4.58/5.00 YES 4.58/5.00 4.58/5.00 DP problem for innermost termination. 4.58/5.00 P = 4.58/5.00 init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 4.58/5.00 f6#(I0, I1, I2, I3, I4) -> f6#(I5, I6, I2, I7, I8) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 2 <= I1] 4.58/5.00 f6#(I9, I10, I11, I12, I13) -> f6#(I14, I15, I11, I16, I17) [-1 <= I15 - 1 /\ 0 <= I14 - 1 /\ 2 <= I10 - 1 /\ 0 <= I9 - 1 /\ 1 <= I11 - 1 /\ I15 + 2 <= I10] 4.58/5.00 f6#(I18, I19, I20, I21, I22) -> f6#(I23, I24, I20, I25, I26) [-1 <= I24 - 1 /\ 0 <= I23 - 1 /\ 2 <= I19 - 1 /\ 0 <= I18 - 1 /\ I24 + 3 <= I19 /\ 1 <= I20 - 1 /\ I23 <= I18] 4.58/5.00 f2#(I27, I28, I29, I30, I31) -> f6#(I32, I33, I29, I34, I35) [0 <= y1 - 1 /\ 1 <= I29 - 1 /\ I32 - 1 <= I27 /\ I32 + 2 <= I28 /\ I33 + 3 <= I28 /\ 0 <= I27 - 1 /\ 3 <= I28 - 1 /\ 1 <= I32 - 1 /\ 0 <= I33 - 1 /\ I31 + 5 <= I28 /\ I30 + 5 <= I28] 4.58/5.00 f5#(I36, I37, I38, I39, I40) -> f5#(I36, I37 + 1, I38, I39, I41) [I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1] 4.58/5.00 f5#(I42, I43, I44, I45, I46) -> f4#(I42 - 1, I45, I46, I47, I48) [I42 - 1 <= I42 - 1 /\ 1 <= I46 - 1 /\ 0 <= I44 - 1 /\ 1 <= I42 - 1 /\ I43 <= I44 - 1] 4.58/5.00 f4#(I49, I50, I51, I52, I53) -> f5#(I49, 0, I54, I50, I51 + 1) [-1 <= I54 - 1 /\ I51 <= I50 - 1 /\ 0 <= I51 - 1 /\ 1 <= I49 - 1 /\ -1 <= I50 - 1] 4.58/5.00 f1#(I55, I56, I57, I58, I59) -> f4#(I60, I56, 1, I61, I62) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1] 4.58/5.00 f3#(I63, I64, I65, I66, I67) -> f2#(I68, I69, I65, I66, I67) [I66 + 5 <= I64 /\ I67 + 5 <= I64 /\ 3 <= I69 - 1 /\ 0 <= I68 - 1 /\ 3 <= I64 - 1 /\ 0 <= I63 - 1 /\ I69 <= I64 /\ I68 + 3 <= I64 /\ I68 <= I63] 4.58/5.00 f1#(I70, I71, I72, I73, I74) -> f2#(I75, I76, I77, I78, I79) [-1 <= I80 - 1 /\ 0 <= I71 - 1 /\ I75 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I75 - 1 /\ 3 <= I76 - 1] 4.58/5.00 R = 4.58/5.00 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 4.58/5.00 f6(I0, I1, I2, I3, I4) -> f6(I5, I6, I2, I7, I8) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 2 <= I1] 4.58/5.00 f6(I9, I10, I11, I12, I13) -> f6(I14, I15, I11, I16, I17) [-1 <= I15 - 1 /\ 0 <= I14 - 1 /\ 2 <= I10 - 1 /\ 0 <= I9 - 1 /\ 1 <= I11 - 1 /\ I15 + 2 <= I10] 4.58/5.00 f6(I18, I19, I20, I21, I22) -> f6(I23, I24, I20, I25, I26) [-1 <= I24 - 1 /\ 0 <= I23 - 1 /\ 2 <= I19 - 1 /\ 0 <= I18 - 1 /\ I24 + 3 <= I19 /\ 