2.00/2.01 YES 2.00/2.01 2.00/2.01 DP problem for innermost termination. 2.00/2.01 P = 2.00/2.01 init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 2.00/2.01 f5#(I0, I1, I2, I3, I4) -> f5#(I5, I6, I7, I8, I9) [-1 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 + 1 <= I0] 2.00/2.01 f4#(I10, I11, I12, I13, I14) -> f5#(I15, I16, I17, I18, I19) [0 <= I15 - 1 /\ 2 <= I10 - 1 /\ I11 <= 1 /\ I15 + 2 <= I10] 2.00/2.01 f4#(I20, I21, I22, I23, I24) -> f4#(I25, I21 - 1, 1, I26, I27) [5 <= I25 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1 /\ I25 - 2 <= I20] 2.00/2.01 f4#(I28, I29, I30, I31, I32) -> f4#(I33, I29 - 1, I34, I35, I36) [2 <= I33 - 1 /\ 2 <= I28 - 1 /\ 1 <= I29 - 1 /\ 0 <= I30 - 1 /\ I30 <= I34 - 1] 2.00/2.01 f3#(I37, I38, I39, I40, I41) -> f4#(I42, I43, 0, I44, I45) [3 <= I42 - 1 /\ 4 <= I37 - 1 /\ I42 + 1 <= I37 /\ -1 <= I43 - 1 /\ 1 <= I38 - 1] 2.00/2.01 f2#(I46, I47, I48, I49, I50) -> f2#(I51, I52, I53, I49 - 1, 1) [5 <= I53 - 1 /\ 7 <= I52 - 1 /\ 0 <= I51 - 1 /\ 3 <= I48 - 1 /\ 5 <= I47 - 1 /\ 0 <= I46 - 1 /\ I53 - 2 <= I48 /\ I53 <= I47 /\ I53 - 5 <= I46 /\ I52 - 4 <= I48 /\ I52 - 2 <= I47 /\ I52 - 7 <= I46 /\ I51 + 3 <= I48 /\ I51 + 5 <= I47 /\ 1 <= I49 - 1 /\ I51 <= I46] 2.00/2.01 f2#(I54, I55, I56, I57, I58) -> f2#(I59, I60, I61, I57 - 1, I62) [2 <= I61 - 1 /\ 4 <= I60 - 1 /\ 0 <= I59 - 1 /\ 2 <= I56 - 1 /\ 4 <= I55 - 1 /\ 0 <= I54 - 1 /\ I59 + 2 <= I56 /\ I59 + 4 <= I55 /\ I59 <= I54 /\ 1 <= I57 - 1 /\ 0 <= I58 - 1 /\ I58 <= I62 - 1] 2.00/2.01 f2#(I63, I64, I65, I66, I67) -> f3#(I68, I69, I70, I71, I72) [6 <= I68 - 1 /\ 3 <= I65 - 1 /\ 5 <= I64 - 1 /\ 0 <= I63 - 1 /\ I68 - 3 <= I65 /\ I68 - 1 <= I64 /\ I66 <= 1 /\ I68 - 6 <= I63] 2.00/2.01 f2#(I73, I74, I75, I76, I77) -> f3#(I78, I79, I80, I81, I82) [I76 <= 1 /\ 0 <= I77 - 1 /\ I77 <= y1 - 1 /\ I77 <= y2 - 1 /\ 0 <= I73 - 1 /\ 4 <= I74 - 1 /\ 2 <= I75 - 1 /\ 4 <= I78 - 1] 2.00/2.01 f1#(I83, I84, I85, I86, I87) -> f2#(I88, I89, I90, I91, 0) [3 <= I90 - 1 /\ 5 <= I89 - 1 /\ 0 <= I88 - 1 /\ 0 <= I83 - 1 /\ I90 - 3 <= I83 /\ I89 - 5 <= I83 /\ I88 <= I83 /\ -1 <= I91 - 1 /\ 0 <= I84 - 1] 2.00/2.01 R = 2.00/2.01 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 2.00/2.01 