118.98/117.67 MAYBE 118.98/117.67 118.98/117.67 DP problem for innermost termination. 118.98/117.67 P = 118.98/117.67 f14#(x1, x2, x3, x4, x5, x6, x7) -> f1#(x1, x2, x3, x4, x5, x6, x7) 118.98/117.67 f13#(I0, I1, I2, I3, I4, I5, I6) -> f2#(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 f12#(I7, I8, I9, I10, I11, I12, I13) -> f13#(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 f11#(I14, I15, I16, I17, I18, I19, I20) -> f12#(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 f2#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 f10#(I28, I29, I30, I31, I32, I33, I34) -> f2#(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2#(I35, I36, I37, I38, I39, I40, I41) -> f10#(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f9#(I43, I44, I45, I46, I47, I48, I49) -> f2#(I43, I44, I45, I46, I47, I48, I49) 118.98/117.67 f8#(I50, I51, I52, I53, I54, I55, I56) -> f9#(I50, I51, I52, I53, I54, 1 + I55, I56) 118.98/117.67 f7#(I57, I58, I59, I60, I61, I62, I63) -> f8#(I57, I58, I59, I60, I61, I62, I63) [I59 = I59] 118.98/117.67 f2#(I64, I65, I66, I67, I68, I69, I70) -> f7#(I64, I65, I66, I67, I71, I69, I70) [I71 = I71 /\ I70 <= I69 /\ I69 <= I70 /\ -1 * I69 + I70 <= 0 /\ -1 * I69 + I70 <= 0] 118.98/117.67 f6#(I72, I73, I74, I75, I76, I77, I78) -> f2#(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2#(I79, I80, I81, I82, I83, I84, I85) -> f6#(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 f3#(I94, I95, I96, I97, I98, I99, I100) -> f4#(I94, I95, I96, I97, I98, I99, I100) [I95 = I95] 118.98/117.67 f2#(I101, I102, I103, I104, I105, I106, I107) -> f3#(I101, I102, I103, I104, I105, I106, I107) [-1 * I106 + I107 <= 0 /\ -1 * I106 + I107 <= 0] 118.98/117.67 f1#(I108, I109, I110, I111, I112, I113, I114) -> f2#(I108, I109, I110, I111, I112, I113, I114) 118.98/117.67 R = 118.98/117.67 f14(x1, x2, x3, x4, x5, x6, x7) -> f1(x1, x2, x3, x4, x5, x6, x7) 118.98/117.67 f13(I0, I1, I2, I3, I4, I5, I6) -> f2(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 f12(I7, I8, I9, I10, I11, I12, I13) -> f13(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 f11(I14, I15, I16, I17, I18, I19, I20) -> f12(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 f2(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 f10(I28, I29, I30, I31, I32, I33, I34) -> f2(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f9(I43, I44, I45, I46, I47, I48, I49) -> f2(I43, I44, I45, I46, I47, I48, I49) 118.98/117.67 f8(I50, I51, I52, I53, I54, I55, I56) -> f9(I50, I51, I52, I53, I54, 1 + I55, I56) 118.98/117.67 f7(I57, I58, I59, I60, I61, I62, I63) -> f8(I57, I58, I59, I60, I61, I62, I63) [I59 = I59] 118.98/117.67 f2(I64, I65, I66, I67, I68, I69, I70) -> f7(I64, I65, I66, I67, I71, I69, I70) [I71 = I71 /\ I70 <= I69 /\ I69 <= I70 /\ -1 * I69 + I70 <= 0 /\ -1 * I69 + I70 <= 0] 118.98/117.67 f6(I72, I73, I74, I75, I76, I77, I78) -> f2(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2(I79, I80, I81, I82, I83, I84, I85) -> f6(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 f4(I87, I88, I89, I90, I91, I92, I93) -> f5(rnd1, I88, I89, I90, I91, I92, I93) [rnd1 = rnd1] 118.98/117.67 f3(I94, I95, I96, I97, I98, I99, I100) -> f4(I94, I95, I96, I97, I98, I99, I100) [I95 = I95] 118.98/117.67 f2(I101, I102, I103, I104, I105, I106, I107) -> f3(I101, I102, I103, I104, I105, I106, I107) [-1 * I106 + I107 <= 0 /\ -1 * I106 + I107 <= 0] 118.98/117.67 f1(I108, I109, I110, I111, I112, I113, I114) -> f2(I108, I109, I110, I111, I112, I113, I114) 118.98/117.67 118.98/117.67 The dependency graph for this problem