73.15/72.05 YES 73.15/72.05 73.15/72.05 DP problem for innermost termination. 73.15/72.05 P = 73.15/72.05 f11#(x1, x2, x3, x4, x5, x6, x7, x8) -> f10#(x1, x2, x3, x4, x5, x6, x7, x8) 73.15/72.05 f10#(I0, I1, I2, I3, I4, I5, I6, I7) -> f4#(I0, rnd2, rnd3, 35, 0, 10, I6, 285) [rnd2 = rnd3 /\ rnd3 = rnd3] 73.15/72.05 f6#(I8, I9, I10, I11, I12, I13, I14, I15) -> f8#(rnd1, I9, I10, I11, I12, I13, 1, I15) [rnd1 = rnd1 /\ 1 + I12 <= I13] 73.15/72.05 f8#(I24, I25, I26, I27, I28, I29, I30, I31) -> f7#(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.05 f7#(I32, I33, I34, I35, I36, I37, I38, I39) -> f8#(I40, I33, I34, I35, I36, I37, 1 + I38, I39) [I40 = I40 /\ 1 + I38 <= I33] 73.15/72.05 f7#(I41, I42, I43, I44, I45, I46, I47, I48) -> f5#(I41, I42, I43, I44, I45, I46, I47, I48) [I42 <= I47] 73.15/72.05 f4#(I49, I50, I51, I52, I53, I54, I55, I56) -> f6#(I49, I50, I51, I52, I53, I54, I55, I56) 73.15/72.05 f5#(I57, I58, I59, I60, I61, I62, I63, I64) -> f3#(I57, I58, I59, I60, I61, I62, I63, I64) 73.15/72.05 f5#(I65, I66, I67, I68, I69, I70, I71, I72) -> f2#(I65, -1 + I66, I67, I68, I69, I70, I71, I72) 73.15/72.05 f5#(I73, I74, I75, I76, I77, I78, I79, I80) -> f3#(I73, I74, I75, I76, I77, I78, I79, I80) 73.15/72.05 f2#(I81, I82, I83, I84, I85, I86, I87, I88) -> f4#(I81, I82, I83, I84, 1 + I85, I86, I87, I88) 73.15/72.05 f3#(I89, I90, I91, I92, I93, I94, I95, I96) -> f1#(I89, 1 + I90, I91, I92, I93, I94, I95, I96) [1 + I90 <= I92] 73.15/72.05 f3#(I97, I98, I99, I100, I101, I102, I103, I104) -> f1#(I97, I98, I99, I100, I101, I102, I103, I104) [I100 <= I98] 73.15/72.05 f1#(I105, I106, I107, I108, I109, I110, I111, I112) -> f2#(I105, I106, I107, I108, I109, I110, I111, I112) 73.15/72.05 R = 73.15/72.05 f11(x1, x2, x3, x4, x5, x6, x7, x8) -> f10(x1, x2, x3, x4, x5, x6, x7, x8) 73.15/72.05 f10(I0, I1, I2, I3, I4, I5, I6, I7) -> f4(I0, rnd2, rnd3, 35, 0, 10, I6, 285) [rnd2 = rnd3 /\ rnd3 = rnd3] 73.15/72.05 f6(I8, I9, I10, I11, I12, I13, I14, I15) -> f8(rnd1, I9, I10, I11, I12, I13, 1, I15) [rnd1 = rnd1 /\ 1 + I12 <= I13] 73.15/72.05 f6(I16, I17, I18, I19, I20, I21, I22, I23) -> f9(I16, I17, I18, I19, I20, I21, I22, I23) [I21 <= I20] 73.15/72.05 f8(I24, I25, I26, I27, I28, I29, I30, I31) -> f7(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.05 f7(I32, I33, I34, I35, I36, I37, I38, I39) -> f8(I40, I33, I34, I35, I36, I37, 1 + I38, I39) [I40 = I40 /\ 1 + I38 <= I33] 73.15/72.05 f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f5(I41, I42, I43, I44, I45, I46, I47, I48) [I42 <= I47] 73.15/72.05 f4(I49, I50, I51, I52, I53, I54, I55, I56) -> f6(I49, I50, I51, I52, I53, I54, I55, I56) 73.15/72.05 f5(I57, I58, I59, I60, I61, I62, I63, I64) -> f3(I57, I58, I59, I60, I61, I62, I63, I64) 73.15/72.05 f5(I65, I66, I67, I68, I69, I70, I71, I72) -> f2(I65, -1 + I66, I67, I68, I69, I70, I71, I72) 