10.78/10.67 YES 10.78/10.67 10.78/10.67 DP problem for innermost termination. 10.78/10.67 P = 10.78/10.67 init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 10.78/10.67 f7#(I36, I37, I38, I39, I40, I41) -> f5#(I42, I40, I43, I44, I45, I46) [-1 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 2 <= I36 - 1 /\ I42 + 1 <= I38 /\ 1 <= I40 - 1 /\ I42 + 3 <= I36] 10.78/10.67 f5#(I47, I48, I49, I50, I51, I52) -> f7#(I53, I54, I55, I56, I48, I57) [-1 <= I55 - 1 /\ 5 <= I54 - 1 /\ 1 <= I53 - 1 /\ 2 <= I47 - 1 /\ I55 + 2 <= I47 /\ 1 <= I48 - 1 /\ I53 <= I47] 10.78/10.67 f5#(I58, I59, I60, I61, I62, I63) -> f7#(I64, I65, I66, I67, I59, I68) [-1 <= I66 - 1 /\ 2 <= I65 - 1 /\ 1 <= I64 - 1 /\ 2 <= I58 - 1 /\ I66 + 2 <= I58 /\ 1 <= I59 - 1 /\ I64 <= I58] 10.78/10.67 f5#(I69, I70, I71, I72, I73, I74) -> f5#(I75, I70, I76, I77, I78, I79) [-1 <= I75 - 1 /\ 3 <= I69 - 1 /\ 1 <= I70 - 1 /\ I75 + 4 <= I69] 10.78/10.67 f5#(I80, I81, I82, I83, I84, I85) -> f5#(I86, I81, I87, I88, I89, I90) [0 <= I86 - 1 /\ 2 <= I80 - 1 /\ 1 <= I81 - 1 /\ I86 + 2 <= I80] 10.78/10.67 f6#(I91, I92, I93, I94, I95, I96) -> f6#(I91, I92, I93 + 1, I94, I95, I97) [I92 - 1 <= I92 - 1 /\ -1 <= I92 - 1 /\ I92 - 1 <= I91 - 1 /\ I92 <= I91 - 1 /\ 1 <= I96 - 1 /\ 0 <= I91 - 1 /\ I93 <= I94 - 1 /\ 0 <= I94 - 1] 10.78/10.67 f6#(I98, I99, I100, I101, I102, I103) -> f6#(I98, I99, I100 + 1, I101, I102, I103) [I99 - 1 <= I99 - 1 /\ -1 <= I99 - 1 /\ I99 - 1 <= I98 - 1 /\ I99 <= I98 - 1 /\ 1 <= I103 - 1 /\ 0 <= I98 - 1 /\ I100 <= I101 - 1 /\ 0 <= I101 - 1] 10.78/10.67 f6#(I104, I105, I106, I107, I108, I109) -> f2#(I105 - 1, I108, I109, I110, I111, I112) [I105 - 1 <= I105 - 1 /\ -1 <= I105 - 1 /\ I105 - 1 <= I104 - 1 /\ I105 <= I104 - 1 /\ 1 <= I109 - 1 /\ 0 <= I104 - 1 /\ I106 <= I107 - 1 /\ 0 <= I107 - 1] 10.78/10.67 f2#(I113, I114, I115, I116, I117, I118) -> f6#(I113, I113 - 1, 0, I119, I114, I115 + 1) [-1 <= I119 - 1 /\ I115 <= I114 - 1 /\ 0 <= I115 - 1 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1] 10.78/10.67 f3#(I120, I121, I122, I123, I124, I125) -> f5#(I126, I122, I127, I128, I129, I130) [0 <= y1 - 1 /\ 1 <= I122 - 1 /\ I126 <= I121 /\ 0 <= I120 - 1 /\ -1 <= I121 - 1 /\ -1 <= I126 - 1] 10.78/10.67 f4#(I131, I132, I133, I134, I135, I136) -> f3#(I137, I138, I132, I139, I140, I141) [-1 <= I138 - 1 /\ 0 <= I137 - 1 /\ 0 <= I131 - 1 /\ I138 + 1 <= I131 /\ I137 <= I131] 10.78/10.67 f1#(I142, I143, I144, I145, I146, I147) -> f3#(I148, I149, I150, I151, I152, I153) [-1 <= I154 - 1 /\ 0 <= I143 - 1 /\ I148 <= I142 /\ 0 <= I142 - 1 /\ 0 <= I148 - 1 /\ -1 <= I149 - 1] 10.78/10.67 f1#(I155, I156, I157, I158, I159, I160) -> f2#(I161, I156, 1, I162, I163, I164) [0 <= I155 - 1 /\ 0 <= I156 - 1 /\ -1 <= I161 - 1] 10.78/10.67 R = 10.78/10.67 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 10.78/10.67 f7(I0, I1, I2, I3, I4, I5) -> f8(I6, I7, I8, I9, I10, I11) [5 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I2 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ 1 <= I4 - 1 /\ I6 <= I1] 10.78/10.67 