is: 118.98/117.67 0 -> 15 118.98/117.67 1 -> 4, 6, 10, 12, 14 118.98/117.67 2 -> 1 118.98/117.67 3 -> 2 118.98/117.67 4 -> 3 118.98/117.67 5 -> 4, 6, 10, 12, 14 118.98/117.67 6 -> 5 118.98/117.67 7 -> 4, 6, 10, 12, 14 118.98/117.67 8 -> 7 118.98/117.67 9 -> 8 118.98/117.67 10 -> 9 118.98/117.67 11 -> 4, 6, 10, 12, 14 118.98/117.67 12 -> 11 118.98/117.67 13 -> 118.98/117.67 14 -> 13 118.98/117.67 15 -> 4, 6, 10, 12, 14 118.98/117.67 Where: 118.98/117.67 0) f14#(x1, x2, x3, x4, x5, x6, x7) -> f1#(x1, x2, x3, x4, x5, x6, x7) 118.98/117.67 1) f13#(I0, I1, I2, I3, I4, I5, I6) -> f2#(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 2) f12#(I7, I8, I9, I10, I11, I12, I13) -> f13#(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 3) f11#(I14, I15, I16, I17, I18, I19, I20) -> f12#(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 4) f2#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 5) f10#(I28, I29, I30, I31, I32, I33, I34) -> f2#(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 6) f2#(I35, I36, I37, I38, I39, I40, I41) -> f10#(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 7) f9#(I43, I44, I45, I46, I47, I48, I49) -> f2#(I43, I44, I45, I46, I47, I48, I49) 118.98/117.67 8) f8#(I50, I51, I52, I53, I54, I55, I56) -> f9#(I50, I51, I52, I53, I54, 1 + I55, I56) 118.98/117.67 9) f7#(I57, I58, I59, I60, I61, I62, I63) -> f8#(I57, I58, I59, I60, I61, I62, I63) [I59 = I59] 118.98/117.67 10) f2#(I64, I65, I66, I67, I68, I69, I70) -> f7#(I64, I65, I66, I67, I71, I69, I70) [I71 = I71 /\ I70 <= I69 /\ I69 <= I70 /\ -1 * I69 + I70 <= 0 /\ -1 * I69 + I70 <= 0] 118.98/117.67 11) f6#(I72, I73, I74, I75, I76, I77, I78) -> f2#(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 12) f2#(I79, I80, I81, I82, I83, I84, I85) -> f6#(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 13) f3#(I94, I95, I96, I97, I98, I99, I100) -> f4#(I94, I95, I96, I97, I98, I99, I100) [I95 = I95] 118.98/117.67 14) f2#(I101, I102, I103, I104, I105, I106, I107) -> f3#(I101, I102, I103, I104, I105, I106, I107) [-1 * I106 + I107 <= 0 /\ -1 * I106 + I107 <= 0] 118.98/117.67 15) f1#(I108, I109, I110, I111, I112, I113, I114) -> f2#(I108, I109, I110, I111, I112, I113, I114) 118.98/117.67 118.98/117.67 We have the following SCCs. 118.98/117.67 { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } 118.98/117.67 118.98/117.67 DP problem for innermost termination. 118.98/117.67 P = 118.98/117.67 f13#(I0, I1, I2, I3, I4, I5, I6) -> f2#(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 f12#(I7, I8, I9, I10, I11, I12, I13) -> f13#(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 f11#(I14, I15, I16, I17, I18, I19, I20) -> f12#(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 f2#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 f10#(I28, I29, I30, I31, I32, I33, I34) -> f2#(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2#(I35, I36, I37, I38, I39, I40, I41) -> f10#(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f9#(I43, I44, I45, I46, I47, I48, I49) -> f2#(I43, I44, I45, I46, I47, I48, I49) 118.98/117.67 f8#(I50, I51, I52, I53, I54, I55, I56) -> f9#(I50, I51, I52, I53, I54, 1 + I55, I56) 118.98/117.67 f7#(I57, I58, I59, I60, I61, I62, I63) -> f8#(I57, I58, I59, I60, I61, I62, I63) [I59 = I59] 118.98/117.67 f2#(I64, I65, I66, I67, I68, I69, I70) -> f7#(I64, I65, I66, I67, I71, I69, I70) [I71 = I71 /\ I70 <= I69 /\ I69 <= I70 /\ -1 * I69 + I70 <= 0 /\ -1 * I69 + I70 <= 0] 118.98/117.67 f6#(I72, I73, I74, I75, I76, I77, I78) -> f2#(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2#(I79, I80, I81, I82, I83, I84, I85) -> f6#(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 