73.15/72.05 f5(I73, I74, I75, I76, I77, I78, I79, I80) -> f3(I73, I74, I75, I76, I77, I78, I79, I80) 73.15/72.05 f2(I81, I82, I83, I84, I85, I86, I87, I88) -> f4(I81, I82, I83, I84, 1 + I85, I86, I87, I88) 73.15/72.05 f3(I89, I90, I91, I92, I93, I94, I95, I96) -> f1(I89, 1 + I90, I91, I92, I93, I94, I95, I96) [1 + I90 <= I92] 73.15/72.05 f3(I97, I98, I99, I100, I101, I102, I103, I104) -> f1(I97, I98, I99, I100, I101, I102, I103, I104) [I100 <= I98] 73.15/72.05 f1(I105, I106, I107, I108, I109, I110, I111, I112) -> f2(I105, I106, I107, I108, I109, I110, I111, I112) 73.15/72.05 73.15/72.05 The dependency graph for this problem is: 73.15/72.05 0 -> 1 73.15/72.05 1 -> 6 73.15/72.05 2 -> 3 73.15/72.05 3 -> 4, 5 73.15/72.05 4 -> 3 73.15/72.05 5 -> 7, 8, 9 73.15/72.05 6 -> 2 73.15/72.05 7 -> 11, 12 73.15/72.05 8 -> 10 73.15/72.05 9 -> 11, 12 73.15/72.05 10 -> 6 73.15/72.05 11 -> 13 73.15/72.05 12 -> 13 73.15/72.05 13 -> 10 73.15/72.05 Where: 73.15/72.05 0) f11#(x1, x2, x3, x4, x5, x6, x7, x8) -> f10#(x1, x2, x3, x4, x5, x6, x7, x8) 73.15/72.05 1) f10#(I0, I1, I2, I3, I4, I5, I6, I7) -> f4#(I0, rnd2, rnd3, 35, 0, 10, I6, 285) [rnd2 = rnd3 /\ rnd3 = rnd3] 73.15/72.05 2) f6#(I8, I9, I10, I11, I12, I13, I14, I15) -> f8#(rnd1, I9, I10, I11, I12, I13, 1, I15) [rnd1 = rnd1 /\ 1 + I12 <= I13] 73.15/72.05 3) f8#(I24, I25, I26, I27, I28, I29, I30, I31) -> f7#(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.05 4) f7#(I32, I33, I34, I35, I36, I37, I38, I39) -> f8#(I40, I33, I34, I35, I36, I37, 1 + I38, I39) [I40 = I40 /\ 1 + I38 <= I33] 73.15/72.05 5) f7#(I41, I42, I43, I44, I45, I46, I47, I48) -> f5#(I41, I42, I43, I44, I45, I46, I47, I48) [I42 <= I47] 73.15/72.05 6) f4#(I49, I50, I51, I52, I53, I54, I55, I56) -> f6#(I49, I50, I51, I52, I53, I54, I55, I56) 73.15/72.05 7) f5#(I57, I58, I59, I60, I61, I62, I63, I64) -> f3#(I57, I58, I59, I60, I61, I62, I63, I64) 73.15/72.05 8) f5#(I65, I66, I67, I68, I69, I70, I71, I72) -> f2#(I65, -1 + I66, I67, I68, I69, I70, I71, I72) 73.15/72.05 9) f5#(I73, I74, I75, I76, I77, I78, I79, I80) -> f3#(I73, I74, I75, I76, I77, I78, I79, I80) 73.15/72.05 10) f2#(I81, I82, I83, I84, I85, I86, I87, I88) -> f4#(I81, I82, I83, I84, 1 + I85, I86, I87, I88) 73.15/72.05 11) f3#(I89, I90, I91, I92, I93, I94, I95, I96) -> f1#(I89, 1 + I90, I91, I92, I93, I94, I95, I96) [1 + I90 <= I92] 73.15/72.05 12) f3#(I97, I98, I99, I100, I101, I102, I103, I104) -> f1#(I97, I98, I99, I100, I101, I102, I103, I104) [I100 <= I98] 73.15/72.05 13) f1#(I105, I106, I107, I108, I109, I110, I111, I112) -> f2#(I105, I106, I107, I108, I109, I110, I111, I112) 73.15/72.05 73.15/72.05 We have the following SCCs. 73.15/72.05 { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 } 73.15/72.05 73.15/72.05 DP problem for innermost termination. 