1 <= I20 - 1 /\ I23 <= I18] 4.58/5.00 f2(I27, I28, I29, I30, I31) -> f6(I32, I33, I29, I34, I35) [0 <= y1 - 1 /\ 1 <= I29 - 1 /\ I32 - 1 <= I27 /\ I32 + 2 <= I28 /\ I33 + 3 <= I28 /\ 0 <= I27 - 1 /\ 3 <= I28 - 1 /\ 1 <= I32 - 1 /\ 0 <= I33 - 1 /\ I31 + 5 <= I28 /\ I30 + 5 <= I28] 4.58/5.00 f5(I36, I37, I38, I39, I40) -> f5(I36, I37 + 1, I38, I39, I41) [I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1] 4.58/5.00 f5(I42, I43, I44, I45, I46) -> f4(I42 - 1, I45, I46, I47, I48) [I42 - 1 <= I42 - 1 /\ 1 <= I46 - 1 /\ 0 <= I44 - 1 /\ 1 <= I42 - 1 /\ I43 <= I44 - 1] 4.58/5.00 f4(I49, I50, I51, I52, I53) -> f5(I49, 0, I54, I50, I51 + 1) [-1 <= I54 - 1 /\ I51 <= I50 - 1 /\ 0 <= I51 - 1 /\ 1 <= I49 - 1 /\ -1 <= I50 - 1] 4.58/5.00 f1(I55, I56, I57, I58, I59) -> f4(I60, I56, 1, I61, I62) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1] 4.58/5.00 f3(I63, I64, I65, I66, I67) -> f2(I68, I69, I65, I66, I67) [I66 + 5 <= I64 /\ I67 + 5 <= I64 /\ 3 <= I69 - 1 /\ 0 <= I68 - 1 /\ 3 <= I64 - 1 /\ 0 <= I63 - 1 /\ I69 <= I64 /\ I68 + 3 <= I64 /\ I68 <= I63] 4.58/5.00 f1(I70, I71, I72, I73, I74) -> f2(I75, I76, I77, I78, I79) [-1 <= I80 - 1 /\ 0 <= I71 - 1 /\ I75 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I75 - 1 /\ 3 <= I76 - 1] 4.58/5.00 4.58/5.00 The dependency graph for this problem is: 4.58/5.00 0 -> 8, 10 4.58/5.00 1 -> 1, 2, 3 4.58/5.00 2 -> 1, 2, 3 4.58/5.00 3 -> 1, 2, 3 4.58/5.00 4 -> 1, 2, 3 4.58/5.00 5 -> 5, 6 4.58/5.00 6 -> 7 4.58/5.00 7 -> 5, 6 4.58/5.00 8 -> 7 4.58/5.00 9 -> 4 4.58/5.00 10 -> 4 4.58/5.00 Where: 4.58/5.00 0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 4.58/5.00 1) f6#(I0, I1, I2, I3, I4) -> f6#(I5, I6, I2, I7, I8) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 2 <= I1] 4.58/5.00 2) f6#(I9, I10, I11, I12, I13) -> f6#(I14, I15, I11, I16, I17) [-1 <= I15 - 1 /\ 0 <= I14 - 1 /\ 2 <= I10 - 1 /\ 0 <= I9 - 1 /\ 1 <= I11 - 1 /\ I15 + 2 <= I10] 4.58/5.00 3) f6#(I18, I19, I20, I21, I22) -> f6#(I23, I24, I20, I25, I26) [-1 <= I24 - 1 /\ 0 <= I23 - 1 /\ 2 <= I19 - 1 /\ 0 <= I18 - 1 /\ I24 + 3 <= I19 /\ 1 <= I20 - 1 /\ I23 <= I18] 4.58/5.00 4) f2#(I27, I28, I29, I30, I31) -> f6#(I32, I33, I29, I34, I35) [0 <= y1 - 1 /\ 1 <= I29 - 1 /\ I32 - 1 <= I27 /\ I32 + 2 <= I28 /\ I33 + 3 <= I28 /\ 0 <= I27 - 1 /\ 3 <= I28 - 1 /\ 1 <= I32 - 1 /\ 0 <= I33 - 1 /\ I31 + 5 <= I28 /\ I30 + 5 <= I28] 4.58/5.00 