R = 118.98/117.67 f14(x1, x2, x3, x4, x5, x6, x7) -> f1(x1, x2, x3, x4, x5, x6, x7) 118.98/117.67 f13(I0, I1, I2, I3, I4, I5, I6) -> f2(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 f12(I7, I8, I9, I10, I11, I12, I13) -> f13(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 f11(I14, I15, I16, I17, I18, I19, I20) -> f12(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 f2(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 f10(I28, I29, I30, I31, I32, I33, I34) -> f2(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f9(I43, I44, I45, I46, I47, I48, I49) -> f2(I43, I44, I45, I46, I47, I48, I49) 118.98/117.67 f8(I50, I51, I52, I53, I54, I55, I56) -> f9(I50, I51, I52, I53, I54, 1 + I55, I56) 118.98/117.67 f7(I57, I58, I59, I60, I61, I62, I63) -> f8(I57, I58, I59, I60, I61, I62, I63) [I59 = I59] 118.98/117.67 f2(I64, I65, I66, I67, I68, I69, I70) -> f7(I64, I65, I66, I67, I71, I69, I70) [I71 = I71 /\ I70 <= I69 /\ I69 <= I70 /\ -1 * I69 + I70 <= 0 /\ -1 * I69 + I70 <= 0] 118.98/117.67 f6(I72, I73, I74, I75, I76, I77, I78) -> f2(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2(I79, I80, I81, I82, I83, I84, I85) -> f6(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 f4(I87, I88, I89, I90, I91, I92, I93) -> f5(rnd1, I88, I89, I90, I91, I92, I93) [rnd1 = rnd1] 118.98/117.67 f3(I94, I95, I96, I97, I98, I99, I100) -> f4(I94, I95, I96, I97, I98, I99, I100) [I95 = I95] 118.98/117.67 f2(I101, I102, I103, I104, I105, I106, I107) -> f3(I101, I102, I103, I104, I105, I106, I107) [-1 * I106 + I107 <= 0 /\ -1 * I106 + I107 <= 0] 118.98/117.67 f1(I108, I109, I110, I111, I112, I113, I114) -> f2(I108, I109, I110, I111, I112, I113, I114) 118.98/117.67 118.98/117.67 We use the extended value criterion with the projection function NU: 118.98/117.67 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 118.98/117.67 NU[f7#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 - 1 118.98/117.67 NU[f8#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 - 1 118.98/117.67 NU[f9#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 118.98/117.67 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 118.98/117.67 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 - 1 118.98/117.67 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 - 1 118.98/117.67 NU[f2#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 118.98/117.67 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 118.98/117.67 118.98/117.67 This gives the following inequalities: 118.98/117.67 ==> -I5 + I6 >= -I5 + I6 118.98/117.67 ==> -I12 + I13 - 1 >= -(1 + I12) + I13 118.98/117.67 I17 = I17 ==> -I19 + I20 - 1 >= -I19 + I20 - 1 118.98/117.67 rnd5 = rnd5 /\ 0 <= -1 - I26 + I27 ==> -I26 + I27 >= -I26 + I27 - 1 118.98/117.67 ==> -I33 + I34 >= -I33 + I34 118.98/117.67 0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41 ==> -I40 + I41 >= -I40 + I41 118.98/117.67 ==> -I48 + I49 >= -I48 + I49 118.98/117.67 ==> -I55 + I56 - 1 >= -(1 + I55) + I56 118.98/117.67 I59 = I59 ==> -I62 + I63 - 1 >= -I62 + I63 - 1 118.98/117.67 I71 = I71 /\ I70 <= I69 /\ I69 <= I70 /\ -1 * I69 + I70 <= 0 /\ -1 * I69 + I70 <= 0 ==> -I69 + I70 > -I69 + I70 - 1 with -I69 + I70 >= 0 118.98/117.67 ==> -I77 + I78 >= -I77 + I78 118.98/117.67 0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0 ==> -I84 + I85 >= -I84 + I85 118.98/117.67 118.98/117.67 We remove all the strictly oriented dependency pairs. 118.98/117.67 118.98/117.67 DP problem for innermost termination. 