143, I144, I145, I146) -> f2(I140, I141, 0, I143, I144, I145, 1) [101 <= I140] We use the reverse value criterion with the projection function NU: NU[f1#(z1,z2,z3,z4,z5,z6,z7)] = 100 + -1 * z1 NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = 100 + -1 * z1 This gives the following inequalities: ==> 100 + -1 * I126 >= 100 + -1 * I126 I133 <= 100 ==> 100 + -1 * I133 > 100 + -1 * (1 + I133) with 100 + -1 * I133 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f3#(I126, I127, I128, I129, I130, I131, I132) -> f1#(I126, I127, I128, I129, I130, I131, I132) R = f16(x1, x2, x3, x4, x5, x6, x7) -> f15(x1, x2, x3, x4, x5, x6, x7) f15(I0, I1, I2, I3, I4, I5, I6) -> f3(1, I1, I2, I3, rnd5, -1, I6) [rnd5 = -1] f11(I7, I8, I9, I10, I11, I12, I13) -> f10(I7, 1, 1, I10, I11, I12, I13) [I13 <= 99] f11(I14, I15, I16, I17, I18, I19, I20) -> f4(I14, I15, I16, I17, I18, I19, I20) [100 <= I20] f10(I21, I22, I23, I24, I25, I26, I27) -> f14(I21, I22, I23, I24, I25, I26, I27) f14(I28, I29, I30, I31, I32, I33, I34) -> f13(I28, I29, I30, I31, I32, I33, I34) [I29 <= 99] f14(I35, I36, I37, I38, I39, I40, I41) -> f7(I35, I36, I37, I38, I39, I40, I41) [100 <= I36] f13(I42, I43, I44, I45, I46, I47, I48) -> f7(I42, I43, I44, I45, I46, I47, I48) [101 - I48 <= I43] f13(I49, I50, I51, I52, I53, I54, I55) -> f12(I49, I50, I51, I52, I53, I54, I55) [I50 <= 100 - I55] f12(I56, I57, I58, I59, I60, I61, I62) -> f9(I56, I57, I58, I59, I60, I61, I62) f12(I63, I64, I65, I66, I67, I68, I69) -> f9(I63, I64, 0, rnd4, I67, I68, I69) [rnd4 = rnd4] f2(I70, I71, I72, I73, I74, I75, I76) -> f11(I70, I71, I72, I73, I74, I75, I76) f9(I77, I78, I79, I80, I81, I82, I83) -> f10(I77, 1 + I78, I79, I80, I81, I82, I83) f8(I84, I85, I86, I87, I88, I89, I90) -> f6(I84, I85, I86, I87, I88, I89, I90) [1 + I86 <= 0] f8(I91, I92, I93, I94, I95, I96, I97) -> f6(I91, I92, I93, I94, I95, I96, I97) [1 <= I93] f8(I98, I99, I100, I101, I102, I103, I104) -> f2(I98, I99, I100, I101, I102, I103, 1 + I104) [0 <= I100 /\ I100 <= 0] f7(I105, I106, I107, I108, I109, I110, I111) -> f8(I105, I106, I107, I108, I109, I110, I111) f6(I112, I113, I114, I115, I116, I117, I118) -> f4(I112, I113, I114, I115, I116, I117, I118) f4(I119, I120, I121, I122, I123, I124, I125) -> f5(I119, I120, I121, I122, I123, I124, I125) f3(I126, I127, I128, I129, I130, I131, I132) -> f1(I126, I127, I128, I129, I130, I131, I132) f1(I133, I134, I135, I136, I137, I138, I139) -> f3(1 + I133, I134, I135, I136, I137, I138, I139) [I133 <= 100] f1(I140, I141, I142, I143, I144, I145, I146) -> f2(I140, I141, 0, I143, I144, I145, 1) [101 <= I140] The dependency graph for this problem is: 18 -> Where: 18) f3#(I126, I127, I128, I129, I130, I131, I132) -> f1#(I126, I127, I128, I129, I130, I131, I132) We have the following SCCs.