73.15/72.05 P = 73.15/72.05 f6#(I8, I9, I10, I11, I12, I13, I14, I15) -> f8#(rnd1, I9, I10, I11, I12, I13, 1, I15) [rnd1 = rnd1 /\ 1 + I12 <= I13] 73.15/72.05 f8#(I24, I25, I26, I27, I28, I29, I30, I31) -> f7#(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.05 f7#(I32, I33, I34, I35, I36, I37, I38, I39) -> f8#(I40, I33, I34, I35, I36, I37, 1 + I38, I39) [I40 = I40 /\ 1 + I38 <= I33] 73.15/72.05 f7#(I41, I42, I43, I44, I45, I46, I47, I48) -> f5#(I41, I42, I43, I44, I45, I46, I47, I48) [I42 <= I47] 73.15/72.05 f4#(I49, I50, I51, I52, I53, I54, I55, I56) -> f6#(I49, I50, I51, I52, I53, I54, I55, I56) 73.15/72.05 f5#(I57, I58, I59, I60, I61, I62, I63, I64) -> f3#(I57, I58, I59, I60, I61, I62, I63, I64) 73.15/72.05 f5#(I65, I66, I67, I68, I69, I70, I71, I72) -> f2#(I65, -1 + I66, I67, I68, I69, I70, I71, I72) 73.15/72.05 f5#(I73, I74, I75, I76, I77, I78, I79, I80) -> f3#(I73, I74, I75, I76, I77, I78, I79, I80) 73.15/72.05 f2#(I81, I82, I83, I84, I85, I86, I87, I88) -> f4#(I81, I82, I83, I84, 1 + I85, I86, I87, I88) 73.15/72.05 f3#(I89, I90, I91, I92, I93, I94, I95, I96) -> f1#(I89, 1 + I90, I91, I92, I93, I94, I95, I96) [1 + I90 <= I92] 73.15/72.05 f3#(I97, I98, I99, I100, I101, I102, I103, I104) -> f1#(I97, I98, I99, I100, I101, I102, I103, I104) [I100 <= I98] 73.15/72.05 f1#(I105, I106, I107, I108, I109, I110, I111, I112) -> f2#(I105, I106, I107, I108, I109, I110, I111, I112) 73.15/72.05 R = 73.15/72.05 f11(x1, x2, x3, x4, x5, x6, x7, x8) -> f10(x1, x2, x3, x4, x5, x6, x7, x8) 73.15/72.05 f10(I0, I1, I2, I3, I4, I5, I6, I7) -> f4(I0, rnd2, rnd3, 35, 0, 10, I6, 285) [rnd2 = rnd3 /\ rnd3 = rnd3] 73.15/72.05 f6(I8, I9, I10, I11, I12, I13, I14, I15) -> f8(rnd1, I9, I10, I11, I12, I13, 1, I15) [rnd1 = rnd1 /\ 1 + I12 <= I13] 73.15/72.05 f6(I16, I17, I18, I19, I20, I21, I22, I23) -> f9(I16, I17, I18, I19, I20, I21, I22, I23) [I21 <= I20] 73.15/72.05 f8(I24, I25, I26, I27, I28, I29, I30, I31) -> f7(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.05 f7(I32, I33, I34, I35, I36, I37, I38, I39) -> f8(I40, I33, I34, I35, I36, I37, 1 + I38, I39) [I40 = I40 /\ 1 + I38 <= I33] 73.15/72.05 f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f5(I41, I42, I43, I44, I45, I46, I47, I48) [I42 <= I47] 73.15/72.05 f4(I49, I50, I51, I52, I53, I54, I55, I56) -> f6(I49, I50, I51, I52, I53, I54, I55, I56) 73.15/72.05 f5(I57, I58, I59, I60, I61, I62, I63, I64) -> f3(I57, I58, I59, I60, I61, I62, I63, I64) 73.15/72.05 f5(I65, I66, I67, I68, I69, I70, I71, I72) -> f2(I65, -1 + I66, I67, I68, I69, I70, I71, I72) 73.15/72.05 f5(I73, I74, I75, I76, I77, I78, I79, I80) -> f3(I73, I74, I75, I76, I77, I78, I79, I80) 73.15/72.05 f2(I81, I82, I83, I84, I85, I86, I87, I88) -> f4(I81, I82, I83, I84, 1 + I85, I86, I87, I88) 73.15/72.05 f3(I89, I90, I91, I92, I93, I94, I95, I96) -> f1(I89, 1 + I90, I91, I92, I93, I94, I95, I96) [1 + I90 <= I92] 73.15/72.05 f3(I97, I98, I99, I100, I101, I102, I103, I104) -> f1(I97, I98, I99, I100, I101, I102, I103, I104) [I100 <= I98] 73.15/72.05 f1(I105, I106, I107, I108, I109, I110, I111, I112) -> f2(I105, I106, I107, I108, I109, I110, I111, I112) 73.15/72.05 73.15/72.05 We use the extended value criterion with the projection function NU: 73.15/72.05 NU[f1#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x4 + x5 73.15/72.05 NU[f2#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x4 + x5 73.15/72.05 NU[f3#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x4 + x5 73.15/72.05 NU[f4#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x4 + x5 + 1 73.15/72.05 NU[f5#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x4 + x5 73.15/72.05 NU[f7#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x4 + x5 73.15/72.05 NU[f8#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x4 + x5 73.15/72.05 NU[f6#(x0,x1,x2,x3,x4,x5,x6,x7)] = -x4 + x5 + 1 73.15/72.05 73.15/72.05 This gives the following inequalities: 73.15/72.05 rnd1 = rnd1 /\ 1 + I12 <= I13 ==> -I12 + I13 + 1 > -I12 + I13 with -I12 + I13 + 1 >= 0 73.15/72.05 ==> -I28 + I29 >= -I28 + I29 73.15/72.05 I40 = I40 /\ 1 + I38 <= I33 ==> -I36 + I37 >= -I36 + I37 73.15/72.05 I42 <= I47 ==> -I45 + I46 >= -I45 + I46 73.15/72.05 ==> -I53 + I54 + 1 >= -I53 + I54 + 1 73.15/72.05 ==> -I61 + I62 >= -I61 + I62 73.15/72.05 ==> -I69 + I70 >= -I69 + I70 73.15/72.05 ==> -I77 + I78 >= -I77 + I78 73.15/72.05 ==> -I85 + I86 >= -(1 + I85) + I86 + 1 73.15/72.05 1 + I90 <= I92 ==> -I93 + I94 >= -I93 + I94 73.15/72.05 I100 <= I98 ==> -I101 + I102 >= -I101 + I102 73.15/72.05 ==> -I109 + I110 >= -I109 + I110 73.15/72.05 73.15/72.05 We remove all the strictly oriented dependency pairs. 73.15/72.05 73.15/72.05 DP problem for innermost termination. 73.15/72.05 P = 73.15/72.05 f8#(I24, I25, I26, I27, I28, I29, I30, I31) -> f7#(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.05 f7#(I32, I33, I34, I35, I36, I37, I38, I39) -> f8#(I40, I33, I34, I35, I36, I37, 1 + I38, I39) [I40 = I40 /\ 1 + I38 <= I33] 73.15/72.05 f7#(I41, I42, I43, I44, I45, I46, I47, I48) -> f5#(I41, I42, I43, I44, I45, I46, I47, I48) [I42 <= I47] 73.15/72.05 f4#(I49, I50, I51, I52, I53, I54, I55, I56) -> f6#(I49, I50, I51, I52, I53, I54, I55, I56) 73.15/72.05 f5#(I57, I58, I59, I60, I61, I62, I63, I64) -> f3#(I57, I58, I59, I60, I61, I62, I63, I64) 73.15/72.05 f5#(I65, I66, I67, I68, I69, I70, I71, I72) -> f2#(I65, -1 + I66, I67, I68, I69, I70, I71, I72) 73.15/72.05 f5#(I73, I74, I75, I76, I77, I78, I79, I80) -> f3#(I73, I74, I75, I76, I77, I78, I79, I80) 73.15/72.05 f2#(I81, I82, I83, I84, I85, I86, I87, I88) -> f4#(I81, I82, I83, I84, 1 + I85, I86, I87, I88) 73.15/72.05 f3#(I89, I90, I91, I92, I93, I94, I95, I96) -> f1#(I89, 1 + I90, I91, I92, I93, I94, I95, I96) [1 + I90 <= I92] 73.15/72.05 f3#(I97, I98, I99, I100, I101, I102, I103, I104) -> f1#(I97, I98, I99, I100, I101, I102, I103, I104) [I100 <= I98] 73.15/72.05 f1#(I105, I106, I107, I108, I109, I110, I111, I112) -> f2#(I105, I106, I107, I108, I109, I110, I111, I112) 73.15/72.05 R = 73.15/72.05 f11(x1, x2, x3, x4, x5, x6, x7, x8) -> f10(x1, x2, x3, x4, x5, x6, x7, x8) 73.15/72.05 f10(I0, I1, I2, I3, I4, I5, I6, I7) -> f4(I0, rnd2, rnd3, 35, 0, 10, I6, 285) [rnd2 = rnd3 /\ rnd3 = rnd3] 73.15/72.05 f6(I8, I9, I10, I11, I12, I13, I14, I15) -> f8(rnd1, I9, I10, I11, I12, I13, 1, I15) [rnd1 = rnd1 /\ 1 + I12 <= I13] 73.15/72.05 f6(I16, I17, I18, I19, I20, I21, I22, I23) -> f9(I16, I17, I18, I19, I20, I21, I22, I23) [I21 <= I20] 73.15/72.05 f8(I24, I25, I26, I27, I28, I29, I30, I31) -> f7(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.05 f7(I32, I33, I34, I35, I36, I37, I38, I39) -> f8(I40, I33, I34, I35, I36, I37, 1 + I38, I39) [I40 = I40 /\ 1 + I38 <= I33] 73.15/72.05 f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f5(I41, I42, I43, I44, I45, I46, I47, I48) [I42 <= I47] 73.15/72.05 f4(I49, I50, I51, I52, I53, I54, I55, I56) -> f6(I49, I50, I51, I52, I53, I54, I55, I56) 73.15/72.05 f5(I57, I58, I59, I60, I61, I62, I63, I64) -> f3(I57, I58, I59, I60, I61, I62, I63, I64) 73.15/72.05 f5(I65, I66, I67, I68, I69, I70, I71, I72) -> f2(I65, -1 + I66, I67, I68, I69, I70, I71, I72) 73.15/72.05 f5(I73, I74, I75, I76, I77, I78, I79, I80) -> f3(I73, I74, I75, I76, I77, I78, I79, I80) 73.15/72.05 f2(I81, I82, I83, I84, I85, I86, I87, I88) -> f4(I81, I82, I83, I84, 1 + I85, I86, I87, I88) 73.15/72.05 f3(I89, I90, I91, I92, I93, I94, I95, I96) -> f1(I89, 1 + I90, I91, I92, I93, I94, I95, I96) [1 + I90 <= I92] 73.15/72.05 f3(I97, I98, I99, I100, I101, I102, I103, I104) -> f1(I97, I98, I99, I100, I101, I102, I103, I104) [I100 <= I98] 73.15/72.05 f1(I105, I106, I107, I108, I109, I110, I111, I112) -> f2(I105, I106, I107, I108, I109, I110, I111, I112) 73.15/72.05 73.15/72.05 The dependency graph for this problem is: 73.15/72.05 3 -> 4, 5 73.15/72.05 4 -> 3 73.15/72.05 5 -> 7, 8, 9 73.15/72.05 6 -> 73.15/72.05 7 -> 11, 12 73.15/72.05 8 -> 10 73.15/72.05 9 -> 11, 12 73.15/72.05 10 -> 6 73.15/72.05 11 -> 13 73.15/72.05 12 -> 13 73.15/72.05 13 -> 10 73.15/72.05 Where: 73.15/72.05 3) f8#(I24, I25, I26, I27, I28, I29, I30, I31) -> f7#(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.05 4) f7#(I32, I33, I34, I35, I36, I37, I38, I39) -> f8#(I40, I33, I34, I35, I36, I37, 1 + I38, I39) [I40 = I40 /\ 1 + I38 <= I33] 73.15/72.05 5) f7#(I41, I42, I43, I44, I45, I46, I47, I48) -> f5#(I41, I42, I43, I44, I45, I46, I47, I48) [I42 <= I47] 73.15/72.05 6) f4#(I49, I50, I51, I52, I53, I54, I55, I56) -> f6#(I49, I50, I51, I52, I53, I54, I55, I56) 73.15/72.05 