118.98/117.67 P = 118.98/117.67 f13#(I0, I1, I2, I3, I4, I5, I6) -> f2#(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 f12#(I7, I8, I9, I10, I11, I12, I13) -> f13#(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 f11#(I14, I15, I16, I17, I18, I19, I20) -> f12#(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 f2#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 f10#(I28, I29, I30, I31, I32, I33, I34) -> f2#(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2#(I35, I36, I37, I38, I39, I40, I41) -> f10#(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f9#(I43, I44, I45, I46, I47, I48, I49) -> f2#(I43, I44, I45, I46, I47, I48, I49) 118.98/117.67 f8#(I50, I51, I52, I53, I54, I55, I56) -> f9#(I50, I51, I52, I53, I54, 1 + I55, I56) 118.98/117.67 f7#(I57, I58, I59, I60, I61, I62, I63) -> f8#(I57, I58, I59, I60, I61, I62, I63) [I59 = I59] 118.98/117.67 f6#(I72, I73, I74, I75, I76, I77, I78) -> f2#(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2#(I79, I80, I81, I82, I83, I84, I85) -> f6#(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 R = 118.98/117.67 f14(x1, x2, x3, x4, x5, x6, x7) -> f1(x1, x2, x3, x4, x5, x6, x7) 118.98/117.67 f13(I0, I1, I2, I3, I4, I5, I6) -> f2(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 f12(I7, I8, I9, I10, I11, I12, I13) -> f13(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 f11(I14, I15, I16, I17, I18, I19, I20) -> f12(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 f2(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 f10(I28, I29, I30, I31, I32, I33, I34) -> f2(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f9(I43, I44, I45, I46, I47, I48, I49) -> f2(I43, I44, I45, I46, I47, I48, I49) 118.98/117.67 f8(I50, I51, I52, I53, I54, I55, I56) -> f9(I50, I51, I52, I53, I54, 1 + I55, I56) 118.98/117.67 f7(I57, I58, I59, I60, I61, I62, I63) -> f8(I57, I58, I59, I60, I61, I62, I63) [I59 = I59] 118.98/117.67 f2(I64, I65, I66, I67, I68, I69, I70) -> f7(I64, I65, I66, I67, I71, I69, I70) [I71 = I71 /\ I70 <= I69 /\ I69 <= I70 /\ -1 * I69 + I70 <= 0 /\ -1 * I69 + I70 <= 0] 118.98/117.67 f6(I72, I73, I74, I75, I76, I77, I78) -> f2(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2(I79, I80, I81, I82, I83, I84, I85) -> f6(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 f4(I87, I88, I89, I90, I91, I92, I93) -> f5(rnd1, I88, I89, I90, I91, I92, I93) [rnd1 = rnd1] 118.98/117.67 f3(I94, I95, I96, I97, I98, I99, I100) -> f4(I94, I95, I96, I97, I98, I99, I100) [I95 = I95] 118.98/117.67 f2(I101, I102, I103, I104, I105, I106, I107) -> f3(I101, I102, I103, I104, I105, I106, I107) [-1 * I106 + I107 <= 0 /\ -1 * I106 + I107 <= 0] 118.98/117.67 f1(I108, I109, I110, I111, I112, I113, I114) -> f2(I108, I109, I110, I111, I112, I113, I114) 118.98/117.67 118.98/117.67 The dependency graph for this problem is: 118.98/117.67 1 -> 4, 6, 12 118.98/117.67 2 -> 1 118.98/117.67 3 -> 2 118.98/117.67 4 -> 3 118.98/117.67 5 -> 4, 6, 12 118.98/117.67 6 -> 5 118.98/117.67 7 -> 4, 6, 12 118.98/117.67 8 -> 7 118.98/117.67 9 -> 8 118.98/117.67 11 -> 4, 6, 12 118.98/117.67 12 -> 11 118.98/117.67 Where: 118.98/117.67 1) f13#(I0, I1, I2, I3, I4, I5, I6) -> f2#(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 2) f12#(I7, I8, I9, I10, I11, I12, I13) -> f13#(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 3) f11#(I14, I15, I16, I17, I18, I19, I20) -> f12#(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 4) f2#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 