54.84/54.20 MAYBE 54.84/54.20 54.84/54.20 DP problem for innermost termination. 54.84/54.20 P = 54.84/54.20 f12#(x1, x2, x3, x4, x5) -> f11#(x1, x2, x3, x4, x5) 54.84/54.20 f11#(I0, I1, I2, I3, I4) -> f4#(I3, 0, I2, I3, I4) 54.84/54.20 f5#(I5, I6, I7, I8, I9) -> f7#(I5, -1 + I6, -1 + I5, I8, I9) [1 <= I6] 54.84/54.20 f5#(I10, I11, I12, I13, I14) -> f4#(I10, I11, I12, I13, I14) [I11 <= 0] 54.84/54.20 f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, I18, rnd5) [rnd5 = rnd5 /\ 1 <= I17] 54.84/54.20 f8#(I20, I21, I22, I23, I24) -> f3#(I20, I21, I22, I23, I24) [I22 <= 0] 54.84/54.20 f10#(I25, I26, I27, I28, I29) -> f9#(I25, I26, I27, I28, I29) [1 + I29 <= 0] 54.84/54.20 f10#(I30, I31, I32, I33, I34) -> f9#(I30, I31, I32, I33, I34) [1 <= I34] 54.84/54.20 f10#(I35, I36, I37, I38, I39) -> f6#(I35, I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0] 54.84/54.20 f9#(I40, I41, I42, I43, I44) -> f6#(-1 + I40, 1 + I41, I42, I43, I44) 54.84/54.20 f7#(I45, I46, I47, I48, I49) -> f8#(I45, I46, I47, I48, I49) 54.84/54.20 f6#(I50, I51, I52, I53, I54) -> f7#(I50, I51, -1 + I52, I53, I54) 54.84/54.20 f3#(I55, I56, I57, I58, I59) -> f5#(I55, I56, I57, I58, I59) 54.84/54.20 f4#(I60, I61, I62, I63, I64) -> f1#(I60, I61, I62, I63, I64) 54.84/54.20 f1#(I65, I66, I67, I68, I69) -> f3#(-1 + I65, 1 + I66, I67, I68, I69) [1 <= I65] 54.84/54.20 R = 54.84/54.20 f12(x1, x2, x3, x4, x5) -> f11(x1, x2, x3, x4, x5) 54.84/54.20 f11(I0, I1, I2, I3, I4) -> f4(I3, 0, I2, I3, I4) 54.84/54.20 f5(I5, I6, I7, I8, I9) -> f7(I5, -1 + I6, -1 + I5, I8, I9) [1 <= I6] 54.84/54.20 f5(I10, I11, I12, I13, I14) -> f4(I10, I11, I12, I13, I14) [I11 <= 0] 54.84/54.20 f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, I18, rnd5) [rnd5 = rnd5 /\ 1 <= I17] 54.84/54.20 f8(I20, I21, I22, I23, I24) -> f3(I20, I21, I22, I23, I24) [I22 <= 0] 54.84/54.20 f10(I25, I26, I27, I28, I29) -> f9(I25, I26, I27, I28, I29) [1 + I29 <= 0] 54.84/54.20 f10(I30, I31, I32, I33, I34) -> f9(I30, I31, I32, I33, I34) [1 <= I34] 54.84/54.20 f10(I35, I36, I37, I38, I39) -> f6(I35, I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0] 54.84/54.20 f9(I40, I41, I42, I43, I44) -> f6(-1 + I40, 1 + I41, I42, I43, I44) 54.84/54.20 f7(I45, I46, I47, I48, I49) -> f8(I45, I46, I47, I48, I49) 54.84/54.20 f6(I50, I51, I52, I53, I54) -> f7(I50, I51, -1 + I52, I53, I54) 54.84/54.20 f3(I55, I56, I57, I58, I59) -> f5(I55, I56, I57, I58, I59) 54.84/54.20 f4(I60, I61, I62, I63, I64) -> f1(I60, I61, I62, I63, I64) 54.84/54.20 f1(I65, I66, I67, I68, I69) -> f3(-1 + I65, 1 + I66, I67, I68, I69) [1 <= I65] 54.84/54.20 f1(I70, I71, I72, I73, I74) -> f2(I70, I71, I72, I73, I74) [I70 <= 0] 54.84/54.20 54.84/54.20 The dependency graph for this problem is: 54.84/54.20 0 -> 1 54.84/54.20 1 -> 13 54.84/54.20 2 -> 10 54.84/54.20 3 -> 13 54.84/54.20 4 -> 6, 7, 8 54.84/54.20 5 -> 12 