/export/starexec/sandbox2/solver/bin/starexec_run_Transition /export/starexec/sandbox2/benchmark/theBenchmark.smt2 /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES DP problem for innermost termination. P = f14#(x1, x2, x3, x4, x5) -> f13#(x1, x2, x3, x4, x5) f13#(I0, I1, I2, I3, I4) -> f4#(0, I1, I2, I3, 400) f5#(I5, I6, I7, I8, I9) -> f7#(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5#(I10, I11, I12, I13, I14) -> f4#(1 + I10, I11, I12, I13, I14) [5 <= I11] f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8#(I20, I21, I22, I23, I24) -> f3#(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11#(I30, I31, I32, I33, I34) -> f7#(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) f12#(I40, I41, I42, I43, I44) -> f2#(I40, I41, I42, I43, I44) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) f7#(I60, I61, I62, I63, I64) -> f8#(I60, I61, I62, I63, I64) f3#(I70, I71, I72, I73, I74) -> f5#(I70, I71, I72, I73, I74) f4#(I75, I76, I77, I78, I79) -> f1#(I75, I76, I77, I78, I79) f1#(I80, I81, I82, I83, I84) -> f3#(I80, 0, I82, I83, I84) [1 + I80 <= 5] f1#(I85, I86, I87, I88, I89) -> f2#(I85, I86, I87, I88, I89) [5 <= I85] R = f14(x1, x2, x3, x4, x5) -> f13(x1, x2, x3, x4, x5) f13(I0, I1, I2, I3, I4) -> f4(0, I1, I2, I3, 400) f5(I5, I6, I7, I8, I9) -> f7(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5(I10, I11, I12, I13, I14) -> f4(1 + I10, I11, I12, I13, I14) [5 <= I11] f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8(I20, I21, I22, I23, I24) -> f3(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11(I25, I26, I27, I28, I29) -> f12(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11(I30, I31, I32, I33, I34) -> f7(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12(I35, I36, I37, I38, I39) -> f9(I35, I36, I37, I38, I39) f12(I40, I41, I42, I43, I44) -> f2(I40, I41, I42, I43, I44) f12(I45, I46, I47, I48, I49) -> f9(I45, I46, I47, I48, I49) f10(I50, I51, I52, I53, I54) -> f11(I50, I51, I52, I53, I54) f9(I55, I56, I57, I58, I59) -> f10(I55, I56, I57, 1 + I58, I59) f7(I60, I61, I62, I63, I64) -> f8(I60, I61, I62, I63, I64) f2(I65, I66, I67, I68, I69) -> f6(I65, I66, I67, I68, I69) f3(I70, I71, I72, I73, I74) -> f5(I70, I71, I72, I73, I74) f4(I75, I76, I77, I78, I79) -> f1(I75, I76, I77, I78, I79) f1(I80, I81, I82, I83, I84) -> f3(I80, 0, I82, I83, I84) [1 + I80 <= 5] f1(I85, I86, I87, I88, I89) -> f2(I85, I86, I87, I88, I89) [5 <= I85] The dependency graph for this problem is: 0 -> 1 1 -> 15 2 -> 13 3 -> 15 4 -> 11 5 -> 14 6 -> 8, 9, 10 7 -> 13 8 -> 12 9 -> 10 -> 12 11 -> 6, 7 12 -> 11 13 -> 4, 5 14 -> 2, 3 15 -> 16, 17 16 -> 14 17 -> Where: 0) f14#(x1, x2, x3, x4, x5) -> f13#(x1, x2, x3, x4, x5) 1) f13#(I0, I1, I2, I3, I4) -> f4#(0, I1, I2, I3, 400) 2) f5#(I5, I6, I7, I8, I9) -> f7#(I5, I6, 0, I8, I9) [1 + I6 <= 5] 3) f5#(I10, I11, I12, I13, I14) -> f4#(1 + I10, I11, I12, I13, I14) [5 <= I11] 4) f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, 0, I19) [1 + I17 <= 5] 5) f8#(I20, I21, I22, I23, I24) -> f3#(I20, 1 + I21, I22, I23, I24) [5 <= I22] 6) f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] 7) f11#(I30, I31, I32, I33, I34) -> f7#(I30, I31, 1 + I32, I33, I34) [5 <= I33] 