5) f10#(I28, I29, I30, I31, I32, I33, I34) -> f2#(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 6) f2#(I35, I36, I37, I38, I39, I40, I41) -> f10#(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 7) f9#(I43, I44, I45, I46, I47, I48, I49) -> f2#(I43, I44, I45, I46, I47, I48, I49) 118.98/117.67 8) f8#(I50, I51, I52, I53, I54, I55, I56) -> f9#(I50, I51, I52, I53, I54, 1 + I55, I56) 118.98/117.67 9) f7#(I57, I58, I59, I60, I61, I62, I63) -> f8#(I57, I58, I59, I60, I61, I62, I63) [I59 = I59] 118.98/117.67 11) f6#(I72, I73, I74, I75, I76, I77, I78) -> f2#(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 12) f2#(I79, I80, I81, I82, I83, I84, I85) -> f6#(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 118.98/117.67 We have the following SCCs. 118.98/117.67 { 1, 2, 3, 4, 5, 6, 11, 12 } 118.98/117.67 118.98/117.67 DP problem for innermost termination. 118.98/117.67 P = 118.98/117.67 f13#(I0, I1, I2, I3, I4, I5, I6) -> f2#(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 f12#(I7, I8, I9, I10, I11, I12, I13) -> f13#(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 f11#(I14, I15, I16, I17, I18, I19, I20) -> f12#(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 f2#(I21, I22, I23, I24, I25, I26, I27) -> f11#(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 f10#(I28, I29, I30, I31, I32, I33, I34) -> f2#(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2#(I35, I36, I37, I38, I39, I40, I41) -> f10#(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f6#(I72, I73, I74, I75, I76, I77, I78) -> f2#(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2#(I79, I80, I81, I82, I83, I84, I85) -> f6#(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 R = 118.98/117.67 f14(x1, x2, x3, x4, x5, x6, x7) -> f1(x1, x2, x3, x4, x5, x6, x7) 118.98/117.67 f13(I0, I1, I2, I3, I4, I5, I6) -> f2(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 f12(I7, I8, I9, I10, I11, I12, I13) -> f13(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 f11(I14, I15, I16, I17, I18, I19, I20) -> f12(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 f2(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 f10(I28, I29, I30, I31, I32, I33, I34) -> f2(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f9(I43, I44, I45, I46, I47, I48, I49) -> f2(I43, I44, I45, I46, I47, I48, I49) 118.98/117.67 f8(I50, I51, I52, I53, I54, I55, I56) -> f9(I50, I51, I52, I53, I54, 1 + I55, I56) 118.98/117.67 f7(I57, I58, I59, I60, I61, I62, I63) -> f8(I57, I58, I59, I60, I61, I62, I63) [I59 = I59] 118.98/117.67 f2(I64, I65, I66, I67, I68, I69, I70) -> f7(I64, I65, I66, I67, I71, I69, I70) [I71 = I71 /\ I70 <= I69 /\ I69 <= I70 /\ -1 * I69 + I70 <= 0 /\ -1 * I69 + I70 <= 0] 118.98/117.67 f6(I72, I73, I74, I75, I76, I77, I78) -> f2(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2(I79, I80, I81, I82, I83, I84, I85) -> f6(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 f4(I87, I88, I89, I90, I91, I92, I93) -> f5(rnd1, I88, I89, I90, I91, I92, I93) [rnd1 = rnd1] 118.98/117.67 f3(I94, I95, I96, I97, I98, I99, I100) -> f4(I94, I95, I96, I97, I98, I99, I100) [I95 = I95] 118.98/117.67 f2(I101, I102, I103, I104, I105, I106, I107) -> f3(I101, I102, I103, I104, I105, I106, I107) [-1 * I106 + I107 <= 0 /\ -1 * I106 + I107 <= 0] 118.98/117.67 f1(I108, I109, I110, I111, I112, I113, I114) -> f2(I108, I109, I110, I111, I112, I113, I114) 118.98/117.67 118.98/117.67 We use the extended value criterion with the projection function NU: 118.98/117.67 NU[f6#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 + 1 118.98/117.67 