5) f5#(I36, I37, I38, I39, I40) -> f5#(I36, I37 + 1, I38, I39, I41) [I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1] 4.58/5.00 6) f5#(I42, I43, I44, I45, I46) -> f4#(I42 - 1, I45, I46, I47, I48) [I42 - 1 <= I42 - 1 /\ 1 <= I46 - 1 /\ 0 <= I44 - 1 /\ 1 <= I42 - 1 /\ I43 <= I44 - 1] 4.58/5.00 7) f4#(I49, I50, I51, I52, I53) -> f5#(I49, 0, I54, I50, I51 + 1) [-1 <= I54 - 1 /\ I51 <= I50 - 1 /\ 0 <= I51 - 1 /\ 1 <= I49 - 1 /\ -1 <= I50 - 1] 4.58/5.00 8) f1#(I55, I56, I57, I58, I59) -> f4#(I60, I56, 1, I61, I62) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1] 4.58/5.00 9) f3#(I63, I64, I65, I66, I67) -> f2#(I68, I69, I65, I66, I67) [I66 + 5 <= I64 /\ I67 + 5 <= I64 /\ 3 <= I69 - 1 /\ 0 <= I68 - 1 /\ 3 <= I64 - 1 /\ 0 <= I63 - 1 /\ I69 <= I64 /\ I68 + 3 <= I64 /\ I68 <= I63] 4.58/5.00 10) f1#(I70, I71, I72, I73, I74) -> f2#(I75, I76, I77, I78, I79) [-1 <= I80 - 1 /\ 0 <= I71 - 1 /\ I75 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I75 - 1 /\ 3 <= I76 - 1] 4.58/5.00 4.58/5.00 We have the following SCCs. 4.58/5.00 { 5, 6, 7 } 4.58/5.00 { 1, 2, 3 } 4.58/5.00 4.58/5.00 DP problem for innermost termination. 4.58/5.00 P = 4.58/5.00 f6#(I0, I1, I2, I3, I4) -> f6#(I5, I6, I2, I7, I8) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 2 <= I1] 4.58/5.00 f6#(I9, I10, I11, I12, I13) -> f6#(I14, I15, I11, I16, I17) [-1 <= I15 - 1 /\ 0 <= I14 - 1 /\ 2 <= I10 - 1 /\ 0 <= I9 - 1 /\ 1 <= I11 - 1 /\ I15 + 2 <= I10] 4.58/5.00 f6#(I18, I19, I20, I21, I22) -> f6#(I23, I24, I20, I25, I26) [-1 <= I24 - 1 /\ 0 <= I23 - 1 /\ 2 <= I19 - 1 /\ 0 <= I18 - 1 /\ I24 + 3 <= I19 /\ 1 <= I20 - 1 /\ I23 <= I18] 4.58/5.00 R = 4.58/5.00 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 4.58/5.00 f6(I0, I1, I2, I3, I4) -> f6(I5, I6, I2, I7, I8) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 2 <= I1] 4.58/5.00 f6(I9, I10, I11, I12, I13) -> f6(I14, I15, I11, I16, I17) [-1 <= I15 - 1 /\ 0 <= I14 - 1 /\ 2 <= I10 - 1 /\ 0 <= I9 - 1 /\ 1 <= I11 - 1 /\ I15 + 2 <= I10] 4.58/5.00 f6(I18, I19, I20, I21, I22) -> f6(I23, I24, I20, I25, I26) [-1 <= I24 - 1 /\ 0 <= I23 - 1 /\ 2 <= I19 - 1 /\ 0 <= I18 - 1 /\ I24 + 3 <= I19 /\ 1 <= I20 - 1 /\ I23 <= I18] 4.58/5.00 f2(I27, I28, I29, I30, I31) -> f6(I32, I33, I29, I34, I35) [0 <= y1 - 1 /\ 1 <= I29 - 1 /\ I32 - 1 <= I27 /\ I32 + 2 <= I28 /\ I33 + 3 <= I28 /\ 0 <= I27 - 1 /\ 3 <= I28 - 1 /\ 1 <= I32 - 1 /\ 0 <= I33 - 1 /\ I31 + 5 <= I28 /\ I30 + 5 <= I28] 4.58/5.00 f5(I36, I37, I38, I39, I40) -> f5(I36, I37 + 1, I38, I39, I41) [I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1] 4.58/5.00 f5(I42, I43, I44, I45, I46) -> f4(I42 - 1, I45, I46, I47, I48) [I42 - 1 <= I42 - 1 /\ 1 <= I46 - 1 /\ 0 <= I44 - 1 /\ 1 <= I42 - 1 /\ I43 <= I44 - 1] 4.58/5.00 f4(I49, I50, I51, I52, I53) -> f5(I49, 0, I54, I50, I51 + 1) [-1 <= I54 - 1 /\ I51 <= I50 - 1 /\ 0 <= I51 - 1 /\ 1 <= I49 - 1 /\ -1 <= I50 - 1] 4.58/5.00 f1(I55, I56, I57, I58, I59) -> f4(I60, I56, 1, I61, I62) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1] 4.58/5.00 f3(I63, I64, I65, I66, I67) -> f2(I68, I69, I65, I66, I67) [I66 + 5 <= I64 /\ I67 + 5 <= I64 /\ 3 <= I69 - 1 /\ 0 <= I68 - 1 /\ 3 <= I64 - 1 /\ 0 <= I63 - 1 /\ I69 <= I64 /\ I68 + 3 <= I64 /\ I68 <= I63] 4.58/5.00 f1(I70, I71, I72, I73, I74) -> f2(I75, I76, I77, I78, I79) [-1 <= I80 - 1 /\ 0 <= I71 - 1 /\ I75 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I75 - 1 /\ 3 <= I76 - 1] 4.58/5.00 4.58/5.00 We use the basic value criterion with the projection function NU: 4.58/5.00 NU[f6#(z1,z2,z3,z4,z5)] = z2 4.58/5.00 4.58/5.00 This gives the following inequalities: 4.58/5.00 -1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 2 <= I1 ==> I1 >! I6 4.58/5.00 -1 <= I15 - 1 /\ 0 <= I14 - 1 /\ 2 <= I10 - 1 /\ 0 <= I9 - 1 /\ 1 <= I11 - 1 /\ I15 + 2 <= I10 ==> I10 >! I15 4.58/5.00 -1 <= I24 - 1 /\ 0 <= I23 - 1 /\ 2 <= I19 - 1 /\ 0 <= I18 - 1 /\ I24 + 3 <= I19 /\ 1 <= I20 - 1 /\ I23 <= I18 ==> I19 >! I24 4.58/5.00 4.58/5.00 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 4.58/5.00 4.58/5.00 DP problem for innermost termination. 4.58/5.00 P = 4.58/5.00 f5#(I36, I37, I38, I39, I40) -> f5#(I36, I37 + 1, I38, I39, I41) [I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1] 4.58/5.00 f5#(I42, I43, I44, I45, I46) -> f4#(I42 - 1, I45, I46, I47, I48) [I42 - 1 <= I42 - 1 /\ 1 <= I46 - 1 /\ 0 <= I44 - 1 /\ 1 <= I42 - 1 /\ I43 <= I44 - 1] 4.58/5.00 f4#(I49, I50, I51, I52, I53) -> f5#(I49, 0, I54, I50, I51 + 1) [-1 <= I54 - 1 /\ I51 <= I50 - 1 /\ 0 <= I51 - 1 /\ 1 <= I49 - 1 /\ -1 <= I50 - 1] 4.58/5.00 R = 4.58/5.00 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 4.58/5.00 f6(I0, I1, I2, I3, I4) -> f6(I5, I6, I2, I7, I8) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 2 <= I1] 4.58/5.00 f6(I9, I10, I11, I12, I13) -> f6(I14, I15, I11, I16, I17) [-1 <= I15 - 1 /\ 0 <= I14 - 1 /\ 2 <= I10 - 1 /\ 0 <= I9 - 1 /\ 1 <= I11 - 1 /\ I15 + 2 <= I10] 4.58/5.00 f6(I18, I19, I20, I21, I22) -> f6(I23, I24, I20, I25, I26) [-1 <= I24 - 1 /\ 0 <= I23 - 1 /\ 2 <= I19 - 1 /\ 0 <= I18 - 1 /\ I24 + 3 <= I19 /\ 1 <= I20 - 1 /\ I23 <= I18] 4.58/5.00 f2(I27, I28, I29, I30, I31) -> f6(I32, I33, I29, I34, I35) [0 <= y1 - 1 /\ 1 <= I29 - 1 /\ I32 - 1 <= I27 /\ I32 + 2 <= I28 /\ I33 + 3 <= I28 /\ 0 <= I27 - 1 /\ 3 <= I28 - 1 /\ 1 <= I32 - 1 /\ 0 <= I33 - 1 /\ I31 + 5 <= I28 /\ I30 + 5 <= I28] 4.58/5.00 f5(I36, I37, I38, I39, I40) -> f5(I36, I37 + 1, I38, I39, I41) [I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1] 4.58/5.00 f5(I42, I43, I44, I45, I46) -> f4(I42 - 1, I45, I46, I47, I48) [I42 - 1 <= I42 - 1 /\ 1 <= I46 - 1 /\ 0 <= I44 - 1 /\ 1 <= I42 - 1 /\ I43 <= I44 - 1] 4.58/5.00 f4(I49, I50, I51, I52, I53) -> f5(I49, 0, I54, I50, I51 + 1) [-1 <= I54 - 1 /\ I51 <= I50 - 1 /\ 0 <= I51 - 1 /\ 1 <= I49 - 1 /\ -1 <= I50 - 1] 4.58/5.00 f1(I55, I56, I57, I58, I59) -> f4(I60, I56, 1, I61, I62) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1] 4.58/5.00 f3(I63, I64, I65, I66, I67) -> f2(I68, I69, I65, I66, I67) [I66 + 5 <= I64 /\ I67 + 5 <= I64 /\ 3 <= I69 - 1 /\ 0 <= I68 - 1 /\ 3 <= I64 - 1 /\ 0 <= I63 - 1 /\ I69 <= I64 /\ I68 + 3 <= I64 /\ I68 <= I63] 4.58/5.00 f1(I70, I71, I72, I73, I74) -> f2(I75, I76, I77, I78, I79) [-1 <= I80 - 1 /\ 0 <= I71 - 1 /\ I75 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I75 - 1 /\ 3 <= I76 - 1] 4.58/5.00 4.58/5.00 We use the basic value criterion with the projection function NU: 4.58/5.00 NU[f4#(z1,z2,z3,z4,z5)] = z1 4.58/5.00 NU[f5#(z1,z2,z3,z4,z5)] = z1 4.58/5.00 4.58/5.00 This gives the following inequalities: 4.58/5.00 I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1 ==> I36 (>! \union =) I36 4.58/5.00 I42 - 1 <= I42 - 1 /\ 1 <= I46 - 1 /\ 0 <= I44 - 1 /\ 1 <= I42 - 1 /\ I43 <= I44 - 1 ==> I42 >! I42 - 1 4.58/5.00 -1 <= I54 - 1 /\ I51 <= I50 - 1 /\ 0 <= I51 - 1 /\ 1 <= I49 - 1 /\ -1 <= I50 - 1 ==> I49 (>! \union =) I49 4.58/5.00 4.58/5.00 We remove all the strictly oriented dependency pairs. 4.58/5.00 4.58/5.00 DP problem for innermost termination. 