54.84/54.20 6 -> 9 54.84/54.20 7 -> 9 54.84/54.20 8 -> 11 54.84/54.20 9 -> 11 54.84/54.20 10 -> 4, 5 54.84/54.20 11 -> 10 54.84/54.20 12 -> 2, 3 54.84/54.20 13 -> 14 54.84/54.20 14 -> 12 54.84/54.20 Where: 54.84/54.20 0) f12#(x1, x2, x3, x4, x5) -> f11#(x1, x2, x3, x4, x5) 54.84/54.20 1) f11#(I0, I1, I2, I3, I4) -> f4#(I3, 0, I2, I3, I4) 54.84/54.20 2) f5#(I5, I6, I7, I8, I9) -> f7#(I5, -1 + I6, -1 + I5, I8, I9) [1 <= I6] 54.84/54.20 3) f5#(I10, I11, I12, I13, I14) -> f4#(I10, I11, I12, I13, I14) [I11 <= 0] 54.84/54.20 4) f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, I18, rnd5) [rnd5 = rnd5 /\ 1 <= I17] 54.84/54.20 5) f8#(I20, I21, I22, I23, I24) -> f3#(I20, I21, I22, I23, I24) [I22 <= 0] 54.84/54.20 6) f10#(I25, I26, I27, I28, I29) -> f9#(I25, I26, I27, I28, I29) [1 + I29 <= 0] 54.84/54.20 7) f10#(I30, I31, I32, I33, I34) -> f9#(I30, I31, I32, I33, I34) [1 <= I34] 54.84/54.20 8) f10#(I35, I36, I37, I38, I39) -> f6#(I35, I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0] 54.84/54.20 9) f9#(I40, I41, I42, I43, I44) -> f6#(-1 + I40, 1 + I41, I42, I43, I44) 54.84/54.20 10) f7#(I45, I46, I47, I48, I49) -> f8#(I45, I46, I47, I48, I49) 54.84/54.20 11) f6#(I50, I51, I52, I53, I54) -> f7#(I50, I51, -1 + I52, I53, I54) 54.84/54.20 12) f3#(I55, I56, I57, I58, I59) -> f5#(I55, I56, I57, I58, I59) 54.84/54.20 13) f4#(I60, I61, I62, I63, I64) -> f1#(I60, I61, I62, I63, I64) 54.84/54.20 14) f1#(I65, I66, I67, I68, I69) -> f3#(-1 + I65, 1 + I66, I67, I68, I69) [1 <= I65] 54.84/54.20 54.84/54.20 We have the following SCCs. 54.84/54.20 { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 } 54.84/54.20 54.84/54.20 DP problem for innermost termination. 54.84/54.20 P = 54.84/54.20 f5#(I5, I6, I7, I8, I9) -> f7#(I5, -1 + I6, -1 + I5, I8, I9) [1 <= I6] 54.84/54.20 f5#(I10, I11, I12, I13, I14) -> f4#(I10, I11, I12, I13, I14) [I11 <= 0] 54.84/54.20 f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, I18, rnd5) [rnd5 = rnd5 /\ 1 <= I17] 54.84/54.20 f8#(I20, I21, I22, I23, I24) -> f3#(I20, I21, I22, I23, I24) [I22 <= 0] 54.84/54.20 f10#(I25, I26, I27, I28, I29) -> f9#(I25, I26, I27, I28, I29) [1 + I29 <= 0] 54.84/54.20 f10#(I30, I31, I32, I33, I34) -> f9#(I30, I31, I32, I33, I34) [1 <= I34] 54.84/54.20 f10#(I35, I36, I37, I38, I39) -> f6#(I35, I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0] 54.84/54.20 f9#(I40, I41, I42, I43, I44) -> f6#(-1 + I40, 1 + I41, I42, I43, I44) 54.84/54.20 f7#(I45, I46, I47, I48, I49) -> f8#(I45, I46, I47, I48, I49) 54.84/54.20 f6#(I50, I51, I52, I53, I54) -> f7#(I50, I51, -1 + I52, I53, I54) 54.84/54.20 f3#(I55, I56, I57, I58, I59) -> f5#(I55, I56, I57, I58, I59) 54.84/54.20 f4#(I60, I61, I62, I63, I64) -> f1#(I60, I61, I62, I63, I64) 54.84/54.20 f1#(I65, I66, I67, I68, I69) -> f3#(-1 + I65, 1 + I66, I67, I68, I69) [1 <= I65] 54.84/54.20 R = 54.84/54.20 