8) f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) 9) f12#(I40, I41, I42, I43, I44) -> f2#(I40, I41, I42, I43, I44) 10) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) 11) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) 12) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) 13) f7#(I60, I61, I62, I63, I64) -> f8#(I60, I61, I62, I63, I64) 14) f3#(I70, I71, I72, I73, I74) -> f5#(I70, I71, I72, I73, I74) 15) f4#(I75, I76, I77, I78, I79) -> f1#(I75, I76, I77, I78, I79) 16) f1#(I80, I81, I82, I83, I84) -> f3#(I80, 0, I82, I83, I84) [1 + I80 <= 5] 17) f1#(I85, I86, I87, I88, I89) -> f2#(I85, I86, I87, I88, I89) [5 <= I85] We have the following SCCs. { 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16 } DP problem for innermost termination. P = f5#(I5, I6, I7, I8, I9) -> f7#(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5#(I10, I11, I12, I13, I14) -> f4#(1 + I10, I11, I12, I13, I14) [5 <= I11] f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8#(I20, I21, I22, I23, I24) -> f3#(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11#(I30, I31, I32, I33, I34) -> f7#(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) f7#(I60, I61, I62, I63, I64) -> f8#(I60, I61, I62, I63, I64) f3#(I70, I71, I72, I73, I74) -> f5#(I70, I71, I72, I73, I74) f4#(I75, I76, I77, I78, I79) -> f1#(I75, I76, I77, I78, I79) f1#(I80, I81, I82, I83, I84) -> f3#(I80, 0, I82, I83, I84) [1 + I80 <= 5] R = f14(x1, x2, x3, x4, x5) -> f13(x1, x2, x3, x4, x5) f13(I0, I1, I2, I3, I4) -> f4(0, I1, I2, I3, 400) f5(I5, I6, I7, I8, I9) -> f7(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5(I10, I11, I12, I13, I14) -> f4(1 + I10, I11, I12, I13, I14) [5 <= I11] f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8(I20, I21, I22, I23, I24) -> f3(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11(I25, I26, I27, I28, I29) -> f12(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11(I30, I31, I32, I33, I34) -> f7(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12(I35, I36, I37, I38, I39) -> f9(I35, I36, I37, I38, I39) f12(I40, I41, I42, I43, I44) -> f2(I40, I41, I42, I43, I44) f12(I45, I46, I47, I48, I49) -> f9(I45, I46, I47, I48, I49) f10(I50, I51, I52, I53, I54) -> f11(I50, I51, I52, I53, I54) f9(I55, I56, I57, I58, I59) -> f10(I55, I56, I57, 1 + I58, I59) f7(I60, I61, I62, I63, I64) -> f8(I60, I61, I62, I63, I64) f2(I65, I66, I67, I68, I69) -> f6(I65, I66, I67, I68, I69) f3(I70, I71, I72, I73, I74) -> f5(I70, I71, I72, I73, I74) f4(I75, I76, I77, I78, I79) -> f1(I75, I76, I77, I78, I79) f1(I80, I81, I82, I83, I84) -> f3(I80, 0, I82, I83, I84) [1 + I80 <= 5] f1(I85, I86, I87, I88, I89) -> f2(I85, I86, I87, I88, I89) [5 <= I85] We use the extended value criterion with the projection function NU: NU[f1#(x0,x1,x2,x3,x4)] = -x0 + 4 NU[f9#(x0,x1,x2,x3,x4)] = -x0 + 3 NU[f12#(x0,x1,x2,x3,x4)] = -x0 + 3 NU[f11#(x0,x1,x2,x3,x4)] = -x0 + 3 NU[f3#(x0,x1,x2,x3,x4)] = -x0 + 3 NU[f10#(x0,x1,x2,x3,x4)] = -x0 + 3 NU[f8#(x0,x1,x2,x3,x4)] = -x0 + 3 NU[f4#(x0,x1,x2,x3,x4)] = -x0 + 4 NU[f7#(x0,x1,x2,x3,x4)] = -x0 + 3 NU[f5#(x0,x1,x2,x3,x4)] = -x0 + 3 This gives the following inequalities: 1 + I6 <= 5 ==> -I5 + 3 >= -I5 + 3 5 <= I11 ==> -I10 + 3 >= -(1 + I10) + 4 1 + I17 <= 5 ==> -I15 + 3 >= -I15 + 3 5 <= I22 ==> -I20 + 3 >= -I20 + 3 1 + I28 <= 5 ==> -I25 + 3 >= -I25 + 3 5 <= I33 ==> -I30 + 3 >= -I30 + 3 ==> -I35 + 3 >= -I35 + 3 ==> -I45 + 3 >= -I45 + 3 ==> -I50 + 3 >= -I50 + 3 ==> -I55 + 3 >= -I55 + 3 ==> -I60 + 3 >= -I60 + 3 ==> -I70 + 3 >= -I70 + 3 ==> -I75 + 4 >= -I75 + 4 1 + I80 <= 5 ==> -I80 + 4 > -I80 + 3 with -I80 + 4 >= 0 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f5#(I5, I6, I7, I8, I9) -> f7#(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5#(I10, I11, I12, I13, I14) -> f4#(1 + I10, I11, I12, I13, I14) [5 <= I11] f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8#(I20, I21, I22, I23, I24) -> f3#(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11#(I30, I31, I32, I33, I34) -> f7#(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) f7#(I60, I61, I62, I63, I64) -> f8#(I60, I61, I62, I63, I64) f3#(I70, I71, I72, I73, I74) -> f5#(I70, I71, I72, I73, I74) f4#(I75, I76, I77, I78, I79) -> f1#(I75, I76, I77, I78, I79) R = f14(x1, x2, x3, x4, x5) -> f13(x1, x2, x3, x4, x5) f13(I0, I1, I2, I3, I4) -> f4(0, I1, I2, I3, 400) f5(I5, I6, I7, I8, I9) -> f7(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5(I10, I11, I12, I13, I14) -> f4(1 + I10, I11, I12, I13, I14) [5 <= I11] f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8(I20, I21, I22, I23, I24) -> f3(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11(I25, I26, I27, I28, I29) -> f12(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11(I30, I31, I32, I33, I34) -> f7(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12(I35, I36, I37, I38, I39) -> f9(I35, I36, I37, I38, I39) f12(I40, I41, I42, I43, I44) -> f2(I40, I41, I42, I43, I44) f12(I45, I46, I47, I48, I49) -> f9(I45, I46, I47, I48, I49) f10(I50, I51, I52, I53, I54) -> f11(I50, I51, I52, I53, I54) f9(I55, I56, I57, I58, I59) -> f10(I55, I56, I57, 1 + I58, I59) f7(I60, I61, I62, I63, I64) -> f8(I60, I61, I62, I63, I64) f2(I65, I66, I67, I68, I69) -> f6(I65, I66, I67, I68, I69) f3(I70, I71, I72, I73, I74) -> f5(I70, I71, I72, I73, I74) f4(I75, I76, I77, I78, I79) -> f1(I75, I76, I77, I78, I79) f1(I80, I81, I82, I83, I84) -> f3(I80, 0, I82, I83, I84) [1 + I80 <= 5] f1(I85, I86, I87, I88, I89) -> f2(I85, I86, I87, I88, I89) [5 <= I85] The dependency graph for this problem is: 2 -> 13 3 -> 15 4 -> 11 5 -> 14 6 -> 8, 10 7 -> 13 8 -> 12 10 -> 12 11 -> 6, 7 12 -> 11 13 -> 4, 5 14 -> 2, 3 15 -> Where: 2) f5#(I5, I6, I7, I8, I9) -> f7#(I5, I6, 0, I8, I9) [1 + I6 <= 5] 3) f5#(I10, I11, I12, I13, I14) -> f4#(1 + I10, I11, I12, I13, I14) [5 <= I11] 4) f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, 0, I19) [1 + I17 <= 5] 5) f8#(I20, I21, I22, I23, I24) -> f3#(I20, 1 + I21, I22, I23, I24) [5 <= I22] 6) f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] 7) f11#(I30, I31, I32, I33, I34) -> f7#(I30, I31, 1 + I32, I33, I34) [5 <= I33] 8) f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) 10) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) 11) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) 12) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) 13) f7#(I60, I61, I62, I63, I64) -> f8#(I60, I61, I62, I63, I64) 14) f3#(I70, I71, I72, I73, I74) -> f5#(I70, I71, I72, I73, I74) 