f5(I0, I1, I2, I3, I4) -> f5(I5, I6, I7, I8, I9) [-1 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 + 1 <= I0] 2.00/2.01 f4(I10, I11, I12, I13, I14) -> f5(I15, I16, I17, I18, I19) [0 <= I15 - 1 /\ 2 <= I10 - 1 /\ I11 <= 1 /\ I15 + 2 <= I10] 2.00/2.01 f4(I20, I21, I22, I23, I24) -> f4(I25, I21 - 1, 1, I26, I27) [5 <= I25 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1 /\ I25 - 2 <= I20] 2.00/2.01 f4(I28, I29, I30, I31, I32) -> f4(I33, I29 - 1, I34, I35, I36) [2 <= I33 - 1 /\ 2 <= I28 - 1 /\ 1 <= I29 - 1 /\ 0 <= I30 - 1 /\ I30 <= I34 - 1] 2.00/2.01 f3(I37, I38, I39, I40, I41) -> f4(I42, I43, 0, I44, I45) [3 <= I42 - 1 /\ 4 <= I37 - 1 /\ I42 + 1 <= I37 /\ -1 <= I43 - 1 /\ 1 <= I38 - 1] 2.00/2.01 f2(I46, I47, I48, I49, I50) -> f2(I51, I52, I53, I49 - 1, 1) [5 <= I53 - 1 /\ 7 <= I52 - 1 /\ 0 <= I51 - 1 /\ 3 <= I48 - 1 /\ 5 <= I47 - 1 /\ 0 <= I46 - 1 /\ I53 - 2 <= I48 /\ I53 <= I47 /\ I53 - 5 <= I46 /\ I52 - 4 <= I48 /\ I52 - 2 <= I47 /\ I52 - 7 <= I46 /\ I51 + 3 <= I48 /\ I51 + 5 <= I47 /\ 1 <= I49 - 1 /\ I51 <= I46] 2.00/2.01 f2(I54, I55, I56, I57, I58) -> f2(I59, I60, I61, I57 - 1, I62) [2 <= I61 - 1 /\ 4 <= I60 - 1 /\ 0 <= I59 - 1 /\ 2 <= I56 - 1 /\ 4 <= I55 - 1 /\ 0 <= I54 - 1 /\ I59 + 2 <= I56 /\ I59 + 4 <= I55 /\ I59 <= I54 /\ 1 <= I57 - 1 /\ 0 <= I58 - 1 /\ I58 <= I62 - 1] 2.00/2.01 f2(I63, I64, I65, I66, I67) -> f3(I68, I69, I70, I71, I72) [6 <= I68 - 1 /\ 3 <= I65 - 1 /\ 5 <= I64 - 1 /\ 0 <= I63 - 1 /\ I68 - 3 <= I65 /\ I68 - 1 <= I64 /\ I66 <= 1 /\ I68 - 6 <= I63] 2.00/2.01 f2(I73, I74, I75, I76, I77) -> f3(I78, I79, I80, I81, I82) [I76 <= 1 /\ 0 <= I77 - 1 /\ I77 <= y1 - 1 /\ I77 <= y2 - 1 /\ 0 <= I73 - 1 /\ 4 <= I74 - 1 /\ 2 <= I75 - 1 /\ 4 <= I78 - 1] 2.00/2.01 f1(I83, I84, I85, I86, I87) -> f2(I88, I89, I90, I91, 0) [3 <= I90 - 1 /\ 5 <= I89 - 1 /\ 0 <= I88 - 1 /\ 0 <= I83 - 1 /\ I90 - 3 <= I83 /\ I89 - 5 <= I83 /\ I88 <= I83 /\ -1 <= I91 - 1 /\ 0 <= I84 - 1] 2.00/2.01 2.00/2.01 The dependency graph for this problem is: 2.00/2.01 0 -> 10 2.00/2.01 1 -> 1 2.00/2.01 2 -> 1 2.00/2.01 3 -> 2, 3, 4 2.00/2.01 4 -> 2, 3, 4 2.00/2.01 5 -> 2, 3 2.00/2.01 6 -> 6, 7, 8, 9 2.00/2.01 7 -> 6, 7, 8, 9 2.00/2.01 8 -> 5 2.00/2.01 9 -> 5 2.00/2.01 10 -> 6, 8 2.00/2.01 Where: 