f12(x1, x2, x3, x4, x5) -> f11(x1, x2, x3, x4, x5) 54.84/54.20 f11(I0, I1, I2, I3, I4) -> f4(I3, 0, I2, I3, I4) 54.84/54.20 f5(I5, I6, I7, I8, I9) -> f7(I5, -1 + I6, -1 + I5, I8, I9) [1 <= I6] 54.84/54.20 f5(I10, I11, I12, I13, I14) -> f4(I10, I11, I12, I13, I14) [I11 <= 0] 54.84/54.20 f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, I18, rnd5) [rnd5 = rnd5 /\ 1 <= I17] 54.84/54.20 f8(I20, I21, I22, I23, I24) -> f3(I20, I21, I22, I23, I24) [I22 <= 0] 54.84/54.20 f10(I25, I26, I27, I28, I29) -> f9(I25, I26, I27, I28, I29) [1 + I29 <= 0] 54.84/54.20 f10(I30, I31, I32, I33, I34) -> f9(I30, I31, I32, I33, I34) [1 <= I34] 54.84/54.20 f10(I35, I36, I37, I38, I39) -> f6(I35, I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0] 54.84/54.20 f9(I40, I41, I42, I43, I44) -> f6(-1 + I40, 1 + I41, I42, I43, I44) 54.84/54.20 f7(I45, I46, I47, I48, I49) -> f8(I45, I46, I47, I48, I49) 54.84/54.20 f6(I50, I51, I52, I53, I54) -> f7(I50, I51, -1 + I52, I53, I54) 54.84/54.20 f3(I55, I56, I57, I58, I59) -> f5(I55, I56, I57, I58, I59) 54.84/54.20 f4(I60, I61, I62, I63, I64) -> f1(I60, I61, I62, I63, I64) 54.84/54.20 f1(I65, I66, I67, I68, I69) -> f3(-1 + I65, 1 + I66, I67, I68, I69) [1 <= I65] 54.84/54.20 f1(I70, I71, I72, I73, I74) -> f2(I70, I71, I72, I73, I74) [I70 <= 0] 54.84/54.20 54.84/54.20 We use the reverse value criterion with the projection function NU: 54.84/54.20 NU[f1#(z1,z2,z3,z4,z5)] = z1 54.84/54.20 NU[f6#(z1,z2,z3,z4,z5)] = z1 54.84/54.20 NU[f9#(z1,z2,z3,z4,z5)] = z1 54.84/54.20 NU[f3#(z1,z2,z3,z4,z5)] = z1 54.84/54.20 NU[f10#(z1,z2,z3,z4,z5)] = z1 54.84/54.20 NU[f8#(z1,z2,z3,z4,z5)] = z1 54.84/54.20 NU[f4#(z1,z2,z3,z4,z5)] = z1 54.84/54.20 NU[f7#(z1,z2,z3,z4,z5)] = z1 54.84/54.20 NU[f5#(z1,z2,z3,z4,z5)] = z1 54.84/54.20 54.84/54.20 This gives the following inequalities: 54.84/54.20 1 <= I6 ==> I5 >= I5 54.84/54.20 I11 <= 0 ==> I10 >= I10 54.84/54.20 rnd5 = rnd5 /\ 1 <= I17 ==> I15 >= I15 54.84/54.20 I22 <= 0 ==> I20 >= I20 54.84/54.20 1 + I29 <= 0 ==> I25 >= I25 54.84/54.20 1 <= I34 ==> I30 >= I30 54.84/54.20 0 <= I39 /\ I39 <= 0 ==> I35 >= I35 54.84/54.20 ==> I40 >= -1 + I40 54.84/54.20 ==> I45 >= I45 54.84/54.20 ==> I50 >= I50 54.84/54.20 ==> I55 >= I55 54.84/54.20 ==> I60 >= I60 54.84/54.20 1 <= I65 ==> I65 > -1 + I65 with I65 >= 0 54.84/54.20 54.84/54.20 We remove all the strictly oriented dependency pairs. 54.84/54.20 54.84/54.20 DP problem for innermost termination. 