281.38/279.03 MAYBE 281.38/279.03 281.38/279.03 DP problem for innermost termination. 281.38/279.03 P = 281.38/279.03 init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 281.38/279.03 f2#(I0, I1, I2, I3, I4) -> f2#(0, 0, -1, I5, I6) [0 = I2 /\ 0 = I0] 281.38/279.03 f2#(I7, I8, I9, I10, I11) -> f2#(2, 1, 1, I12, I13) [0 = I9 /\ 3 = I7] 281.38/279.03 f5#(I14, I15, I16, I17, I18) -> f2#(I14 - 1, 0, I15, I19, I20) [I15 = I16 /\ I15 <= I14 - 1 /\ I15 <= I14 - 1] 281.38/279.03 f2#(I21, I22, I23, I24, I25) -> f2#(I21, 1, 1, I26, I27) [0 = I23 /\ 3 <= I21 - 1] 281.38/279.03 f2#(I28, I29, I30, I31, I32) -> f2#(I28, 1, 1, I33, I34) [0 = I30 /\ I28 <= 2 /\ 0 <= I28 - 1] 281.38/279.03 f5#(I35, I36, I37, I38, I39) -> f2#(I35, 0, I36, I40, I41) [I37 <= I36 - 1] 281.38/279.03 f5#(I42, I43, I44, I45, I46) -> f2#(I42, 0, I43, I47, I48) [I43 <= I44 - 1] 281.38/279.03 f4#(I49, I50, I51, I52, I53) -> f2#(I50 - 1, 0, I51, I54, I55) [I51 = I52 /\ I51 <= I50 - 1 /\ 0 <= I49 - 1] 281.38/279.03 f3#(I56, I57, I58, I59, I60) -> f2#(I57 - 1, I58, I59, I61, I62) [I59 = I60 /\ I59 <= I57 - 1 /\ 0 <= I56 - 1] 281.38/279.03 f4#(I63, I64, I65, I66, I67) -> f2#(I64, 0, I65, I68, I69) [I66 <= I65 - 1 /\ I64 <= I63 - 1 /\ 0 <= I63 - 1] 281.38/279.03 f4#(I70, I71, I72, I73, I74) -> f2#(I71, 0, I72, I75, I76) [I73 <= I72 - 1 /\ I70 <= I71 - 1 /\ 0 <= I70 - 1] 281.38/279.03 f4#(I77, I78, I79, I80, I81) -> f2#(I78, 0, I79, I82, I83) [I79 <= I80 - 1 /\ I78 <= I77 - 1 /\ 0 <= I77 - 1] 281.38/279.03 f4#(I84, I85, I86, I87, I88) -> f2#(I85, 0, I86, I89, I90) [I86 <= I87 - 1 /\ I84 <= I85 - 1 /\ 0 <= I84 - 1] 281.38/279.03 f3#(I91, I92, I93, I94, I95) -> f2#(I92, I93, I94, I96, I97) [I95 <= I94 - 1 /\ I92 <= I91 - 1 /\ 1 <= I94 - 1 /\ 0 <= I91 - 1] 281.38/279.03 f3#(I98, I99, I100, I101, I102) -> f2#(I99, I100, I101, I103, I104) [I102 <= I101 - 1 /\ I98 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= I98 - 1] 281.38/279.03 f3#(I105, I106, I107, I108, I109) -> f2#(I106, I107, I108, I110, I111) [I108 <= I109 - 1 /\ I106 <= I105 - 1 /\ 1 <= I108 - 1 /\ 0 <= I105 - 1] 281.38/279.03 f3#(I112, I113, I114, I115, I116) -> f2#(I113, I114, I115, I117, I118) [I115 <= I116 - 1 /\ I112 <= I113 - 1 /\ 1 <= I115 - 1 /\ 0 <= I112 - 1] 281.38/279.03 f2#(I119, I120, I121, I122, I123) -> f5#(I119, I119 - 1, I119 - 2, I124, I125) [I119 = I121 /\ 0 <= I119 - 1] 281.38/279.03 f2#(I126, I127, I128, I129, I130) -> f4#(I128, I126, I128 - 1, I126 - 2, I131) [0 = I127 /\ I128 <= I126 - 1 /\ 0 <= I128 - 1 /\ -1 <= I126 - 1] 281.38/279.03 f2#(I132, I133, I134, I135, I136) -> f3#(I134, I132, I133, I134 + 1, I132 - 2) [0 <= I133 - 1 /\ -1 <= I132 - 1 /\ I134 <= I132 - 1 /\ 0 <= I134 - 1] 281.38/279.03 f2#(I137, I138, I139, I140, I141) -> f3#(I139, I137, I138, I139 + 1, I137 - 2) [I138 <= -1 /\ -1 <= I137 - 1 /\ I139 <= I137 - 1 /\ 0 <= I139 - 1] 281.38/279.03 f1#(I142, I143, I144, I145, I146) -> f2#(20, 0, I143 + 15, I147, I148) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ I143 <= I143 + 15 - 1] 281.38/279.03 R = 281.38/279.03 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 281.38/279.03 f2(I0, I1, I2, I3, I4) -> f2(0, 0, -1, I5, I6) [0 = I2 /\ 0 = I0] 281.38/279.03 f2(I7, I8, I9, I10, I11) -> f2(2, 1, 1, I12, I13) [0 = I9 /\ 3 = I7] 281.38/279.03 f5(I14, I15, I16, I17, I18) -> f2(I14 - 1, 0, I15, I19, I20) [I15 = I16 /\ I15 <= I14 - 1 /\ I15 <= I14 - 1] 281.38/279.03 f2(I21, I22, I23, I24, I25) -> f2(I21, 1, 1, I26, I27) [0 = I23 /\ 3 <= I21 - 1] 281.38/279.03 f2(I28, I29, I30, I31, I32) -> f2(I28, 1, 1, I33, I34) [0 = I30 /\ I28 <= 2 /\ 0 <= I28 - 1] 281.38/279.03 f5(I35, I36, I37, I38, I39) -> f2(I35, 0, I36, I40, I41) [I37 <= I36 - 1] 281.38/279.03 f5(I42, I43, I44, I45, I46) -> f2(I42, 0, I43, I47, I48) [I43 <= I44 - 1] 281.38/279.03 f4(I49, I50, I51, I52, I53) -> f2(I50 - 1, 0, I51, I54, I55) [I51 = I52 /\ I51 <= I50 - 1 /\ 0 <= I49 - 1] 281.38/279.03 f3(I56, I57, I58, I59, I60) -> f2(I57 - 1, I58, I59, I61, I62) [I59 = I60 /\ I59 <= I57 - 1 /\ 0 <= I56 - 1] 281.38/279.03 f4(I63, I64, I65, I66, I67) -> f2(I64, 0, I65, I68, I69) [I66 <= I65 - 1 /\ I64 <= I63 - 1 /\ 0 <= I63 - 1] 281.38/279.03 f4(I70, I71, I72, I73, I74) -> f2(I71, 0, I72, I75, I76) [I73 <= I72 - 1 /\ I70 <= I71 - 1 /\ 0 <= I70 - 1] 281.38/279.03 f4(I77, I78, I79, I80, I81) -> f2(I78, 0, I79, I82, I83) [I79 <= I80 - 1 /\ I78 <= I77 - 1 /\ 0 <= I77 - 1] 281.38/279.03 f4(I84, I85, I86, I87, I88) -> f2(I85, 0, I86, I89, I90) [I86 <= I87 - 1 /\ I84 <= I85 - 1 /\ 0 <= I84 - 1] 281.38/279.03 f3(I91, I92, I93, I94, I95) -> f2(I92, I93, I94, I96, I97) [I95 <= I94 - 1 /\ I92 <= I91 - 1 /\ 1 <= I94 - 1 /\ 0 <= I91 - 1] 281.38/279.03 f3(I98, I99, I100, I101, I102) -> f2(I99, I100, I101, I103, I104) [I102 <= I101 - 1 /\ I98 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= I98 - 1] 281.38/279.03 f3(I105, I106, I107, I108, I109) -> f2(I106, I107, I108, I110, I111) [I108 <= I109 - 1 /\ I106 <= I105 - 1 /\ 1 <= I108 - 1 /\ 0 <= I105 - 1] 281.38/279.03 f3(I112, I113, I114, I115, I116) -> f2(I113, I114, I115, I117, I118) [I115 <= I116 - 1 /\ I112 <= I113 - 1 /\ 1 <= I115 - 1 /\ 0 <= I112 - 1] 281.38/279.03 f2(I119, I120, I121, I122, I123) -> f5(I119, I119 - 1, I119 - 2, I124, I125) [I119 = I121 /\ 0 <= I119 - 1] 281.38/279.03 f2(I126, I127, I128, I129, I130) -> f4(I128, I126, I128 - 1, I126 - 2, I131) [0 = I127 /\ I128 <= I126 - 1 /\ 0 <= I128 - 1 /\ -1 <= I126 - 1] 281.38/279.03 f2(I132, I133, I134, I135, I136) -> f3(I134, I132, I133, I134 + 1, I132 - 2) [0 <= I133 - 1 /\ -1 <= I132 - 1 /\ I134 <= I132 - 1 /\ 0 <= I134 - 1] 281.38/279.03 f2(I137, I138, I139, I140, I141) -> f3(I139, I137, I138, I139 + 1, I137 - 2) [I138 <= -1 /\ -1 <= I137 - 1 /\ I139 <= I137 - 1 /\ 0 <= I139 - 1] 281.38/279.03 f1(I142, I143, I144, I145, I146) -> f2(20, 0, I143 + 15, I147, I148) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ I143 <= I143 + 15 - 1] 281.38/279.03 281.38/279.03 The dependency graph for this problem is: 281.38/279.03 0 -> 22 281.38/279.03 1 -> 281.38/279.03 2 -> 20 281.38/279.03 3 -> 1, 2, 4, 5, 18, 19 281.38/279.03 4 -> 20 281.38/279.03 5 -> 18, 20 281.38/279.03 6 -> 1, 2, 4, 5, 18, 19 281.38/279.03 7 -> 1, 2, 4, 5, 18, 19 281.38/279.03 8 -> 1, 2, 4, 5, 18, 19 281.38/279.03 9 -> 1, 2, 4, 5, 18, 19, 20, 21 281.38/279.03 10 -> 1, 2, 4, 5, 18, 19 281.38/279.03 11 -> 2, 4, 5, 18, 19 281.38/279.03 12 -> 1, 2, 4, 5, 18, 19 281.38/279.03 13 -> 2, 4, 5, 18, 19 281.38/279.03 14 -> 18, 19, 20, 21 281.38/279.03 15 -> 18, 19, 20, 21 281.38/279.03 16 -> 18, 19, 20, 21 281.38/279.03 17 -> 18, 19, 20, 21 281.38/279.03 18 -> 6 281.38/279.03 19 -> 8, 13 281.38/279.03 20 -> 9, 15, 17 281.38/279.03 21 -> 9, 15, 17 281.38/279.03 22 -> 18, 19 281.38/279.03 Where: 281.38/279.03 0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 281.38/279.03 1) f2#(I0, I1, I2, I3, I4) -> f2#(0, 0, -1, I5, I6) [0 = I2 /\ 0 = I0] 281.38/279.03 2) f2#(I7, I8, I9, I10, I11) -> f2#(2, 1, 1, I12, I13) [0 = I9 /\ 3 = I7] 281.38/279.03 3) f5#(I14, I15, I16, I17, I18) -> f2#(I14 - 1, 0, I15, I19, I20) [I15 = I16 /\ I15 <= I14 - 1 /\ I15 <= I14 - 1] 281.38/279.03 4) f2#(I21, I22, I23, I24, I25) -> f2#(I21, 1, 1, I26, I27) [0 = I23 /\ 3 <= I21 - 1] 281.38/279.03 5) f2#(I28, I29, I30, I31, I32) -> f2#(I28, 1, 1, I33, I34) [0 = I30 /\ I28 <= 2 /\ 0 <= I28 - 1] 281.38/279.04 6) f5#(I35, I36, I37, I38, I39) -> f2#(I35, 0, I36, I40, I41) [I37 <= I36 - 1] 281.38/279.04 7) f5#(I42, I43, I44, I45, I46) -> f2#(I42, 0, I43, I47, I48) [I43 <= I44 - 1] 281.38/279.04 8) f4#(I49, I50, I51, I52, I53) -> f2#(I50 - 1, 0, I51, I54, I55) [I51 = I52 /\ I51 <= I50 - 1 /\ 0 <= I49 - 1] 281.38/279.04 9) f3#(I56, I57, I58, I59, I60) -> f2#(I57 - 1, I58, I59, I61, I62) [I59 = I60 /\ I59 <= I57 - 1 /\ 0 <= I56 - 1] 