2.00/2.01 0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 2.00/2.01 1) f5#(I0, I1, I2, I3, I4) -> f5#(I5, I6, I7, I8, I9) [-1 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 + 1 <= I0] 2.00/2.01 2) f4#(I10, I11, I12, I13, I14) -> f5#(I15, I16, I17, I18, I19) [0 <= I15 - 1 /\ 2 <= I10 - 1 /\ I11 <= 1 /\ I15 + 2 <= I10] 2.00/2.01 3) f4#(I20, I21, I22, I23, I24) -> f4#(I25, I21 - 1, 1, I26, I27) [5 <= I25 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1 /\ I25 - 2 <= I20] 2.00/2.01 4) f4#(I28, I29, I30, I31, I32) -> f4#(I33, I29 - 1, I34, I35, I36) [2 <= I33 - 1 /\ 2 <= I28 - 1 /\ 1 <= I29 - 1 /\ 0 <= I30 - 1 /\ I30 <= I34 - 1] 2.00/2.01 5) f3#(I37, I38, I39, I40, I41) -> f4#(I42, I43, 0, I44, I45) [3 <= I42 - 1 /\ 4 <= I37 - 1 /\ I42 + 1 <= I37 /\ -1 <= I43 - 1 /\ 1 <= I38 - 1] 2.00/2.01 6) f2#(I46, I47, I48, I49, I50) -> f2#(I51, I52, I53, I49 - 1, 1) [5 <= I53 - 1 /\ 7 <= I52 - 1 /\ 0 <= I51 - 1 /\ 3 <= I48 - 1 /\ 5 <= I47 - 1 /\ 0 <= I46 - 1 /\ I53 - 2 <= I48 /\ I53 <= I47 /\ I53 - 5 <= I46 /\ I52 - 4 <= I48 /\ I52 - 2 <= I47 /\ I52 - 7 <= I46 /\ I51 + 3 <= I48 /\ I51 + 5 <= I47 /\ 1 <= I49 - 1 /\ I51 <= I46] 2.00/2.01 7) f2#(I54, I55, I56, I57, I58) -> f2#(I59, I60, I61, I57 - 1, I62) [2 <= I61 - 1 /\ 4 <= I60 - 1 /\ 0 <= I59 - 1 /\ 2 <= I56 - 1 /\ 4 <= I55 - 1 /\ 0 <= I54 - 1 /\ I59 + 2 <= I56 /\ I59 + 4 <= I55 /\ I59 <= I54 /\ 1 <= I57 - 1 /\ 0 <= I58 - 1 /\ I58 <= I62 - 1] 2.00/2.01 8) f2#(I63, I64, I65, I66, I67) -> f3#(I68, I69, I70, I71, I72) [6 <= I68 - 1 /\ 3 <= I65 - 1 /\ 5 <= I64 - 1 /\ 0 <= I63 - 1 /\ I68 - 3 <= I65 /\ I68 - 1 <= I64 /\ I66 <= 1 /\ I68 - 6 <= I63] 2.00/2.01 9) f2#(I73, I74, I75, I76, I77) -> f3#(I78, I79, I80, I81, I82) [I76 <= 1 /\ 0 <= I77 - 1 /\ I77 <= y1 - 1 /\ I77 <= y2 - 1 /\ 0 <= I73 - 1 /\ 4 <= I74 - 1 /\ 2 <= I75 - 1 /\ 4 <= I78 - 1] 2.00/2.01 10) f1#(I83, I84, I85, I86, I87) -> f2#(I88, I89, I90, I91, 0) [3 <= I90 - 1 /\ 5 <= I89 - 1 /\ 0 <= I88 - 1 /\ 0 <= I83 - 1 /\ I90 - 3 <= I83 /\ I89 - 5 <= I83 /\ I88 <= I83 /\ -1 <= I91 - 1 /\ 0 <= I84 - 1] 2.00/2.01 2.00/2.01 We have the following SCCs. 2.00/2.01 { 6, 7 } 2.00/2.01 { 3, 4 } 2.00/2.01 { 1 } 2.00/2.01 2.00/2.01 DP problem for innermost termination. 