54.84/54.20 P = 54.84/54.20 f5#(I5, I6, I7, I8, I9) -> f7#(I5, -1 + I6, -1 + I5, I8, I9) [1 <= I6] 54.84/54.20 f5#(I10, I11, I12, I13, I14) -> f4#(I10, I11, I12, I13, I14) [I11 <= 0] 54.84/54.20 f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, I18, rnd5) [rnd5 = rnd5 /\ 1 <= I17] 54.84/54.20 f8#(I20, I21, I22, I23, I24) -> f3#(I20, I21, I22, I23, I24) [I22 <= 0] 54.84/54.20 f10#(I25, I26, I27, I28, I29) -> f9#(I25, I26, I27, I28, I29) [1 + I29 <= 0] 54.84/54.20 f10#(I30, I31, I32, I33, I34) -> f9#(I30, I31, I32, I33, I34) [1 <= I34] 54.84/54.20 f10#(I35, I36, I37, I38, I39) -> f6#(I35, I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0] 54.84/54.20 f9#(I40, I41, I42, I43, I44) -> f6#(-1 + I40, 1 + I41, I42, I43, I44) 54.84/54.20 f7#(I45, I46, I47, I48, I49) -> f8#(I45, I46, I47, I48, I49) 54.84/54.20 f6#(I50, I51, I52, I53, I54) -> f7#(I50, I51, -1 + I52, I53, I54) 54.84/54.20 f3#(I55, I56, I57, I58, I59) -> f5#(I55, I56, I57, I58, I59) 54.84/54.20 f4#(I60, I61, I62, I63, I64) -> f1#(I60, I61, I62, I63, I64) 54.84/54.20 R = 54.84/54.20 f12(x1, x2, x3, x4, x5) -> f11(x1, x2, x3, x4, x5) 54.84/54.20 f11(I0, I1, I2, I3, I4) -> f4(I3, 0, I2, I3, I4) 54.84/54.20 f5(I5, I6, I7, I8, I9) -> f7(I5, -1 + I6, -1 + I5, I8, I9) [1 <= I6] 54.84/54.20 f5(I10, I11, I12, I13, I14) -> f4(I10, I11, I12, I13, I14) [I11 <= 0] 54.84/54.20 f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, I18, rnd5) [rnd5 = rnd5 /\ 1 <= I17] 54.84/54.20 f8(I20, I21, I22, I23, I24) -> f3(I20, I21, I22, I23, I24) [I22 <= 0] 54.84/54.20 f10(I25, I26, I27, I28, I29) -> f9(I25, I26, I27, I28, I29) [1 + I29 <= 0] 54.84/54.20 f10(I30, I31, I32, I33, I34) -> f9(I30, I31, I32, I33, I34) [1 <= I34] 54.84/54.20 f10(I35, I36, I37, I38, I39) -> f6(I35, I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0] 54.84/54.20 f9(I40, I41, I42, I43, I44) -> f6(-1 + I40, 1 + I41, I42, I43, I44) 54.84/54.20 f7(I45, I46, I47, I48, I49) -> f8(I45, I46, I47, I48, I49) 54.84/54.20 f6(I50, I51, I52, I53, I54) -> f7(I50, I51, -1 + I52, I53, I54) 54.84/54.20 f3(I55, I56, I57, I58, I59) -> f5(I55, I56, I57, I58, I59) 54.84/54.20 f4(I60, I61, I62, I63, I64) -> f1(I60, I61, I62, I63, I64) 54.84/54.20 f1(I65, I66, I67, I68, I69) -> f3(-1 + I65, 1 + I66, I67, I68, I69) [1 <= I65] 54.84/54.20 f1(I70, I71, I72, I73, I74) -> f2(I70, I71, I72, I73, I74) [I70 <= 0] 54.84/54.20 54.84/54.20 The dependency graph for this problem is: 54.84/54.20 2 -> 10 54.84/54.20 3 -> 13 54.84/54.20 4 -> 6, 7, 8 54.84/54.20 5 -> 12 54.84/54.20 6 -> 9 54.84/54.20 7 -> 9 54.84/54.20 8 -> 11 54.84/54.20 9 -> 11 54.84/54.20 10 -> 4, 5 54.84/54.20 11 -> 10 54.84/54.20 12 -> 2, 3 54.84/54.20 13 -> 54.84/54.20 Where: 54.84/54.20 2) f5#(I5, I6, I7, I8, I9) -> f7#(I5, -1 + I6, -1 + I5, I8, I9) [1 <= I6] 54.84/54.20 3) f5#(I10, I11, I12, I13, I14) -> f4#(I10, I11, I12, I13, I14) [I11 <= 0] 54.84/54.20 4) f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, I18, rnd5) [rnd5 = rnd5 /\ 1 <= I17] 54.84/54.20 5) f8#(I20, I21, I22, I23, I24) -> f3#(I20, I21, I22, I23, I24) [I22 <= 0] 54.84/54.20 6) f10#(I25, I26, I27, I28, I29) -> f9#(I25, I26, I27, I28, I29) [1 + I29 <= 0] 54.84/54.20 7) f10#(I30, I31, I32, I33, I34) -> f9#(I30, I31, I32, I33, I34) [1 <= I34] 54.84/54.20 