26.20/25.87 MAYBE 26.20/25.87 26.20/25.87 DP problem for innermost termination. 26.20/25.87 P = 26.20/25.87 f11#(x1, x2, x3, x4, x5, x6) -> f10#(x1, x2, x3, x4, x5, x6) 26.20/25.87 f10#(I0, I1, I2, I3, I4, I5) -> f4#(I0, I1, I2, rnd4, rnd5, I5) [rnd4 = rnd5 /\ rnd5 = rnd5] 26.20/25.87 f5#(I6, I7, I8, I9, I10, I11) -> f9#(I6, I7, I8, I9, I10, I11) [1 + I7 <= I9] 26.20/25.87 f5#(I12, I13, I14, I15, I16, I17) -> f9#(I12, I13, I14, I15, I16, I17) [1 + I15 <= I13] 26.20/25.87 f5#(I18, I19, I20, I21, I22, I23) -> f8#(I18, I19, I20, I21, I22, I23) [I21 <= I19 /\ I19 <= I21] 26.20/25.87 f9#(I24, I25, I26, I27, I28, I29) -> f8#(I24, I25, I26, I27, I28, I29) 26.20/25.87 f9#(I30, I31, I32, I33, I34, I35) -> f2#(I30, 1 + I31, I32, I33, I34, I35) 26.20/25.87 f7#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 26.20/25.87 f8#(I42, I43, I44, I45, I46, I47) -> f7#(I42, -1 + I43, 0, I45, I46, I47) 26.20/25.87 f6#(I48, I49, I50, I51, I52, I53) -> f7#(I48, I49, 1 + I50, I51, I52, I53) [1 + I50 <= I49] 26.20/25.87 f2#(I60, I61, I62, I63, I64, I65) -> f5#(I60, I61, I62, I63, I64, I65) 26.20/25.87 f4#(I72, I73, I74, I75, I76, I77) -> f1#(I72, I73, I74, I75, I76, I77) [1 <= I75] 26.20/25.87 f1#(I84, I85, I86, I87, I88, I89) -> f2#(I84, 0, I86, I87, I88, rnd6) [rnd6 = rnd6 /\ I87 <= I84] 26.20/25.87 R = 26.20/25.87 f11(x1, x2, x3, x4, x5, x6) -> f10(x1, x2, x3, x4, x5, x6) 26.20/25.87 f10(I0, I1, I2, I3, I4, I5) -> f4(I0, I1, I2, rnd4, rnd5, I5) [rnd4 = rnd5 /\ rnd5 = rnd5] 26.20/25.87 f5(I6, I7, I8, I9, I10, I11) -> f9(I6, I7, I8, I9, I10, I11) [1 + I7 <= I9] 26.20/25.87 f5(I12, I13, I14, I15, I16, I17) -> f9(I12, I13, I14, I15, I16, I17) [1 + I15 <= I13] 26.20/25.87 f5(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) [I21 <= I19 /\ I19 <= I21] 26.20/25.87 f9(I24, I25, I26, I27, I28, I29) -> f8(I24, I25, I26, I27, I28, I29) 26.20/25.87 f9(I30, I31, I32, I33, I34, I35) -> f2(I30, 1 + I31, I32, I33, I34, I35) 26.20/25.87 f7(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 26.20/25.87 f8(I42, I43, I44, I45, I46, I47) -> f7(I42, -1 + I43, 0, I45, I46, I47) 26.20/25.87 f6(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, 1 + I50, I51, I52, I53) [1 + I50 <= I49] 26.20/25.87 f6(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) [I55 <= I56] 26.20/25.87 f2(I60, I61, I62, I63, I64, I65) -> f5(I60, I61, I62, I63, I64, I65) 26.20/25.87 f4(I66, I67, I68, I69, I70, I71) -> f3(I66, I67, I68, I69, I70, I71) [I69 <= 0] 26.20/25.87 f4(I72, I73, I74, I75, I76, I77) -> f1(I72, I73, I74, I75, I76, I77) [1 <= I75] 26.20/25.87 