2.00/2.01 P = 2.00/2.01 f5#(I0, I1, I2, I3, I4) -> f5#(I5, I6, I7, I8, I9) [-1 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 + 1 <= I0] 2.00/2.01 R = 2.00/2.01 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 2.00/2.01 f5(I0, I1, I2, I3, I4) -> f5(I5, I6, I7, I8, I9) [-1 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 + 1 <= I0] 2.00/2.01 f4(I10, I11, I12, I13, I14) -> f5(I15, I16, I17, I18, I19) [0 <= I15 - 1 /\ 2 <= I10 - 1 /\ I11 <= 1 /\ I15 + 2 <= I10] 2.00/2.01 f4(I20, I21, I22, I23, I24) -> f4(I25, I21 - 1, 1, I26, I27) [5 <= I25 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1 /\ I25 - 2 <= I20] 2.00/2.01 f4(I28, I29, I30, I31, I32) -> f4(I33, I29 - 1, I34, I35, I36) [2 <= I33 - 1 /\ 2 <= I28 - 1 /\ 1 <= I29 - 1 /\ 0 <= I30 - 1 /\ I30 <= I34 - 1] 2.00/2.01 f3(I37, I38, I39, I40, I41) -> f4(I42, I43, 0, I44, I45) [3 <= I42 - 1 /\ 4 <= I37 - 1 /\ I42 + 1 <= I37 /\ -1 <= I43 - 1 /\ 1 <= I38 - 1] 2.00/2.01 f2(I46, I47, I48, I49, I50) -> f2(I51, I52, I53, I49 - 1, 1) [5 <= I53 - 1 /\ 7 <= I52 - 1 /\ 0 <= I51 - 1 /\ 3 <= I48 - 1 /\ 5 <= I47 - 1 /\ 0 <= I46 - 1 /\ I53 - 2 <= I48 /\ I53 <= I47 /\ I53 - 5 <= I46 /\ I52 - 4 <= I48 /\ I52 - 2 <= I47 /\ I52 - 7 <= I46 /\ I51 + 3 <= I48 /\ I51 + 5 <= I47 /\ 1 <= I49 - 1 /\ I51 <= I46] 2.00/2.01 f2(I54, I55, I56, I57, I58) -> f2(I59, I60, I61, I57 - 1, I62) [2 <= I61 - 1 /\ 4 <= I60 - 1 /\ 0 <= I59 - 1 /\ 2 <= I56 - 1 /\ 4 <= I55 - 1 /\ 0 <= I54 - 1 /\ I59 + 2 <= I56 /\ I59 + 4 <= I55 /\ I59 <= I54 /\ 1 <= I57 - 1 /\ 0 <= I58 - 1 /\ I58 <= I62 - 1] 2.00/2.01 f2(I63, I64, I65, I66, I67) -> f3(I68, I69, I70, I71, I72) [6 <= I68 - 1 /\ 3 <= I65 - 1 /\ 5 <= I64 - 1 /\ 0 <= I63 - 1 /\ I68 - 3 <= I65 /\ I68 - 1 <= I64 /\ I66 <= 1 /\ I68 - 6 <= I63] 2.00/2.01 f2(I73, I74, I75, I76, I77) -> f3(I78, I79, I80, I81, I82) [I76 <= 1 /\ 0 <= I77 - 1 /\ I77 <= y1 - 1 /\ I77 <= y2 - 1 /\ 0 <= I73 - 1 /\ 4 <= I74 - 1 /\ 2 <= I75 - 1 /\ 4 <= I78 - 1] 2.00/2.01 f1(I83, I84, I85, I86, I87) -> f2(I88, I89, I90, I91, 0) [3 <= I90 - 1 /\ 5 <= I89 - 1 /\ 0 <= I88 - 1 /\ 0 <= I83 - 1 /\ I90 - 3 <= I83 /\ I89 - 5 <= I83 /\ I88 <= I83 /\ -1 <= I91 - 1 /\ 0 <= I84 - 1] 2.00/2.01 2.00/2.01 We use the basic value criterion with the