f7(I12, I13, I14, I15, I16, I17) -> f8(I18, I19, I20, I21, I22, I23) [5 <= I19 - 1 /\ 0 <= I18 - 1 /\ 3 <= I14 - 1 /\ 0 <= I13 - 1 /\ 5 <= I12 - 1 /\ I19 - 2 <= I14 /\ I19 <= I12 /\ 1 <= I16 - 1 /\ I18 <= I13] 10.78/10.67 f7(I24, I25, I26, I27, I28, I29) -> f8(I30, I31, I32, I33, I34, I35) [3 <= I31 - 1 /\ 0 <= I30 - 1 /\ 1 <= I26 - 1 /\ 0 <= I25 - 1 /\ 3 <= I24 - 1 /\ I31 - 2 <= I26 /\ I31 - 3 <= I25 /\ I31 <= I24 /\ 1 <= I28 - 1 /\ I30 <= I25] 10.78/10.67 f7(I36, I37, I38, I39, I40, I41) -> f5(I42, I40, I43, I44, I45, I46) [-1 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 2 <= I36 - 1 /\ I42 + 1 <= I38 /\ 1 <= I40 - 1 /\ I42 + 3 <= I36] 10.78/10.67 f5(I47, I48, I49, I50, I51, I52) -> f7(I53, I54, I55, I56, I48, I57) [-1 <= I55 - 1 /\ 5 <= I54 - 1 /\ 1 <= I53 - 1 /\ 2 <= I47 - 1 /\ I55 + 2 <= I47 /\ 1 <= I48 - 1 /\ I53 <= I47] 10.78/10.67 f5(I58, I59, I60, I61, I62, I63) -> f7(I64, I65, I66, I67, I59, I68) [-1 <= I66 - 1 /\ 2 <= I65 - 1 /\ 1 <= I64 - 1 /\ 2 <= I58 - 1 /\ I66 + 2 <= I58 /\ 1 <= I59 - 1 /\ I64 <= I58] 10.78/10.67 f5(I69, I70, I71, I72, I73, I74) -> f5(I75, I70, I76, I77, I78, I79) [-1 <= I75 - 1 /\ 3 <= I69 - 1 /\ 1 <= I70 - 1 /\ I75 + 4 <= I69] 10.78/10.67 f5(I80, I81, I82, I83, I84, I85) -> f5(I86, I81, I87, I88, I89, I90) [0 <= I86 - 1 /\ 2 <= I80 - 1 /\ 1 <= I81 - 1 /\ I86 + 2 <= I80] 10.78/10.67 f6(I91, I92, I93, I94, I95, I96) -> f6(I91, I92, I93 + 1, I94, I95, I97) [I92 - 1 <= I92 - 1 /\ -1 <= I92 - 1 /\ I92 - 1 <= I91 - 1 /\ I92 <= I91 - 1 /\ 1 <= I96 - 1 /\ 0 <= I91 - 1 /\ I93 <= I94 - 1 /\ 0 <= I94 - 1] 10.78/10.67 f6(I98, I99, I100, I101, I102, I103) -> f6(I98, I99, I100 + 1, I101, I102, I103) [I99 - 1 <= I99 - 1 /\ -1 <= I99 - 1 /\ I99 - 1 <= I98 - 1 /\ I99 <= I98 - 1 /\ 1 <= I103 - 1 /\ 0 <= I98 - 1 /\ I100 <= I101 - 1 /\ 0 <= I101 - 1] 10.78/10.67 f6(I104, I105, I106, I107, I108, I109) -> f2(I105 - 1, I108, I109, I110, I111, I112) [I105 - 1 <= I105 - 1 /\ -1 <= I105 - 1 /\ I105 - 1 <= I104 - 1 /\ I105 <= I104 - 1 /\ 1 <= I109 - 1 /\ 0 <= I104 - 1 /\ I106 <= I107 - 1 /\ 0 <= I107 - 1] 10.78/10.67 f2(I113, I114, I115, I116, I117, I118) -> f6(I113, I113 - 1, 0, I119, I114, I115 + 1) [-1 <= I119 - 1 /\ I115 <= I114 - 1 /\ 0 <= I115 - 1 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1] 10.78/10.67 f3(I120, I121, I122, I123, I124, I125) -> f5(I126, I122, I127, I128, I129, I130) [0 <= y1 - 1 /\ 1 <= I122 - 1 /\ I126 <= I121 /\ 0 <= I120 - 1 /\ -1 <= I121 - 1 /\ -1 <= I126 - 1] 10.78/10.67 f4(I131, I132, I133, I134, I135, I136) -> f3(I137, I138, I132, I139, I140, I141) [-1 <= I138 - 1 /\ 0 <= I137 - 1 /\ 0 <= I131 - 1 /\ I138 + 1 <= I131 /\ I137 <= I131] 10.78/10.67 f1(I142, I143, I144, I145, I146, I147) -> f3(I148, I149, I150, I151, I152, I153) [-1 <= I154 - 1 /\ 0 <= I143 - 1 /\ I148 <= I142 /\ 0 <= I142 - 1 /\ 0 <= I148 - 1 /\ -1 <= I149 - 1] 10.78/10.67 f1(I155, I156, I157, I158, I159, I160) -> f2(I161, I156, 1, I162, I163, I164) [0 <= I155 - 1 /\ 0 <= I156 - 1 /\ -1 <= I161 - 1] 10.78/10.67 10.78/10.67 The dependency graph for this problem is: 