f1(I78, I79, I80, I81, I82, I83) -> f3(I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 26.20/25.87 f1(I84, I85, I86, I87, I88, I89) -> f2(I84, 0, I86, I87, I88, rnd6) [rnd6 = rnd6 /\ I87 <= I84] 26.20/25.87 26.20/25.87 The dependency graph for this problem is: 26.20/25.87 0 -> 1 26.20/25.87 1 -> 11 26.20/25.87 2 -> 5, 6 26.20/25.87 3 -> 5, 6 26.20/25.87 4 -> 8 26.20/25.87 5 -> 8 26.20/25.87 6 -> 10 26.20/25.87 7 -> 9 26.20/25.87 8 -> 7 26.20/25.87 9 -> 7 26.20/25.87 10 -> 2, 3, 4 26.20/25.87 11 -> 12 26.20/25.87 12 -> 10 26.20/25.87 Where: 26.20/25.87 0) f11#(x1, x2, x3, x4, x5, x6) -> f10#(x1, x2, x3, x4, x5, x6) 26.20/25.87 1) f10#(I0, I1, I2, I3, I4, I5) -> f4#(I0, I1, I2, rnd4, rnd5, I5) [rnd4 = rnd5 /\ rnd5 = rnd5] 26.20/25.87 2) f5#(I6, I7, I8, I9, I10, I11) -> f9#(I6, I7, I8, I9, I10, I11) [1 + I7 <= I9] 26.20/25.87 3) f5#(I12, I13, I14, I15, I16, I17) -> f9#(I12, I13, I14, I15, I16, I17) [1 + I15 <= I13] 26.20/25.87 4) f5#(I18, I19, I20, I21, I22, I23) -> f8#(I18, I19, I20, I21, I22, I23) [I21 <= I19 /\ I19 <= I21] 26.20/25.87 5) f9#(I24, I25, I26, I27, I28, I29) -> f8#(I24, I25, I26, I27, I28, I29) 26.20/25.87 6) f9#(I30, I31, I32, I33, I34, I35) -> f2#(I30, 1 + I31, I32, I33, I34, I35) 26.20/25.87 7) f7#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 26.20/25.87 8) f8#(I42, I43, I44, I45, I46, I47) -> f7#(I42, -1 + I43, 0, I45, I46, I47) 26.20/25.87 9) f6#(I48, I49, I50, I51, I52, I53) -> f7#(I48, I49, 1 + I50, I51, I52, I53) [1 + I50 <= I49] 26.20/25.87 10) f2#(I60, I61, I62, I63, I64, I65) -> f5#(I60, I61, I62, I63, I64, I65) 26.20/25.87 11) f4#(I72, I73, I74, I75, I76, I77) -> f1#(I72, I73, I74, I75, I76, I77) [1 <= I75] 26.20/25.87 12) f1#(I84, I85, I86, I87, I88, I89) -> f2#(I84, 0, I86, I87, I88, rnd6) [rnd6 = rnd6 /\ I87 <= I84] 26.20/25.87 26.20/25.87 We have the following SCCs. 26.20/25.87 { 2, 3, 6, 10 } 26.20/25.87 { 7, 9 } 26.20/25.87 26.20/25.87 DP problem for innermost termination. 26.20/25.87 P = 26.20/25.87 f7#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 26.20/25.87 f6#(I48, I49, I50, I51, I52, I53) -> f7#(I48, I49, 1 + I50, I51, I52, I53) [1 + I50 <= I49] 26.20/25.87 R = 26.20/25.87 f11(x1, x2, x3, x4, x5, x6) -> f10(x1, x2, x3, x4, x5, x6) 26.20/25.87 f10(I0, I1, I2, I3, I4, I5) -> f4(I0, I1, I2, rnd4, rnd5, I5) [rnd4 = rnd5 /\ rnd5 = rnd5] 26.20/25.87 f5(I6, I7, I8, I9, I10, I11) -> f9(I6, I7, I8, I9, I10, I11) [1 + I7 <= I9] 26.20/25.87 f5(I12, I13, I14, I15, I16, I17) -> f9(I12, I13, I14, I15, I16, I17) [1 + I15 <= I13] 26.20/25.87 f5(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) [I21 <= I19 /\ I19 <= I21] 26.20/25.87 