7) f5#(I57, I58, I59, I60, I61, I62, I63, I64) -> f3#(I57, I58, I59, I60, I61, I62, I63, I64) 73.15/72.05 8) f5#(I65, I66, I67, I68, I69, I70, I71, I72) -> f2#(I65, -1 + I66, I67, I68, I69, I70, I71, I72) 73.15/72.06 9) f5#(I73, I74, I75, I76, I77, I78, I79, I80) -> f3#(I73, I74, I75, I76, I77, I78, I79, I80) 73.15/72.06 10) f2#(I81, I82, I83, I84, I85, I86, I87, I88) -> f4#(I81, I82, I83, I84, 1 + I85, I86, I87, I88) 73.15/72.06 11) f3#(I89, I90, I91, I92, I93, I94, I95, I96) -> f1#(I89, 1 + I90, I91, I92, I93, I94, I95, I96) [1 + I90 <= I92] 73.15/72.06 12) f3#(I97, I98, I99, I100, I101, I102, I103, I104) -> f1#(I97, I98, I99, I100, I101, I102, I103, I104) [I100 <= I98] 73.15/72.06 13) f1#(I105, I106, I107, I108, I109, I110, I111, I112) -> f2#(I105, I106, I107, I108, I109, I110, I111, I112) 73.15/72.06 73.15/72.06 We have the following SCCs. 73.15/72.06 { 3, 4 } 73.15/72.06 73.15/72.06 DP problem for innermost termination. 73.15/72.06 P = 73.15/72.06 f8#(I24, I25, I26, I27, I28, I29, I30, I31) -> f7#(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.06 f7#(I32, I33, I34, I35, I36, I37, I38, I39) -> f8#(I40, I33, I34, I35, I36, I37, 1 + I38, I39) [I40 = I40 /\ 1 + I38 <= I33] 73.15/72.06 R = 73.15/72.06 f11(x1, x2, x3, x4, x5, x6, x7, x8) -> f10(x1, x2, x3, x4, x5, x6, x7, x8) 73.15/72.06 f10(I0, I1, I2, I3, I4, I5, I6, I7) -> f4(I0, rnd2, rnd3, 35, 0, 10, I6, 285) [rnd2 = rnd3 /\ rnd3 = rnd3] 73.15/72.06 f6(I8, I9, I10, I11, I12, I13, I14, I15) -> f8(rnd1, I9, I10, I11, I12, I13, 1, I15) [rnd1 = rnd1 /\ 1 + I12 <= I13] 73.15/72.06 f6(I16, I17, I18, I19, I20, I21, I22, I23) -> f9(I16, I17, I18, I19, I20, I21, I22, I23) [I21 <= I20] 73.15/72.06 f8(I24, I25, I26, I27, I28, I29, I30, I31) -> f7(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.06 f7(I32, I33, I34, I35, I36, I37, I38, I39) -> f8(I40, I33, I34, I35, I36, I37, 1 + I38, I39) [I40 = I40 /\ 1 + I38 <= I33] 73.15/72.06 f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f5(I41, I42, I43, I44, I45, I46, I47, I48) [I42 <= I47] 73.15/72.06 f4(I49, I50, I51, I52, I53, I54, I55, I56) -> f6(I49, I50, I51, I52, I53, I54, I55, I56) 73.15/72.06 f5(I57, I58, I59, I60, I61, I62, I63, I64) -> f3(I57, I58, I59, I60, I61, I62, I63, I64) 73.15/72.06 f5(I65, I66, I67, I68, I69, I70, I71, I72) -> f2(I65, -1 + I66, I67, I68, I69, I70, I71, I72) 73.15/72.06 f5(I73, I74, I75, I76, I77, I78, I79, I80) -> f3(I73, I74, I75, I76, I77, I78, I79, I80) 73.15/72.06 f2(I81, I82, I83, I84, I85, I86, I87, I88) -> f4(I81, I82, I83, I84, 1 + I85, I86, I87, I88) 73.15/72.06 f3(I89, I90, I91, I92, I93, I94, I95, I96) -> f1(I89, 1 + I90, I91, I92, I93, I94, I95, I96) [1 + I90 <= I92] 73.15/72.06 f3(I97, I98, I99, I100, I101, I102, I103, I104) -> f1(I97, I98, I99, I100, I101, I102, I103, I104) [I100 <= I98] 73.15/72.06 