4.58/5.00 P = 4.58/5.00 f5#(I36, I37, I38, I39, I40) -> f5#(I36, I37 + 1, I38, I39, I41) [I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1] 4.58/5.00 f4#(I49, I50, I51, I52, I53) -> f5#(I49, 0, I54, I50, I51 + 1) [-1 <= I54 - 1 /\ I51 <= I50 - 1 /\ 0 <= I51 - 1 /\ 1 <= I49 - 1 /\ -1 <= I50 - 1] 4.58/5.00 R = 4.58/5.00 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 4.58/5.00 f6(I0, I1, I2, I3, I4) -> f6(I5, I6, I2, I7, I8) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 2 <= I1] 4.58/5.00 f6(I9, I10, I11, I12, I13) -> f6(I14, I15, I11, I16, I17) [-1 <= I15 - 1 /\ 0 <= I14 - 1 /\ 2 <= I10 - 1 /\ 0 <= I9 - 1 /\ 1 <= I11 - 1 /\ I15 + 2 <= I10] 4.58/5.00 f6(I18, I19, I20, I21, I22) -> f6(I23, I24, I20, I25, I26) [-1 <= I24 - 1 /\ 0 <= I23 - 1 /\ 2 <= I19 - 1 /\ 0 <= I18 - 1 /\ I24 + 3 <= I19 /\ 1 <= I20 - 1 /\ I23 <= I18] 4.58/5.00 f2(I27, I28, I29, I30, I31) -> f6(I32, I33, I29, I34, I35) [0 <= y1 - 1 /\ 1 <= I29 - 1 /\ I32 - 1 <= I27 /\ I32 + 2 <= I28 /\ I33 + 3 <= I28 /\ 0 <= I27 - 1 /\ 3 <= I28 - 1 /\ 1 <= I32 - 1 /\ 0 <= I33 - 1 /\ I31 + 5 <= I28 /\ I30 + 5 <= I28] 4.58/5.00 f5(I36, I37, I38, I39, I40) -> f5(I36, I37 + 1, I38, I39, I41) [I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1] 4.58/5.00 f5(I42, I43, I44, I45, I46) -> f4(I42 - 1, I45, I46, I47, I48) [I42 - 1 <= I42 - 1 /\ 1 <= I46 - 1 /\ 0 <= I44 - 1 /\ 1 <= I42 - 1 /\ I43 <= I44 - 1] 4.58/5.00 f4(I49, I50, I51, I52, I53) -> f5(I49, 0, I54, I50, I51 + 1) [-1 <= I54 - 1 /\ I51 <= I50 - 1 /\ 0 <= I51 - 1 /\ 1 <= I49 - 1 /\ -1 <= I50 - 1] 4.58/5.00 f1(I55, I56, I57, I58, I59) -> f4(I60, I56, 1, I61, I62) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1] 4.58/5.00 f3(I63, I64, I65, I66, I67) -> f2(I68, I69, I65, I66, I67) [I66 + 5 <= I64 /\ I67 + 5 <= I64 /\ 3 <= I69 - 1 /\ 0 <= I68 - 1 /\ 3 <= I64 - 1 /\ 0 <= I63 - 1 /\ I69 <= I64 /\ I68 + 3 <= I64 /\ I68 <= I63] 4.58/5.00 f1(I70, I71, I72, I73, I74) -> f2(I75, I76, I77, I78, I79) [-1 <= I80 - 1 /\ 0 <= I71 - 1 /\ I75 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I75 - 1 /\ 3 <= I76 - 1] 4.58/5.00 4.58/5.00 The dependency graph for this problem is: 4.58/5.00 5 -> 5 4.58/5.00 7 -> 5 4.58/5.00 Where: 4.58/5.00 5) f5#(I36, I37, I38, I39, I40) -> f5#(I36, I37 + 1, I38, I39, I41) [I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1] 4.58/5.00 7) f4#(I49, I50, I51, I52, I53) -> f5#(I49, 0, I54, I50, I51 + 1) [-1 <= I54 - 1 /\ I51 <= I50 - 1 /\ 0 <= I51 - 1 /\ 1 <= I49 - 1 /\ -1 <= I50 - 1] 4.58/5.01 4.58/5.01 We have the following SCCs. 4.58/5.01 { 5 } 4.58/5.01 4.58/5.01 DP problem for innermost termination. 