f9(I24, I25, I26, I27, I28, I29) -> f8(I24, I25, I26, I27, I28, I29) 26.20/25.87 f9(I30, I31, I32, I33, I34, I35) -> f2(I30, 1 + I31, I32, I33, I34, I35) 26.20/25.87 f7(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 26.20/25.87 f8(I42, I43, I44, I45, I46, I47) -> f7(I42, -1 + I43, 0, I45, I46, I47) 26.20/25.87 f6(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, 1 + I50, I51, I52, I53) [1 + I50 <= I49] 26.20/25.87 f6(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) [I55 <= I56] 26.20/25.87 f2(I60, I61, I62, I63, I64, I65) -> f5(I60, I61, I62, I63, I64, I65) 26.20/25.87 f4(I66, I67, I68, I69, I70, I71) -> f3(I66, I67, I68, I69, I70, I71) [I69 <= 0] 26.20/25.87 f4(I72, I73, I74, I75, I76, I77) -> f1(I72, I73, I74, I75, I76, I77) [1 <= I75] 26.20/25.87 f1(I78, I79, I80, I81, I82, I83) -> f3(I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 26.20/25.87 f1(I84, I85, I86, I87, I88, I89) -> f2(I84, 0, I86, I87, I88, rnd6) [rnd6 = rnd6 /\ I87 <= I84] 26.20/25.87 26.20/25.87 We use the reverse value criterion with the projection function NU: 26.20/25.87 NU[f6#(z1,z2,z3,z4,z5,z6)] = z2 + -1 * (1 + z3) 26.20/25.87 NU[f7#(z1,z2,z3,z4,z5,z6)] = z2 + -1 * (1 + z3) 26.20/25.87 26.20/25.87 This gives the following inequalities: 26.20/25.87 ==> I37 + -1 * (1 + I38) >= I37 + -1 * (1 + I38) 26.20/25.87 1 + I50 <= I49 ==> I49 + -1 * (1 + I50) > I49 + -1 * (1 + (1 + I50)) with I49 + -1 * (1 + I50) >= 0 26.20/25.87 26.20/25.87 We remove all the strictly oriented dependency pairs. 26.20/25.87 26.20/25.87 DP problem for innermost termination. 26.20/25.87 P = 26.20/25.87 f7#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 26.20/25.87 R = 26.20/25.87 f11(x1, x2, x3, x4, x5, x6) -> f10(x1, x2, x3, x4, x5, x6) 26.20/25.87 f10(I0, I1, I2, I3, I4, I5) -> f4(I0, I1, I2, rnd4, rnd5, I5) [rnd4 = rnd5 /\ rnd5 = rnd5] 26.20/25.87 f5(I6, I7, I8, I9, I10, I11) -> f9(I6, I7, I8, I9, I10, I11) [1 + I7 <= I9] 26.20/25.87 f5(I12, I13, I14, I15, I16, I17) -> f9(I12, I13, I14, I15, I16, I17) [1 + I15 <= I13] 26.20/25.87 f5(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) [I21 <= I19 /\ I19 <= I21] 26.20/25.87 f9(I24, I25, I26, I27, I28, I29) -> f8(I24, I25, I26, I27, I28, I29) 26.20/25.87 f9(I30, I31, I32, I33, I34, I35) -> f2(I30, 1 + I31, I32, I33, I34, I35) 26.20/25.87 f7(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 26.20/25.87 f8(I42, I43, I44, I45, I46, I47) -> f7(I42, -1 + I43, 0, I45, I46, I47) 26.20/25.87 f6(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, 1 + I50, I51, I52, I53) [1 + I50 <= I49] 26.20/25.87 