f1(I105, I106, I107, I108, I109, I110, I111, I112) -> f2(I105, I106, I107, I108, I109, I110, I111, I112) 73.15/72.06 73.15/72.06 We use the reverse value criterion with the projection function NU: 73.15/72.06 NU[f7#(z1,z2,z3,z4,z5,z6,z7,z8)] = z2 + -1 * (1 + z7) 73.15/72.06 NU[f8#(z1,z2,z3,z4,z5,z6,z7,z8)] = z2 + -1 * (1 + z7) 73.15/72.06 73.15/72.06 This gives the following inequalities: 73.15/72.06 ==> I25 + -1 * (1 + I30) >= I25 + -1 * (1 + I30) 73.15/72.06 I40 = I40 /\ 1 + I38 <= I33 ==> I33 + -1 * (1 + I38) > I33 + -1 * (1 + (1 + I38)) with I33 + -1 * (1 + I38) >= 0 73.15/72.06 73.15/72.06 We remove all the strictly oriented dependency pairs. 73.15/72.06 73.15/72.06 DP problem for innermost termination. 73.15/72.06 P = 73.15/72.06 f8#(I24, I25, I26, I27, I28, I29, I30, I31) -> f7#(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.06 R = 73.15/72.06 f11(x1, x2, x3, x4, x5, x6, x7, x8) -> f10(x1, x2, x3, x4, x5, x6, x7, x8) 73.15/72.06 f10(I0, I1, I2, I3, I4, I5, I6, I7) -> f4(I0, rnd2, rnd3, 35, 0, 10, I6, 285) [rnd2 = rnd3 /\ rnd3 = rnd3] 73.15/72.06 f6(I8, I9, I10, I11, I12, I13, I14, I15) -> f8(rnd1, I9, I10, I11, I12, I13, 1, I15) [rnd1 = rnd1 /\ 1 + I12 <= I13] 73.15/72.06 f6(I16, I17, I18, I19, I20, I21, I22, I23) -> f9(I16, I17, I18, I19, I20, I21, I22, I23) [I21 <= I20] 73.15/72.06 f8(I24, I25, I26, I27, I28, I29, I30, I31) -> f7(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.06 f7(I32, I33, I34, I35, I36, I37, I38, I39) -> f8(I40, I33, I34, I35, I36, I37, 1 + I38, I39) [I40 = I40 /\ 1 + I38 <= I33] 73.15/72.06 f7(I41, I42, I43, I44, I45, I46, I47, I48) -> f5(I41, I42, I43, I44, I45, I46, I47, I48) [I42 <= I47] 73.15/72.06 f4(I49, I50, I51, I52, I53, I54, I55, I56) -> f6(I49, I50, I51, I52, I53, I54, I55, I56) 73.15/72.06 f5(I57, I58, I59, I60, I61, I62, I63, I64) -> f3(I57, I58, I59, I60, I61, I62, I63, I64) 73.15/72.06 f5(I65, I66, I67, I68, I69, I70, I71, I72) -> f2(I65, -1 + I66, I67, I68, I69, I70, I71, I72) 73.15/72.06 f5(I73, I74, I75, I76, I77, I78, I79, I80) -> f3(I73, I74, I75, I76, I77, I78, I79, I80) 73.15/72.06 f2(I81, I82, I83, I84, I85, I86, I87, I88) -> f4(I81, I82, I83, I84, 1 + I85, I86, I87, I88) 73.15/72.06 f3(I89, I90, I91, I92, I93, I94, I95, I96) -> f1(I89, 1 + I90, I91, I92, I93, I94, I95, I96) [1 + I90 <= I92] 73.15/72.06 f3(I97, I98, I99, I100, I101, I102, I103, I104) -> f1(I97, I98, I99, I100, I101, I102, I103, I104) [I100 <= I98] 73.15/72.06 f1(I105, I106, I107, I108, I109, I110, I111, I112) -> f2(I105, I106, I107, I108, I109, I110, I111, I112) 73.15/72.06 73.15/72.06 The dependency graph for this problem is: 73.15/72.06 3 -> 73.15/72.06 Where: 73.15/72.06 3) f8#(I24, I25, I26, I27, I28, I29, I30, I31) -> f7#(I24, I25, I26, I27, I28, I29, I30, I31) 73.15/72.06 73.15/72.06 We have the following SCCs. 73.15/72.06 73.15/75.03 EOF