4.58/5.01 P = 4.58/5.01 f5#(I36, I37, I38, I39, I40) -> f5#(I36, I37 + 1, I38, I39, I41) [I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1] 4.58/5.01 R = 4.58/5.01 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 4.58/5.01 f6(I0, I1, I2, I3, I4) -> f6(I5, I6, I2, I7, I8) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 2 <= I1] 4.58/5.01 f6(I9, I10, I11, I12, I13) -> f6(I14, I15, I11, I16, I17) [-1 <= I15 - 1 /\ 0 <= I14 - 1 /\ 2 <= I10 - 1 /\ 0 <= I9 - 1 /\ 1 <= I11 - 1 /\ I15 + 2 <= I10] 4.58/5.01 f6(I18, I19, I20, I21, I22) -> f6(I23, I24, I20, I25, I26) [-1 <= I24 - 1 /\ 0 <= I23 - 1 /\ 2 <= I19 - 1 /\ 0 <= I18 - 1 /\ I24 + 3 <= I19 /\ 1 <= I20 - 1 /\ I23 <= I18] 4.58/5.01 f2(I27, I28, I29, I30, I31) -> f6(I32, I33, I29, I34, I35) [0 <= y1 - 1 /\ 1 <= I29 - 1 /\ I32 - 1 <= I27 /\ I32 + 2 <= I28 /\ I33 + 3 <= I28 /\ 0 <= I27 - 1 /\ 3 <= I28 - 1 /\ 1 <= I32 - 1 /\ 0 <= I33 - 1 /\ I31 + 5 <= I28 /\ I30 + 5 <= I28] 4.58/5.01 f5(I36, I37, I38, I39, I40) -> f5(I36, I37 + 1, I38, I39, I41) [I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1] 4.58/5.01 f5(I42, I43, I44, I45, I46) -> f4(I42 - 1, I45, I46, I47, I48) [I42 - 1 <= I42 - 1 /\ 1 <= I46 - 1 /\ 0 <= I44 - 1 /\ 1 <= I42 - 1 /\ I43 <= I44 - 1] 4.58/5.01 f4(I49, I50, I51, I52, I53) -> f5(I49, 0, I54, I50, I51 + 1) [-1 <= I54 - 1 /\ I51 <= I50 - 1 /\ 0 <= I51 - 1 /\ 1 <= I49 - 1 /\ -1 <= I50 - 1] 4.58/5.01 f1(I55, I56, I57, I58, I59) -> f4(I60, I56, 1, I61, I62) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1] 4.58/5.01 f3(I63, I64, I65, I66, I67) -> f2(I68, I69, I65, I66, I67) [I66 + 5 <= I64 /\ I67 + 5 <= I64 /\ 3 <= I69 - 1 /\ 0 <= I68 - 1 /\ 3 <= I64 - 1 /\ 0 <= I63 - 1 /\ I69 <= I64 /\ I68 + 3 <= I64 /\ I68 <= I63] 4.58/5.01 f1(I70, I71, I72, I73, I74) -> f2(I75, I76, I77, I78, I79) [-1 <= I80 - 1 /\ 0 <= I71 - 1 /\ I75 <= I70 /\ 0 <= I70 - 1 /\ 0 <= I75 - 1 /\ 3 <= I76 - 1] 4.58/5.01 4.58/5.01 We use the reverse value criterion with the projection function NU: 4.58/5.01 NU[f5#(z1,z2,z3,z4,z5)] = z3 - 1 + -1 * z2 4.58/5.01 4.58/5.01 This gives the following inequalities: 4.58/5.01 I36 - 1 <= I36 - 1 /\ 1 <= I40 - 1 /\ 0 <= I38 - 1 /\ 1 <= I36 - 1 /\ I37 <= I38 - 1 ==> I38 - 1 + -1 * I37 > I38 - 1 + -1 * (I37 + 1) with I38 - 1 + -1 * I37 >= 0 4.58/5.01 4.58/5.01 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 4.58/5.01 EOF