NU[f10#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 + 1 118.98/117.67 NU[f11#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 118.98/117.67 NU[f12#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 118.98/117.67 NU[f2#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 + 1 118.98/117.67 NU[f13#(x0,x1,x2,x3,x4,x5,x6)] = -x5 + x6 + 1 118.98/117.67 118.98/117.67 This gives the following inequalities: 118.98/117.67 ==> -I5 + I6 + 1 >= -I5 + I6 + 1 118.98/117.67 ==> -I12 + I13 >= -(1 + I12) + I13 + 1 118.98/117.67 I17 = I17 ==> -I19 + I20 >= -I19 + I20 118.98/117.67 rnd5 = rnd5 /\ 0 <= -1 - I26 + I27 ==> -I26 + I27 + 1 > -I26 + I27 with -I26 + I27 + 1 >= 0 118.98/117.67 ==> -I33 + I34 + 1 >= -I33 + I34 + 1 118.98/117.67 0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41 ==> -I40 + I41 + 1 >= -I40 + I41 + 1 118.98/117.67 ==> -I77 + I78 + 1 >= -I77 + I78 + 1 118.98/117.67 0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0 ==> -I84 + I85 + 1 >= -I84 + I85 + 1 118.98/117.67 118.98/117.67 We remove all the strictly oriented dependency pairs. 118.98/117.67 118.98/117.67 DP problem for innermost termination. 118.98/117.67 P = 118.98/117.67 f13#(I0, I1, I2, I3, I4, I5, I6) -> f2#(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 f12#(I7, I8, I9, I10, I11, I12, I13) -> f13#(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 f11#(I14, I15, I16, I17, I18, I19, I20) -> f12#(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 f10#(I28, I29, I30, I31, I32, I33, I34) -> f2#(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2#(I35, I36, I37, I38, I39, I40, I41) -> f10#(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f6#(I72, I73, I74, I75, I76, I77, I78) -> f2#(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2#(I79, I80, I81, I82, I83, I84, I85) -> f6#(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 R = 118.98/117.67 f14(x1, x2, x3, x4, x5, x6, x7) -> f1(x1, x2, x3, x4, x5, x6, x7) 118.98/117.67 f13(I0, I1, I2, I3, I4, I5, I6) -> f2(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 f12(I7, I8, I9, I10, I11, I12, I13) -> f13(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 f11(I14, I15, I16, I17, I18, I19, I20) -> f12(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 f2(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 f10(I28, I29, I30, I31, I32, I33, I34) -> f2(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f9(I43, I44, I45, I46, I47, I48, I49) -> f2(I43, I44, I45, I46, I47, I48, I49) 118.98/117.67 f8(I50, I51, I52, I53, I54, I55, I56) -> f9(I50, I51, I52, I53, I54, 1 + I55, I56) 118.98/117.67 f7(I57, I58, I59, I60, I61, I62, I63) -> f8(I57, I58, I59, I60, I61, I62, I63) [I59 = I59] 118.98/117.67 f2(I64, I65, I66, I67, I68, I69, I70) -> f7(I64, I65, I66, I67, I71, I69, I70) [I71 = I71 /\ I70 <= I69 /\ I69 <= I70 /\ -1 * I69 + I70 <= 0 /\ -1 * I69 + I70 <= 0] 118.98/117.67 f6(I72, I73, I74, I75, I76, I77, I78) -> f2(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2(I79, I80, I81, I82, I83, I84, I85) -> f6(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 f4(I87, I88, I89, I90, I91, I92, I93) -> f5(rnd1, I88, I89, I90, I91, I92, I93) [rnd1 = rnd1] 118.98/117.67 f3(I94, I95, I96, I97, I98, I99, I100) -> f4(I94, I95, I96, I97, I98, I99, I100) [I95 = I95] 118.98/117.67 f2(I101, I102, I103, I104, I105, I106, I107) -> f3(I101, I102, I103, I104, I105, I106, I107) [-1 * I106 + I107 <= 0 /\ -1 * I106 + I107 <= 0] 118.98/117.67 f1(I108, I109, I110, I111, I112, I113, I114) -> f2(I108, I109, I110, I111, I112, I113, I114) 118.98/117.67 118.98/117.67 