4.96/4.97 YES 4.96/4.97 4.96/4.97 DP problem for innermost termination. 4.96/4.97 P = 4.96/4.97 init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.96/4.97 f6#(I0, I1, I2, I3, I4, I5) -> f6#(I6, I1, I2, I7, I8, I9) [I7 + 4 <= I0 /\ I3 + 2 <= I0 /\ 0 <= I6 - 1 /\ 2 <= I0 - 1 /\ I6 + 2 <= I0 /\ I1 <= I3 /\ 1 <= I2 - 1] 4.96/4.97 f6#(I10, I11, I12, I13, I14, I15) -> f6#(I16, I11, I12, I17, I18, I19) [I17 + 4 <= I10 /\ I13 + 2 <= I10 /\ 0 <= I16 - 1 /\ 2 <= I10 - 1 /\ I16 + 2 <= I10 /\ I13 <= I11 - 1 /\ 1 <= I12 - 1] 4.96/4.97 f5#(I20, I21, I22, I23, I24, I25) -> f6#(I26, I27, I23, I25, I28, I29) [I25 + 2 <= I20 /\ 0 <= I26 - 1 /\ 0 <= I20 - 1 /\ I26 <= I20 /\ I24 <= I23 - 1 /\ -1 <= I27 - 1 /\ 1 <= I23 - 1 /\ 0 <= I22 - 1 /\ I21 <= I22 - 1 /\ -1 <= I24 - 1] 4.96/4.97 f4#(I30, I31, I32, I33, I34, I35) -> f4#(I36, I37, I38, I39, I40, I41) [-1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 2 <= I31 /\ I37 + 2 <= I30 /\ I36 + 2 <= I31 /\ I36 + 2 <= I30] 4.96/4.97 f4#(I42, I43, I44, I45, I46, I47) -> f4#(I48, I49, I50, I51, I52, I53) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 2 <= I43 - 1 /\ 2 <= I42 - 1 /\ I49 + 3 <= I43 /\ I49 + 3 <= I42 /\ I48 + 3 <= I43 /\ I48 + 3 <= I42] 4.96/4.97 f5#(I54, I55, I56, I57, I58, I59) -> f5#(I60, I55 + 1, I56, I57, I58 + 1, I61) [-1 <= I58 - 1 /\ I55 <= I56 - 1 /\ 0 <= I56 - 1 /\ 1 <= I57 - 1 /\ -1 <= y1 - 1 /\ I58 <= I57 - 1 /\ 0 <= I54 - 1 /\ 2 <= I60 - 1 /\ I59 + 2 <= I54] 4.96/4.97 f5#(I62, I63, I64, I65, I66, I67) -> f5#(I68, I63 + 1, I64, I65, I66 + 1, I69) [-1 <= I66 - 1 /\ I63 <= I64 - 1 /\ 0 <= I64 - 1 /\ 1 <= I65 - 1 /\ -1 <= I70 - 1 /\ I66 <= I65 - 1 /\ 0 <= I62 - 1 /\ 2 <= I68 - 1 /\ I67 + 2 <= I62] 4.96/4.97 f5#(I71, I72, I73, I74, I75, I76) -> f5#(I77, I72 + 1, I73, I74, I75 + 1, I78) [-1 <= I75 - 1 /\ I72 <= I73 - 1 /\ 0 <= I73 - 1 /\ 1 <= I74 - 1 /\ -1 <= I79 - 1 /\ I75 <= I74 - 1 /\ 0 <= I71 - 1 /\ 3 <= I77 - 1 /\ I76 + 2 <= I71] 4.96/4.97 f5#(I80, I81, I82, I83, I84, I85) -> f5#(I86, I81 + 1, I82, I83, I84 + 1, I87) [-1 <= I84 - 1 /\ I81 <= I82 - 1 /\ 0 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= I88 - 1 /\ I84 <= I83 - 1 /\ 0 <= I80 - 1 /\ 3 <= I86 - 1 /\ I85 + 2 <= I80] 4.96/4.97 f1#(I89, I90, I91, I92, I93, I94) -> f5#(I95, 0, I96, I90, 2, I97) [1 <= I95 - 1 /\ 0 <= I89 - 1 /\ -1 <= I96 - 1 /\ 1 <= I90 - 1 /\ -1 <= I97 - 1] 4.96/4.97 f2#(I98, I99, I100, I101, I102, I103) -> f4#(I104, I105, I106, I107, I108, I109) [I104 <= I99 /\ 1 <= I110 - 1 /\ I105 <= I99 /\ 0 <= I98 - 1 /\ 0 <= I99 - 1 /\ 0 <= I104 - 1 /\ 0 <= I105 - 1 /\ I100 + 2 <= I99 /\ I102 + 2 <= I99 /\ I101 + 2 <= I99] 4.96/4.97 f3#(I111, I112, I113, I114, I115, I116) -> f2#(I117, I118, I113, I114, I115, I119) [I114 + 2 <= I112 /\ I115 + 2 <= I112 /\ I113 + 2 <= I112 /\ 0 <= I118 - 1 /\ 0 <= I117 - 1 /\ 0 <= I112 - 1 /\ 0 <= I111 - 1 /\ I118 <= I112 /\ I117 <= I112 /\ I117 <= I111] 4.96/4.97 f1#(I120, I121, I122, I123, I124, I125) -> f2#(I126, I127, I128, I129, I130, I131) [-1 <= I132 - 1 /\ 0 <= I121 - 1 /\ I126 <= I120 /\ 0 <= I120 - 1 /\ 0 <= I126 - 1 /\ 0 <= I127 - 1] 4.96/4.97 R = 4.96/4.97 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.96/4.97 f6(I0, I1, I2, I3, I4, I5) -> f6(I6, I1, I2, I7, I8, I9) [I7 + 4 <= I0 /\ I3 + 2 <= I0 /\ 0 <= I6 - 1 /\ 2 <= I0 - 1 /\ I6 + 2 <= I0 /\ I1 <= I3 /\ 1 <= I2 - 1] 4.96/4.97 f6(I10, I11, I12, I13, I14, I15) -> f6(I16, I11, I12, I17, I18, I19) [I17 + 4 <= I10 /\ I13 + 2 <= I10 /\ 0 <= I16 - 1 /\ 2 <= I10 - 1 /\ I16 + 2 <= I10 /\ I13 <= I11 - 1 /\ 1 <= I12 - 1] 4.96/4.97 f5(I20, I21, I22, I23, I24, I25) -> f6(I26, I27, I23, I25, I28, I29) [I25 + 2 <= I20 /\ 0 <= I26 - 1 /\ 0 <= I20 - 1 /\ I26 <= I20 /\ I24 <= I23 - 1 /\ -1 <= I27 - 1 /\ 1 <= I23 - 1 /\ 0 <= I22 - 1 /\ I21 <= I22 - 1 /\ -1 <= I24 - 1] 4.96/4.97 f4(I30, I31, I32, I33, I34, I35) -> f4(I36, I37, I38, I39, I40, I41) [-1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 2 <= I31 /\ I37 + 2 <= I30 /\ I36 + 2 <= I31 /\ I36 + 2 <= I30] 4.96/4.97 f4(I42, I43, I44, I45, I46, I47) -> f4(I48, I49, I50, I51, I52, I53) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 2 <= I43 - 1 /\ 2 <= I42 - 1 /\ I49 + 3 <= I43 /\ I49 + 3 <= I42 /\ I48 + 3 <= I43 /\ I48 + 3 <= I42] 4.96/4.97 f5(I54, I55, I56, I57, I58, I59) -> f5(I60, I55 + 1, I56, I57, I58 + 1, I61) [-1 <= I58 - 1 /\ I55 <= I56 - 1 /\ 0 <= I56 - 1 /\ 1 <= I57 - 1 /\ -1 <= y1 - 1 /\ I58 <= I57 - 1 /\ 0 <= I54 - 1 /\ 2 <= I60 - 1 /\ I59 + 2 <= I54] 4.96/4.97 f5(I62, I63, I64, I65, I66, I67) -> f5(I68, I63 + 1, I64, I65, I66 + 1, I69) [-1 <= I66 - 1 /\ I63 <= I64 - 1 /\ 0 <= I64 - 1 /\ 1 <= I65 - 1 /\ -1 <= I70 - 1 /\ I66 <= I65 - 1 /\ 0 <= I62 - 1 /\ 2 <= I68 - 1 /\ I67 + 2 <= I62] 4.96/4.97 f5(I71, I72, I73, I74, I75, I76) -> f5(I77, I72 + 1, I73, I74, I75 + 1, I78) [-1 <= I75 - 1 /\ I72 <= I73 - 1 /\ 0 <= I73 - 1 /\ 1 <= I74 - 1 /\ -1 <= I79 - 1 /\ I75 <= I74 - 1 /\ 0 <= I71 - 1 /\ 3 <= I77 - 1 /\ I76 + 2 <= I71] 4.96/4.97 f5(I80, I81, I82, I83, I84, I85) -> f5(I86, I81 + 1, I82, I83, I84 + 1, I87) [-1 <= I84 - 1 /\ I81 <= I82 - 1 /\ 0 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= I88 - 1 /\ I84 <= I83 - 1 /\ 0 <= I80 - 1 /\ 3 <= I86 - 1 /\ I85 + 2 <= I80] 4.96/4.97 f1(I89, I90, I91, I92, I93, I94) -> f5(I95, 0, I96, I90, 2, I97) [1 <= I95 - 1 /\ 0 <= I89 - 1 /\ -1 <= I96 - 1 /\ 1 <= I90 - 1 /\ -1 <= I97 - 1] 4.96/4.97 f2(I98, I99, I100, I101, I102, I103) -> f4(I104, I105, I106, I107, I108, I109) [I104 <= I99 /\ 1 <= I110 - 1 /\ I105 <= I99 /\ 0 <= I98 - 1 /\ 0 <= I99 - 1 /\ 0 <= I104 - 1 /\ 0 <= I105 - 1 /\ I100 + 2 <= I99 /\ I102 + 2 <= I99 /\ I101 + 2 <= I99] 4.96/4.97 f3(I111, I112, I113, I114, I115, I116) -> f2(I117, I118, I113, I114, I115, I119) [I114 + 2 <= I112 /\ I115 + 2 <= I112 /\ I113 + 2 <= I112 /\ 0 <= I118 - 1 /\ 0 <= I117 - 1 /\ 0 <= I112 - 1 /\ 0 <= I111 - 1 /\ I118 <= I112 /\ I117 <= I112 /\ I117 <= I111] 4.96/4.97 f1(I120, I121, I122, I123, I124, I125) -> f2(I126, I127, I128, I129, I130, I131) [-1 <= I132 - 1 /\ 0 <= I121 - 1 /\ I126 <= I120 /\ 0 <= I120 - 1 /\ 0 <= I126 - 1 /\ 0 <= I127 - 1] 4.96/4.97 4.96/4.97 The dependency graph for this problem is: 4.96/4.97 0 -> 10, 13 4.96/4.97 1 -> 1, 2 4.96/4.97 2 -> 1, 2 4.96/4.97 3 -> 1, 2 4.96/4.97 4 -> 4, 5 4.96/4.97 5 -> 4, 5 4.96/4.97 6 -> 3, 6, 7, 8, 9 4.96/4.97 7 -> 3, 6, 7, 8, 9 4.96/4.97 8 -> 3, 6, 7, 8, 9 4.96/4.97 9 -> 3, 6, 7, 8, 9 4.96/4.97 10 -> 3, 6, 7, 8, 9 4.96/4.97 11 -> 4, 5 4.96/4.97 12 -> 11 4.96/4.97 13 -> 11 4.96/4.97 Where: 4.96/4.97 0) init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.96/4.97 1) f6#(I0, I1, I2, I3, I4, I5) -> f6#(I6, I1, I2, I7, I8, I9) [I7 + 4 <= I0 /\ I3 + 2 <= I0 /\ 0 <= I6 - 1 /\ 2 <= I0 - 1 /\ I6 + 2 <= I0 /\ I1 <= I3 /\ 1 <= I2 - 1] 4.96/4.97 2) f6#(I10, I11, I12, I13, I14, I15) -> f6#(I16, I11, I12, I17, I18, I19) [I17 + 4 <= I10 /\ I13 + 2 <= I10 /\ 0 <= I16 - 1 /\ 2 <= I10 - 1 /\ I16 + 2 <= I10 /\ I13 <= I11 - 1 /\ 1 <= I12 - 1] 4.96/4.97 3) f5#(I20, I21, I22, I23, I24, I25) -> f6#(I26, I27, I23, I25, I28, I29) [I25 + 2 <= I20 /\ 0 <= I26 - 1 /\ 0 <= I20 - 1 /\ I26 <= I20 /\ I24 <= I23 - 1 /\ -1 <= I27 - 1 /\ 1 <= I23 - 1 /\ 0 <= I22 - 1 /\ I21 <= I22 - 1 /\ -1 <= I24 - 1] 4.96/4.97 4) f4#(I30, I31, I32, I33, I34, I35) -> f4#(I36, I37, I38, I39, I40, I41) [-1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 2 <= I31 /\ I37 + 2 <= I30 /\ I36 + 2 <= I31 /\ I36 + 2 <= I30] 4.96/4.97 5) f4#(I42, I43, I44, I45, I46, I47) -> f4#(I48, I49, I50, I51, I52, I53) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 2 <= I43 - 1 /\ 2 <= I42 - 1 /\ I49 + 3 <= I43 /\ I49 + 3 <= I42 /\ I48 + 3 <= I43 /\ I48 + 3 <= I42] 4.96/4.97 6) f5#(I54, I55, I56, I57, I58, I59) -> f5#(I60, I55 + 1, I56, I57, I58 + 1, I61) [-1 <= I58 - 1 /\ I55 <= I56 - 1 /\ 0 <= I56 - 1 /\ 1 <= I57 - 1 /\ -1 <= y1 - 1 /\ I58 <= I57 - 1 /\ 0 <= I54 - 1 /\ 2 <= I60 - 1 /\ I59 + 2 <= I54] 4.96/4.97 7) f5#(I62, I63, I64, I65, I66, I67) -> f5#(I68, I63 + 1, I64, I65, I66 + 1, I69) [-1 <= I66 - 1 /\ I63 <= I64 - 1 /\ 0 <= I64 - 1 /\ 1 <= I65 - 1 /\ -1 <= I70 - 1 /\ I66 <= I65 - 1 /\ 0 <= I62 - 1 /\ 2 <= I68 - 1 /\ I67 + 2 <= I62] 4.96/4.97 8) f5#(I71, I72, I73, I74, I75, I76) -> f5#(I77, I72 + 1, I73, I74, I75 + 1, I78) [-1 <= I75 - 1 /\ I72 <= I73 - 1 /\ 0 <= I73 - 1 /\ 1 <= I74 - 1 /\ -1 <= I79 - 1 /\ I75 <= I74 - 1 /\ 0 <= I71 - 1 /\ 3 <= I77 - 1 /\ I76 + 2 <= I71] 4.96/4.97 9) f5#(I80, I81, I82, I83, I84, I85) -> f5#(I86, I81 + 1, I82, I83, I84 + 1, I87) [-1 <= I84 - 1 /\ I81 <= I82 - 1 /\ 0 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= I88 - 1 /\ I84 <= I83 - 1 /\ 0 <= I80 - 1 /\ 3 <= I86 - 1 /\ I85 + 2 <= I80] 4.96/4.97 10) f1#(I89, I90, I91, I92, I93, I94) -> f5#(I95, 0, I96, I90, 2, I97) [1 <= I95 - 1 /\ 0 <= I89 - 1 /\ -1 <= I96 - 1 /\ 1 <= I90 - 1 /\ -1 <= I97 - 1] 4.96/4.97 11) f2#(I98, I99, I100, I101, I102, I103) -> f4#(I104, I105, I106, I107, I108, I109) [I104 <= I99 /\ 1 <= I110 - 1 /\ I105 <= I99 /\ 0 <= I98 - 1 /\ 0 <= I99 - 1 /\ 0 <= I104 - 1 /\ 0 <= I105 - 1 /\ I100 + 2 <= I99 /\ I102 + 2 <= I99 /\ I101 + 2 <= I99] 4.96/4.97 12) f3#(I111, I112, I113, I114, I115, I116) -> f2#(I117, I118, I113, I114, I115, I119) [I114 + 2 <= I112 /\ I115 + 2 <= I112 /\ I113 + 2 <= I112 /\ 0 <= I118 - 1 /\ 0 <= I117 - 1 /\ 0 <= I112 - 1 /\ 0 <= I111 - 1 /\ I118 <= I112 /\ I117 <= I112 /\ I117 <= I111] 4.96/4.97 13) f1#(I120, I121, I122, I123, I124, I125) -> f2#(I126, I127, I128, I129, I130, I131) [-1 <= I132 - 1 /\ 0 <= I121 - 1 /\ I126 <= I120 /\ 0 <= I120 - 1 /\ 0 <= I126 - 1 /\ 0 <= I127 - 1] 4.96/4.97 4.96/4.97 We have the following SCCs. 4.96/4.97 { 6, 7, 8, 9 } 4.96/4.97 { 1, 2 } 4.96/4.97 { 4, 5 } 4.96/4.97 4.96/4.97 DP problem for innermost termination. 4.96/4.97 P = 4.96/4.97 f4#(I30, I31, I32, I33, I34, I35) -> f4#(I36, I37, I38, I39, I40, I41) [-1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 2 <= I31 /\ I37 + 2 <= I30 /\ I36 + 2 <= I31 /\ I36 + 2 <= I30] 4.96/4.97 f4#(I42, I43, I44, I45, I46, I47) -> f4#(I48, I49, I50, I51, I52, I53) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 2 <= I43 - 1 /\ 2 <= I42 - 1 /\ I49 + 3 <= I43 /\ I49 + 3 <= I42 /\ I48 + 3 <= I43 /\ I48 + 3 <= I42] 4.96/4.97 R = 4.96/4.97 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.96/4.97 f6(I0, I1, I2, I3, I4, I5) -> f6(I6, I1, I2, I7, I8, I9) [I7 + 4 <= I0 /\ I3 + 2 <= I0 /\ 0 <= I6 - 1 /\ 2 <= I0 - 1 /\ I6 + 2 <= I0 /\ I1 <= I3 /\ 1 <= I2 - 1] 4.96/4.97 f6(I10, I11, I12, I13, I14, I15) -> f6(I16, I11, I12, I17, I18, I19) [I17 + 4 <= I10 /\ I13 + 2 <= I10 /\ 0 <= I16 - 1 /\ 2 <= I10 - 1 /\ I16 + 2 <= I10 /\ I13 <= I11 - 1 /\ 1 <= I12 - 1] 4.96/4.97 f5(I20, I21, I22, I23, I24, I25) -> f6(I26, I27, I23, I25, I28, I29) [I25 + 2 <= I20 /\ 0 <= I26 - 1 /\ 0 <= I20 - 1 /\ I26 <= I20 /\ I24 <= I23 - 1 /\ -1 <= I27 - 1 /\ 1 <= I23 - 1 /\ 0 <= I22 - 1 /\ I21 <= I22 - 1 /\ -1 <= I24 - 1] 4.96/4.97 f4(I30, I31, I32, I33, I34, I35) -> f4(I36, I37, I38, I39, I40, I41) [-1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 2 <= I31 /\ I37 + 2 <= I30 /\ I36 + 2 <= I31 /\ I36 + 2 <= I30] 4.96/4.97 f4(I42, I43, I44, I45, I46, I47) -> f4(I48, I49, I50, I51, I52, I53) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 2 <= I43 - 1 /\ 2 <= I42 - 1 /\ I49 + 3 <= I43 /\ I49 + 3 <= I42 /\ I48 + 3 <= I43 /\ I48 + 3 <= I42] 4.96/4.97 f5(I54, I55, I56, I57, I58, I59) -> f5(I60, I55 + 1, I56, I57, I58 + 1, I61) [-1 <= I58 - 1 /\ I55 <= I56 - 1 /\ 0 <= I56 - 1 /\ 1 <= I57 - 1 /\ -1 <= y1 - 1 /\ I58 <= I57 - 1 /\ 0 <= I54 - 1 /\ 2 <= I60 - 1 /\ I59 + 2 <= I54] 4.96/4.97 f5(I62, I63, I64, I65, I66, I67) -> f5(I68, I63 + 1, I64, I65, I66 + 1, I69) [-1 <= I66 - 1 /\ I63 <= I64 - 1 /\ 0 <= I64 - 1 /\ 1 <= I65 - 1 /\ -1 <= I70 - 1 /\ I66 <= I65 - 1 /\ 0 <= I62 - 1 /\ 2 <= I68 - 1 /\ I67 + 2 <= I62] 4.96/4.97 f5(I71, I72, I73, I74, I75, I76) -> f5(I77, I72 + 1, I73, I74, I75 + 1, I78) [-1 <= I75 - 1 /\ I72 <= I73 - 1 /\ 0 <= I73 - 1 /\ 1 <= I74 - 1 /\ -1 <= I79 - 1 /\ I75 <= I74 - 1 /\ 0 <= I71 - 1 /\ 3 <= I77 - 1 /\ I76 + 2 <= I71] 4.96/4.97 f5(I80, I81, I82, I83, I84, I85) -> f5(I86, I81 + 1, I82, I83, I84 + 1, I87) [-1 <= I84 - 1 /\ I81 <= I82 - 1 /\ 0 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= I88 - 1 /\ I84 <= I83 - 1 /\ 0 <= I80 - 1 /\ 3 <= I86 - 1 /\ I85 + 2 <= I80] 4.96/4.97 f1(I89, I90, I91, I92, I93, I94) -> f5(I95, 0, I96, I90, 2, I97) [1 <= I95 - 1 /\ 0 <= I89 - 1 /\ -1 <= I96 - 1 /\ 1 <= I90 - 1 /\ -1 <= I97 - 1] 4.96/4.97 f2(I98, I99, I100, I101, I102, I103) -> f4(I104, I105, I106, I107, I108, I109) [I104 <= I99 /\ 1 <= I110 - 1 /\ I105 <= I99 /\ 0 <= I98 - 1 /\ 0 <= I99 - 1 /\ 0 <= I104 - 1 /\ 0 <= I105 - 1 /\ I100 + 2 <= I99 /\ I102 + 2 <= I99 /\ I101 + 2 <= I99] 4.96/4.97 f3(I111, I112, I113, I114, I115, I116) -> f2(I117, I118, I113, I114, I115, I119) [I114 + 2 <= I112 /\ I115 + 2 <= I112 /\ I113 + 2 <= I112 /\ 0 <= I118 - 1 /\ 0 <= I117 - 1 /\ 0 <= I112 - 1 /\ 0 <= I111 - 1 /\ I118 <= I112 /\ I117 <= I112 /\ I117 <= I111] 4.96/4.97 f1(I120, I121, I122, I123, I124, I125) -> f2(I126, I127, I128, I129, I130, I131) [-1 <= I132 - 1 /\ 0 <= I121 - 1 /\ I126 <= I120 /\ 0 <= I120 - 1 /\ 0 <= I126 - 1 /\ 0 <= I127 - 1] 4.96/4.97 4.96/4.97 We use the basic value criterion with the projection function NU: 4.96/4.97 NU[f4#(z1,z2,z3,z4,z5,z6)] = z2 4.96/4.97 4.96/4.97 This gives the following inequalities: 4.96/4.97 -1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 2 <= I31 /\ I37 + 2 <= I30 /\ I36 + 2 <= I31 /\ I36 + 2 <= I30 ==> I31 >! I37 4.96/4.97 -1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 2 <= I43 - 1 /\ 2 <= I42 - 1 /\ I49 + 3 <= I43 /\ I49 + 3 <= I42 /\ I48 + 3 <= I43 /\ I48 + 3 <= I42 ==> I43 >! I49 4.96/4.97 4.96/4.97 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 4.96/4.97 4.96/4.97 DP problem for innermost termination. 4.96/4.97 P = 4.96/4.97 f6#(I0, I1, I2, I3, I4, I5) -> f6#(I6, I1, I2, I7, I8, I9) [I7 + 4 <= I0 /\ I3 + 2 <= I0 /\ 0 <= I6 - 1 /\ 2 <= I0 - 1 /\ I6 + 2 <= I0 /\ I1 <= I3 /\ 1 <= I2 - 1] 4.96/4.97 f6#(I10, I11, I12, I13, I14, I15) -> f6#(I16, I11, I12, I17, I18, I19) [I17 + 4 <= I10 /\ I13 + 2 <= I10 /\ 0 <= I16 - 1 /\ 2 <= I10 - 1 /\ I16 + 2 <= I10 /\ I13 <= I11 - 1 /\ 1 <= I12 - 1] 4.96/4.97 R = 4.96/4.97 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.96/4.97 f6(I0, I1, I2, I3, I4, I5) -> f6(I6, I1, I2, I7, I8, I9) [I7 + 4 <= I0 /\ I3 + 2 <= I0 /\ 0 <= I6 - 1 /\ 2 <= I0 - 1 /\ I6 + 2 <= I0 /\ I1 <= I3 /\ 1 <= I2 - 1] 4.96/4.97 f6(I10, I11, I12, I13, I14, I15) -> f6(I16, I11, I12, I17, I18, I19) [I17 + 4 <= I10 /\ I13 + 2 <= I10 /\ 0 <= I16 - 1 /\ 2 <= I10 - 1 /\ I16 + 2 <= I10 /\ I13 <= I11 - 1 /\ 1 <= I12 - 1] 4.96/4.97 f5(I20, I21, I22, I23, I24, I25) -> f6(I26, I27, I23, I25, I28, I29) [I25 + 2 <= I20 /\ 0 <= I26 - 1 /\ 0 <= I20 - 1 /\ I26 <= I20 /\ I24 <= I23 - 1 /\ -1 <= I27 - 1 /\ 1 <= I23 - 1 /\ 0 <= I22 - 1 /\ I21 <= I22 - 1 /\ -1 <= I24 - 1] 4.96/4.97 f4(I30, I31, I32, I33, I34, I35) -> f4(I36, I37, I38, I39, I40, I41) [-1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 2 <= I31 /\ I37 + 2 <= I30 /\ I36 + 2 <= I31 /\ I36 + 2 <= I30] 4.96/4.97 f4(I42, I43, I44, I45, I46, I47) -> f4(I48, I49, I50, I51, I52, I53) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 2 <= I43 - 1 /\ 2 <= I42 - 1 /\ I49 + 3 <= I43 /\ I49 + 3 <= I42 /\ I48 + 3 <= I43 /\ I48 + 3 <= I42] 4.96/4.97 f5(I54, I55, I56, I57, I58, I59) -> f5(I60, I55 + 1, I56, I57, I58 + 1, I61) [-1 <= I58 - 1 /\ I55 <= I56 - 1 /\ 0 <= I56 - 1 /\ 1 <= I57 - 1 /\ -1 <= y1 - 1 /\ I58 <= I57 - 1 /\ 0 <= I54 - 1 /\ 2 <= I60 - 1 /\ I59 + 2 <= I54] 4.96/4.97 f5(I62, I63, I64, I65, I66, I67) -> f5(I68, I63 + 1, I64, I65, I66 + 1, I69) [-1 <= I66 - 1 /\ I63 <= I64 - 1 /\ 0 <= I64 - 1 /\ 1 <= I65 - 1 /\ -1 <= I70 - 1 /\ I66 <= I65 - 1 /\ 0 <= I62 - 1 /\ 2 <= I68 - 1 /\ I67 + 2 <= I62] 4.96/4.97 f5(I71, I72, I73, I74, I75, I76) -> f5(I77, I72 + 1, I73, I74, I75 + 1, I78) [-1 <= I75 - 1 /\ I72 <= I73 - 1 /\ 0 <= I73 - 1 /\ 1 <= I74 - 1 /\ -1 <= I79 - 1 /\ I75 <= I74 - 1 /\ 0 <= I71 - 1 /\ 3 <= I77 - 1 /\ I76 + 2 <= I71] 4.96/4.97 f5(I80, I81, I82, I83, I84, I85) -> f5(I86, I81 + 1, I82, I83, I84 + 1, I87) [-1 <= I84 - 1 /\ I81 <= I82 - 1 /\ 0 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= I88 - 1 /\ I84 <= I83 - 1 /\ 0 <= I80 - 1 /\ 3 <= I86 - 1 /\ I85 + 2 <= I80] 4.96/4.97 f1(I89, I90, I91, I92, I93, I94) -> f5(I95, 0, I96, I90, 2, I97) [1 <= I95 - 1 /\ 0 <= I89 - 1 /\ -1 <= I96 - 1 /\ 1 <= I90 - 1 /\ -1 <= I97 - 1] 4.96/4.97 f2(I98, I99, I100, I101, I102, I103) -> f4(I104, I105, I106, I107, I108, I109) [I104 <= I99 /\ 1 <= I110 - 1 /\ I105 <= I99 /\ 0 <= I98 - 1 /\ 0 <= I99 - 1 /\ 0 <= I104 - 1 /\ 0 <= I105 - 1 /\ I100 + 2 <= I99 /\ I102 + 2 <= I99 /\ I101 + 2 <= I99] 4.96/4.97 f3(I111, I112, I113, I114, I115, I116) -> f2(I117, I118, I113, I114, I115, I119) [I114 + 2 <= I112 /\ I115 + 2 <= I112 /\ I113 + 2 <= I112 /\ 0 <= I118 - 1 /\ 0 <= I117 - 1 /\ 0 <= I112 - 1 /\ 0 <= I111 - 1 /\ I118 <= I112 /\ I117 <= I112 /\ I117 <= I111] 4.96/4.97 f1(I120, I121, I122, I123, I124, I125) -> f2(I126, I127, I128, I129, I130, I131) [-1 <= I132 - 1 /\ 0 <= I121 - 1 /\ I126 <= I120 /\ 0 <= I120 - 1 /\ 0 <= I126 - 1 /\ 0 <= I127 - 1] 4.96/4.97 4.96/4.97 We use the basic value criterion with the projection