15) f4#(I75, I76, I77, I78, I79) -> f1#(I75, I76, I77, I78, I79) We have the following SCCs. { 2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14 } DP problem for innermost termination. P = f5#(I5, I6, I7, I8, I9) -> f7#(I5, I6, 0, I8, I9) [1 + I6 <= 5] f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8#(I20, I21, I22, I23, I24) -> f3#(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11#(I30, I31, I32, I33, I34) -> f7#(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) f7#(I60, I61, I62, I63, I64) -> f8#(I60, I61, I62, I63, I64) f3#(I70, I71, I72, I73, I74) -> f5#(I70, I71, I72, I73, I74) R = f14(x1, x2, x3, x4, x5) -> f13(x1, x2, x3, x4, x5) f13(I0, I1, I2, I3, I4) -> f4(0, I1, I2, I3, 400) f5(I5, I6, I7, I8, I9) -> f7(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5(I10, I11, I12, I13, I14) -> f4(1 + I10, I11, I12, I13, I14) [5 <= I11] f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8(I20, I21, I22, I23, I24) -> f3(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11(I25, I26, I27, I28, I29) -> f12(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11(I30, I31, I32, I33, I34) -> f7(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12(I35, I36, I37, I38, I39) -> f9(I35, I36, I37, I38, I39) f12(I40, I41, I42, I43, I44) -> f2(I40, I41, I42, I43, I44) f12(I45, I46, I47, I48, I49) -> f9(I45, I46, I47, I48, I49) f10(I50, I51, I52, I53, I54) -> f11(I50, I51, I52, I53, I54) f9(I55, I56, I57, I58, I59) -> f10(I55, I56, I57, 1 + I58, I59) f7(I60, I61, I62, I63, I64) -> f8(I60, I61, I62, I63, I64) f2(I65, I66, I67, I68, I69) -> f6(I65, I66, I67, I68, I69) f3(I70, I71, I72, I73, I74) -> f5(I70, I71, I72, I73, I74) f4(I75, I76, I77, I78, I79) -> f1(I75, I76, I77, I78, I79) f1(I80, I81, I82, I83, I84) -> f3(I80, 0, I82, I83, I84) [1 + I80 <= 5] f1(I85, I86, I87, I88, I89) -> f2(I85, I86, I87, I88, I89) [5 <= I85] We use the extended value criterion with the projection function NU: NU[f9#(x0,x1,x2,x3,x4)] = -x1 + 3 NU[f12#(x0,x1,x2,x3,x4)] = -x1 + 3 NU[f11#(x0,x1,x2,x3,x4)] = -x1 + 3 NU[f3#(x0,x1,x2,x3,x4)] = -x1 + 4 NU[f10#(x0,x1,x2,x3,x4)] = -x1 + 3 NU[f8#(x0,x1,x2,x3,x4)] = -x1 + 3 NU[f7#(x0,x1,x2,x3,x4)] = -x1 + 3 NU[f5#(x0,x1,x2,x3,x4)] = -x1 + 4 This gives the following inequalities: 1 + I6 <= 5 ==> -I6 + 4 > -I6 + 3 with -I6 + 4 >= 0 1 + I17 <= 5 ==> -I16 + 3 >= -I16 + 3 5 <= I22 ==> -I21 + 3 >= -(1 + I21) + 4 1 + I28 <= 5 ==> -I26 + 3 >= -I26 + 3 5 <= I33 ==> -I31 + 3 >= -I31 + 3 ==> -I36 + 3 >= -I36 + 3 ==> -I46 + 3 >= -I46 + 3 ==> -I51 + 3 >= -I51 + 3 ==> -I56 + 3 >= -I56 + 3 ==> -I61 + 3 >= -I61 + 3 ==> -I71 + 4 >= -I71 + 4 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8#(I20, I21, I22, I23, I24) -> f3#(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11#(I30, I31, I32, I33, I34) -> f7#(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) f7#(I60, I61, I62, I63, I64) -> f8#(I60, I61, I62, I63, I64) f3#(I70, I71, I72, I73, I74) -> f5#(I70, I71, I72, I73, I74) R = f14(x1, x2, x3, x4, x5) -> f13(x1, x2, x3, x4, x5) f13(I0, I1, I2, I3, I4) -> f4(0, I1, I2, I3, 400) f5(I5, I6, I7, I8, I9) -> f7(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5(I10, I11, I12, I13, I14) -> f4(1 + I10, I11, I12, I13, I14) [5 <= I11] f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8(I20, I21, I22, I23, I24) -> f3(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11(I25, I26, I27, I28, I29) -> f12(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11(I30, I31, I32, I33, I34) -> f7(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12(I35, I36, I37, I38, I39) -> f9(I35, I36, I37, I38, I39) f12(I40, I41, I42, I43, I44) -> f2(I40, I41, I42, I43, I44) f12(I45, I46, I47, I48, I49) -> f9(I45, I46, I47, I48, I49) f10(I50, I51, I52, I53, I54) -> f11(I50, I51, I52, I53, I54) f9(I55, I56, I57, I58, I59) -> f10(I55, I56, I57, 1 + I58, I59) f7(I60, I61, I62, I63, I64) -> f8(I60, I61, I62, I63, I64) f2(I65, I66, I67, I68, I69) -> f6(I65, I66, I67, I68, I69) f3(I70, I71, I72, I73, I74) -> f5(I70, I71, I72, I73, I74) f4(I75, I76, I77, I78, I79) -> f1(I75, I76, I77, I78, I79) f1(I80, I81, I82, I83, I84) -> f3(I80, 0, I82, I83, I84) [1 + I80 <= 5] f1(I85, I86, I87, I88, I89) -> f2(I85, I86, I87, I88, I89) [5 <= I85] The dependency graph for this problem is: 4 -> 11 5 -> 14 6 -> 8, 10 7 -> 13 8 -> 12 10 -> 12 11 -> 6, 7 12 -> 11 13 -> 4, 5 14 -> Where: 4) f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, 0, I19) [1 + I17 <= 5] 5) f8#(I20, I21, I22, I23, I24) -> f3#(I20, 1 + I21, I22, I23, I24) [5 <= I22] 6) f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] 7) f11#(I30, I31, I32, I33, I34) -> f7#(I30, I31, 1 + I32, I33, I34) [5 <= I33] 8) f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) 10) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) 11) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) 12) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) 13) f7#(I60, I61, I62, I63, I64) -> f8#(I60, I61, I62, I63, I64) 14) f3#(I70, I71, I72, I73, I74) -> f5#(I70, I71, I72, I73, I74) We have the following SCCs. { 4, 6, 7, 8, 10, 11, 12, 13 } DP problem for innermost termination. P = f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, 0, I19) [1 + I17 <= 5] f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11#(I30, I31, I32, I33, I34) -> f7#(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) f7#(I60, I61, I62, I63, I64) -> f8#(I60, I61, I62, I63, I64) R = f14(x1, x2, x3, x4, x5) -> f13(x1, x2, x3, x4, x5) f13(I0, I1, I2, I3, I4) -> f4(0, I1, I2, I3, 400) f5(I5, I6, I7, I8, I9) -> f7(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5(I10, I11, I12, I13, I14) -> f4(1 + I10, I11, I12, I13, I14) [5 <= I11] f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8(I20, I21, I22, I23, I24) -> f3(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11(I25, I26, I27, I28, I29) -> f12(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11(I30, I31, I32, I33, I34) -> f7(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12(I35, I36, I37, I38, I39) -> f9(I35, I36, I37, I38, I39) f12(I40, I41, I42, I43, I44) -> f2(I40, I41, I42, I43, I44) f12(I45, I46, I47, I48, I49) -> f9(I45, I46, I47, I48, I49) f10(I50, I51, I52, I53, I54) -> f11(I50, I51, I52, I53, I54) f9(I55, I56, I57, I58, I59) -> f10(I55, I56, I57, 1 + I58, I59) f7(I60, I61, I62, I63, I64) -> f8(I60, I61, I62, I63, I64) f2(I65, I66, I67, I68, I69) -> f6(I65, I66, I67, I68, I69) f3(I70, I71, I72, I73, I74) -> f5(I70, I71, I72, I73, I74) f4(I75, I76, I77, I78, I79) -> f1(I75, I76, I77, I78, I79) f1(I80, I81, I82, I83, I84) -> f3(I80, 0, I82, I83, I84) [1 + I80 <= 5] f1(I85, I86, I87, I88, I89) -> f2(I85, I86, I87, I88, I89) [5 <= I85] We use the extended value criterion with the projection function NU: NU[f9#(x0,x1,x2,x3,x4)] = -x2 + 3 NU[f7#(x0,x1,x2,x3,x4)] = -x2 + 4 NU[f12#(x0,x1,x2,x3,x4)] = -x2 + 3 NU[f11#(x0,x1,x2,x3,x4)] = -x2 + 3 NU[f10#(x0,x1,x2,x3,x4)] = -x2 + 3 NU[f8#(x0,x1,x2,x3,x4)] = -x2 + 4 This gives the following inequalities: 1 + I17 <= 5 ==> -I17 + 4 > -I17 + 3 with -I17 + 4 >= 0 1 + I28 <= 5 ==> -I27 + 3 >= -I27 + 3 5 <= I33 ==> -I32 + 3 >= -(1 + I32) + 4 ==> -I37 + 3 >= -I37 + 3 ==> -I47 + 3 >= -I47 + 3 ==> -I52 + 3 >= -I52 + 3 ==> -I57 + 3 >= -I57 + 3 ==> -I62 + 4 >= -I62 + 4 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11#(I30, I31, I32, I33, I34) -> f7#(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) f7#(I60, I61, I62, I63, I64) -> f8#(I60, I61, I62, I63, I64) R = f14(x1, x2, x3, x4, x5) -> f13(x1, x2, x3, x4, x5) f13(I0, I1, I2, I3, I4) -> f4(0, I1, I2, I3, 400) f5(I5, I6, I7, I8, I9) -> f7(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5(I10, I11, I12, I13, I14) -> f4(1 + I10, I11, I12, I13, I14) [5 <= I11] f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8(I20, I21, I22, I23, I24) -> f3(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11(I25, I26, I27, I28, I29) -> f12(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11(I30, I31, I32, I33, I34) -> f7(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12(I35, I36, I37, I38, I39) -> f9(I35, I36, I37, I38, I39) f12(I40, I41, I42, I43, I44) -> f2(I40, I41, I42, I43, I44) f12(I45, I46, I47, I48, I49) -> f9(I45, I46, I47, I48, I49) f10(I50, I51, I52, I53, I54) -> f11(I50, I51, I52, I53, I54) f9(I55, I56, I57, I58, I59) -> f10(I55, I56, I57, 1 + I58, I59) f7(I60, I61, I62, I63, I64) -> f8(I60, I61, I62, I63, I64) f2(I65, I66, I67, I68, I69) -> f6(I65, I66, I67, I68, I69) f3(I70, I71, I72, I73, I74) -> f5(I70, I71, I72, I73, I74) f4(I75, I76, I77, I78, I79) -> f1(I75, I76, I77, I78, I79) f1(I80, I81, I82, I83, I84) -> f3(I80, 0, I82, I83, I84) [1 + I80 <= 5] f1(I85, I86, I87, I88, I89) -> f2(I85, I86, I87, I88, I89) [5 <= I85] The dependency graph for this problem is: 6 -> 8, 10 7 -> 13 8 -> 12 10 -> 12 11 -> 6, 7 12 -> 11 13 -> Where: 6) f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] 7) f11#(I30, I31, I32, I33, I34) -> f7#(I30, I31, 1 + I32, I33, I34) [5 <= I33] 8) f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) 10) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) 11) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) 12) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) 13) f7#(I60, I61, I62, I63, I64) -> f8#(I60, I61, I62, I63, I64) We have the following SCCs. { 6, 8, 10, 11, 12 } DP problem for innermost termination. P = f11#(I25, I26, I27, I28, I29) -> f12#(I25, I26, I27, I28, I29) [1 + I28 <= 5] f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) R = f14(x1, x2, x3, x4, x5) -> f13(x1, x2, x3, x4, x5) f13(I0, I1, I2, I3, I4) -> f4(0, I1, I2, I3, 