The dependency graph for this problem is: 118.98/117.67 1 -> 6, 12 118.98/117.67 2 -> 1 118.98/117.67 3 -> 2 118.98/117.67 5 -> 6, 12 118.98/117.67 6 -> 5 118.98/117.67 11 -> 6, 12 118.98/117.67 12 -> 11 118.98/117.67 Where: 118.98/117.67 1) f13#(I0, I1, I2, I3, I4, I5, I6) -> f2#(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 2) f12#(I7, I8, I9, I10, I11, I12, I13) -> f13#(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 3) f11#(I14, I15, I16, I17, I18, I19, I20) -> f12#(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 5) f10#(I28, I29, I30, I31, I32, I33, I34) -> f2#(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 6) f2#(I35, I36, I37, I38, I39, I40, I41) -> f10#(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 11) f6#(I72, I73, I74, I75, I76, I77, I78) -> f2#(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 12) f2#(I79, I80, I81, I82, I83, I84, I85) -> f6#(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 118.98/117.67 We have the following SCCs. 118.98/117.67 { 5, 6, 11, 12 } 118.98/117.67 118.98/117.67 DP problem for innermost termination. 118.98/117.67 P = 118.98/117.67 f10#(I28, I29, I30, I31, I32, I33, I34) -> f2#(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2#(I35, I36, I37, I38, I39, I40, I41) -> f10#(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f6#(I72, I73, I74, I75, I76, I77, I78) -> f2#(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2#(I79, I80, I81, I82, I83, I84, I85) -> f6#(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 R = 118.98/117.67 f14(x1, x2, x3, x4, x5, x6, x7) -> f1(x1, x2, x3, x4, x5, x6, x7) 118.98/117.67 f13(I0, I1, I2, I3, I4, I5, I6) -> f2(I0, I1, I2, I3, I4, I5, I6) 118.98/117.67 f12(I7, I8, I9, I10, I11, I12, I13) -> f13(I7, I8, I9, I10, I11, 1 + I12, I13) 118.98/117.67 f11(I14, I15, I16, I17, I18, I19, I20) -> f12(I14, I15, I16, I17, I18, I19, I20) [I17 = I17] 118.98/117.67 f2(I21, I22, I23, I24, I25, I26, I27) -> f11(I21, I22, I23, I24, rnd5, I26, I27) [rnd5 = rnd5 /\ 0 <= -1 - I26 + I27] 118.98/117.67 f10(I28, I29, I30, I31, I32, I33, I34) -> f2(I28, I29, I30, I31, I32, I33, I34) 118.98/117.67 f2(I35, I36, I37, I38, I39, I40, I41) -> f10(I35, I36, I37, I38, I42, I40, I41) [0 <= I42 /\ I42 <= 0 /\ I42 = I42 /\ 0 <= -1 - I40 + I41] 118.98/117.67 f9(I43, I44, I45, I46, I47, I48, I49) -> f2(I43, I44, I45, I46, I47, I48, I49) 118.98/117.67 f8(I50, I51, I52, I53, I54, I55, I56) -> f9(I50, I51, I52, I53, I54, 1 + I55, I56) 118.98/117.67 f7(I57, I58, I59, I60, I61, I62, I63) -> f8(I57, I58, I59, I60, I61, I62, I63) [I59 = I59] 118.98/117.67 f2(I64, I65, I66, I67, I68, I69, I70) -> f7(I64, I65, I66, I67, I71, I69, I70) [I71 = I71 /\ I70 <= I69 /\ I69 <= I70 /\ -1 * I69 + I70 <= 0 /\ -1 * I69 + I70 <= 0] 118.98/117.67 f6(I72, I73, I74, I75, I76, I77, I78) -> f2(I72, I73, I74, I75, I76, I77, I78) 118.98/117.67 f2(I79, I80, I81, I82, I83, I84, I85) -> f6(I79, I80, I81, I82, I86, I84, I85) [0 <= I86 /\ I86 <= 0 /\ I86 = I86 /\ I85 <= I84 /\ I84 <= I85 /\ -1 * I84 + I85 <= 0 /\ -1 * I84 + I85 <= 0] 118.98/117.67 f4(I87, I88, I89, I90, I91, I92, I93) -> f5(rnd1, I88, I89, I90, I91, I92, I93) [rnd1 = rnd1] 118.98/117.67 f3(I94, I95, I96, I97, I98, I99, I100) -> f4(I94, I95, I96, I97, I98, I99, I100) [I95 = I95] 118.98/117.67 f2(I101, I102, I103, I104, I105, I106, I107) -> f3(I101, I102, I103, I104, I105, I106, I107) [-1 * I106 + I107 <= 0 /\ -1 * I106 + I107 <= 0] 118.98/117.67 f1(I108, I109, I110, I111, I112, I113, I114) -> f2(I108, I109, I110, I111, I112, I113, I114) 118.98/117.67 118.98/120.64 EOF