56.69/56.51 YES 56.69/56.51 56.69/56.51 DP problem for innermost termination. 56.69/56.51 P = 56.69/56.51 init#(x1, x2, x3, x4, x5, x6, x7) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 56.69/56.51 f8#(I0, I1, I2, I3, I4, I5, I6) -> f8#(I7, I1 + 1, I2, I3 + 1, I3 + 1, I5, I6) [I3 <= I5 /\ I1 <= I6 - 1 /\ I2 <= I6 - 1 /\ y2 <= y1 - 1 /\ I3 <= I6 - 1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I3 = I4] 56.69/56.51 f8#(I8, I9, I10, I11, I12, I13, I14) -> f8#(I15, I9, I10 - 1, I11 + 1, I11 + 1, I13, I14) [I11 <= I13 /\ I9 <= I14 - 1 /\ I10 <= I14 - 1 /\ I16 <= I17 /\ I11 <= I14 - 1 /\ I15 <= I8 /\ 0 <= I8 - 1 /\ 0 <= I15 - 1 /\ I11 = I12] 56.69/56.51 f7#(I18, I19, I20, I21, I22, I23, I24) -> f8#(I25, I18, I22, I18, I18, I22, I23) [0 <= I25 - 1 /\ 0 <= I20 - 1 /\ I22 <= I21 - 1 /\ I25 <= I20] 56.69/56.51 f7#(I26, I27, I28, I29, I30, I31, I32) -> f7#(I26, I27, I33, I29 + 1, I30, I31, I34) [0 <= I33 - 1 /\ 0 <= I28 - 1 /\ I33 <= I28 /\ I29 <= I31 - 1 /\ I29 <= I30 /\ I30 + I27 + 1 - I29 <= I31 - 1] 56.69/56.51 f6#(I35, I36, I37, I38, I39, I40, I41) -> f6#(I35, I36, I42, I38 + 1, I38 + 1, I40, I41) [I38 = I39 /\ 0 <= I42 - 1 /\ 0 <= I37 - 1 /\ I42 <= I37 /\ I38 <= I41 - 1 /\ I38 <= I40] 56.69/56.51 f6#(I43, I44, I45, I46, I47, I48, I49) -> f7#(I43, I48, I50, I48 + 1, I44, I49, I51) [I46 = I47 /\ 0 <= I50 - 1 /\ 0 <= I45 - 1 /\ I48 <= I46 - 1 /\ I50 <= I45] 56.69/56.51 f5#(I52, I53, I54, I55, I56, I57, I58) -> f6#(I52, I53, I59, I52, I52, I54, I56) [0 <= I59 - 1 /\ 0 <= I55 - 1 /\ -1 <= I56 - 1 /\ I59 <= I55] 56.69/56.51 f4#(I60, I61, I62, I63, I64, I65, I66) -> f6#(I62, I63, I67, I62, I62, I68, I64) [0 <= I62 + I63 - 2 * I68 /\ I62 + I63 - 2 * I68 <= 1 /\ 0 <= I67 - 1 /\ 0 <= I61 - 1 /\ 0 <= I60 - 1 /\ I67 <= I61 /\ I67 <= I60 /\ -1 <= I64 - 1 /\ I68 <= I68 + 1 - 1 /\ I63 - (I68 + 1) <= I63 - I62 - 1 /\ I63 - I62 <= I68 - I62 /\ I62 <= I63 - 1] 56.69/56.51 f3#(I69, I70, I71, I72, I73, I74, I75) -> f4#(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 f4#(I80, I81, I82, I83, I84, I85, I86) -> f6#(I82, I83, I87, I82, I82, I88, I84) [0 <= I82 + I83 - 2 * I88 /\ I82 + I83 - 2 * I88 <= 1 /\ 0 <= I87 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I87 <= I81 /\ I87 <= I80 /\ -1 <= I84 - 1 /\ I83 - I82 <= I83 - (I88 + 1) /\ I83 - I82 <= I88 - I82 /\ I82 <= I83 - 1] 56.69/56.51 f3#(I89, I90, I91, I92, I93, I94, I95) -> f4#(I89, I90, I91, I92, I93, I96, I97) [I91 <= I92 - 1 /\ I92 - I91 <= I98 - I91 /\ I92 - I91 <= I92 - (I98 + 1) /\ -1 <= I93 - 1 /\ I99 <= I89 /\ I99 <= I90 /\ 0 <= I89 - 1 /\ 0 <= I90 - 1 /\ 0 <= I99 - 1] 56.69/56.51 f4#(I100, I101, I102, I103, I104, I105, I106) -> f5#(I102, I103, I107, I108, I104, I109, I110) [0 <= I102 + I103 - 2 * I107 /\ I102 + I103 - 2 * I107 <= 1 /\ 0 <= I108 - 1 /\ 0 <= I101 - 1 /\ 0 <= I100 - 1 /\ I108 <= I101 /\ I108 <= I100 /\ I103 - (I107 + 1) <= I103 - I102 - 1 /\ I107 <= I107 + 1 - 1 /\ I107 - I102 <= I103 - I102 - 1 /\ I102 <= I103 - 1] 56.69/56.51 f3#(I111, I112, I113, I114, I115, I116, I117) -> f4#(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 f4#(I122, I123, I124, I125, I126, I127, I128) -> f5#(I124, I125, I129, I130, I126, I131, I132) [0 <= I124 + I125 - 2 * I129 /\ I124 + I125 - 2 * I129 <= 1 /\ 0 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1 /\ I130 <= I123 /\ I130 <= I122 /\ I125 - I124 <= I125 - (I129 + 1) /\ I129 - I124 <= I125 - I124 - 1 /\ I124 <= I125 - 1] 56.69/56.51 f3#(I133, I134, I135, I136, I137, I138, I139) -> f4#(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 f4#(I144, I145, I146, I147, I148, I149, I150) -> f3#(I151, I152, I153, I147, I148, I154, I155) [I146 <= I147 - 1 /\ I156 - I146 <= I147 - I146 - 1 /\ I156 <= I156 + 1 - 1 /\ I147 - (I156 + 1) <= I147 - I146 - 1 /\ I151 <= I144 /\ I151 <= I145 /\ I152 <= I144 /\ I152 <= I145 /\ 0 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I151 - 1 /\ 0 <= I152 - 1 /\ I146 + I147 - 2 * I156 <= 1 /\ 0 <= I146 + I147 - 2 * I156 /\ I156 + 1 = I153] 56.69/56.51 f3#(I157, I158, I159, I160, I161, I162, I163) -> f4#(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 f4#(I168, I169, I170, I171, I172, I173, I174) -> f3#(I175, I176, I177, I171, I172, I178, I179) [I170 <= I171 - 1 /\ I171 - I170 <= I180 - I170 /\ I171 - (I180 + 1) <= I171 - I170 - 1 /\ I180 <= I180 + 1 - 1 /\ I175 <= I168 /\ I175 <= I169 /\ I176 <= I168 /\ I176 <= I169 /\ 0 <= I168 - 1 /\ 0 <= I169 - 1 /\ 0 <= I175 - 1 /\ 0 <= I176 - 1 /\ I170 + I171 - 2 * I180 <= 1 /\ 0 <= I170 + I171 - 2 * I180 /\ I180 + 1 = I177] 56.69/56.51 f3#(I181, I182, I183, I184, I185, I186, I187) -> f4#(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 f4#(I193, I194, I195, I196, I197, I198, I199) -> f3#(I200, I201, I195, I202, I197, I203, I204) [0 <= I195 + I196 - 2 * I202 /\ I195 + I196 - 2 * I202 <= 1 /\ 0 <= I201 - 1 /\ 0 <= I200 - 1 /\ 0 <= I194 - 1 /\ 0 <= I193 - 1 /\ I201 <= I194 /\ I201 <= I193 /\ I200 <= I194 /\ I200 <= I193 /\ I202 - I195 <= I196 - I195 - 1 /\ I195 <= I196 - 1] 56.69/56.51 f3#(I205, I206, I207, I208, I209, I210, I211) -> f4#(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 f2#(I217, I218, I219, I220, I221, I222, I223) -> f3#(I224, I225, 0, I219 - 1, I219, I226, I227) [0 <= I225 - 1 /\ 0 <= I224 - 1 /\ 0 <= I217 - 1 /\ I225 <= I217 /\ I224 <= I217 /\ I219 <= I218 /\ -1 <= I219 - 1 /\ I219 - 1 <= I219 - 1] 56.69/56.51 f2#(I228, I229, I230, I231, I232, I233, I234) -> f2#(I235, I229 + 1, I230, I236, I237, I238, I239) [0 <= I235 - 1 /\ 0 <= I228 - 1 /\ I229 <= I230 - 1 /\ I235 <= I228] 56.69/56.51 f1#(I240, I241, I242, I243, I244, I245, I246) -> f2#(I247, 0, I241, I248, I249, I250, I251) [0 <= I247 - 1 /\ 0 <= I240 - 1 /\ -1 <= I241 - 1 /\ I247 <= I240] 56.69/56.51 R = 56.69/56.51 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 56.69/56.51 f8(I0, I1, I2, I3, I4, I5, I6) -> f8(I7, I1 + 1, I2, I3 + 1, I3 + 1, I5, I6) [I3 <= I5 /\ I1 <= I6 - 1 /\ I2 <= I6 - 1 /\ y2 <= y1 - 1 /\ I3 <= I6 - 1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I3 = I4] 56.69/56.51 f8(I8, I9, I10, I11, I12, I13, I14) -> f8(I15, I9, I10 - 1, I11 + 1, I11 + 1, I13, I14) [I11 <= I13 /\ I9 <= I14 - 1 /\ I10 <= I14 - 1 /\ I16 <= I17 /\ I11 <= I14 - 1 /\ I15 <= I8 /\ 0 <= I8 - 1 /\ 0 <= I15 - 1 /\ I11 = I12] 56.69/56.51 f7(I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I18, I22, I18, I18, I22, I23) [0 <= I25 - 1 /\ 0 <= I20 - 1 /\ I22 <= I21 - 1 /\ I25 <= I20] 56.69/56.51 f7(I26, I27, I28, I29, I30, I31, I32) -> f7(I26, I27, I33, I29 + 1, I30, I31, I34) [0 <= I33 - 1 /\ 0 <= I28 - 1 /\ I33 <= I28 /\ I29 <= I31 - 1 /\ I29 <= I30 /\ I30 + I27 + 1 - I29 <= I31 - 1] 56.69/56.51 f6(I35, I36, I37, I38, I39, I40, I41) -> f6(I35, I36, I42, I38 + 1, I38 + 1, I40, I41) [I38 = I39 /\ 0 <= I42 - 1 /\ 0 <= I37 - 1 /\ I42 <= I37 /\ I38 <= I41 - 1 /\ I38 <= I40] 56.69/56.51 f6(I43, I44, I45, I46, I47, I48, I49) -> f7(I43, I48, I50, I48 + 1, I44, I49, I51) [I46 = I47 /\ 0 <= I50 - 1 /\ 0 <= I45 - 1 /\ I48 <= I46 - 1 /\ I50 <= I45] 56.69/56.51 f5(I52, I53, I54, I55, I56, I57, I58) -> f6(I52, I53, I59, I52, I52, I54, I56) [0 <= I59 - 1 /\ 0 <= I55 - 1 /\ -1 <= I56 - 1 /\ I59 <= I55] 56.69/56.51 f4(I60, I61, I62, I63, I64, I65, I66) -> f6(I62, I63, I67, I62, I62, I68, I64) [0 <= I62 + I63 - 2 * I68 /\ I62 + I63 - 2 * I68 <= 1 /\ 0 <= I67 - 1 /\ 0 <= I61 - 1 /\ 0 <= I60 - 1 /\ I67 <= I61 /\ I67 <= I60 /\ -1 <= I64 - 1 /\ I68 <= I68 + 1 - 1 /\ I63 - (I68 + 1) <= I63 - I62 - 1 /\ I63 - I62 <= I68 - I62 /\ I62 <= I63 - 1] 56.69/56.51 f3(I69, I70, I71, I72, I73, I74, I75) -> f4(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 f4(I80, I81, I82, I83, I84, I85, I86) -> f6(I82, I83, I87, I82, I82, I88, I84) [0 <= I82 + I83 - 2 * I88 /\ I82 + I83 - 2 * I88 <= 1 /\ 0 <= I87 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I87 <= I81 /\ I87 <= I80 /\ -1 <= I84 - 1 /\ I83 - I82 <= I83 - (I88 + 1) /\ I83 - I82 <= I88 - I82 /\ I82 <= I83 - 1] 56.69/56.51 f3(I89, I90, I91, I92, I93, I94, I95) -> f4(I89, I90, I91, I92, I93, I96, I97) [I91 <= I92 - 1 /\ I92 - I91 <= I98 - I91 /\ I92 - I91 <= I92 - (I98 + 1) /\ -1 <= I93 - 1 /\ I99 <= I89 /\ I99 <= I90 /\ 0 <= I89 - 1 /\ 0 <= I90 - 1 /\ 0 <= I99 - 1] 56.69/56.51 f4(I100, I101, I102, I103, I104, I105, I106) -> f5(I102, I103, I107, I108, I104, I109, I110) [0 <= I102 + I103 - 2 * I107 /\ I102 + I103 - 2 * I107 <= 1 /\ 0 <= I108 - 1 /\ 0 <= I101 - 1 /\ 0 <= I100 - 1 /\ I108 <= I101 /\ I108 <= I100 /\ I103 - (I107 + 1) <= I103 - I102 - 1 /\ I107 <= I107 + 1 - 1 /\ I107 - I102 <= I103 - I102 - 1 /\ I102 <= I103 - 1] 56.69/56.51 f3(I111, I112, I113, I114, I115, I116, I117) -> f4(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 f4(I122, I123, I124, I125, I126, I127, I128) -> f5(I124, I125, I129, I130, I126, I131, I132) [0 <= I124 + I125 - 2 * I129 /\ I124 + I125 - 2 * I129 <= 1 /\ 0 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1 /\ I130 <= I123 /\ I130 <= I122 /\ I125 - I124 <= I125 - (I129 + 1) /\ I129 - I124 <= I125 - I124 - 1 /\ I124 <= I125 - 1] 56.69/56.51 f3(I133, I134, I135, I136, I137, I138, I139) -> f4(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 f4(I144, I145, I146, I147, I148, I149, I150) -> f3(I151, I152, I153, I147, I148, I154, I155) [I146 <= I147 - 1 /\ I156 - I146 <= I147 - I146 - 1 /\ I156 <= I156 + 1 - 1 /\ I147 - (I156 + 1) <= I147 - I146 - 1 /\ I151 <= I144 /\ I151 <= I145 /\ I152 <= I144 /\ I152 <= I145 /\ 0 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I151 - 1 /\ 0 <= I152 - 1 /\ I146 + I147 - 2 * I156 <= 1 /\ 0 <= I146 + I147 - 2 * I156 /\ I156 + 1 = I153] 56.69/56.51 f3(I157, I158, I159, I160, I161, I162, I163) -> f4(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 f4(I168, I169, I170, I171, I172, I173, I174) -> f3(I175, I176, I177, I171, I172, I178, I179) [I170 <= I171 - 1 /\ I171 - I170 <= I180 - I170 /\ I171 - (I180 + 1) <= I171 - I170 - 1 /\ I180 <= I180 + 1 - 1 /\ I175 <= I168 /\ I175 <= I169 /\ I176 <= I168 /\ I176 <= I169 /\ 0 <= I168 - 1 /\ 0 <= I169 - 1 /\ 0 <= I175 - 1 /\ 0 <= I176 - 1 /\ I170 + I171 - 2 * I180 <= 1 /\ 0 <= I170 + I171 - 2 * I180 /\ I180 + 1 = I177] 56.69/56.51 f3(I181, I182, I183, I184, I185, I186, I187) -> f4(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 f4(I193, I194, I195, I196, I197, I198, I199) -> f3(I200, I201, I195, I202, I197, I203, I204) [0 <= I195 + I196 - 2 * I202 /\ I195 + I196 - 2 * I202 <= 1 /\ 0 <= I201 - 1 /\ 0 <= I200 - 1 /\ 0 <= I194 - 1 /\ 0 <= I193 - 1 /\ I201 <= I194 /\ I201 <= I193 /\ I200 <= I194 /\ I200 <= I193 /\ I202 - I195 <= I196 - I195 - 1 /\ I195 <= I196 - 1] 56.69/56.51 f3(I205, I206, I207, I208, I209, I210, I211) -> f4(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 f2(I217, I218, I219, I220, I221, I222, I223) -> f3(I224, I225, 0, I219 - 1, I219, I226, I227) [0 <= I225 - 1 /\ 0 <= I224 - 1 /\ 0 <= I217 - 1 /\ I225 <= I217 /\ I224 <= I217 /\ I219 <= I218 /\ -1 <= I219 - 1 /\ I219 - 1 <= I219 - 1] 56.69/56.51 f2(I228, I229, I230, I231, I232, I233, I234) -> f2(I235, I229 + 1, I230, I236, I237, I238, I239) [0 <= I235 - 1 /\ 0 <= I228 - 1 /\ I229 <= I230 - 1 /\ I235 <= I228] 56.69/56.51 f1(I240, I241, I242, I243, I244, I245, I246) -> f2(I247, 0, I241, I248, I249, I250, I251) [0 <= I247 - 1 /\ 0 <= I240 - 1 /\ -1 <= I241 - 1 /\ I247 <= I240] 56.69/56.51 56.69/56.51 The dependency graph for this problem is: 56.69/56.51 0 -> 24 56.69/56.51 1 -> 1, 2 56.69/56.51 2 -> 1, 2 56.69/56.51 3 -> 1, 2 56.69/56.51 4 -> 3, 4 56.69/56.51 5 -> 5, 6 56.69/56.51 6 -> 3, 4 56.69/56.51 7 -> 5, 6 56.69/56.51 8 -> 56.69/56.51 9 -> 12, 16, 20 56.69/56.51 10 -> 56.69/56.51 11 -> 56.69/56.51 12 -> 7 56.69/56.51 13 -> 12, 16, 20 56.69/56.51 14 -> 56.69/56.51 15 -> 12, 16, 20 56.69/56.51 16 -> 9, 13, 15, 17, 19, 21 56.69/56.51 17 -> 12, 16, 20 56.69/56.51 18 -> 56.69/56.51 19 -> 12, 16, 20 56.69/56.51 20 -> 9, 13, 15, 17, 19, 21 56.69/56.51 21 -> 12, 16, 20 56.69/56.51 22 -> 9, 13, 15, 17, 19, 21 56.69/56.51 23 -> 22, 23 56.69/56.51 24 -> 22, 23 56.69/56.51 Where: 56.69/56.51 0) init#(x1, x2, x3, x4, x5, x6, x7) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 56.69/56.51 1) f8#(I0, I1, I2, I3, I4, I5, I6) -> f8#(I7, I1 + 1, I2, I3 + 1, I3 + 1, I5, I6) [I3 <= I5 /\ I1 <= I6 - 1 /\ I2 <= I6 - 1 /\ y2 <= y1 - 1 /\ I3 <= I6 - 1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I3 = I4] 56.69/56.51 