10.78/10.67 0 -> 12, 13 10.78/10.67 1 -> 2, 3, 4, 5 10.78/10.67 2 -> 1 10.78/10.67 3 -> 1 10.78/10.67 4 -> 2, 3, 4, 5 10.78/10.67 5 -> 2, 3, 4, 5 10.78/10.67 6 -> 6, 7, 8 10.78/10.67 7 -> 6, 7, 8 10.78/10.67 8 -> 9 10.78/10.67 9 -> 6, 7, 8 10.78/10.67 10 -> 2, 3, 4, 5 10.78/10.67 11 -> 10 10.78/10.67 12 -> 10 10.78/10.67 13 -> 9 10.78/10.67 Where: 10.78/10.67 0) init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 10.78/10.67 1) f7#(I36, I37, I38, I39, I40, I41) -> f5#(I42, I40, I43, I44, I45, I46) [-1 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 2 <= I36 - 1 /\ I42 + 1 <= I38 /\ 1 <= I40 - 1 /\ I42 + 3 <= I36] 10.78/10.67 2) f5#(I47, I48, I49, I50, I51, I52) -> f7#(I53, I54, I55, I56, I48, I57) [-1 <= I55 - 1 /\ 5 <= I54 - 1 /\ 1 <= I53 - 1 /\ 2 <= I47 - 1 /\ I55 + 2 <= I47 /\ 1 <= I48 - 1 /\ I53 <= I47] 10.78/10.67 3) f5#(I58, I59, I60, I61, I62, I63) -> f7#(I64, I65, I66, I67, I59, I68) [-1 <= I66 - 1 /\ 2 <= I65 - 1 /\ 1 <= I64 - 1 /\ 2 <= I58 - 1 /\ I66 + 2 <= I58 /\ 1 <= I59 - 1 /\ I64 <= I58] 10.78/10.67 4) f5#(I69, I70, I71, I72, I73, I74) -> f5#(I75, I70, I76, I77, I78, I79) [-1 <= I75 - 1 /\ 3 <= I69 - 1 /\ 1 <= I70 - 1 /\ I75 + 4 <= I69] 10.78/10.67 5) f5#(I80, I81, I82, I83, I84, I85) -> f5#(I86, I81, I87, I88, I89, I90) [0 <= I86 - 1 /\ 2 <= I80 - 1 /\ 1 <= I81 - 1 /\ I86 + 2 <= I80] 10.78/10.67 6) f6#(I91, I92, I93, I94, I95, I96) -> f6#(I91, I92, I93 + 1, I94, I95, I97) [I92 - 1 <= I92 - 1 /\ -1 <= I92 - 1 /\ I92 - 1 <= I91 - 1 /\ I92 <= I91 - 1 /\ 1 <= I96 - 1 /\ 0 <= I91 - 1 /\ I93 <= I94 - 1 /\ 0 <= I94 - 1] 10.78/10.67 7) f6#(I98, I99, I100, I101, I102, I103) -> f6#(I98, I99, I100 + 1, I101, I102, I103) [I99 - 1 <= I99 - 1 /\ -1 <= I99 - 1 /\ I99 - 1 <= I98 - 1 /\ I99 <= I98 - 1 /\ 1 <= I103 - 1 /\ 0 <= I98 - 1 /\ I100 <= I101 - 1 /\ 0 <= I101 - 1] 10.78/10.67 8) f6#(I104, I105, I106, I107, I108, I109) -> f2#(I105 - 1, I108, I109, I110, I111, I112) [I105 - 1 <= I105 - 1 /\ -1 <= I105 - 1 /\ I105 - 1 <= I104 - 1 /\ I105 <= I104 - 1 /\ 1 <= I109 - 1 /\ 0 <= I104 - 1 /\ I106 <= I107 - 1 /\ 0 <= I107 - 1] 10.78/10.67 9) f2#(I113, I114, I115, I116, I117, I118) -> f6#(I113, I113 - 1, 0, I119, I114, I115 + 1) [-1 <= I119 - 1 /\ I115 <= I114 - 1 /\ 0 <= I115 - 1 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1] 10.78/10.67 10) f3#(I120, I121, I122, I123, I124, I125) -> f5#(I126, I122, I127, I128, I129, I130) [0 <= y1 - 1 /\ 1 <= I122 - 1 /\ I126 <= I121 /\ 0 <= I120 - 1 /\ -1 <= I121 - 1 /\ -1 <= I126 - 1] 10.78/10.67 11) f4#(I131, I132, I133, I134, I135, I136) -> f3#(I137, I138, I132, I139, I140, I141) [-1 <= I138 - 1 /\ 0 <= I137 - 1 /\ 0 <= I131 - 1 /\ I138 + 1 <= I131 /\ I137 <= I131] 10.78/10.67 12) f1#(I142, I143, I144, I145, I146, I147) -> f3#(I148, I149, I150, I151, I152, I153) [-1 <= I154 - 1 /\ 0 <= I143 - 1 /\ I148 <= I142 /\ 0 <= I142 - 1 /\ 0 <= I148 - 1 /\ -1 <= I149 - 1] 10.78/10.67 13) f1#(I155, I156, I157, I158, I159, I160) -> f2#(I161, I156, 1, I162, I163, I164) [0 <= I155 - 1 /\ 0 <= I156 - 1 /\ -1 <= I161 - 1] 10.78/10.67 10.78/10.67 We have the following SCCs. 10.78/10.67 { 1, 2, 3, 4, 5 } 10.78/10.67 { 6, 7, 8, 9 } 10.78/10.67 10.78/10.67 DP problem for innermost termination. 