400) f5(I5, I6, I7, I8, I9) -> f7(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5(I10, I11, I12, I13, I14) -> f4(1 + I10, I11, I12, I13, I14) [5 <= I11] f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8(I20, I21, I22, I23, I24) -> f3(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11(I25, I26, I27, I28, I29) -> f12(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11(I30, I31, I32, I33, I34) -> f7(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12(I35, I36, I37, I38, I39) -> f9(I35, I36, I37, I38, I39) f12(I40, I41, I42, I43, I44) -> f2(I40, I41, I42, I43, I44) f12(I45, I46, I47, I48, I49) -> f9(I45, I46, I47, I48, I49) f10(I50, I51, I52, I53, I54) -> f11(I50, I51, I52, I53, I54) f9(I55, I56, I57, I58, I59) -> f10(I55, I56, I57, 1 + I58, I59) f7(I60, I61, I62, I63, I64) -> f8(I60, I61, I62, I63, I64) f2(I65, I66, I67, I68, I69) -> f6(I65, I66, I67, I68, I69) f3(I70, I71, I72, I73, I74) -> f5(I70, I71, I72, I73, I74) f4(I75, I76, I77, I78, I79) -> f1(I75, I76, I77, I78, I79) f1(I80, I81, I82, I83, I84) -> f3(I80, 0, I82, I83, I84) [1 + I80 <= 5] f1(I85, I86, I87, I88, I89) -> f2(I85, I86, I87, I88, I89) [5 <= I85] We use the extended value criterion with the projection function NU: NU[f10#(x0,x1,x2,x3,x4)] = -x3 + 4 NU[f9#(x0,x1,x2,x3,x4)] = -x3 + 3 NU[f12#(x0,x1,x2,x3,x4)] = -x3 + 3 NU[f11#(x0,x1,x2,x3,x4)] = -x3 + 4 This gives the following inequalities: 1 + I28 <= 5 ==> -I28 + 4 > -I28 + 3 with -I28 + 4 >= 0 ==> -I38 + 3 >= -I38 + 3 ==> -I48 + 3 >= -I48 + 3 ==> -I53 + 4 >= -I53 + 4 ==> -I58 + 3 >= -(1 + I58) + 4 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) R = f14(x1, x2, x3, x4, x5) -> f13(x1, x2, x3, x4, x5) f13(I0, I1, I2, I3, I4) -> f4(0, I1, I2, I3, 400) f5(I5, I6, I7, I8, I9) -> f7(I5, I6, 0, I8, I9) [1 + I6 <= 5] f5(I10, I11, I12, I13, I14) -> f4(1 + I10, I11, I12, I13, I14) [5 <= I11] f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, 0, I19) [1 + I17 <= 5] f8(I20, I21, I22, I23, I24) -> f3(I20, 1 + I21, I22, I23, I24) [5 <= I22] f11(I25, I26, I27, I28, I29) -> f12(I25, I26, I27, I28, I29) [1 + I28 <= 5] f11(I30, I31, I32, I33, I34) -> f7(I30, I31, 1 + I32, I33, I34) [5 <= I33] f12(I35, I36, I37, I38, I39) -> f9(I35, I36, I37, I38, I39) f12(I40, I41, I42, I43, I44) -> f2(I40, I41, I42, I43, I44) f12(I45, I46, I47, I48, I49) -> f9(I45, I46, I47, I48, I49) f10(I50, I51, I52, I53, I54) -> f11(I50, I51, I52, I53, I54) f9(I55, I56, I57, I58, I59) -> f10(I55, I56, I57, 1 + I58, I59) f7(I60, I61, I62, I63, I64) -> f8(I60, I61, I62, I63, I64) f2(I65, I66, I67, I68, I69) -> f6(I65, I66, I67, I68, I69) f3(I70, I71, I72, I73, I74) -> f5(I70, I71, I72, I73, I74) f4(I75, I76, I77, I78, I79) -> f1(I75, I76, I77, I78, I79) f1(I80, I81, I82, I83, I84) -> f3(I80, 0, I82, I83, I84) [1 + I80 <= 5] f1(I85, I86, I87, I88, I89) -> f2(I85, I86, I87, I88, I89) [5 <= I85] The dependency graph for this problem is: 8 -> 12 10 -> 12 11 -> 12 -> 11 Where: 8) f12#(I35, I36, I37, I38, I39) -> f9#(I35, I36, I37, I38, I39) 10) f12#(I45, I46, I47, I48, I49) -> f9#(I45, I46, I47, I48, I49) 11) f10#(I50, I51, I52, I53, I54) -> f11#(I50, I51, I52, I53, I54) 12) f9#(I55, I56, I57, I58, I59) -> f10#(I55, I56, I57, 1 + I58, I59) We have the following SCCs.