projection function NU: 2.00/2.01 NU[f5#(z1,z2,z3,z4,z5)] = z1 2.00/2.01 2.00/2.01 This gives the following inequalities: 2.00/2.01 -1 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 + 1 <= I0 ==> I0 >! I5 2.00/2.01 2.00/2.01 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 2.00/2.01 2.00/2.01 DP problem for innermost termination. 2.00/2.01 P = 2.00/2.01 f4#(I20, I21, I22, I23, I24) -> f4#(I25, I21 - 1, 1, I26, I27) [5 <= I25 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1 /\ I25 - 2 <= I20] 2.00/2.01 f4#(I28, I29, I30, I31, I32) -> f4#(I33, I29 - 1, I34, I35, I36) [2 <= I33 - 1 /\ 2 <= I28 - 1 /\ 1 <= I29 - 1 /\ 0 <= I30 - 1 /\ I30 <= I34 - 1] 2.00/2.01 R = 2.00/2.01 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 2.00/2.01 f5(I0, I1, I2, I3, I4) -> f5(I5, I6, I7, I8, I9) [-1 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 + 1 <= I0] 2.00/2.01 f4(I10, I11, I12, I13, I14) -> f5(I15, I16, I17, I18, I19) [0 <= I15 - 1 /\ 2 <= I10 - 1 /\ I11 <= 1 /\ I15 + 2 <= I10] 2.00/2.01 f4(I20, I21, I22, I23, I24) -> f4(I25, I21 - 1, 1, I26, I27) [5 <= I25 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1 /\ I25 - 2 <= I20] 2.00/2.01 f4(I28, I29, I30, I31, I32) -> f4(I33, I29 - 1, I34, I35, I36) [2 <= I33 - 1 /\ 2 <= I28 - 1 /\ 1 <= I29 - 1 /\ 0 <= I30 - 1 /\ I30 <= I34 - 1] 2.00/2.01 f3(I37, I38, I39, I40, I41) -> f4(I42, I43, 0, I44, I45) [3 <= I42 - 1 /\ 4 <= I37 - 1 /\ I42 + 1 <= I37 /\ -1 <= I43 - 1 /\ 1 <= I38 - 1] 2.00/2.01 f2(I46, I47, I48, I49, I50) -> f2(I51, I52, I53, I49 - 1, 1) [5 <= I53 - 1 /\ 7 <= I52 - 1 /\ 0 <= I51 - 1 /\ 3 <= I48 - 1 /\ 5 <= I47 - 1 /\ 0 <= I46 - 1 /\ I53 - 2 <= I48 /\ I53 <= I47 /\ I53 - 5 <= I46 /\ I52 - 4 <= I48 /\ I52 - 2 <= I47 /\ I52 - 7 <= I46 /\ I51 + 3 <= I48 /\ I51 + 5 <= I47 /\ 1 <= I49 - 1 /\ I51 <= I46] 2.00/2.01 f2(I54, I55, I56, I57, I58) -> f2(I59, I60, I61, I57 - 1, I62) [2 <= I61 - 1 /\ 4 <= I60 - 1 /\ 0 <= I59 - 1 /\ 2 <= I56 - 1 /\ 4 <= I55 - 1 /\ 0 <= I54 - 1 /\ I59 + 2 <= I56 /\ I59 + 4 <= I55 /\ I59 <= I54 /\ 1 <= I57 - 1 /\ 0 <= I58 - 1 /\ I58 <= I62 - 1] 2.00/2.01 f2(I63, I64, I65, I66, I67) -> f3(I68, I69, I70, I71, I72) [6 <= I68 - 1 /\ 3 <= I65 - 1 /\ 5 <= I64 - 1 /\ 0 <= I63 - 1 /\ I68 - 