10.78/10.67 P = 10.78/10.67 f6#(I91, I92, I93, I94, I95, I96) -> f6#(I91, I92, I93 + 1, I94, I95, I97) [I92 - 1 <= I92 - 1 /\ -1 <= I92 - 1 /\ I92 - 1 <= I91 - 1 /\ I92 <= I91 - 1 /\ 1 <= I96 - 1 /\ 0 <= I91 - 1 /\ I93 <= I94 - 1 /\ 0 <= I94 - 1] 10.78/10.67 f6#(I98, I99, I100, I101, I102, I103) -> f6#(I98, I99, I100 + 1, I101, I102, I103) [I99 - 1 <= I99 - 1 /\ -1 <= I99 - 1 /\ I99 - 1 <= I98 - 1 /\ I99 <= I98 - 1 /\ 1 <= I103 - 1 /\ 0 <= I98 - 1 /\ I100 <= I101 - 1 /\ 0 <= I101 - 1] 10.78/10.67 f6#(I104, I105, I106, I107, I108, I109) -> f2#(I105 - 1, I108, I109, I110, I111, I112) [I105 - 1 <= I105 - 1 /\ -1 <= I105 - 1 /\ I105 - 1 <= I104 - 1 /\ I105 <= I104 - 1 /\ 1 <= I109 - 1 /\ 0 <= I104 - 1 /\ I106 <= I107 - 1 /\ 0 <= I107 - 1] 10.78/10.67 f2#(I113, I114, I115, I116, I117, I118) -> f6#(I113, I113 - 1, 0, I119, I114, I115 + 1) [-1 <= I119 - 1 /\ I115 <= I114 - 1 /\ 0 <= I115 - 1 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1] 10.78/10.67 R = 10.78/10.67 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 10.78/10.67 f7(I0, I1, I2, I3, I4, I5) -> f8(I6, I7, I8, I9, I10, I11) [5 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I2 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ 1 <= I4 - 1 /\ I6 <= I1] 10.78/10.67 f7(I12, I13, I14, I15, I16, I17) -> f8(I18, I19, I20, I21, I22, I23) [5 <= I19 - 1 /\ 0 <= I18 - 1 /\ 3 <= I14 - 1 /\ 0 <= I13 - 1 /\ 5 <= I12 - 1 /\ I19 - 2 <= I14 /\ I19 <= I12 /\ 1 <= I16 - 1 /\ I18 <= I13] 10.78/10.67 f7(I24, I25, I26, I27, I28, I29) -> f8(I30, I31, I32, I33, I34, I35) [3 <= I31 - 1 /\ 0 <= I30 - 1 /\ 1 <= I26 - 1 /\ 0 <= I25 - 1 /\ 3 <= I24 - 1 /\ I31 - 2 <= I26 /\ I31 - 3 <= I25 /\ I31 <= I24 /\ 1 <= I28 - 1 /\ I30 <= I25] 10.78/10.67 f7(I36, I37, I38, I39, I40, I41) -> f5(I42, I40, I43, I44, I45, I46) [-1 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 2 <= I36 - 1 /\ I42 + 1 <= I38 /\ 1 <= I40 - 1 /\ I42 + 3 <= I36] 10.78/10.67 f5(I47, I48, I49, I50, I51, I52) -> f7(I53, I54, I55, I56, I48, I57) [-1 <= I55 - 1 /\ 5 <= I54 - 1 /\ 1 <= I53 - 1 /\ 2 <= I47 - 1 /\ I55 + 2 <= I47 /\ 1 <= I48 - 1 /\ I53 <= I47] 10.78/10.67 f5(I58, I59, I60, I61, I62, I63) -> f7(I64, I65, I66, I67, I59, I68) [-1 <= I66 - 1 /\ 2 <= I65 - 1 /\ 1 <= I64 - 1 /\ 2 <= I58 - 1 /\ I66 + 2 <= I58 /\ 1 <= I59 - 1 /\ I64 <= I58] 10.78/10.67 f5(I69, I70, I71, I72, I73, I74) -> f5(I75, I70, I76, I77, I78, I79) [-1 <= I75 - 1 /\ 3 <= I69 - 1 /\ 1 <= I70 - 1 /\ I75 + 4 <= I69] 10.78/10.67 f5(I80, I81, I82, I83, I84, I85) -> f5(I86, I81, I87, I88, I89, I90) [0 <= I86 - 1 /\ 2 <= I80 - 1 /\ 1 <= I81 - 1 /\ I86 + 2 <= I80] 10.78/10.67 f6(I91, I92, I93, I94, I95, I96) -> f6(I91, I92, I93 + 1, I94, I95, I97) [I92 - 1 <= I92 - 1 /\ -1 <= I92 - 1 /\ I92 - 1 <= I91 - 1 /\ I92 <= I91 - 1 /\ 1 <= I96 - 1 /\ 0 <= I91 - 1 /\ I93 <= I94 - 1 /\ 0 <= I94 - 1] 10.78/10.67 f6(I98, I99, I100, I101, I102, I103) -> f6(I98, I99, I100 + 1, I101, I102, I103) [I99 - 1 <= I99 - 1 /\ -1 <= I99 - 1 /\ I99 - 1 <= I98 - 1 /\ I99 <= I98 - 1 /\ 1 <= I103 - 1 /\ 0 <= I98 - 1 /\ I100 <= I101 - 1 /\ 0 <= I101 - 1] 10.78/10.67 f6(I104, I105, I106, I107, I108, I109) -> f2(I105 - 1, I108, I109, I110, I111, I112) [I105 - 1 <= I105 - 1 /\ -1 <= I105 - 1 /\ I105 - 1 <= I104 - 1 /\ I105 <= I104 - 1 /\ 1 <= I109 - 1 /\ 0 <= I104 - 1 /\ I106 <= I107 - 1 /\ 0 <= I107 - 1] 10.78/10.67 f2(I113, I114, I115, I116, I117, I118) -> f6(I113, I113 - 1, 0, I119, I114, I115 + 1) [-1 <= I119 - 1 /\ I115 <= I114 - 1 /\ 0 <= I115 - 1 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1] 10.78/10.67 f3(I120, I121, I122, I123, I124, I125) -> f5(I126, I122, I127, I128, I129, I130) [0 <= y1 - 1 /\ 1 <= I122 - 1 /\ I126 <= I121 /\ 0 <= I120 - 1 /\ -1 <= I121 - 1 /\ -1 <= I126 - 1] 10.78/10.67 f4(I131, I132, I133, I134, I135, I136) -> f3(I137, I138, I132, I139, I140, I141) [-1 <= I138 - 1 /\ 0 <= I137 - 1 /\ 0 <= I131 - 1 /\ I138 + 1 <= I131 /\ I137 <= I131] 10.78/10.67 f1(I142, I143, I144, I145, I146, I147) -> f3(I148, I149, I150, I151, I152, I153) [-1 <= I154 - 1 /\ 0 <= I143 - 1 /\ I148 <= I142 /\ 0 <= I142 - 1 /\ 0 <= I148 - 1 /\ -1 <= I149 - 1] 10.78/10.67 f1(I155, I156, I157, I158, I159, I160) -> f2(I161, I156, 1, I162, I163, I164) [0 <= I155 - 1 /\ 0 <= I156 - 1 /\ -1 <= I161 - 1] 10.78/10.67 10.78/10.67 We use the basic value criterion with the projection function NU: 10.78/10.67 NU[f2#(z1,z2,z3,z4,z5,z6)] = z1 10.78/10.67 NU[f6#(z1,z2,z3,z4,z5,z6)] = z2 10.78/10.67 10.78/10.67 This gives the following inequalities: 10.78/10.67 I92 - 1 <= I92 - 1 /\ -1 <= I92 - 1 /\ I92 - 1 <= I91 - 1 /\ I92 <= I91 - 1 /\ 1 <= I96 - 1 /\ 0 <= I91 - 1 /\ I93 <= I94 - 1 /\ 0 <= I94 - 1 ==> I92 (>! \union =) I92 10.78/10.67 I99 - 1 <= I99 - 1 /\ -1 <= I99 - 1 /\ I99 - 1 <= I98 - 1 /\ I99 <= I98 - 1 /\ 1 <= I103 - 1 /\ 0 <= I98 - 1 /\ I100 <= I101 - 1 /\ 0 <= I101 - 1 ==> I99 (>! \union =) I99 10.78/10.67 I105 - 1 <= I105 - 1 /\ -1 <= I105 - 1 /\ I105 - 1 <= I104 - 1 /\ I105 <= I104 - 1 /\ 1 <= I109 - 1 /\ 0 <= I104 - 1 /\ I106 <= I107 - 1 /\ 0 <= I107 - 1 ==> I105 >! I105 - 1 10.78/10.67 -1 <= I119 - 1 /\ I115 <= I114 - 1 /\ 0 <= I115 - 1 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1 ==> I113 >! I113 - 1 10.78/10.67 10.78/10.67 We remove all the strictly oriented dependency pairs. 10.78/10.67 10.78/10.67 DP problem for innermost termination. 10.78/10.67 P = 10.78/10.67 f6#(I91, I92, I93, I94, I95, I96) -> f6#(I91, I92, I93 + 1, I94, I95, I97) [I92 - 1 <= I92 - 1 /\ -1 <= I92 - 1 /\ I92 - 1 <= I91 - 1 /\ I92 <= I91 - 1 /\ 1 <= I96 - 1 /\ 0 <= I91 - 1 /\ I93 <= I94 - 1 /\ 0 <= I94 - 1] 10.78/10.67 f6#(I98, I99, I100, I101, I102, I103) -> f6#(I98, I99, I100 + 1, I101, I102, I103) [I99 - 1 <= I99 - 1 /\ -1 <= I99 - 1 /\ I99 - 1 <= I98 - 1 /\ I99 <= I98 - 1 /\ 1 <= I103 - 1 /\ 0 <= I98 - 1 /\ I100 <= I101 - 1 /\ 0 <= I101 - 1] 10.78/10.67 R = 10.78/10.67 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 10.78/10.67 