8) f10#(I35, I36, I37, I38, I39) -> f6#(I35, I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0] 54.84/54.20 9) f9#(I40, I41, I42, I43, I44) -> f6#(-1 + I40, 1 + I41, I42, I43, I44) 54.84/54.20 10) f7#(I45, I46, I47, I48, I49) -> f8#(I45, I46, I47, I48, I49) 54.84/54.20 11) f6#(I50, I51, I52, I53, I54) -> f7#(I50, I51, -1 + I52, I53, I54) 54.84/54.20 12) f3#(I55, I56, I57, I58, I59) -> f5#(I55, I56, I57, I58, I59) 54.84/54.20 13) f4#(I60, I61, I62, I63, I64) -> f1#(I60, I61, I62, I63, I64) 54.84/54.20 54.84/54.20 We have the following SCCs. 54.84/54.20 { 2, 4, 5, 6, 7, 8, 9, 10, 11, 12 } 54.84/54.20 54.84/54.20 DP problem for innermost termination. 54.84/54.20 P = 54.84/54.20 f5#(I5, I6, I7, I8, I9) -> f7#(I5, -1 + I6, -1 + I5, I8, I9) [1 <= I6] 54.84/54.20 f8#(I15, I16, I17, I18, I19) -> f10#(I15, I16, I17, I18, rnd5) [rnd5 = rnd5 /\ 1 <= I17] 54.84/54.20 f8#(I20, I21, I22, I23, I24) -> f3#(I20, I21, I22, I23, I24) [I22 <= 0] 54.84/54.20 f10#(I25, I26, I27, I28, I29) -> f9#(I25, I26, I27, I28, I29) [1 + I29 <= 0] 54.84/54.20 f10#(I30, I31, I32, I33, I34) -> f9#(I30, I31, I32, I33, I34) [1 <= I34] 54.84/54.20 f10#(I35, I36, I37, I38, I39) -> f6#(I35, I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0] 54.84/54.20 f9#(I40, I41, I42, I43, I44) -> f6#(-1 + I40, 1 + I41, I42, I43, I44) 54.84/54.20 f7#(I45, I46, I47, I48, I49) -> f8#(I45, I46, I47, I48, I49) 54.84/54.20 f6#(I50, I51, I52, I53, I54) -> f7#(I50, I51, -1 + I52, I53, I54) 54.84/54.20 f3#(I55, I56, I57, I58, I59) -> f5#(I55, I56, I57, I58, I59) 54.84/54.20 R = 54.84/54.20 f12(x1, x2, x3, x4, x5) -> f11(x1, x2, x3, x4, x5) 54.84/54.20 f11(I0, I1, I2, I3, I4) -> f4(I3, 0, I2, I3, I4) 54.84/54.20 f5(I5, I6, I7, I8, I9) -> f7(I5, -1 + I6, -1 + I5, I8, I9) [1 <= I6] 54.84/54.20 f5(I10, I11, I12, I13, I14) -> f4(I10, I11, I12, I13, I14) [I11 <= 0] 54.84/54.20 f8(I15, I16, I17, I18, I19) -> f10(I15, I16, I17, I18, rnd5) [rnd5 = rnd5 /\ 1 <= I17] 54.84/54.20 f8(I20, I21, I22, I23, I24) -> f3(I20, I21, I22, I23, I24) [I22 <= 0] 54.84/54.20 f10(I25, I26, I27, I28, I29) -> f9(I25, I26, I27, I28, I29) [1 + I29 <= 0] 54.84/54.20 f10(I30, I31, I32, I33, I34) -> f9(I30, I31, I32, I33, I34) [1 <= I34] 54.84/54.20 f10(I35, I36, I37, I38, I39) -> f6(I35, I36, I37, I38, I39) [0 <= I39 /\ I39 <= 0] 54.84/54.20 f9(I40, I41, I42, I43, I44) -> f6(-1 + I40, 1 + I41, I42, I43, I44) 54.84/54.20 f7(I45, I46, I47, I48, I49) -> f8(I45, I46, I47, I48, I49) 54.84/54.20 f6(I50, I51, I52, I53, I54) -> f7(I50, I51, -1 + I52, I53, I54) 54.84/54.20 f3(I55, I56, I57, I58, I59) -> f5(I55, I56, I57, I58, I59) 54.84/54.20 f4(I60, I61, I62, I63, I64) -> f1(I60, I61, I62, I63, I64) 54.84/54.20 f1(I65, I66, I67, I68, I69) -> f3(-1 + I65, 1 + I66, I67, I68, I69) [1 <= I65] 54.84/54.20 f1(I70, I71, I72, I73, I74) -> f2(I70, I71, I72, I73, I74) [I70 <= 0] 54.84/54.20 54.84/57.17 EOF