84.70/83.53 MAYBE 84.70/83.53 84.70/83.53 DP problem for innermost termination. 84.70/83.53 P = 84.70/83.53 f8#(x1, x2, x3, x4, x5, x6, x7, x8) -> f7#(x1, x2, x3, x4, x5, x6, x7, x8) 84.70/83.53 f7#(I0, I1, I2, I3, I4, I5, I6, I7) -> f1#(I0, I1, I2, 0, 1, rnd6, I6, I7) [rnd6 = rnd6] 84.70/83.53 f6#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, I11, I12, I13, I14, I15) 84.70/83.53 f1#(I16, I17, I18, I19, I20, I21, I22, I23) -> f6#(I16, I17, I18, I19, -1 + I20, -1 * I17 + I21, I22, I23) [1 + I16 <= I21 /\ 1 <= I20] 84.70/83.53 f5#(I24, I25, I26, I27, I28, I29, I30, I31) -> f1#(I24, I25, I26, I27, I28, I29, I30, I31) 84.70/83.53 f1#(I32, I33, I34, I35, I36, I37, I38, I39) -> f5#(I32, I33, I34, I35, 1 + I36, I34 + I37, I38, I39) [I37 <= I32 /\ 1 <= I36] 84.70/83.53 f4#(I40, I41, I42, I43, I44, I45, I46, I47) -> f1#(I40, I41, I42, I43, I44, I45, I46, I47) 84.70/83.53 f1#(I48, I49, I50, I51, I52, I53, I54, I55) -> f4#(I48, I49, I50, 1, -1 + I52, -1 * I49 + I53, I52, I53) [1 + I48 <= I53 /\ 1 <= I52 /\ I51 <= 0] 84.70/83.53 f3#(I56, I57, I58, I59, I60, I61, I62, I63) -> f1#(I56, I57, I58, I59, I60, I61, I62, I63) 84.70/83.53 f1#(I64, I65, I66, I67, I68, I69, I70, I71) -> f3#(I64, I65, I66, 1, 1 + I68, I66 + I69, I68, I69) [I69 <= I64 /\ 1 <= I68 /\ I67 <= 0] 84.70/83.53 R = 84.70/83.53 f8(x1, x2, x3, x4, x5, x6, x7, x8) -> f7(x1, x2, x3, x4, x5, x6, x7, x8) 84.70/83.53 f7(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, 1, rnd6, I6, I7) [rnd6 = rnd6] 84.70/83.53 f6(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, I11, I12, I13, I14, I15) 84.70/83.53 f1(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, -1 + I20, -1 * I17 + I21, I22, I23) [1 + I16 <= I21 /\ 1 <= I20] 84.70/83.53 f5(I24, I25, I26, I27, I28, I29, I30, I31) -> f1(I24, I25, I26, I27, I28, I29, I30, I31) 84.70/83.53 f1(I32, I33, I34, I35, I36, I37, I38, I39) -> f5(I32, I33, I34, I35, 1 + I36, I34 + I37, I38, I39) [I37 <= I32 /\ 1 <= I36] 84.70/83.53 f4(I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I40, I41, I42, I43, I44, I45, I46, I47) 84.70/83.53 f1(I48, I49, I50, I51, I52, I53, I54, I55) -> f4(I48, I49, I50, 1, -1 + I52, -1 * I49 + I53, I52, I53) [1 + I48 <= I53 /\ 1 <= I52 /\ I51 <= 0] 84.70/83.53 f3(I56, I57, I58, I59, I60, I61, I62, I63) -> f1(I56, I57, I58, I59, I60, I61, I62, I63) 84.70/83.53 f1(I64, I65, I66, I67, I68, I69, I70, I71) -> f3(I64, I65, I66, 1, 1 + I68, I66 + I69, I68, I69) [I69 <= I64 /\ 1 <= I68 /\ I67 <= 0] 84.70/83.53 f1(I72, I73, I74, I75, I76, I77, I78, I79) -> f2(I72, I73, I74, I75, I76, I77, I78, I79) [I77 <= I79 /\ I78 <= I76 /\ 1 <= I75] 84.70/83.53 84.70/83.53 The dependency graph for this problem is: 84.70/83.53 0 -> 1 84.70/83.53 1 -> 3, 5, 7, 9 84.70/83.53 2 -> 3, 5, 7, 9 84.70/83.53 3 -> 2 84.70/83.53 4 -> 3, 5, 7, 9 84.70/83.53 5 -> 4 84.70/83.53 6 -> 3, 5, 7, 9 84.70/83.53 7 -> 6 84.70/83.53 8 -> 3, 5, 7, 9 84.70/83.53 9 -> 8 84.70/83.53 Where: 84.70/83.53 0) f8#(x1, x2, x3, x4, x5, x6, x7, x8) -> f7#(x1, x2, x3, x4, x5, x6, x7, x8) 84.70/83.53 1) f7#(I0, I1, I2, I3, I4, I5, I6, I7) -> f1#(I0, I1, I2, 0, 1, rnd6, I6, I7) [rnd6 = rnd6] 84.70/83.53 2) f6#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, I11, I12, I13, I14, I15) 84.70/83.53 3) f1#(I16, I17, I18, I19, I20, I21, I22, I23) -> f6#(I16, I17, I18, I19, -1 + I20, -1 * I17 + I21, I22, I23) [1 + I16 <= I21 /\ 1 <= I20] 84.70/83.53 4) f5#(I24, I25, I26, I27, I28, I29, I30, I31) -> f1#(I24, I25, I26, I27, I28, I29, I30, I31) 84.70/83.53 5) f1#(I32, I33, I34, I35, I36, I37, I38, I39) -> f5#(I32, I33, I34, I35, 1 + I36, I34 + I37, I38, I39) [I37 <= I32 /\ 1 <= I36] 84.70/83.53 6) f4#(I40, I41, I42, I43, I44, I45, I46, I47) -> f1#(I40, I41, I42, I43, I44, I45, I46, I47) 84.70/83.53 7) f1#(I48, I49, I50, I51, I52, I53, I54, I55) -> f4#(I48, I49, I50, 1, -1 + I52, -1 * I49 + I53, I52, I53) [1 + I48 <= I53 /\ 1 <= I52 /\ I51 <= 0] 84.70/83.53 8) f3#(I56, I57, I58, I59, I60, I61, I62, I63) -> f1#(I56, I57, I58, I59, I60, I61, I62, I63) 84.70/83.53 9) f1#(I64, I65, I66, I67, I68, I69, I70, I71) -> f3#(I64, I65, I66, 1, 1 + I68, I66 + I69, I68, I69) [I69 <= I64 /\ 1 <= I68 /\ I67 <= 0] 84.70/83.53 84.70/83.53 We have the following SCCs. 84.70/83.53 { 2, 3, 4, 5, 6, 7, 8, 9 } 84.70/83.53 84.70/83.53 DP problem for innermost termination. 84.70/83.53 P = 84.70/83.53 f6#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, I11, I12, I13, I14, I15) 84.70/83.53 f1#(I16, I17, I18, I19, I20, I21, I22, I23) -> f6#(I16, I17, I18, I19, -1 + I20, -1 * I17 + I21, I22, I23) [1 + I16 <= I21 /\ 1 <= I20] 84.70/83.53 f5#(I24, I25, I26, I27, I28, I29, I30, I31) -> f1#(I24, I25, I26, I27, I28, I29, I30, I31) 84.70/83.53 f1#(I32, I33, I34, I35, I36, I37, I38, I39) -> f5#(I32, I33, I34, I35, 1 + I36, I34 + I37, I38, I39) [I37 <= I32 /\ 1 <= I36] 84.70/83.53 f4#(I40, I41, I42, I43, I44, I45, I46, I47) -> f1#(I40, I41, I42, I43, I44, I45, I46, I47) 84.70/83.53 f1#(I48, I49, I50, I51, I52, I53, I54, I55) -> f4#(I48, I49, I50, 1, -1 + I52, -1 * I49 + I53, I52, I53) [1 + I48 <= I53 /\ 1 <= I52 /\ I51 <= 0] 84.70/83.53 