f7(I0, I1, I2, I3, I4, I5) -> f8(I6, I7, I8, I9, I10, I11) [5 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I2 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ 1 <= I4 - 1 /\ I6 <= I1] 10.78/10.67 f7(I12, I13, I14, I15, I16, I17) -> f8(I18, I19, I20, I21, I22, I23) [5 <= I19 - 1 /\ 0 <= I18 - 1 /\ 3 <= I14 - 1 /\ 0 <= I13 - 1 /\ 5 <= I12 - 1 /\ I19 - 2 <= I14 /\ I19 <= I12 /\ 1 <= I16 - 1 /\ I18 <= I13] 10.78/10.67 f7(I24, I25, I26, I27, I28, I29) -> f8(I30, I31, I32, I33, I34, I35) [3 <= I31 - 1 /\ 0 <= I30 - 1 /\ 1 <= I26 - 1 /\ 0 <= I25 - 1 /\ 3 <= I24 - 1 /\ I31 - 2 <= I26 /\ I31 - 3 <= I25 /\ I31 <= I24 /\ 1 <= I28 - 1 /\ I30 <= I25] 10.78/10.67 f7(I36, I37, I38, I39, I40, I41) -> f5(I42, I40, I43, I44, I45, I46) [-1 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 2 <= I36 - 1 /\ I42 + 1 <= I38 /\ 1 <= I40 - 1 /\ I42 + 3 <= I36] 10.78/10.67 f5(I47, I48, I49, I50, I51, I52) -> f7(I53, I54, I55, I56, I48, I57) [-1 <= I55 - 1 /\ 5 <= I54 - 1 /\ 1 <= I53 - 1 /\ 2 <= I47 - 1 /\ I55 + 2 <= I47 /\ 1 <= I48 - 1 /\ I53 <= I47] 10.78/10.67 f5(I58, I59, I60, I61, I62, I63) -> f7(I64, I65, I66, I67, I59, I68) [-1 <= I66 - 1 /\ 2 <= I65 - 1 /\ 1 <= I64 - 1 /\ 2 <= I58 - 1 /\ I66 + 2 <= I58 /\ 1 <= I59 - 1 /\ I64 <= I58] 10.78/10.67 f5(I69, I70, I71, I72, I73, I74) -> f5(I75, I70, I76, I77, I78, I79) [-1 <= I75 - 1 /\ 3 <= I69 - 1 /\ 1 <= I70 - 1 /\ I75 + 4 <= I69] 10.78/10.67 f5(I80, I81, I82, I83, I84, I85) -> f5(I86, I81, I87, I88, I89, I90) [0 <= I86 - 1 /\ 2 <= I80 - 1 /\ 1 <= I81 - 1 /\ I86 + 2 <= I80] 10.78/10.67 f6(I91, I92, I93, I94, I95, I96) -> f6(I91, I92, I93 + 1, I94, I95, I97) [I92 - 1 <= I92 - 1 /\ -1 <= I92 - 1 /\ I92 - 1 <= I91 - 1 /\ I92 <= I91 - 1 /\ 1 <= I96 - 1 /\ 0 <= I91 - 1 /\ I93 <= I94 - 1 /\ 0 <= I94 - 1] 10.78/10.67 f6(I98, I99, I100, I101, I102, I103) -> f6(I98, I99, I100 + 1, I101, I102, I103) [I99 - 1 <= I99 - 1 /\ -1 <= I99 - 1 /\ I99 - 1 <= I98 - 1 /\ I99 <= I98 - 1 /\ 1 <= I103 - 1 /\ 0 <= I98 - 1 /\ I100 <= I101 - 1 /\ 0 <= I101 - 1] 10.78/10.67 f6(I104, I105, I106, I107, I108, I109) -> f2(I105 - 1, I108, I109, I110, I111, I112) [I105 - 1 <= I105 - 1 /\ -1 <= I105 - 1 /\ I105 - 1 <= I104 - 1 /\ I105 <= I104 - 1 /\ 1 <= I109 - 1 /\ 0 <= I104 - 1 /\ I106 <= I107 - 1 /\ 0 <= I107 - 1] 10.78/10.67 f2(I113, I114, I115, I116, I117, I118) -> f6(I113, I113 - 1, 0, I119, I114, I115 + 1) [-1 <= I119 - 1 /\ I115 <= I114 - 1 /\ 0 <= I115 - 1 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1] 10.78/10.67 f3(I120, I121, I122, I123, I124, I125) -> f5(I126, I122, I127, I128, I129, I130) [0 <= y1 - 1 /\ 1 <= I122 - 1 /\ I126 <= I121 /\ 0 <= I120 - 1 /\ -1 <= I121 - 1 /\ -1 <= I126 - 1] 10.78/10.67 f4(I131, I132, I133, I134, I135, I136) -> f3(I137, I138, I132, I139, I140, I141) [-1 <= I138 - 1 /\ 0 <= I137 - 1 /\ 0 <= I131 - 1 /\ I138 + 1 <= I131 /\ I137 <= I131] 10.78/10.67 f1(I142, I143, I144, I145, I146, I147) -> f3(I148, I149, I150, I151, I152, I153) [-1 <= I154 - 1 /\ 0 <= I143 - 1 /\ I148 <= I142 /\ 0 <= I142 - 1 /\ 0 <= I148 - 1 /\ -1 <= I149 - 1] 10.78/10.67 