4.44/4.48 MAYBE 4.44/4.48 4.44/4.48 DP problem for innermost termination. 4.44/4.48 P = 4.44/4.48 init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.44/4.48 f5#(I0, I1, I2, I3, I4, I5) -> f5#(I6, I7, I2 - 1, I3, I4 + 1, I8) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] 4.44/4.48 f5#(I9, I10, I11, I12, I13, I14) -> f5#(I15, I16, I11 - 1, I12, I13 + 1, I17) [4 <= I16 - 1 /\ 4 <= I15 - 1 /\ 2 <= I10 - 1 /\ 2 <= I9 - 1 /\ I16 - 2 <= I10 /\ I16 - 2 <= I9 /\ I15 - 2 <= I10 /\ I15 - 2 <= I9 /\ I13 <= I12 - 1 /\ -1 <= I13 - 1 /\ 0 <= I11 - 1] 4.44/4.48 f5#(I18, I19, I20, I21, I22, I23) -> f5#(I24, I25, I20 - 1, I21, I22 + 1, I26) [2 <= I25 - 1 /\ 2 <= I24 - 1 /\ 1 <= I19 - 1 /\ 2 <= I18 - 1 /\ I22 <= I21 - 1 /\ -1 <= I22 - 1 /\ 0 <= I20 - 1] 4.44/4.48 f5#(I27, I28, I29, I30, I31, I32) -> f5#(I33, I34, I29 - 1, I30, I31 + 1, I35) [-1 <= I31 - 1 /\ 0 <= I36 - 1 /\ 0 <= I29 - 1 /\ I31 <= I30 - 1 /\ 2 <= I27 - 1 /\ 1 <= I28 - 1 /\ 2 <= I33 - 1 /\ 2 <= I34 - 1] 4.44/4.48 f5#(I37, I38, I39, I40, I41, I42) -> f5#(I43, I44, I39 - 1, I40, I41 + 1, I45) [-1 <= I41 - 1 /\ 0 <= I46 - 1 /\ 0 <= I39 - 1 /\ I41 <= I40 - 1 /\ I43 <= I37 /\ I44 + 2 <= I38 /\ 2 <= I37 - 1 /\ 2 <= I38 - 1 /\ 2 <= I43 - 1 /\ 0 <= I44 - 1] 4.44/4.48 f5#(I47, I48, I49, I50, I51, I52) -> f5#(I53, I54, I49 - 1, I50, I51 + 1, I55) [0 <= I54 - 1 /\ 2 <= I53 - 1 /\ 2 <= I48 - 1 /\ 2 <= I47 - 1 /\ I54 + 2 <= I48 /\ I53 <= I47 /\ I51 <= I50 - 1 /\ -1 <= I51 - 1 /\ 0 <= I49 - 1] 4.44/4.48 f2#(I56, I57, I58, I59, I60, I61) -> f5#(I62, I63, I64, I65, I59 + 1, I66) [2 <= I63 - 1 /\ 2 <= I62 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ I63 - 3 <= I57 /\ I63 - 2 <= I56 /\ I62 - 3 <= I57 /\ I62 - 2 <= I56 /\ -1 <= I59 - 1 /\ I59 <= I65 - 1 /\ 0 <= I58 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1] 4.44/4.48 f3#(I67, I68, I69, I70, I71, I72) -> f3#(I73, I74, I75, I76, I77, I78) [2 <= I73 - 1 /\ 2 <= I67 - 1 /\ I73 - 2 <= I67] 4.44/4.48 f3#(I79, I80, I81, I82, I83, I84) -> f3#(I85, I86, I87, I88, I89, I90) [-1 <= I85 - 1 /\ 1 <= I79 - 1 /\ I85 + 2 <= I79] 4.44/4.48 f4#(I91, I92, I93, I94, I95, I96) -> f2#(I97, I98, I93 - 1, I95, I99, I100) [I96 + 2 <= I94 /\ 4 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I94 - 1 /\ 0 <= I91 - 1 /\ I97 + 2 <= I94 /\ I97 <= I91] 4.44/4.48 f2#(I101, I102, I103, I104, I105, I106) -> f2#(I107, I108, I103 - 1, I109, I110, I111) [0 <= I103 - 1 /\ 0 <= I112 - 1 /\ I107 <= I101 /\ I107 - 1 <= I102 /\ 0 <= I101 - 1 /\ -1 <= I102 - 1 /\ 0 <= I107 - 1 /\ 4 <= I108 - 1] 4.44/4.48 f2#(I113, I114, I115, I116, I117, I118) -> f2#(I119, I120, I115 - 1, I121, I122, I123) [0 <= I115 - 1 /\ 0 <= I124 - 1 /\ I119 <= I113 /\ I119 - 1 <= I114 /\ I120 - 2 <= I114 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1 /\ 0 <= I119 - 1 /\ 1 <= I120 - 1] 4.44/4.48 f2#(I125, I126, I127, I128, I129, I130) -> f3#(I131, I132, I133, I134, I135, I136) [I131 <= I126 /\ 0 <= I137 - 1 /\ 0 <= I125 - 1 /\ -1 <= I126 - 1 /\ -1 <= I131 - 1 /\ 0 = I127] 4.44/4.48 f1#(I138, I139, I140, I141, I142, I143) -> f2#(I144, I145, I146, 1, I147, I148) [-1 <= I145 - 1 /\ 0 <= I144 - 1 /\ 0 <= I138 - 1 /\ I145 + 1 <= I138 /\ I144 <= I138 /\ -1 <= I146 - 1 /\ 0 <= I139 - 1] 4.44/4.48 R = 4.44/4.48 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.44/4.48 f5(I0, I1, I2, I3, I4, I5) -> f5(I6, I7, I2 - 1, I3, I4 + 1, I8) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] 4.44/4.48 f5(I9, I10, I11, I12, I13, I14) -> f5(I15, I16, I11 - 1, I12, I13 + 1, I17) [4 <= I16 - 1 /\ 4 <= I15 - 1 /\ 2 <= I10 - 1 /\ 2 <= I9 - 1 /\ I16 - 2 <= I10 /\ I16 - 2 <= I9 /\ I15 - 2 <= I10 /\ I15 - 2 <= I9 /\ I13 <= I12 - 1 /\ -1 <= I13 - 1 /\ 0 <= I11 - 1] 4.44/4.48 f5(I18, I19, I20, I21, I22, I23) -> f5(I24, I25, I20 - 1, I21, I22 + 1, I26) [2 <= I25 - 1 /\ 2 <= I24 - 1 /\ 1 <= I19 - 1 /\ 2 <= I18 - 1 /\ I22 <= I21 - 1 /\ -1 <= I22 - 1 /\ 0 <= I20 - 1] 4.44/4.48 f5(I27, I28, I29, I30, I31, I32) -> f5(I33, I34, I29 - 1, I30, I31 + 1, I35) [-1 <= I31 - 1 /\ 0 <= I36 - 1 /\ 0 <= I29 - 1 /\ I31 <= I30 - 1 /\ 2 <= I27 - 1 /\ 1 <= I28 - 1 /\ 2 <= I33 - 1 /\ 2 <= I34 - 1] 4.44/4.48 f5(I37, I38, I39, I40, I41, I42) -> f5(I43, I44, I39 - 1, I40, I41 + 1, I45) [-1 <= I41 - 1 /\ 0 <= I46 - 1 /\ 0 <= I39 - 1 /\ I41 <= I40 - 1 /\ I43 <= I37 /\ I44 + 2 <= I38 /\ 2 <= I37 - 1 /\ 2 <= I38 - 1 /\ 2 <= I43 - 1 /\ 0 <= I44 - 1] 4.44/4.48 f5(I47, I48, I49, I50, I51, I52) -> f5(I53, I54, I49 - 1, I50, I51 + 1, I55) [0 <= I54 - 1 /\ 2 <= I53 - 1 /\ 2 <= I48 - 1 /\ 2 <= I47 - 1 /\ I54 + 2 <= I48 /\ I53 <= I47 /\ I51 <= I50 - 1 /\ -1 <= I51 - 1 /\ 0 <= I49 - 1] 4.44/4.48 f2(I56, I57, I58, I59, I60, I61) -> f5(I62, I63, I64, I65, I59 + 1, I66) [2 <= I63 - 1 /\ 2 <= I62 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ I63 - 3 <= I57 /\ I63 - 2 <= I56 /\ I62 - 3 <= I57 /\ I62 - 2 <= I56 /\ -1 <= I59 - 1 /\ I59 <= I65 - 1 /\ 0 <= I58 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1] 4.44/4.48 f3(I67, I68, I69, I70, I71, I72) -> f3(I73, I74, I75, I76, I77, I78) [2 <= I73 - 1 /\ 2 <= I67 - 1 /\ I73 - 2 <= I67] 4.44/4.48 f3(I79, I80, I81, I82, I83, I84) -> f3(I85, I86, I87, I88, I89, I90) [-1 <= I85 - 1 /\ 1 <= I79 - 1 /\ I85 + 2 <= I79] 4.44/4.48 f4(I91, I92, I93, I94, I95, I96) -> f2(I97, I98, I93 - 1, I95, I99, I100) [I96 + 2 <= I94 /\ 4 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I94 - 1 /\ 0 <= I91 - 1 /\ I97 + 2 <= I94 /\ I97 <= I91] 4.44/4.48 f2(I101, I102, I103, I104, I105, I106) -> f2(I107, I108, I103 - 1, I109, I110, I111) [0 <= I103 - 1 /\ 0 <= I112 - 1 /\ I107 <= I101 /\ I107 - 1 <= I102 /\ 0 <= I101 - 1 /\ -1 <= I102 - 1 /\ 0 <= I107 - 1 /\ 4 <= I108 - 1] 4.44/4.48 f2(I113, I114, I115, I116, I117, I118) -> f2(I119, I120, I115 - 1, I121, I122, I123) [0 <= I115 - 1 /\ 0 <= I124 - 1 /\ I119 <= I113 /\ I119 - 1 <= I114 /\ I120 - 2 <= I114 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1 /\ 0 <= I119 - 1 /\ 1 <= I120 - 1] 4.44/4.48 f2(I125, I126, I127, I128, I129, I130) -> f3(I131, I132, I133, I134, I135, I136) [I131 <= I126 /\ 0 <= I137 - 1 /\ 0 <= I125 - 1 /\ -1 <= I126 - 1 /\ -1 <= I131 - 1 /\ 0 = I127] 4.44/4.48 f1(I138, I139, I140, I141, I142, I143) -> f2(I144, I145, I146, 1, I147, I148) [-1 <= I145 - 1 /\ 0 <= I144 - 1 /\ 0 <= I138 - 1 /\ I145 + 1 <= I138 /\ I144 <= I138 /\ -1 <= I146 - 1 /\ 0 <= I139 - 1] 4.44/4.48 4.44/4.48 The dependency graph for this problem is: 4.44/4.48 0 -> 14 4.44/4.48 1 -> 1, 2, 3, 4, 5, 6 4.44/4.48 2 -> 1, 2, 3, 4, 5, 6 4.44/4.48 3 -> 1, 2, 3, 4, 5, 6 4.44/4.48 4 -> 1, 2, 3, 4, 5, 6 4.44/4.48 5 -> 1, 2, 3, 4, 5, 6 4.44/4.48 6 -> 1, 2, 3, 4, 5, 6 4.44/4.48 7 -> 1, 2, 3, 4, 5, 6 4.44/4.48 8 -> 8, 9 4.44/4.48 9 -> 8, 9 4.44/4.48 10 -> 7, 11, 12, 13 4.44/4.48 11 -> 7, 11, 12, 13 4.44/4.48 12 -> 7, 11, 12, 13 4.44/4.48 13 -> 8, 9 4.44/4.48 14 -> 7, 11, 12, 13 4.44/4.48 Where: 4.44/4.48 0) init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.44/4.48 1) f5#(I0, I1, I2, I3, I4, I5) -> f5#(I6, I7, I2 - 1, I3, I4 + 1, I8) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] 4.44/4.48 2) f5#(I9, I10, I11, I12, I13, I14) -> f5#(I15, I16, I11 - 1, I12, I13 + 1, I17) [4 <= I16 - 1 /\ 4 <= I15 - 1 /\ 2 <= I10 - 1 /\ 2 <= I9 - 1 /\ I16 - 2 <= I10 /\ I16 - 2 <= I9 /\ I15 - 2 <= I10 /\ I15 - 2 <= I9 /\ I13 <= I12 - 1 /\ -1 <= I13 - 1 /\ 0 <= I11 - 1] 4.44/4.48 3) f5#(I18, I19, I20, I21, I22, I23) -> f5#(I24, I25, I20 - 1, I21, I22 + 1, I26) [2 <= I25 - 1 /\ 2 <= I24 - 1 /\ 1 <= I19 - 1 /\ 2 <= I18 - 1 /\ I22 <= I21 - 1 /\ -1 <= I22 - 1 /\ 0 <= I20 - 1] 4.44/4.48 4) f5#(I27, I28, I29, I30, I31, I32) -> f5#(I33, I34, I29 - 1, I30, I31 + 1, I35) [-1 <= I31 - 1 /\ 0 <= I36 - 1 /\ 0 <= I29 - 1 /\ I31 <= I30 - 1 /\ 2 <= I27 - 1 /\ 1 <= I28 - 1 /\ 2 <= I33 - 1 /\ 2 <= I34 - 1] 4.44/4.48 5) f5#(I37, I38, I39, I40, I41, I42) -> f5#(I43, I44, I39 - 1, I40, I41 + 1, I45) [-1 <= I41 - 1 /\ 0 <= I46 - 1 /\ 0 <= I39 - 1 /\ I41 <= I40 - 1 /\ I43 <= I37 /\ I44 + 2 <= I38 /\ 2 <= I37 - 1 /\ 2 <= I38 - 1 /\ 2 <= I43 - 1 /\ 0 <= I44 - 1] 4.44/4.48 6) f5#(I47, I48, I49, I50, I51, I52) -> f5#(I53, I54, I49 - 1, I50, I51 + 1, I55) [0 <= I54 - 1 /\ 2 <= I53 - 1 /\ 2 <= I48 - 1 /\ 2 <= I47 - 1 /\ I54 + 2 <= I48 /\ I53 <= I47 /\ I51 <= I50 - 1 /\ -1 <= I51 - 1 /\ 0 <= I49 - 1] 4.44/4.48 7) f2#(I56, I57, I58, I59, I60, I61) -> f5#(I62, I63, I64, I65, I59 + 1, I66) [2 <= I63 - 1 /\ 2 <= I62 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ I63 - 3 <= I57 /\ I63 - 2 <= I56 /\ I62 - 3 <= I57 /\ I62 - 2 <= I56 /\ -1 <= I59 - 1 /\ I59 <= I65 - 1 /\ 0 <= I58 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1] 4.44/4.48 8) f3#(I67, I68, I69, I70, I71, I72) -> f3#(I73, I74, I75, I76, I77, I78) [2 <= I73 - 1 /\ 2 <= I67 - 1 /\ I73 - 2 <= I67] 4.44/4.48 9) f3#(I79, I80, I81, I82, I83, I84) -> f3#(I85, I86, I87, I88, I89, I90) [-1 <= I85 - 1 /\ 1 <= I79 - 1 /\ I85 + 2 <= I79] 4.44/4.48 10) f4#(I91, I92, I93, I94, I95, I96) -> f2#(I97, I98, I93 - 1, I95, I99, I100) [I96 + 2 <= I94 /\ 4 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I94 - 1 /\ 0 <= I91 - 1 /\ I97 + 2 <= I94 /\ I97 <= I91] 4.44/4.48 11) f2#(I101, I102, I103, I104, I105, I106) -> f2#(I107, I108, I103 - 1, I109, I110, I111) [0 <= I103 - 1 /\ 0 <= I112 - 1 /\ I107 <= I101 /\ I107 - 1 <= I102 /\ 0 <= I101 - 1 /\ -1 <= I102 - 1 /\ 0 <= I107 - 1 /\ 4 <= I108 - 1] 4.44/4.48 12) f2#(I113, I114, I115, I116, I117, I118) -> f2#(I119, I120, I115 - 1, I121, I122, I123) [0 <= I115 - 1 /\ 0 <= I124 - 1 /\ I119 <= I113 /\ I119 - 1 <= I114 /\ I120 - 2 <= I114 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1 /\ 0 <= I119 - 1 /\ 1 <= I120 - 1] 4.44/4.48 13) f2#(I125, I126, I127, I128, I129, I130) -> f3#(I131, I132, I133, I134, I135, I136) [I131 <= I126 /\ 0 <= I137 - 1 /\ 0 <= I125 - 1 /\ -1 <= I126 - 1 /\ -1 <= I131 - 1 /\ 0 = I127] 4.44/4.48 14) f1#(I138, I139, I140, I141, I142, I143) -> f2#(I144, I145, I146, 1, I147, I148) [-1 <= I145 - 1 /\ 0 <= I144 - 1 /\ 0 <= I138 - 1 /\ I145 + 1 <= I138 /\ I144 <= I138 /\ -1 <= I146 - 1 /\ 0 <= I139 - 1] 4.44/4.48 4.44/4.48 We have the following SCCs. 4.44/4.48 { 11, 12 } 4.44/4.48 { 8, 9 } 4.44/4.48 { 1, 2, 3, 4, 5, 6 } 4.44/4.48 4.44/4.48 DP problem for innermost termination. 4.44/4.48 P = 4.44/4.48 f5#(I0, I1, I2, I3, I4, I5) -> f5#(I6, I7, I2 - 1, I3, I4 + 1, I8) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] 4.44/4.48 f5#(I9, I10, I11, I12, I13, I14) -> f5#(I15, I16, I11 - 1, I12, I13 + 1, I17) [4 <= I16 - 1 /\ 4 <= I15 - 1 /\ 2 <= I10 - 1 /\ 2 <= I9 - 1 /\ I16 - 2 <= I10 /\ I16 - 2 <= I9 /\ I15 - 2 <= I10 /\ I15 - 2 <= I9 /\ I13 <= I12 - 1 /\ -1 <= I13 - 1 /\ 0 <= I11 - 1] 4.44/4.48 f5#(I18, I19, I20, I21, I22, I23) -> f5#(I24, I25, I20 - 1, I21, I22 + 1, I26) [2 <= I25 - 1 /\ 2 <= I24 - 1 /\ 1 <= I19 - 1 /\ 2 <= I18 - 1 /\ I22 <= I21 - 1 /\ -1 <= I22 - 1 /\ 0 <= I20 - 1] 4.44/4.48 f5#(I27, I28, I29, I30, I31, I32) -> f5#(I33, I34, I29 - 1, I30, I31 + 1, I35) [-1 <= I31 - 1 /\ 0 <= I36 - 1 /\ 0 <= I29 - 1 /\ I31 <= I30 - 1 /\ 2 <= I27 - 1 /\ 1 <= I28 - 1 /\ 2 <= I33 - 1 /\ 2 <= I34 - 1] 4.44/4.48 f5#(I37, I38, I39, I40, I41, I42) -> f5#(I43, I44, I39 - 1, I40, I41 + 1, I45) [-1 <= I41 - 1 /\ 0 <= I46 - 1 /\ 0 <= I39 - 1 /\ I41 <= I40 - 1 /\ I43 <= I37 /\ I44 + 2 <= I38 /\ 2 <= I37 - 1 /\ 2 <= I38 - 1 /\ 2 <= I43 - 1 /\ 0 <= I44 - 1] 4.44/4.48 f5#(I47, I48, I49, I50, I51, I52) -> f5#(I53, I54, I49 - 1, I50, I51 + 1, I55) [0 <= I54 - 1 /\ 2 <= I53 - 1 /\ 2 <= I48 - 1 /\ 2 <= I47 - 1 /\ I54 + 2 <= I48 /\ I53 <= I47 /\ I51 <= I50 - 1 /\ -1 <= I51 - 1 /\ 0 <= I49 - 1] 4.44/4.48 R = 4.44/4.48 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.44/4.48 f5(I0, I1, I2, I3, I4, I5) -> f5(I6, I7, I2 - 1, I3, I4 + 1, I8) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] 4.44/4.48 f5(I9, I10, I11, I12, I13, I14) -> f5(I15, I16, I11 - 1, I12, I13 + 1, I17) [4 <= I16 - 1 /\ 4 <= I15 - 1 /\ 2 <= I10 - 1 /\ 2 <= I9 - 1 /\ I16 - 2 <= I10 /\ I16 - 2 <= I9 /\ I15 - 2 <= I10 /\ I15 - 2 <= I9 /\ I13 <= I12 - 1 /\ -1 <= I13 - 1 /\ 0 <= I11 - 1] 4.44/4.48 f5(I18, I19, I20, I21, I22, I23) -> f5(I24, I25, I20 - 1, I21, I22 + 1, I26) [2 <= I25 - 1 /\ 2 <= I24 - 1 /\ 1 <= I19 - 1 /\ 2 <= I18 - 1 /\ I22 <= I21 - 1 /\ -1 <= I22 - 1 /\ 0 <= I20 - 1] 4.44/4.48 f5(I27, I28, I29, I30, I31, I32) -> f5(I33, I34, I29 - 1, I30, I31 + 1, I35) [-1 <= I31 - 1 /\ 0 <= I36 - 1 /\ 0 <= I29 - 1 /\ I31 <= I30 - 1 /\ 2 <= I27 - 1 /\ 1 <= I28 - 1 /\ 2 <= I33 - 1 /\ 2 <= I34 - 1] 4.44/4.48 f5(I37, I38, I39, I40, I41, I42) -> f5(I43, I44, I39 - 1, I40, I41 + 1, I45) [-1 <= I41 - 1 /\ 0 <= I46 - 1 /\ 0 <= I39 - 1 /\ I41 <= I40 - 1 /\ I43 <= I37 /\ I44 + 2 <= I38 /\ 2 <= I37 - 1 /\ 2 <= I38 - 1 /\ 2 <= I43 - 1 /\ 0 <= I44 - 1] 4.44/4.48 f5(I47, I48, I49, I50, I51, I52) -> f5(I53, I54, I49 - 1, I50, I51 + 1, I55) [0 <= I54 - 1 /\ 2 <= I53 - 1 /\ 2 <= I48 - 1 /\ 2 <= I47 - 1 /\ I54 + 2 <= I48 /\ I53 <= I47 /\ I51 <= I50 - 1 /\ -1 <= I51 - 1 /\ 0 <= I49 - 1] 4.44/4.48 f2(I56, I57, I58, I59, I60, I61) -> f5(I62, I63, I64, I65, I59 + 1, I66) [2 <= I63 - 1 /\ 2 <= I62 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ I63 - 3 <= I57 /\ I63 - 2 <= I56 /\ I62 - 3 <= I57 /\ I62 - 2 <= I56 /\ -1 <= I59 - 1 /\ I59 <= I65 - 1 /\ 0 <= I58 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1] 4.44/4.48 f3(I67, I68, I69, I70, I71, I72) -> f3(I73, I74, I75, I76, I77, I78) [2 <= I73 - 1 /\ 2 <= I67 - 1 /\ I73 - 2 <= I67] 4.44/4.48 f3(I79, I80, I81, I82, I83, I84) -> f3(I85, I86, I87, I88, I89, I90) [-1 <= I85 - 1 /\ 1 <= I79 - 1 /\ I85 + 2 <= I79] 4.44/4.48 f4(I91, I92, I93, I94, I95, I96) -> f2(I97, I98, I93 - 1, I95, I99, I100) [I96 + 2 <= I94 /\ 4 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I94 - 1 /\ 0 <= I91 - 1 /\ I97 + 2 <= I94 /\ I97 <= I91] 4.44/4.48 f2(I101, I102, I103, I104, I105, I106) -> f2(I107, I108, I103 - 1, I109, I110, I111) [0 <= I103 - 1 /\ 0 <= I112 - 1 /\ I107 <= I101 /\ I107 - 1 <= I102 /\ 0 <= I101 - 1 /\ -1 <= I102 - 1 /\ 0 <= I107 - 1 /\ 4 <= I108 - 1] 4.44/4.48 f2(I113, I114, I115, I116, I117, I118) -> f2(I119, I120, I115 - 1, I121, I122, I123) [0 <= I115 - 1 /\ 0 <= I124 - 1 /\ I119 <= I113 /\ I119 - 1 <= I114 /\ I120 - 2 <= I114 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1 /\ 0 <= I119 - 1 /\ 1 <= I120 - 1] 4.44/4.48 f2(I125, I126, I127, I128, I129, I130) -> f3(I131, I132, I133, I134, I135, I136) [I131 <= I126 /\ 0 <= I137 - 1 /\ 0 <= I125 - 1 /\ -1 <= I126 - 1 /\ -1 <= I131 - 1 /\ 0 = I127] 4.44/4.48 f1(I138, I139, I140, I141, I142, I143) -> f2(I144, I145, I146, 1, I147, I148) [-1 <= I145 - 1 /\ 0 <= I144 - 1 /\ 0 <= I138 - 1 /\ I145 + 1 <= I138 /\ I144 <= I138 /\ -1 <= I146 - 1 /\ 0 <= I139 - 1] 4.44/4.48 4.44/4.48 We use the basic value criterion with the projection function NU: 4.44/4.48 NU[f5#(z1,z2,z3,z4,z5,z6)] = z3 4.44/4.48 4.44/4.48 This gives the following inequalities: 4.44/4.48 -1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1 ==> I2 >! I2 - 1 4.44/4.48 4 <= I16 - 1 /\ 4 <= I15 - 1 /\ 2 <= I10 - 1 /\ 2 <= I9 - 1 /\ I16 - 2 <= I10 /\ I16 - 2 <= I9 /\ I15 - 2 <= I10 /\ I15 - 2 <= I9 /\ I13 <= I12 - 1 /\ -1 <= I13 - 1 /\ 0 <= I11 - 1 ==> I11 >! I11 - 1 4.44/4.48 2 <= I25 - 1 /\ 2 <= I24 - 1 /\ 1 <= I19 - 1 /\ 2 <= I18 - 1 /\ I22 <= I21 - 1 /\ -1 <= I22 - 1 /\ 0 <= I20 - 1 ==> I20 >! I20 - 1 4.44/4.48 -1 <= I31 - 1 /\ 0 <= I36 - 1 /\ 0 <= I29 - 1 /\ I31 <= I30 - 1 /\ 2 <= I27 - 1 /\ 1 <= I28 - 1 /\ 2 <= I33 - 1 /\ 2 <= I34 - 1 ==> I29 >! I29 - 1 4.44/4.48 -1 <= I41 - 1 /\ 0 <= I46 - 1 /\ 0 <= I39 - 1 /\ I41 <= I40 - 1 /\ I43 <= I37 /\ I44 + 2 <= I38 /\ 2 <= I37 - 1 /\ 2 <= I38 - 1 /\ 2 <= I43 - 1 /\ 0 <= I44 - 1 ==> I39 >! I39 - 1 4.44/4.48 0 <= I54 - 1 /\ 2 <= I53 - 1 /\ 2 <= I48 - 1 /\ 2 <= I47 - 1 /\ I54 + 2 <= I48 /\ I53 <= I47 /\ I51 <= I50 - 1 /\ -1 <= I51 - 1 /\ 0 <= I49 - 1 ==> I49 >! I49 - 1 4.44/4.48 4.44/4.48 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 4.44/4.48 4.44/4.48 DP problem for innermost termination. 4.44/4.48 P = 4.44/4.48 f3#(I67, I68, I69, I70, I71, I72) -> f3#(I73, I74, I75, I76, I77, I78) [2 <= I73 - 1 /\ 2 <= I67 - 1 /\ I73 - 2 <= I67] 4.44/4.48 f3#(I79, I80, I81, I82, I83, I84) -> f3#(I85, I86, I87, I88, I89, I90) [-1 <= I85 - 1 /\ 1 <= I79 - 1 /\ I85 + 2 <= I79] 4.44/4.48 R = 4.44/4.48 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.44/4.48 f5(I0, I1, I2, I3, I4, I5) -> f5(I6, I7, I2 - 1, I3, I4 + 1, I8) [-1 <= I4 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I4 <= I3 - 1 /\ I6 - 2 <= I0 /\ I6 - 2 <= I1 /\ I7 - 2 <= I0 /\ I7 - 2 <= I1 /\ 2 <= I0 - 1 /\ 2 <= I1 - 1 /\ 4 <= I6 - 1 /\ 4 <= I7 - 1] 4.44/4.48 f5(I9, I10, I11, I12, I13, I14) -> f5(I15, I16, I11 - 1, I12, I13 + 1, I17) [4 <= I16 - 1 /\ 4 <= I15 - 1 /\ 2 <= I10 - 1 /\ 2 <= I9 - 1 /\ I16 - 2 <= I10 /\ I16 - 2 <= I9 /\ I15 - 2 <= I10 /\ I15 - 2 <= I9 /\ I13 <= I12 - 1 /\ -1 <= I13 - 1 /\ 0 <= I11 - 1] 4.44/4.48 f5(I18, I19, I20, I21, I22, I23) -> f5(I24, I25, I20 - 1, I21, I22 + 1, I26) [2 <= I25 - 1 /\ 2 <= I24 - 1 /\ 1 <= I19 - 1 /\ 2 <= I18 - 1 /\ I22 <= I21 - 1 /\ -1 <= I22 - 1 /\ 0 <= I20 - 1] 4.44/4.48 f5(I27, I28, I29, I30, I31, I32) -> f5(I33, I34, I29 - 1, I30, I31 + 1, I35) [-1 <= I31 - 1 /\ 0 <= I36 - 1 /\ 0 <= I29 - 1 /\ I31 <= I30 - 1 /\ 2 <= I27 - 1 /\ 1 <= I28 - 1 /\ 2 <= I33 - 1 /\ 2 <= I34 - 1] 4.44/4.48 f5(I37, I38, I39, I40, I41, I42) -> f5(I43, I44, I39 - 1, I40, I41 + 1, I45) [-1 <= I41 - 1 /\ 0 <= I46 - 1 /\ 0 <= I39 - 1 /\ I41 <= I40 - 1 /\ I43 <= I37 /\ I44 + 2 <= I38 /\ 2 <= I37 - 1 /\ 2 <= I38 - 1 /\ 2 <= I43 - 1 /\ 0 <= I44 - 1] 4.44/4.48 f5(I47, I48, I49, I50, I51, I52) -> f5(I53, I54, I49 - 1, I50, I51 + 1, I55) [0 <= I54 - 1 /\ 2 <= I53 - 1 /\ 2 <= I48 - 1 /\ 2 <= I47 - 1 /\ I54 + 2 <= I48 /\ I53 <= I47 /\ I51 <= I50 - 1 /\ -1 <= I51 - 1 /\ 0 <= I49 - 1] 4.44/4.48 f2(I56, I57, I58, I59, I60, I61) -> f5(I62, I63, I64, I65, I59 + 1, I66) [2 <= I63 - 1 /\ 2 <= I62 - 1 /\ -1 <= I57 - 1 /\ 0 <= I56 - 1 /\ I63 - 3 <= I57 /\ I63 - 2 <= I56 /\ I62 - 3 <= I57 /\ I62 - 2 <= I56 /\ -1 <= I59 - 1 /\ I59 <= I65 - 1 /\ 0 <= I58 - 1 /\ 0 <= I65 - 1 /\ 0 <= I64 - 1] 4.44/4.48 f3(I67, I68, I69, I70, I71, I72) -> f3(I73, I74, I75, I76, I77, I78) [2 <= I73 - 1 /\ 2 <= I67 - 1 /\ I73 - 2 <= I67] 4.44/4.48 f3(I79, I80, I81, I82, I83, I84) -> f3(I85, I86, I87, I88, I89, I90) [-1 <= I85 - 1 /\ 1 <= I79 - 1 /\ I85 + 2 <= I79] 4.44/4.48 f4(I91, I92, I93, I94, I95, I96) -> f2(I97, I98, I93 - 1, I95, I99, I100) [I96 + 2 <= I94 /\ 4 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I94 - 1 /\ 0 <= I91 - 1 /\ I97 + 2 <= I94 /\ I97 <= I91] 4.44/4.48 f2(I101, I102, I103, I104, I105, I106) -> f2(I107, I108, I103 - 1, I109, I110, I111) [0 <= I103 - 1 /\ 0 <= I112 - 1 /\ I107 <= I101 /\ I107 - 1 <= I102 /\ 0 <= I101 - 1 /\ -1 <= I102 - 1 /\ 0 <= I107 - 1 /\ 4 <= I108 - 1] 4.44/4.48 f2(I113, I114, I115, I116, I117, I118) -> f2(I119, I120, I115 - 1, I121, I122, I123) [0 <= I115 - 1 /\ 0 <= I124 - 1 /\ I119 <= I113 /\ I119 - 1 <= I114 /\ I120 - 2 <= I114 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1 /\ 0 <= I119 - 1 /\ 1 <= I120 - 1] 4.44/4.48 f2(I125, I126, I127, I128, I129, I130) -> f3(I131, I132, I133, I134, I135, I136) [I131 <= I126 /\ 0 <= I137 - 1 /\ 0 <= I125 - 1 /\ -1 <= I126 - 1 /\ -1 <= I131 - 1 /\ 0 = I127] 4.44/4.48 f1(I138, I139, I140, I141, I142, I143) -> f2(I144, I145, I146, 1, I147, I148) [-1 <= I145 - 1 /\ 0 <= I144 - 1 /\ 0 <= I138 - 1 /\ I145 + 1 <= I138 /\ I144 <= I138 /\ -1 <= I146 - 1 /\ 0 <= I139 - 1] 4.44/4.48 4.44/7.46 EOF