3 <= I65 /\ I68 - 1 <= I64 /\ I66 <= 1 /\ I68 - 6 <= I63] 2.00/2.01 f2(I73, I74, I75, I76, I77) -> f3(I78, I79, I80, I81, I82) [I76 <= 1 /\ 0 <= I77 - 1 /\ I77 <= y1 - 1 /\ I77 <= y2 - 1 /\ 0 <= I73 - 1 /\ 4 <= I74 - 1 /\ 2 <= I75 - 1 /\ 4 <= I78 - 1] 2.00/2.01 f1(I83, I84, I85, I86, I87) -> f2(I88, I89, I90, I91, 0) [3 <= I90 - 1 /\ 5 <= I89 - 1 /\ 0 <= I88 - 1 /\ 0 <= I83 - 1 /\ I90 - 3 <= I83 /\ I89 - 5 <= I83 /\ I88 <= I83 /\ -1 <= I91 - 1 /\ 0 <= I84 - 1] 2.00/2.01 2.00/2.01 We use the basic value criterion with the projection function NU: 2.00/2.01 NU[f4#(z1,z2,z3,z4,z5)] = z2 2.00/2.01 2.00/2.01 This gives the following inequalities: 2.00/2.01 5 <= I25 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1 /\ I25 - 2 <= I20 ==> I21 >! I21 - 1 2.00/2.01 2 <= I33 - 1 /\ 2 <= I28 - 1 /\ 1 <= I29 - 1 /\ 0 <= I30 - 1 /\ I30 <= I34 - 1 ==> I29 >! I29 - 1 2.00/2.01 2.00/2.01 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 2.00/2.01 2.00/2.01 DP problem for innermost termination. 2.00/2.01 P = 2.00/2.01 f2#(I46, I47, I48, I49, I50) -> f2#(I51, I52, I53, I49 - 1, 1) [5 <= I53 - 1 /\ 7 <= I52 - 1 /\ 0 <= I51 - 1 /\ 3 <= I48 - 1 /\ 5 <= I47 - 1 /\ 0 <= I46 - 1 /\ I53 - 2 <= I48 /\ I53 <= I47 /\ I53 - 5 <= I46 /\ I52 - 4 <= I48 /\ I52 - 2 <= I47 /\ I52 - 7 <= I46 /\ I51 + 3 <= I48 /\ I51 + 5 <= I47 /\ 1 <= I49 - 1 /\ I51 <= I46] 2.00/2.01 f2#(I54, I55, I56, I57, I58) -> f2#(I59, I60, I61, I57 - 1, I62) [2 <= I61 - 1 /\ 4 <= I60 - 1 /\ 0 <= I59 - 1 /\ 2 <= I56 - 1 /\ 4 <= I55 - 1 /\ 0 <= I54 - 1 /\ I59 + 2 <= I56 /\ I59 + 4 <= I55 /\ I59 <= I54 /\ 1 <= I57 - 1 /\ 0 <= I58 - 1 /\ I58 <= I62 - 1] 2.00/2.01 R = 2.00/2.01 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 2.00/2.01 f5(I0, I1, I2, I3, I4) -> f5(I5, I6, I7, I8, I9) [-1 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 + 1 <= I0] 2.00/2.01 f4(I10, I11, I12, I13, I14) -> f5(I15, I16, I17, I18, I19) [0 <= I15 - 1 /\ 2 <= I10 - 1 /\ I11 <= 1 /\ I15 + 2 <= I10] 2.00/2.01 f4(I20, I21, I22, I23, I24) -> f4(I25, I21 - 1, 1, I26, I27) [5 <= I25 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1 /\ I25 - 2 <= I20] 2.00/2.01 f4(I28, I29, I30, I31, I32) -> f4(I33, I29 - 1, I34, I35, I36) [2 <= I33 - 1 /\ 2 <= I28 - 1 /\ 1 <= I29 - 1 /\ 0 <= I30 - 1 /\ I30 <= I34 - 1] 2.00/2.01 f3(I37, I38, I39, I40, I41) -> f4(I42, I43, 0, I44, I45) [3 <= I42 - 1 /\ 4 <= I37 - 1 /\ I42 + 1 <= I37 /\ -1 <= I43 - 1 /\ 1 <= I38 - 1] 2.00/2.01 f2(I46, I47, I48, I49, I50) -> f2(I51, I52, I53, I49 - 1, 1) [5 <= I53 - 1 /\ 7 <= I52 - 1 /\ 0 <= I51 - 1 /\ 3 <= I48 - 1 /\ 5 <= I47 - 1 /\ 0 <= I46 - 1 /\ I53 - 2 <= I48 /\ I53 <= I47 /\ I53 - 5 <= I46 /\ I52 - 4 <= I48 /\ I52 - 2 <= I47 /\ I52 - 7 <= I46 /\ I51 + 3 <= I48 /\ I51 + 5 <= I47 /\ 1 <= I49 - 1 /\ I51 <= I46] 2.00/2.01 f2(I54, I55, I56, I57, I58) -> f2(I59, I60, I61, I57 - 1, I62) [2 <= I61 - 1 /\ 4 <= I60 - 1 /\ 0 <= I59 - 1 /\ 2 <= I56 - 1 /\ 4 <= I55 - 1 /\ 0 <= I54 - 1 /\ I59 + 2 <= I56 /\ I59 + 4 <= I55 /\ I59 <= I54 /\ 1 <= I57 - 1 /\ 0 <= I58 - 1 /\ I58 <= I62 - 1] 2.00/2.01 f2(I63, I64, I65, I66, I67) -> f3(I68, I69, I70, I71, I72) [6 <= I68 - 1 /\ 3 <= I65 - 1 /\ 5 <= I64 - 1 /\ 0 <= I63 - 1 /\ I68 - 3 <= I65 /\ I68 - 1 <= I64 /\ I66 <= 1 /\ I68 - 6 <= I63] 2.00/2.01 f2(I73, I74, I75, I76, I77) -> f3(I78, I79, I80, I81, I82) [I76 <= 1 /\ 0 <= I77 - 1 /\ I77 <= y1 - 1 /\ I77 <= y2 - 1 /\ 0 <= I73 - 1 /\ 4 <= I74 - 1 /\ 2 <= I75 - 1 /\ 4 <= I78 - 1] 2.00/2.01 f1(I83, I84, I85, I86, I87) -> f2(I88, I89, I90, I91, 0) [3 <= I90 - 1 /\ 5 <= I89 - 1 /\ 0 <= I88 - 1 /\ 0 <= I83 - 1 /\ I90 - 3 <= I83 /\ I89 - 5 <= I83 /\ I88 <= I83 /\ -1 <= I91 - 1 /\ 0 <= I84 - 1] 2.00/2.01 2.00/2.01 We use the basic value criterion with the projection function NU: 2.00/2.01 NU[f2#(z1,z2,z3,z4,z5)] = z4 2.00/2.01 2.00/2.01 This gives the following inequalities: 2.00/2.01 5 <= I53 - 1 /\ 7 <= I52 - 1 /\ 0 <= I51 - 1 /\ 3 <= I48 - 1 /\ 5 <= I47 - 1 /\ 0 <= I46 - 1 /\ I53 - 2 <= I48 /\ I53 <= I47 /\ I53 - 5 <= I46 /\ I52 - 4 <= I48 /\ I52 - 2 <= I47 /\ I52 - 7 <= I46 /\ I51 + 3 <= I48 /\ I51 + 5 <= I47 /\ 1 <= I49 - 1 /\ I51 <= I46 ==> I49 >! I49 - 1 2.00/2.01 2 <= I61 - 1 /\ 4 <= I60 - 1 /\ 0 <= I59 - 1 /\ 2 <= I56 - 1 /\ 4 <= I55 - 1 /\ 0 <= I54 - 1 /\ I59 + 2 <= I56 /\ I59 + 4 <= I55 /\ I59 <= I54 /\ 1 <= I57 - 1 /\ 0 <= I58 - 1 /\ I58 <= I62 - 1 ==> I57 >! I57 - 1 2.00/2.01 2.00/2.01 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 2.00/4.99 EOF