function NU: 4.96/4.97 NU[f6#(z1,z2,z3,z4,z5,z6)] = z1 4.96/4.97 4.96/4.97 This gives the following inequalities: 4.96/4.97 I7 + 4 <= I0 /\ I3 + 2 <= I0 /\ 0 <= I6 - 1 /\ 2 <= I0 - 1 /\ I6 + 2 <= I0 /\ I1 <= I3 /\ 1 <= I2 - 1 ==> I0 >! I6 4.96/4.97 I17 + 4 <= I10 /\ I13 + 2 <= I10 /\ 0 <= I16 - 1 /\ 2 <= I10 - 1 /\ I16 + 2 <= I10 /\ I13 <= I11 - 1 /\ 1 <= I12 - 1 ==> I10 >! I16 4.96/4.97 4.96/4.97 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 4.96/4.97 4.96/4.97 DP problem for innermost termination. 4.96/4.97 P = 4.96/4.97 f5#(I54, I55, I56, I57, I58, I59) -> f5#(I60, I55 + 1, I56, I57, I58 + 1, I61) [-1 <= I58 - 1 /\ I55 <= I56 - 1 /\ 0 <= I56 - 1 /\ 1 <= I57 - 1 /\ -1 <= y1 - 1 /\ I58 <= I57 - 1 /\ 0 <= I54 - 1 /\ 2 <= I60 - 1 /\ I59 + 2 <= I54] 4.96/4.97 f5#(I62, I63, I64, I65, I66, I67) -> f5#(I68, I63 + 1, I64, I65, I66 + 1, I69) [-1 <= I66 - 1 /\ I63 <= I64 - 1 /\ 0 <= I64 - 1 /\ 1 <= I65 - 1 /\ -1 <= I70 - 1 /\ I66 <= I65 - 1 /\ 0 <= I62 - 1 /\ 2 <= I68 - 1 /\ I67 + 2 <= I62] 4.96/4.97 f5#(I71, I72, I73, I74, I75, I76) -> f5#(I77, I72 + 1, I73, I74, I75 + 1, I78) [-1 <= I75 - 1 /\ I72 <= I73 - 1 /\ 0 <= I73 - 1 /\ 1 <= I74 - 1 /\ -1 <= I79 - 1 /\ I75 <= I74 - 1 /\ 0 <= I71 - 1 /\ 3 <= I77 - 1 /\ I76 + 2 <= I71] 4.96/4.97 f5#(I80, I81, I82, I83, I84, I85) -> f5#(I86, I81 + 1, I82, I83, I84 + 1, I87) [-1 <= I84 - 1 /\ I81 <= I82 - 1 /\ 0 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= I88 - 1 /\ I84 <= I83 - 1 /\ 0 <= I80 - 1 /\ 3 <= I86 - 1 /\ I85 + 2 <= I80] 4.96/4.97 R = 4.96/4.97 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.96/4.97 f6(I0, I1, I2, I3, I4, I5) -> f6(I6, I1, I2, I7, I8, I9) [I7 + 4 <= I0 /\ I3 + 2 <= I0 /\ 0 <= I6 - 1 /\ 2 <= I0 - 1 /\ I6 + 2 <= I0 /\ I1 <= I3 /\ 1 <= I2 - 1] 4.96/4.97 f6(I10, I11, I12, I13, I14, I15) -> f6(I16, I11, I12, I17, I18, I19) [I17 + 4 <= I10 /\ I13 + 2 <= I10 /\ 0 <= I16 - 1 /\ 2 <= I10 - 1 /\ I16 + 2 <= I10 /\ I13 <= I11 - 1 /\ 1 <= I12 - 1] 4.96/4.97 f5(I20, I21, I22, I23, I24, I25) -> f6(I26, I27, I23, I25, I28, I29) [I25 + 2 <= I20 /\ 0 <= I26 - 1 /\ 0 <= I20 - 1 /\ I26 <= I20 /\ I24 <= I23 - 1 /\ -1 <= I27 - 1 /\ 1 <= I23 - 1 /\ 0 <= I22 - 1 /\ I21 <= I22 - 1 /\ -1 <= I24 - 1] 4.96/4.97 f4(I30, I31, I32, I33, I34, I35) -> f4(I36, I37, I38, I39, I40, I41) [-1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 2 <= I31 /\ I37 + 2 <= I30 /\ I36 + 2 <= I31 /\ I36 + 2 <= I30] 4.96/4.97 f4(I42, I43, I44, I45, I46, I47) -> f4(I48, I49, I50, I51, I52, I53) [-1 <= I49 - 1 /\ -1 <= I48 - 1 /\ 2 <= I43 - 1 /\ 2 <= I42 - 1 /\ I49 + 3 <= I43 /\ I49 + 3 <= I42 /\ I48 + 3 <= I43 /\ I48 + 3 <= I42] 4.96/4.97 f5(I54, I55, I56, I57, I58, I59) -> f5(I60, I55 + 1, I56, I57, I58 + 1, I61) [-1 <= I58 - 1 /\ I55 <= I56 - 1 /\ 0 <= I56 - 1 /\ 1 <= I57 - 1 /\ -1 <= y1 - 1 /\ I58 <= I57 - 1 /\ 0 <= I54 - 1 /\ 2 <= I60 - 1 /\ I59 + 2 <= I54] 4.96/4.97 