f1(I155, I156, I157, I158, I159, I160) -> f2(I161, I156, 1, I162, I163, I164) [0 <= I155 - 1 /\ 0 <= I156 - 1 /\ -1 <= I161 - 1] 10.78/10.67 10.78/10.67 We use the reverse value criterion with the projection function NU: 10.78/10.67 NU[f6#(z1,z2,z3,z4,z5,z6)] = z4 - 1 + -1 * z3 10.78/10.67 10.78/10.67 This gives the following inequalities: 10.78/10.67 I92 - 1 <= I92 - 1 /\ -1 <= I92 - 1 /\ I92 - 1 <= I91 - 1 /\ I92 <= I91 - 1 /\ 1 <= I96 - 1 /\ 0 <= I91 - 1 /\ I93 <= I94 - 1 /\ 0 <= I94 - 1 ==> I94 - 1 + -1 * I93 > I94 - 1 + -1 * (I93 + 1) with I94 - 1 + -1 * I93 >= 0 10.78/10.67 I99 - 1 <= I99 - 1 /\ -1 <= I99 - 1 /\ I99 - 1 <= I98 - 1 /\ I99 <= I98 - 1 /\ 1 <= I103 - 1 /\ 0 <= I98 - 1 /\ I100 <= I101 - 1 /\ 0 <= I101 - 1 ==> I101 - 1 + -1 * I100 > I101 - 1 + -1 * (I100 + 1) with I101 - 1 + -1 * I100 >= 0 10.78/10.67 10.78/10.67 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 10.78/10.67 10.78/10.67 DP problem for innermost termination. 10.78/10.67 P = 10.78/10.67 f7#(I36, I37, I38, I39, I40, I41) -> f5#(I42, I40, I43, I44, I45, I46) [-1 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 2 <= I36 - 1 /\ I42 + 1 <= I38 /\ 1 <= I40 - 1 /\ I42 + 3 <= I36] 10.78/10.67 f5#(I47, I48, I49, I50, I51, I52) -> f7#(I53, I54, I55, I56, I48, I57) [-1 <= I55 - 1 /\ 5 <= I54 - 1 /\ 1 <= I53 - 1 /\ 2 <= I47 - 1 /\ I55 + 2 <= I47 /\ 1 <= I48 - 1 /\ I53 <= I47] 10.78/10.67 f5#(I58, I59, I60, I61, I62, I63) -> f7#(I64, I65, I66, I67, I59, I68) [-1 <= I66 - 1 /\ 2 <= I65 - 1 /\ 1 <= I64 - 1 /\ 2 <= I58 - 1 /\ I66 + 2 <= I58 /\ 1 <= I59 - 1 /\ I64 <= I58] 10.78/10.67 f5#(I69, I70, I71, I72, I73, I74) -> f5#(I75, I70, I76, I77, I78, I79) [-1 <= I75 - 1 /\ 3 <= I69 - 1 /\ 1 <= I70 - 1 /\ I75 + 4 <= I69] 10.78/10.67 f5#(I80, I81, I82, I83, I84, I85) -> f5#(I86, I81, I87, I88, I89, I90) [0 <= I86 - 1 /\ 2 <= I80 - 1 /\ 1 <= I81 - 1 /\ I86 + 2 <= I80] 10.78/10.67 R = 10.78/10.67 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 10.78/10.67 f7(I0, I1, I2, I3, I4, I5) -> f8(I6, I7, I8, I9, I10, I11) [5 <= I7 - 1 /\ 0 <= I6 - 1 /\ 0 <= I2 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ 1 <= I4 - 1 /\ I6 <= I1] 10.78/10.67 f7(I12, I13, I14, I15, I16, I17) -> f8(I18, I19, I20, I21, I22, I23) [5 <= I19 - 1 /\ 0 <= I18 - 1 /\ 3 <= I14 - 1 /\ 0 <= I13 - 1 /\ 5 <= I12 - 1 /\ I19 - 2 <= I14 /\ I19 <= I12 /\ 1 <= I16 - 1 /\ I18 <= I13] 10.78/10.67 f7(I24, I25, I26, I27, I28, I29) -> f8(I30, I31, I32, I33, I34, I35) [3 <= I31 - 1 /\ 0 <= I30 - 1 /\ 1 <= I26 - 1 /\ 0 <= I25 - 1 /\ 3 <= I24 - 1 /\ I31 - 2 <= I26 /\ I31 - 3 <= I25 /\ I31 <= I24 /\ 1 <= I28 - 1 /\ I30 <= I25] 10.78/10.67 f7(I36, I37, I38, I39, I40, I41) -> f5(I42, I40, I43, I44, I45, I46) [-1 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 2 <= I36 - 1 /\ I42 + 1 <= I38 /\ 1 <= I40 - 1 /\ I42 + 3 <= I36] 10.78/10.67 f5(I47, I48, I49, I50, I51, I52) -> f7(I53, I54, I55, I56, I48, I57) [-1 <= I55 - 1 /\ 5 <= I54 - 1 /\ 1 <= I53 - 1 /\ 2 <= I47 - 1 /\ I55 + 2 <= I47 /\ 1 <= I48 - 1 /\ I53 <= I47] 10.78/10.67 