281.38/279.04 10) f4#(I63, I64, I65, I66, I67) -> f2#(I64, 0, I65, I68, I69) [I66 <= I65 - 1 /\ I64 <= I63 - 1 /\ 0 <= I63 - 1] 281.38/279.04 11) f4#(I70, I71, I72, I73, I74) -> f2#(I71, 0, I72, I75, I76) [I73 <= I72 - 1 /\ I70 <= I71 - 1 /\ 0 <= I70 - 1] 281.38/279.04 12) f4#(I77, I78, I79, I80, I81) -> f2#(I78, 0, I79, I82, I83) [I79 <= I80 - 1 /\ I78 <= I77 - 1 /\ 0 <= I77 - 1] 281.38/279.04 13) f4#(I84, I85, I86, I87, I88) -> f2#(I85, 0, I86, I89, I90) [I86 <= I87 - 1 /\ I84 <= I85 - 1 /\ 0 <= I84 - 1] 281.38/279.04 14) f3#(I91, I92, I93, I94, I95) -> f2#(I92, I93, I94, I96, I97) [I95 <= I94 - 1 /\ I92 <= I91 - 1 /\ 1 <= I94 - 1 /\ 0 <= I91 - 1] 281.38/279.04 15) f3#(I98, I99, I100, I101, I102) -> f2#(I99, I100, I101, I103, I104) [I102 <= I101 - 1 /\ I98 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= I98 - 1] 281.38/279.04 16) f3#(I105, I106, I107, I108, I109) -> f2#(I106, I107, I108, I110, I111) [I108 <= I109 - 1 /\ I106 <= I105 - 1 /\ 1 <= I108 - 1 /\ 0 <= I105 - 1] 281.38/279.04 17) f3#(I112, I113, I114, I115, I116) -> f2#(I113, I114, I115, I117, I118) [I115 <= I116 - 1 /\ I112 <= I113 - 1 /\ 1 <= I115 - 1 /\ 0 <= I112 - 1] 281.38/279.04 18) f2#(I119, I120, I121, I122, I123) -> f5#(I119, I119 - 1, I119 - 2, I124, I125) [I119 = I121 /\ 0 <= I119 - 1] 281.38/279.04 19) f2#(I126, I127, I128, I129, I130) -> f4#(I128, I126, I128 - 1, I126 - 2, I131) [0 = I127 /\ I128 <= I126 - 1 /\ 0 <= I128 - 1 /\ -1 <= I126 - 1] 281.38/279.04 20) f2#(I132, I133, I134, I135, I136) -> f3#(I134, I132, I133, I134 + 1, I132 - 2) [0 <= I133 - 1 /\ -1 <= I132 - 1 /\ I134 <= I132 - 1 /\ 0 <= I134 - 1] 281.38/279.04 21) f2#(I137, I138, I139, I140, I141) -> f3#(I139, I137, I138, I139 + 1, I137 - 2) [I138 <= -1 /\ -1 <= I137 - 1 /\ I139 <= I137 - 1 /\ 0 <= I139 - 1] 281.38/279.04 22) f1#(I142, I143, I144, I145, I146) -> f2#(20, 0, I143 + 15, I147, I148) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ I143 <= I143 + 15 - 1] 281.38/279.04 281.38/279.04 We have the following SCCs. 281.38/279.04 { 2, 4, 5, 6, 8, 9, 13, 15, 17, 18, 19, 20, 21 } 281.38/279.04 281.38/279.04 DP problem for innermost termination. 281.38/279.04 P = 281.38/279.04 f2#(I7, I8, I9, I10, I11) -> f2#(2, 1, 1, I12, I13) [0 = I9 /\ 3 = I7] 281.38/279.04 f2#(I21, I22, I23, I24, I25) -> f2#(I21, 1, 1, I26, I27) [0 = I23 /\ 3 <= I21 - 1] 281.38/279.04 f2#(I28, I29, I30, I31, I32) -> f2#(I28, 1, 1, I33, I34) [0 = I30 /\ I28 <= 2 /\ 0 <= I28 - 1] 281.38/279.04 f5#(I35, I36, I37, I38, I39) -> f2#(I35, 0, I36, I40, I41) [I37 <= I36 - 1] 281.38/279.04 f4#(I49, I50, I51, I52, I53) -> f2#(I50 - 1, 0, I51, I54, I55) [I51 = I52 /\ I51 <= I50 - 1 /\ 0 <= I49 - 1] 281.38/279.04 f3#(I56, I57, I58, I59, I60) -> f2#(I57 - 1, I58, I59, I61, I62) [I59 = I60 /\ I59 <= I57 - 1 /\ 0 <= I56 - 1] 281.38/279.04 f4#(I84, I85, I86, I87, I88) -> f2#(I85, 0, I86, I89, I90) [I86 <= I87 - 1 /\ I84 <= I85 - 1 /\ 0 <= I84 - 1] 281.38/279.04 f3#(I98, I99, I100, I101, I102) -> f2#(I99, I100, I101, I103, I104) [I102 <= I101 - 1 /\ I98 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= I98 - 1] 281.38/279.04 f3#(I112, I113, I114, I115, I116) -> f2#(I113, I114, I115, I117, I118) [I115 <= I116 - 1 /\ I112 <= I113 - 1 /\ 1 <= I115 - 1 /\ 0 <= I112 - 1] 281.38/279.04 f2#(I119, I120, I121, I122, I123) -> f5#(I119, I119 - 1, I119 - 2, I124, I125) [I119 = I121 /\ 0 <= I119 - 1] 281.38/279.04 f2#(I126, I127, I128, I129, I130) -> f4#(I128, I126, I128 - 1, I126 - 2, I131) [0 = I127 /\ I128 <= I126 - 1 /\ 0 <= I128 - 1 /\ -1 <= I126 - 1] 281.38/279.04 f2#(I132, I133, I134, I135, I136) -> f3#(I134, I132, I133, I134 + 1, I132 - 2) [0 <= I133 - 1 /\ -1 <= I132 - 1 /\ I134 <= I132 - 1 /\ 0 <= I134 - 1] 281.38/279.04 f2#(I137, I138, I139, I140, I141) -> f3#(I139, I137, I138, I139 + 1, I137 - 2) [I138 <= -1 /\ -1 <= I137 - 1 /\ I139 <= I137 - 1 /\ 0 <= I139 - 1] 281.38/279.04 R = 281.38/279.04 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 281.38/279.04 f2(I0, I1, I2, I3, I4) -> f2(0, 0, -1, I5, I6) [0 = I2 /\ 0 = I0] 281.38/279.04 f2(I7, I8, I9, I10, I11) -> f2(2, 1, 1, I12, I13) [0 = I9 /\ 3 = I7] 281.38/279.04 f5(I14, I15, I16, I17, I18) -> f2(I14 - 1, 0, I15, I19, I20) [I15 = I16 /\ I15 <= I14 - 1 /\ I15 <= I14 - 1] 281.38/279.04 f2(I21, I22, I23, I24, I25) -> f2(I21, 1, 1, I26, I27) [0 = I23 /\ 3 <= I21 - 1] 281.38/279.04 f2(I28, I29, I30, I31, I32) -> f2(I28, 1, 1, I33, I34) [0 = I30 /\ I28 <= 2 /\ 0 <= I28 - 1] 281.38/279.04 f5(I35, I36, I37, I38, I39) -> f2(I35, 0, I36, I40, I41) [I37 <= I36 - 1] 281.38/279.04 f5(I42, I43, I44, I45, I46) -> f2(I42, 0, I43, I47, I48) [I43 <= I44 - 1] 281.38/279.04 f4(I49, I50, I51, I52, I53) -> f2(I50 - 1, 0, I51, I54, I55) [I51 = I52 /\ I51 <= I50 - 1 /\ 0 <= I49 - 1] 281.38/279.04 f3(I56, I57, I58, I59, I60) -> f2(I57 - 1, I58, I59, I61, I62) [I59 = I60 /\ I59 <= I57 - 1 /\ 0 <= I56 - 1] 281.38/279.04 f4(I63, I64, I65, I66, I67) -> f2(I64, 0, I65, I68, I69) [I66 <= I65 - 1 /\ I64 <= I63 - 1 /\ 0 <= I63 - 1] 281.38/279.04 f4(I70, I71, I72, I73, I74) -> f2(I71, 0, I72, I75, I76) [I73 <= I72 - 1 /\ I70 <= I71 - 1 /\ 0 <= I70 - 1] 281.38/279.04 f4(I77, I78, I79, I80, I81) -> f2(I78, 0, I79, I82, I83) [I79 <= I80 - 1 /\ I78 <= I77 - 1 /\ 0 <= I77 - 1] 281.38/279.04 f4(I84, I85, I86, I87, I88) -> f2(I85, 0, I86, I89, I90) [I86 <= I87 - 1 /\ I84 <= I85 - 1 /\ 0 <= I84 - 1] 281.38/279.04 f3(I91, I92, I93, I94, I95) -> f2(I92, I93, I94, I96, I97) [I95 <= I94 - 1 /\ I92 <= I91 - 1 /\ 1 <= I94 - 1 /\ 0 <= I91 - 1] 281.38/279.04 f3(I98, I99, I100, I101, I102) -> f2(I99, I100, I101, I103, I104) [I102 <= I101 - 1 /\ I98 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= I98 - 1] 281.38/279.04 f3(I105, I106, I107, I108, I109) -> f2(I106, I107, I108, I110, I111) [I108 <= I109 - 1 /\ I106 <= I105 - 1 /\ 1 <= I108 - 1 /\ 0 <= I105 - 1] 281.38/279.04 f3(I112, I113, I114, I115, I116) -> f2(I113, I114, I115, I117, I118) [I115 <= I116 - 1 /\ I112 <= I113 - 1 /\ 1 <= I115 - 1 /\ 0 <= I112 - 1] 281.38/279.04 f2(I119, I120, I121, I122, I123) -> f5(I119, I119 - 1, I119 - 2, I124, I125) [I119 = I121 /\ 0 <= I119 - 1] 281.38/279.04 f2(I126, I127, I128, I129, I130) -> f4(I128, I126, I128 - 1, I126 - 2, I131) [0 = I127 /\ I128 <= I126 - 1 /\ 0 <= I128 - 1 /\ -1 <= I126 - 1] 281.38/279.04 f2(I132, I133, I134, I135, I136) -> f3(I134, I132, I133, I134 + 1, I132 - 2) [0 <= I133 - 1 /\ -1 <= I132 - 1 /\ I134 <= I132 - 1 /\ 0 <= I134 - 1] 281.38/279.04 f2(I137, I138, I139, I140, I141) -> f3(I139, I137, I138, I139 + 1, I137 - 2) [I138 <= -1 /\ -1 <= I137 - 1 /\ I139 <= I137 - 1 /\ 0 <= I139 - 1] 281.38/279.04 f1(I142, I143, I144, I145, I146) -> f2(20, 0, I143 + 15, I147, I148) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ I143 <= I143 + 15 - 1] 281.38/279.04 281.38/279.04 We use the reverse value criterion with the projection function NU: 281.38/279.04 NU[f3#(z1,z2,z3,z4,z5)] = z2 - 1 + -1 * -1 281.38/279.04 NU[f4#(z1,z2,z3,z4,z5)] = z2 - 1 + -1 * -1 281.38/279.04 NU[f5#(z1,z2,z3,z4,z5)] = z1 281.38/279.04 NU[f2#(z1,z2,z3,z4,z5)] = z1 281.38/279.04 281.38/279.04 This gives the following inequalities: 281.38/279.04 0 = I9 /\ 3 = I7 ==> I7 > 2 with I7 >= 0 281.38/279.04 0 = I23 /\ 3 <= I21 - 1 ==> I21 >= I21 281.38/279.04 0 = I30 /\ I28 <= 2 /\ 0 <= I28 - 1 ==> I28 >= I28 281.38/279.04 I37 <= I36 - 1 ==> I35 >= I35 281.38/279.04 I51 = I52 /\ I51 <= I50 - 1 /\ 0 <= I49 - 1 ==> I50 - 1 + -1 * -1 >= I50 - 1 281.38/279.04 I59 = I60 /\ I59 <= I57 - 1 /\ 0 <= I56 - 1 ==> I57 - 1 + -1 * -1 >= I57 - 1 281.38/279.04 I86 <= I87 - 1 /\ I84 <= I85 - 1 /\ 0 <= I84 - 1 ==> I85 - 1 + -1 * -1 >= I85 281.38/279.04 I102 <= I101 - 1 /\ I98 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= I98 - 1 ==> I99 - 1 + -1 * -1 >= I99 281.38/279.04 I115 <= I116 - 1 /\ I112 <= I113 - 1 /\ 1 <= I115 - 1 /\ 0 <= I112 - 1 ==> I113 - 1 + -1 * -1 >= I113 281.38/279.04 I119 = I121 /\ 0 <= I119 - 1 ==> I119 >= I119 281.38/279.04 0 = I127 /\ I128 <= I126 - 1 /\ 0 <= I128 - 1 /\ -1 <= I126 - 1 ==> I126 >= I126 - 1 + -1 * -1 281.38/279.04 0 <= I133 - 1 /\ -1 <= I132 - 1 /\ I134 <= I132 - 1 /\ 0 <= I134 - 1 ==> I132 >= I132 - 1 + -1 * -1 281.38/279.04 I138 <= -1 /\ -1 <= I137 - 1 /\ I139 <= I137 - 1 /\ 0 <= I139 - 1 ==> I137 >= I137 - 1 + -1 * -1 281.38/279.04 281.38/279.04 We remove all the strictly oriented dependency pairs. 281.38/279.04 281.38/279.04 DP problem for innermost termination. 281.38/279.04 P = 281.38/279.04 f2#(I21, I22, I23, I24, I25) -> f2#(I21, 1, 1, I26, I27) [0 = I23 /\ 3 <= I21 - 1] 281.38/279.04 f2#(I28, I29, I30, I31, I32) -> f2#(I28, 1, 1, I33, I34) [0 = I30 /\ I28 <= 2 /\ 0 <= I28 - 1] 281.38/279.04 f5#(I35, I36, I37, I38, I39) -> f2#(I35, 0, I36, I40, I41) [I37 <= I36 - 1] 281.38/279.04 f4#(I49, I50, I51, I52, I53) -> f2#(I50 - 1, 0, I51, I54, I55) [I51 = I52 /\ I51 <= I50 - 1 /\ 0 <= I49 - 1] 281.38/279.04 f3#(I56, I57, I58, I59, I60) -> f2#(I57 - 1, I58, I59, I61, I62) [I59 = I60 /\ I59 <= I57 - 1 /\ 0 <= I56 - 1] 281.38/279.04 f4#(I84, I85, I86, I87, I88) -> f2#(I85, 0, I86, I89, I90) [I86 <= I87 - 1 /\ I84 <= I85 - 1 /\ 0 <= I84 - 1] 281.38/279.04 f3#(I98, I99, I100, I101, I102) -> f2#(I99, I100, I101, I103, I104) [I102 <= I101 - 1 /\ I98 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= I98 - 1] 281.38/279.04 f3#(I112, I113, I114, I115, I116) -> f2#(I113, I114, I115, I117, I118) [I115 <= I116 - 1 /\ I112 <= I113 - 1 /\ 1 <= I115 - 1 /\ 0 <= I112 - 1] 281.38/279.04 f2#(I119, I120, I121, I122, I123) -> f5#(I119, I119 - 1, I119 - 2, I124, I125) [I119 = I121 /\ 0 <= I119 - 1] 281.38/279.04 f2#(I126, I127, I128, I129, I130) -> f4#(I128, I126, I128 - 1, I126 - 2, I131) [0 = I127 /\ I128 <= I126 - 1 /\ 0 <= I128 - 1 /\ -1 <= I126 - 1] 281.38/279.04 f2#(I132, I133, I134, I135, I136) -> f3#(I134, I132, I133, I134 + 1, I132 - 2) [0 <= I133 - 1 /\ -1 <= I132 - 1 /\ I134 <= I132 - 1 /\ 0 <= I134 - 1] 281.38/279.04 f2#(I137, I138, I139, I140, I141) -> f3#(I139, I137, I138, I139 + 1, I137 - 2) [I138 <= -1 /\ -1 <= I137 - 1 /\ I139 <= I137 - 1 /\ 0 <= I139 - 1] 281.38/279.04 R = 281.38/279.04 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 281.38/279.04 f2(I0, I1, I2, I3, I4) -> f2(0, 0, -1, I5, I6) [0 = I2 /\ 0 = I0] 281.38/279.04 f2(I7, I8, I9, I10, I11) -> f2(2, 1, 1, I12, I13) [0 = I9 /\ 3 = I7] 281.38/279.04 f5(I14, I15, I16, I17, I18) -> f2(I14 - 1, 0, I15, I19, I20) [I15 = I16 /\ I15 <= I14 - 1 /\ I15 <= I14 - 1] 281.38/279.04 f2(I21, I22, I23, I24, I25) -> f2(I21, 1, 1, I26, I27) [0 = I23 /\ 3 <= I21 - 1] 281.38/279.04 f2(I28, I29, I30, I31, I32) -> f2(I28, 1, 1, I33, I34) [0 = I30 /\ I28 <= 2 /\ 0 <= I28 - 1] 281.38/279.04 f5(I35, I36, I37, I38, I39) -> f2(I35, 0, I36, I40, I41) [I37 <= I36 - 1] 281.38/279.04 f5(I42, I43, I44, I45, I46) -> f2(I42, 0, I43, I47, I48) [I43 <= I44 - 1] 281.38/279.04 f4(I49, I50, I51, I52, I53) -> f2(I50 - 1, 0, I51, I54, I55) [I51 = I52 /\ I51 <= I50 - 1 /\ 0 <= I49 - 1] 281.38/279.04 f3(I56, I57, I58, I59, I60) -> f2(I57 - 1, I58, I59, I61, I62) [I59 = I60 /\ I59 <= I57 - 1 /\ 0 <= I56 - 1] 281.38/279.04 f4(I63, I64, I65, I66, I67) -> f2(I64, 0, I65, I68, I69) [I66 <= I65 - 1 /\ I64 <= I63 - 1 /\ 0 <= I63 - 1] 281.38/279.04 f4(I70, I71, I72, I73, I74) -> f2(I71, 0, I72, I75, I76) [I73 <= I72 - 1 /\ I70 <= I71 - 1 /\ 0 <= I70 - 1] 281.38/279.04 f4(I77, I78, I79, I80, I81) -> f2(I78, 0, I79, I82, I83) [I79 <= I80 - 1 /\ I78 <= I77 - 1 /\ 0 <= I77 - 1] 281.38/279.04 f4(I84, I85, I86, I87, I88) -> f2(I85, 0, I86, I89, I90) [I86 <= I87 - 1 /\ I84 <= I85 - 1 /\ 0 <= I84 - 1] 281.38/279.04 f3(I91, I92, I93, I94, I95) -> f2(I92, I93, I94, I96, I97) [I95 <= I94 - 1 /\ I92 <= I91 - 1 /\ 1 <= I94 - 1 /\ 0 <= I91 - 1] 281.38/279.04 f3(I98, I99, I100, I101, I102) -> f2(I99, I100, I101, I103, I104) [I102 <= I101 - 1 /\ I98 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= I98 - 1] 281.38/279.04 f3(I105, I106, I107, I108, I109) -> f2(I106, I107, I108, I110, I111) [I108 <= I109 - 1 /\ I106 <= I105 - 1 /\ 1 <= I108 - 1 /\ 0 <= I105 - 1] 281.38/279.04 f3(I112, I113, I114, I115, I116) -> f2(I113, I114, I115, I117, I118) [I115 <= I116 - 1 /\ I112 <= I113 - 1 /\ 1 <= I115 - 1 /\ 0 <= I112 - 1] 281.38/279.04 f2(I119, I120, I121, I122, I123) -> f5(I119, I119 - 1, I119 - 2, I124, I125) [I119 = I121 /\ 0 <= I119 - 1] 281.38/279.04 f2(I126, I127, I128, I129, I130) -> f4(I128, I126, I128 - 1, I126 - 2, I131) [0 = I127 /\ I128 <= I126 - 1 /\ 0 <= I128 - 1 /\ -1 <= I126 - 1] 281.38/279.04 f2(I132, I133, I134, I135, I136) -> f3(I134, I132, I133, I134 + 1, I132 - 2) [0 <= I133 - 1 /\ -1 <= I132 - 1 /\ I134 <= I132 - 1 /\ 0 <= I134 - 1] 281.38/279.04 f2(I137, I138, I139, I140, I141) -> f3(I139, I137, I138, I139 + 1, I137 - 2) [I138 <= -1 /\ -1 <= I137 - 1 /\ I139 <= I137 - 1 /\ 0 <= I139 - 1] 281.38/279.04 f1(I142, I143, I144, I145, I146) -> f2(20, 0, I143 + 15, I147, I148) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ I143 <= I143 + 15 - 1] 281.38/279.04 281.38/282.00 EOF