f5(I62, I63, I64, I65, I66, I67) -> f5(I68, I63 + 1, I64, I65, I66 + 1, I69) [-1 <= I66 - 1 /\ I63 <= I64 - 1 /\ 0 <= I64 - 1 /\ 1 <= I65 - 1 /\ -1 <= I70 - 1 /\ I66 <= I65 - 1 /\ 0 <= I62 - 1 /\ 2 <= I68 - 1 /\ I67 + 2 <= I62] 4.96/4.97 f5(I71, I72, I73, I74, I75, I76) -> f5(I77, I72 + 1, I73, I74, I75 + 1, I78) [-1 <= I75 - 1 /\ I72 <= I73 - 1 /\ 0 <= I73 - 1 /\ 1 <= I74 - 1 /\ -1 <= I79 - 1 /\ I75 <= I74 - 1 /\ 0 <= I71 - 1 /\ 3 <= I77 - 1 /\ I76 + 2 <= I71] 4.96/4.97 f5(I80, I81, I82, I83, I84, I85) -> f5(I86, I81 + 1, I82, I83, I84 + 1, I87) [-1 <= I84 - 1 /\ I81 <= I82 - 1 /\ 0 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= I88 - 1 /\ I84 <= I83 - 1 /\ 0 <= I80 - 1 /\ 3 <= I86 - 1 /\ I85 + 2 <= I80] 4.96/4.97 f1(I89, I90, I91, I92, I93, I94) -> f5(I95, 0, I96, I90, 2, I97) [1 <= I95 - 1 /\ 0 <= I89 - 1 /\ -1 <= I96 - 1 /\ 1 <= I90 - 1 /\ -1 <= I97 - 1] 4.96/4.97 f2(I98, I99, I100, I101, I102, I103) -> f4(I104, I105, I106, I107, I108, I109) [I104 <= I99 /\ 1 <= I110 - 1 /\ I105 <= I99 /\ 0 <= I98 - 1 /\ 0 <= I99 - 1 /\ 0 <= I104 - 1 /\ 0 <= I105 - 1 /\ I100 + 2 <= I99 /\ I102 + 2 <= I99 /\ I101 + 2 <= I99] 4.96/4.97 f3(I111, I112, I113, I114, I115, I116) -> f2(I117, I118, I113, I114, I115, I119) [I114 + 2 <= I112 /\ I115 + 2 <= I112 /\ I113 + 2 <= I112 /\ 0 <= I118 - 1 /\ 0 <= I117 - 1 /\ 0 <= I112 - 1 /\ 0 <= I111 - 1 /\ I118 <= I112 /\ I117 <= I112 /\ I117 <= I111] 4.96/4.97 f1(I120, I121, I122, I123, I124, I125) -> f2(I126, I127, I128, I129, I130, I131) [-1 <= I132 - 1 /\ 0 <= I121 - 1 /\ I126 <= I120 /\ 0 <= I120 - 1 /\ 0 <= I126 - 1 /\ 0 <= I127 - 1] 4.96/4.97 4.96/4.97 We use the reverse value criterion with the projection function NU: 4.96/4.97 NU[f5#(z1,z2,z3,z4,z5,z6)] = z3 - 1 + -1 * z2 4.96/4.97 4.96/4.97 This gives the following inequalities: 4.96/4.97 -1 <= I58 - 1 /\ I55 <= I56 - 1 /\ 0 <= I56 - 1 /\ 1 <= I57 - 1 /\ -1 <= y1 - 1 /\ I58 <= I57 - 1 /\ 0 <= I54 - 1 /\ 2 <= I60 - 1 /\ I59 + 2 <= I54 ==> I56 - 1 + -1 * I55 > I56 - 1 + -1 * (I55 + 1) with I56 - 1 + -1 * I55 >= 0 4.96/4.97 -1 <= I66 - 1 /\ I63 <= I64 - 1 /\ 0 <= I64 - 1 /\ 1 <= I65 - 1 /\ -1 <= I70 - 1 /\ I66 <= I65 - 1 /\ 0 <= I62 - 1 /\ 2 <= I68 - 1 /\ I67 + 2 <= I62 ==> I64 - 1 + -1 * I63 > I64 - 1 + -1 * (I63 + 1) with I64 - 1 + -1 * I63 >= 0 4.96/4.97 -1 <= I75 - 1 /\ I72 <= I73 - 1 /\ 0 <= I73 - 1 /\ 1 <= I74 - 1 /\ -1 <= I79 - 1 /\ I75 <= I74 - 1 /\ 0 <= I71 - 1 /\ 3 <= I77 - 1 /\ I76 + 2 <= I71 ==> I73 - 1 + -1 * I72 > I73 - 1 + -1 * (I72 + 1) with I73 - 1 + -1 * I72 >= 0 4.96/4.97 -1 <= I84 - 1 /\ I81 <= I82 - 1 /\ 0 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= I88 - 1 /\ I84 <= I83 - 1 /\ 0 <= I80 - 1 /\ 3 <= I86 - 1 /\ I85 + 2 <= I80 ==> I82 - 1 + -1 * I81 > I82 - 1 + -1 * (I81 + 1) with I82 - 1 + -1 * I81 >= 0 4.96/4.97 4.96/4.97 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 4.96/7.95 EOF