f5(I58, I59, I60, I61, I62, I63) -> f7(I64, I65, I66, I67, I59, I68) [-1 <= I66 - 1 /\ 2 <= I65 - 1 /\ 1 <= I64 - 1 /\ 2 <= I58 - 1 /\ I66 + 2 <= I58 /\ 1 <= I59 - 1 /\ I64 <= I58] 10.78/10.67 f5(I69, I70, I71, I72, I73, I74) -> f5(I75, I70, I76, I77, I78, I79) [-1 <= I75 - 1 /\ 3 <= I69 - 1 /\ 1 <= I70 - 1 /\ I75 + 4 <= I69] 10.78/10.67 f5(I80, I81, I82, I83, I84, I85) -> f5(I86, I81, I87, I88, I89, I90) [0 <= I86 - 1 /\ 2 <= I80 - 1 /\ 1 <= I81 - 1 /\ I86 + 2 <= I80] 10.78/10.67 f6(I91, I92, I93, I94, I95, I96) -> f6(I91, I92, I93 + 1, I94, I95, I97) [I92 - 1 <= I92 - 1 /\ -1 <= I92 - 1 /\ I92 - 1 <= I91 - 1 /\ I92 <= I91 - 1 /\ 1 <= I96 - 1 /\ 0 <= I91 - 1 /\ I93 <= I94 - 1 /\ 0 <= I94 - 1] 10.78/10.67 f6(I98, I99, I100, I101, I102, I103) -> f6(I98, I99, I100 + 1, I101, I102, I103) [I99 - 1 <= I99 - 1 /\ -1 <= I99 - 1 /\ I99 - 1 <= I98 - 1 /\ I99 <= I98 - 1 /\ 1 <= I103 - 1 /\ 0 <= I98 - 1 /\ I100 <= I101 - 1 /\ 0 <= I101 - 1] 10.78/10.67 f6(I104, I105, I106, I107, I108, I109) -> f2(I105 - 1, I108, I109, I110, I111, I112) [I105 - 1 <= I105 - 1 /\ -1 <= I105 - 1 /\ I105 - 1 <= I104 - 1 /\ I105 <= I104 - 1 /\ 1 <= I109 - 1 /\ 0 <= I104 - 1 /\ I106 <= I107 - 1 /\ 0 <= I107 - 1] 10.78/10.67 f2(I113, I114, I115, I116, I117, I118) -> f6(I113, I113 - 1, 0, I119, I114, I115 + 1) [-1 <= I119 - 1 /\ I115 <= I114 - 1 /\ 0 <= I115 - 1 /\ 0 <= I113 - 1 /\ -1 <= I114 - 1] 10.78/10.67 f3(I120, I121, I122, I123, I124, I125) -> f5(I126, I122, I127, I128, I129, I130) [0 <= y1 - 1 /\ 1 <= I122 - 1 /\ I126 <= I121 /\ 0 <= I120 - 1 /\ -1 <= I121 - 1 /\ -1 <= I126 - 1] 10.78/10.67 f4(I131, I132, I133, I134, I135, I136) -> f3(I137, I138, I132, I139, I140, I141) [-1 <= I138 - 1 /\ 0 <= I137 - 1 /\ 0 <= I131 - 1 /\ I138 + 1 <= I131 /\ I137 <= I131] 10.78/10.67 f1(I142, I143, I144, I145, I146, I147) -> f3(I148, I149, I150, I151, I152, I153) [-1 <= I154 - 1 /\ 0 <= I143 - 1 /\ I148 <= I142 /\ 0 <= I142 - 1 /\ 0 <= I148 - 1 /\ -1 <= I149 - 1] 10.78/10.67 f1(I155, I156, I157, I158, I159, I160) -> f2(I161, I156, 1, I162, I163, I164) [0 <= I155 - 1 /\ 0 <= I156 - 1 /\ -1 <= I161 - 1] 10.78/10.67 10.78/10.67 We use the basic value criterion with the projection function NU: 10.78/10.67 NU[f5#(z1,z2,z3,z4,z5,z6)] = z1 10.78/10.67 NU[f7#(z1,z2,z3,z4,z5,z6)] = z3 10.78/10.67 10.78/10.67 This gives the following inequalities: 10.78/10.67 -1 <= I42 - 1 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 2 <= I36 - 1 /\ I42 + 1 <= I38 /\ 1 <= I40 - 1 /\ I42 + 3 <= I36 ==> I38 >! I42 10.78/10.67 -1 <= I55 - 1 /\ 5 <= I54 - 1 /\ 1 <= I53 - 1 /\ 2 <= I47 - 1 /\ I55 + 2 <= I47 /\ 1 <= I48 - 1 /\ I53 <= I47 ==> I47 >! I55 10.78/10.67 -1 <= I66 - 1 /\ 2 <= I65 - 1 /\ 1 <= I64 - 1 /\ 2 <= I58 - 1 /\ I66 + 2 <= I58 /\ 1 <= I59 - 1 /\ I64 <= I58 ==> I58 >! I66 10.78/10.67 -1 <= I75 - 1 /\ 3 <= I69 - 1 /\ 1 <= I70 - 1 /\ I75 + 4 <= I69 ==> I69 >! I75 10.78/10.67 0 <= I86 - 1 /\ 2 <= I80 - 1 /\ 1 <= I81 - 1 /\ I86 + 2 <= I80 ==> I80 >! I86 10.78/10.67 10.78/10.67 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 10.78/13.65 EOF