f6(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) [I55 <= I56] 26.20/25.87 f2(I60, I61, I62, I63, I64, I65) -> f5(I60, I61, I62, I63, I64, I65) 26.20/25.87 f4(I66, I67, I68, I69, I70, I71) -> f3(I66, I67, I68, I69, I70, I71) [I69 <= 0] 26.20/25.87 f4(I72, I73, I74, I75, I76, I77) -> f1(I72, I73, I74, I75, I76, I77) [1 <= I75] 26.20/25.87 f1(I78, I79, I80, I81, I82, I83) -> f3(I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 26.20/25.87 f1(I84, I85, I86, I87, I88, I89) -> f2(I84, 0, I86, I87, I88, rnd6) [rnd6 = rnd6 /\ I87 <= I84] 26.20/25.87 26.20/25.87 The dependency graph for this problem is: 26.20/25.87 7 -> 26.20/25.87 Where: 26.20/25.87 7) f7#(I36, I37, I38, I39, I40, I41) -> f6#(I36, I37, I38, I39, I40, I41) 26.20/25.87 26.20/25.87 We have the following SCCs. 26.20/25.87 26.20/25.87 26.20/25.87 DP problem for innermost termination. 26.20/25.87 P = 26.20/25.87 f5#(I6, I7, I8, I9, I10, I11) -> f9#(I6, I7, I8, I9, I10, I11) [1 + I7 <= I9] 26.20/25.87 f5#(I12, I13, I14, I15, I16, I17) -> f9#(I12, I13, I14, I15, I16, I17) [1 + I15 <= I13] 26.20/25.87 f9#(I30, I31, I32, I33, I34, I35) -> f2#(I30, 1 + I31, I32, I33, I34, I35) 26.20/25.87 f2#(I60, I61, I62, I63, I64, I65) -> f5#(I60, I61, I62, I63, I64, I65) 26.20/25.87 R = 26.20/25.87 f11(x1, x2, x3, x4, x5, x6) -> f10(x1, x2, x3, x4, x5, x6) 26.20/25.87 f10(I0, I1, I2, I3, I4, I5) -> f4(I0, I1, I2, rnd4, rnd5, I5) [rnd4 = rnd5 /\ rnd5 = rnd5] 26.20/25.87 f5(I6, I7, I8, I9, I10, I11) -> f9(I6, I7, I8, I9, I10, I11) [1 + I7 <= I9] 26.20/25.87 f5(I12, I13, I14, I15, I16, I17) -> f9(I12, I13, I14, I15, I16, I17) [1 + I15 <= I13] 26.20/25.87 f5(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) [I21 <= I19 /\ I19 <= I21] 26.20/25.87 f9(I24, I25, I26, I27, I28, I29) -> f8(I24, I25, I26, I27, I28, I29) 26.20/25.87 f9(I30, I31, I32, I33, I34, I35) -> f2(I30, 1 + I31, I32, I33, I34, I35) 26.20/25.87 f7(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 26.20/25.87 f8(I42, I43, I44, I45, I46, I47) -> f7(I42, -1 + I43, 0, I45, I46, I47) 26.20/25.87 f6(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, 1 + I50, I51, I52, I53) [1 + I50 <= I49] 26.20/25.87 f6(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) [I55 <= I56] 26.20/25.87 f2(I60, I61, I62, I63, I64, I65) -> f5(I60, I61, I62, I63, I64, I65) 26.20/25.87 f4(I66, I67, I68, I69, I70, I71) -> f3(I66, I67, I68, I69, I70, I71) [I69 <= 0] 26.20/25.87 f4(I72, I73, I74, I75, I76, I77) -> f1(I72, I73, I74, I75, I76, I77) [1 <= I75] 26.20/25.87 f1(I78, I79, I80, I81, I82, I83) -> f3(I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 26.20/25.87 