2) f8#(I8, I9, I10, I11, I12, I13, I14) -> f8#(I15, I9, I10 - 1, I11 + 1, I11 + 1, I13, I14) [I11 <= I13 /\ I9 <= I14 - 1 /\ I10 <= I14 - 1 /\ I16 <= I17 /\ I11 <= I14 - 1 /\ I15 <= I8 /\ 0 <= I8 - 1 /\ 0 <= I15 - 1 /\ I11 = I12] 56.69/56.51 3) f7#(I18, I19, I20, I21, I22, I23, I24) -> f8#(I25, I18, I22, I18, I18, I22, I23) [0 <= I25 - 1 /\ 0 <= I20 - 1 /\ I22 <= I21 - 1 /\ I25 <= I20] 56.69/56.51 4) f7#(I26, I27, I28, I29, I30, I31, I32) -> f7#(I26, I27, I33, I29 + 1, I30, I31, I34) [0 <= I33 - 1 /\ 0 <= I28 - 1 /\ I33 <= I28 /\ I29 <= I31 - 1 /\ I29 <= I30 /\ I30 + I27 + 1 - I29 <= I31 - 1] 56.69/56.51 5) f6#(I35, I36, I37, I38, I39, I40, I41) -> f6#(I35, I36, I42, I38 + 1, I38 + 1, I40, I41) [I38 = I39 /\ 0 <= I42 - 1 /\ 0 <= I37 - 1 /\ I42 <= I37 /\ I38 <= I41 - 1 /\ I38 <= I40] 56.69/56.51 6) f6#(I43, I44, I45, I46, I47, I48, I49) -> f7#(I43, I48, I50, I48 + 1, I44, I49, I51) [I46 = I47 /\ 0 <= I50 - 1 /\ 0 <= I45 - 1 /\ I48 <= I46 - 1 /\ I50 <= I45] 56.69/56.51 7) f5#(I52, I53, I54, I55, I56, I57, I58) -> f6#(I52, I53, I59, I52, I52, I54, I56) [0 <= I59 - 1 /\ 0 <= I55 - 1 /\ -1 <= I56 - 1 /\ I59 <= I55] 56.69/56.51 8) f4#(I60, I61, I62, I63, I64, I65, I66) -> f6#(I62, I63, I67, I62, I62, I68, I64) [0 <= I62 + I63 - 2 * I68 /\ I62 + I63 - 2 * I68 <= 1 /\ 0 <= I67 - 1 /\ 0 <= I61 - 1 /\ 0 <= I60 - 1 /\ I67 <= I61 /\ I67 <= I60 /\ -1 <= I64 - 1 /\ I68 <= I68 + 1 - 1 /\ I63 - (I68 + 1) <= I63 - I62 - 1 /\ I63 - I62 <= I68 - I62 /\ I62 <= I63 - 1] 56.69/56.51 9) f3#(I69, I70, I71, I72, I73, I74, I75) -> f4#(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 10) f4#(I80, I81, I82, I83, I84, I85, I86) -> f6#(I82, I83, I87, I82, I82, I88, I84) [0 <= I82 + I83 - 2 * I88 /\ I82 + I83 - 2 * I88 <= 1 /\ 0 <= I87 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I87 <= I81 /\ I87 <= I80 /\ -1 <= I84 - 1 /\ I83 - I82 <= I83 - (I88 + 1) /\ I83 - I82 <= I88 - I82 /\ I82 <= I83 - 1] 56.69/56.51 11) f3#(I89, I90, I91, I92, I93, I94, I95) -> f4#(I89, I90, I91, I92, I93, I96, I97) [I91 <= I92 - 1 /\ I92 - I91 <= I98 - I91 /\ I92 - I91 <= I92 - (I98 + 1) /\ -1 <= I93 - 1 /\ I99 <= I89 /\ I99 <= I90 /\ 0 <= I89 - 1 /\ 0 <= I90 - 1 /\ 0 <= I99 - 1] 56.69/56.51 12) f4#(I100, I101, I102, I103, I104, I105, I106) -> f5#(I102, I103, I107, I108, I104, I109, I110) [0 <= I102 + I103 - 2 * I107 /\ I102 + I103 - 2 * I107 <= 1 /\ 0 <= I108 - 1 /\ 0 <= I101 - 1 /\ 0 <= I100 - 1 /\ I108 <= I101 /\ I108 <= I100 /\ I103 - (I107 + 