f3#(I56, I57, I58, I59, I60, I61, I62, I63) -> f1#(I56, I57, I58, I59, I60, I61, I62, I63) 84.70/83.53 f1#(I64, I65, I66, I67, I68, I69, I70, I71) -> f3#(I64, I65, I66, 1, 1 + I68, I66 + I69, I68, I69) [I69 <= I64 /\ 1 <= I68 /\ I67 <= 0] 84.70/83.53 R = 84.70/83.53 f8(x1, x2, x3, x4, x5, x6, x7, x8) -> f7(x1, x2, x3, x4, x5, x6, x7, x8) 84.70/83.53 f7(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, 1, rnd6, I6, I7) [rnd6 = rnd6] 84.70/83.53 f6(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, I11, I12, I13, I14, I15) 84.70/83.53 f1(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, -1 + I20, -1 * I17 + I21, I22, I23) [1 + I16 <= I21 /\ 1 <= I20] 84.70/83.53 f5(I24, I25, I26, I27, I28, I29, I30, I31) -> f1(I24, I25, I26, I27, I28, I29, I30, I31) 84.70/83.53 f1(I32, I33, I34, I35, I36, I37, I38, I39) -> f5(I32, I33, I34, I35, 1 + I36, I34 + I37, I38, I39) [I37 <= I32 /\ 1 <= I36] 84.70/83.53 f4(I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I40, I41, I42, I43, I44, I45, I46, I47) 84.70/83.53 f1(I48, I49, I50, I51, I52, I53, I54, I55) -> f4(I48, I49, I50, 1, -1 + I52, -1 * I49 + I53, I52, I53) [1 + I48 <= I53 /\ 1 <= I52 /\ I51 <= 0] 84.70/83.53 f3(I56, I57, I58, I59, I60, I61, I62, I63) -> f1(I56, I57, I58, I59, I60, I61, I62, I63) 84.70/83.53 f1(I64, I65, I66, I67, I68, I69, I70, I71) -> f3(I64, I65, I66, 1, 1 + I68, I66 + I69, I68, I69) [I69 <= I64 /\ 1 <= I68 /\ I67 <= 0] 84.70/83.53 f1(I72, I73, I74, I75, I76, I77, I78, I79) -> f2(I72, I73, I74, I75, I76, I77, I78, I79) [I77 <= I79 /\ I78 <= I76 /\ 1 <= I75] 84.70/83.53 84.70/83.53 We use the reverse value criterion with the projection function NU: 84.70/83.53 NU[f3#(z1,z2,z3,z4,z5,z6,z7,z8)] = 0 + -1 * z4 84.70/83.53 NU[f4#(z1,z2,z3,z4,z5,z6,z7,z8)] = 0 + -1 * z4 84.70/83.53 NU[f5#(z1,z2,z3,z4,z5,z6,z7,z8)] = 0 + -1 * z4 84.70/83.53 NU[f1#(z1,z2,z3,z4,z5,z6,z7,z8)] = 0 + -1 * z4 84.70/83.53 NU[f6#(z1,z2,z3,z4,z5,z6,z7,z8)] = 0 + -1 * z4 84.70/83.53 84.70/83.53 This gives the following inequalities: 84.70/83.53 ==> 0 + -1 * I11 >= 0 + -1 * I11 84.70/83.53 1 + I16 <= I21 /\ 1 <= I20 ==> 0 + -1 * I19 >= 0 + -1 * I19 84.70/83.53 ==> 0 + -1 * I27 >= 0 + -1 * I27 84.70/83.53 I37 <= I32 /\ 1 <= I36 ==> 0 + -1 * I35 >= 0 + -1 * I35 84.70/83.53 ==> 0 + -1 * I43 >= 0 + -1 * I43 84.70/83.53 1 + I48 <= I53 /\ 1 <= I52 /\ I51 <= 0 ==> 0 + -1 * I51 > 0 + -1 * 1 with 0 + -1 * I51 >= 0 84.70/83.53 ==> 0 + -1 * I59 >= 0 + -1 * I59 84.70/83.53 I69 <= I64 /\ 1 <= I68 /\ I67 <= 0 ==> 0 + -1 * I67 > 0 + -1 * 1 with 0 + -1 * I67 >= 0 84.70/83.53 84.70/83.53 We remove all the strictly oriented dependency pairs. 