f1(I84, I85, I86, I87, I88, I89) -> f2(I84, 0, I86, I87, I88, rnd6) [rnd6 = rnd6 /\ I87 <= I84] 26.20/25.87 26.20/25.87 We use the extended value criterion with the projection function NU: 26.20/25.87 NU[f2#(x0,x1,x2,x3,x4,x5)] = -x1 + x3 - 1 26.20/25.87 NU[f9#(x0,x1,x2,x3,x4,x5)] = -x1 + x3 - 2 26.20/25.87 NU[f5#(x0,x1,x2,x3,x4,x5)] = -x1 + x3 - 1 26.20/25.87 26.20/25.87 This gives the following inequalities: 26.20/25.87 1 + I7 <= I9 ==> -I7 + I9 - 1 > -I7 + I9 - 2 with -I7 + I9 - 1 >= 0 26.20/25.87 1 + I15 <= I13 ==> -I13 + I15 - 1 >= -I13 + I15 - 2 26.20/25.87 ==> -I31 + I33 - 2 >= -(1 + I31) + I33 - 1 26.20/25.87 ==> -I61 + I63 - 1 >= -I61 + I63 - 1 26.20/25.87 26.20/25.87 We remove all the strictly oriented dependency pairs. 26.20/25.87 26.20/25.87 DP problem for innermost termination. 26.20/25.87 P = 26.20/25.87 f5#(I12, I13, I14, I15, I16, I17) -> f9#(I12, I13, I14, I15, I16, I17) [1 + I15 <= I13] 26.20/25.87 f9#(I30, I31, I32, I33, I34, I35) -> f2#(I30, 1 + I31, I32, I33, I34, I35) 26.20/25.87 f2#(I60, I61, I62, I63, I64, I65) -> f5#(I60, I61, I62, I63, I64, I65) 26.20/25.87 R = 26.20/25.87 f11(x1, x2, x3, x4, x5, x6) -> f10(x1, x2, x3, x4, x5, x6) 26.20/25.87 f10(I0, I1, I2, I3, I4, I5) -> f4(I0, I1, I2, rnd4, rnd5, I5) [rnd4 = rnd5 /\ rnd5 = rnd5] 26.20/25.87 f5(I6, I7, I8, I9, I10, I11) -> f9(I6, I7, I8, I9, I10, I11) [1 + I7 <= I9] 26.20/25.87 f5(I12, I13, I14, I15, I16, I17) -> f9(I12, I13, I14, I15, I16, I17) [1 + I15 <= I13] 26.20/25.87 f5(I18, I19, I20, I21, I22, I23) -> f8(I18, I19, I20, I21, I22, I23) [I21 <= I19 /\ I19 <= I21] 26.20/25.87 f9(I24, I25, I26, I27, I28, I29) -> f8(I24, I25, I26, I27, I28, I29) 26.20/25.87 f9(I30, I31, I32, I33, I34, I35) -> f2(I30, 1 + I31, I32, I33, I34, I35) 26.20/25.87 f7(I36, I37, I38, I39, I40, I41) -> f6(I36, I37, I38, I39, I40, I41) 26.20/25.87 f8(I42, I43, I44, I45, I46, I47) -> f7(I42, -1 + I43, 0, I45, I46, I47) 26.20/25.87 f6(I48, I49, I50, I51, I52, I53) -> f7(I48, I49, 1 + I50, I51, I52, I53) [1 + I50 <= I49] 26.20/25.87 f6(I54, I55, I56, I57, I58, I59) -> f3(I54, I55, I56, I57, I58, I59) [I55 <= I56] 26.20/25.87 f2(I60, I61, I62, I63, I64, I65) -> f5(I60, I61, I62, I63, I64, I65) 26.20/25.87 f4(I66, I67, I68, I69, I70, I71) -> f3(I66, I67, I68, I69, I70, I71) [I69 <= 0] 26.20/25.87 f4(I72, I73, I74, I75, I76, I77) -> f1(I72, I73, I74, I75, I76, I77) [1 <= I75] 26.20/25.87 f1(I78, I79, I80, I81, I82, I83) -> f3(I78, I79, I80, I81, I82, I83) [1 + I78 <= I81] 26.20/25.87 f1(I84, I85, I86, I87, I88, I89) -> f2(I84, 0, I86, I87, I88, rnd6) [rnd6 = rnd6 /\ I87 <= I84] 26.20/25.87 26.20/28.85 EOF