84.70/83.53 84.70/83.53 DP problem for innermost termination. 84.70/83.53 P = 84.70/83.53 f6#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, I11, I12, I13, I14, I15) 84.70/83.53 f1#(I16, I17, I18, I19, I20, I21, I22, I23) -> f6#(I16, I17, I18, I19, -1 + I20, -1 * I17 + I21, I22, I23) [1 + I16 <= I21 /\ 1 <= I20] 84.70/83.53 f5#(I24, I25, I26, I27, I28, I29, I30, I31) -> f1#(I24, I25, I26, I27, I28, I29, I30, I31) 84.70/83.53 f1#(I32, I33, I34, I35, I36, I37, I38, I39) -> f5#(I32, I33, I34, I35, 1 + I36, I34 + I37, I38, I39) [I37 <= I32 /\ 1 <= I36] 84.70/83.53 f4#(I40, I41, I42, I43, I44, I45, I46, I47) -> f1#(I40, I41, I42, I43, I44, I45, I46, I47) 84.70/83.53 f3#(I56, I57, I58, I59, I60, I61, I62, I63) -> f1#(I56, I57, I58, I59, I60, I61, I62, I63) 84.70/83.53 R = 84.70/83.53 f8(x1, x2, x3, x4, x5, x6, x7, x8) -> f7(x1, x2, x3, x4, x5, x6, x7, x8) 84.70/83.53 f7(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, 1, rnd6, I6, I7) [rnd6 = rnd6] 84.70/83.53 f6(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, I11, I12, I13, I14, I15) 84.70/83.53 f1(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, -1 + I20, -1 * I17 + I21, I22, I23) [1 + I16 <= I21 /\ 1 <= I20] 84.70/83.53 f5(I24, I25, I26, I27, I28, I29, I30, I31) -> f1(I24, I25, I26, I27, I28, I29, I30, I31) 84.70/83.53 f1(I32, I33, I34, I35, I36, I37, I38, I39) -> f5(I32, I33, I34, I35, 1 + I36, I34 + I37, I38, I39) [I37 <= I32 /\ 1 <= I36] 84.70/83.53 f4(I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I40, I41, I42, I43, I44, I45, I46, I47) 84.70/83.53 f1(I48, I49, I50, I51, I52, I53, I54, I55) -> f4(I48, I49, I50, 1, -1 + I52, -1 * I49 + I53, I52, I53) [1 + I48 <= I53 /\ 1 <= I52 /\ I51 <= 0] 84.70/83.53 f3(I56, I57, I58, I59, I60, I61, I62, I63) -> f1(I56, I57, I58, I59, I60, I61, I62, I63) 84.70/83.53 f1(I64, I65, I66, I67, I68, I69, I70, I71) -> f3(I64, I65, I66, 1, 1 + I68, I66 + I69, I68, I69) [I69 <= I64 /\ 1 <= I68 /\ I67 <= 0] 84.70/83.53 f1(I72, I73, I74, I75, I76, I77, I78, I79) -> f2(I72, I73, I74, I75, I76, I77, I78, I79) [I77 <= I79 /\ I78 <= I76 /\ 1 <= I75] 84.70/83.53 84.70/83.53 The dependency graph for this problem is: 84.70/83.53 2 -> 3, 5 84.70/83.53 3 -> 2 84.70/83.53 4 -> 3, 5 84.70/83.53 5 -> 4 84.70/83.53 6 -> 3, 5 84.70/83.53 8 -> 3, 5 84.70/83.53 Where: 84.70/83.53 2) f6#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, I11, I12, I13, I14, I15) 84.70/83.53 3) f1#(I16, I17, I18, I19, I20, I21, I22, I23) -> f6#(I16, I17, I18, I19, -1 + I20, -1 * I17 + I21, I22, I23) [1 + I16 <= I21 /\ 1 <= I20] 84.70/83.53 4) f5#(I24, I25, I26, I27, I28, I29, I30, I31) -> f1#(I24, I25, I26, I27, I28, I29, I30, I31) 84.70/83.53 5) f1#(I32, I33, I34, I35, I36, I37, I38, I39) -> f5#(I32, I33, I34, I35, 1 + I36, I34 + I37, I38, I39) [I37 <= I32 /\ 1 <= I36] 84.70/83.53 6) f4#(I40, I41, I42, I43, I44, I45, I46, I47) -> f1#(I40, I41, I42, I43, I44, I45, I46, I47) 84.70/83.53 8) f3#(I56, I57, I58, I59, I60, I61, I62, I63) -> f1#(I56, I57, I58, I59, I60, I61, I62, I63) 84.70/83.53 84.70/83.53 We have the following SCCs. 84.70/83.53 { 2, 3, 4, 5 } 84.70/83.53 84.70/83.53 DP problem for innermost termination. 84.70/83.53 P = 84.70/83.53 f6#(I8, I9, I10, I11, I12, I13, I14, I15) -> f1#(I8, I9, I10, I11, I12, I13, I14, I15) 84.70/83.53 f1#(I16, I17, I18, I19, I20, I21, I22, I23) -> f6#(I16, I17, I18, I19, -1 + I20, -1 * I17 + I21, I22, I23) [1 + I16 <= I21 /\ 1 <= I20] 84.70/83.53 f5#(I24, I25, I26, I27, I28, I29, I30, I31) -> f1#(I24, I25, I26, I27, I28, I29, I30, I31) 84.70/83.53 f1#(I32, I33, I34, I35, I36, I37, I38, I39) -> f5#(I32, I33, I34, I35, 1 + I36, I34 + I37, I38, I39) [I37 <= I32 /\ 1 <= I36] 84.70/83.53 R = 84.70/83.53 f8(x1, x2, x3, x4, x5, x6, x7, x8) -> f7(x1, x2, x3, x4, x5, x6, x7, x8) 84.70/83.53 f7(I0, I1, I2, I3, I4, I5, I6, I7) -> f1(I0, I1, I2, 0, 1, rnd6, I6, I7) [rnd6 = rnd6] 84.70/83.53 f6(I8, I9, I10, I11, I12, I13, I14, I15) -> f1(I8, I9, I10, I11, I12, I13, I14, I15) 84.70/83.53 f1(I16, I17, I18, I19, I20, I21, I22, I23) -> f6(I16, I17, I18, I19, -1 + I20, -1 * I17 + I21, I22, I23) [1 + I16 <= I21 /\ 1 <= I20] 84.70/83.53 f5(I24, I25, I26, I27, I28, I29, I30, I31) -> f1(I24, I25, I26, I27, I28, I29, I30, I31) 84.70/83.53 f1(I32, I33, I34, I35, I36, I37, I38, I39) -> f5(I32, I33, I34, I35, 1 + I36, I34 + I37, I38, I39) [I37 <= I32 /\ 1 <= I36] 84.70/83.53 f4(I40, I41, I42, I43, I44, I45, I46, I47) -> f1(I40, I41, I42, I43, I44, I45, I46, I47) 84.70/83.53 f1(I48, I49, I50, I51, I52, I53, I54, I55) -> f4(I48, I49, I50, 1, -1 + I52, -1 * I49 + I53, I52, I53) [1 + I48 <= I53 /\ 1 <= I52 /\ I51 <= 0] 84.70/83.53 f3(I56, I57, I58, I59, I60, I61, I62, I63) -> f1(I56, I57, I58, I59, I60, I61, I62, I63) 84.70/83.53 f1(I64, I65, I66, I67, I68, I69, I70, I71) -> f3(I64, I65, I66, 1, 1 + I68, I66 + I69, I68, I69) [I69 <= I64 /\ 1 <= I68 /\ I67 <= 0] 84.70/83.53 f1(I72, I73, I74, I75, I76, I77, I78, I79) -> f2(I72, I73, I74, I75, I76, I77, I78, I79) [I77 <= I79 /\ I78 <= I76 /\ 1 <= I75] 84.70/83.53 84.70/86.51 EOF