1) <= I103 - I102 - 1 /\ I107 <= I107 + 1 - 1 /\ I107 - I102 <= I103 - I102 - 1 /\ I102 <= I103 - 1] 56.69/56.51 13) f3#(I111, I112, I113, I114, I115, I116, I117) -> f4#(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 14) f4#(I122, I123, I124, I125, I126, I127, I128) -> f5#(I124, I125, I129, I130, I126, I131, I132) [0 <= I124 + I125 - 2 * I129 /\ I124 + I125 - 2 * I129 <= 1 /\ 0 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1 /\ I130 <= I123 /\ I130 <= I122 /\ I125 - I124 <= I125 - (I129 + 1) /\ I129 - I124 <= I125 - I124 - 1 /\ I124 <= I125 - 1] 56.69/56.51 15) f3#(I133, I134, I135, I136, I137, I138, I139) -> f4#(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 16) f4#(I144, I145, I146, I147, I148, I149, I150) -> f3#(I151, I152, I153, I147, I148, I154, I155) [I146 <= I147 - 1 /\ I156 - I146 <= I147 - I146 - 1 /\ I156 <= I156 + 1 - 1 /\ I147 - (I156 + 1) <= I147 - I146 - 1 /\ I151 <= I144 /\ I151 <= I145 /\ I152 <= I144 /\ I152 <= I145 /\ 0 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I151 - 1 /\ 0 <= I152 - 1 /\ I146 + I147 - 2 * I156 <= 1 /\ 0 <= I146 + I147 - 2 * I156 /\ I156 + 1 = I153] 56.69/56.51 17) f3#(I157, I158, I159, I160, I161, I162, I163) -> f4#(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 18) f4#(I168, I169, I170, I171, I172, I173, I174) -> f3#(I175, I176, I177, I171, I172, I178, I179) [I170 <= I171 - 1 /\ I171 - I170 <= I180 - I170 /\ I171 - (I180 + 1) <= I171 - I170 - 1 /\ I180 <= I180 + 1 - 1 /\ I175 <= I168 /\ I175 <= I169 /\ I176 <= I168 /\ I176 <= I169 /\ 0 <= I168 - 1 /\ 0 <= I169 - 1 /\ 0 <= I175 - 1 /\ 0 <= I176 - 1 /\ I170 + I171 - 2 * I180 <= 1 /\ 0 <= I170 + I171 - 2 * I180 /\ I180 + 1 = I177] 56.69/56.51 19) f3#(I181, I182, I183, I184, I185, I186, I187) -> f4#(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 20) f4#(I193, I194, I195, I196, I197, I198, I199) -> f3#(I200, I201, I195, I202, I197, I203, I204) [0 <= I195 + I196 - 2 * I202 /\ I195 + I196 - 2 * I202 <= 1 /\ 0 <= I201 - 1 /\ 0 <= I200 - 1 /\ 0 <= I194 - 1 /\ 0 <= I193 - 1 /\ I201 <= I194 /\ I201 <= I193 /\ I200 <= I194 /\ I200 <= I193 /\ I202 - I195 <= I196 - I195 - 1 /\ I195 <= I196 - 1] 56.69/56.51 21) f3#(I205, I206, I207, I208, I209, I210, I211) -> f4#(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 22) f2#(I217, I218, I219, I220, I221, I222, I223) -> f3#(I224, I225, 0, I219 - 1, I219, I226, I227) [0 <= I225 - 1 /\ 0 <= I224 - 1 /\ 0 <= I217 - 1 /\ I225 <= I217 /\ I224 <= I217 /\ I219 <= I218 /\ -1 <= I219 - 1 /\ I219 - 1 <= I219 - 1] 56.69/56.51 23) f2#(I228, I229, I230, I231, I232, I233, I234) -> f2#(I235, I229 + 1, I230, I236, I237, I238, I239) [0 <= I235 - 1 /\ 0 <= I228 - 1 /\ I229 <= I230 - 1 /\ I235 <= I228] 56.69/56.51 24) f1#(I240, I241, I242, I243, I244, I245, I246) -> f2#(I247, 0, I241, I248, I249, I250, I251) [0 <= I247 - 1 /\ 0 <= I240 - 1 /\ -1 <= I241 - 1 /\ I247 <= I240] 56.69/56.51 56.69/56.51 We have the following SCCs. 56.69/56.51 { 23 } 56.69/56.51 { 9, 13, 15, 16, 17, 19, 20, 21 } 56.69/56.51 { 5 } 56.69/56.51 { 4 } 56.69/56.51 { 1, 2 } 56.69/56.51 56.69/56.51 DP problem for innermost termination. 56.69/56.51 P = 56.69/56.51 f8#(I0, I1, I2, I3, I4, I5, I6) -> f8#(I7, I1 + 1, I2, I3 + 1, I3 + 1, I5, I6) [I3 <= I5 /\ I1 <= I6 - 1 /\ I2 <= I6 - 1 /\ y2 <= y1 - 1 /\ I3 <= I6 - 1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I3 = I4] 56.69/56.51 f8#(I8, I9, I10, I11, I12, I13, I14) -> f8#(I15, I9, I10 - 1, I11 + 1, I11 + 1, I13, I14) [I11 <= I13 /\ I9 <= I14 - 1 /\ I10 <= I14 - 1 /\ I16 <= I17 /\ I11 <= I14 - 1 /\ I15 <= I8 /\ 0 <= I8 - 1 /\ 0 <= I15 - 1 /\ I11 = I12] 56.69/56.51 R = 56.69/56.51 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 56.69/56.51 f8(I0, I1, I2, I3, I4, I5, I6) -> f8(I7, I1 + 1, I2, I3 + 1, I3 + 1, I5, I6) [I3 <= I5 /\ I1 <= I6 - 1 /\ I2 <= I6 - 1 /\ y2 <= y1 - 1 /\ I3 <= I6 - 1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I3 = I4] 56.69/56.51 f8(I8, I9, I10, I11, I12, I13, I14) -> f8(I15, I9, I10 - 1, I11 + 1, I11 + 1, I13, I14) [I11 <= I13 /\ I9 <= I14 - 1 /\ I10 <= I14 - 1 /\ I16 <= I17 /\ I11 <= I14 - 1 /\ I15 <= I8 /\ 0 <= I8 - 1 /\ 0 <= I15 - 1 /\ I11 = I12] 56.69/56.51 f7(I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I18, I22, I18, I18, I22, I23) [0 <= I25 - 1 /\ 0 <= I20 - 1 /\ I22 <= I21 - 1 /\ I25 <= I20] 56.69/56.51 f7(I26, I27, I28, I29, I30, I31, I32) -> f7(I26, I27, I33, I29 + 1, I30, I31, I34) [0 <= I33 - 1 /\ 0 <= I28 - 1 /\ I33 <= I28 /\ I29 <= I31 - 1 /\ I29 <= I30 /\ I30 + I27 + 1 - I29 <= I31 - 1] 56.69/56.51 f6(I35, I36, I37, I38, I39, I40, I41) -> f6(I35, I36, I42, I38 + 1, I38 + 1, I40, I41) [I38 = I39 /\ 0 <= I42 - 1 /\ 0 <= I37 - 1 /\ I42 <= I37 /\ I38 <= I41 - 1 /\ I38 <= I40] 56.69/56.51 f6(I43, I44, I45, I46, I47, I48, I49) -> f7(I43, I48, I50, I48 + 1, I44, I49, I51) [I46 = I47 /\ 0 <= I50 - 1 /\ 0 <= I45 - 1 /\ I48 <= I46 - 1 /\ I50 <= I45] 56.69/56.51 f5(I52, I53, I54, I55, I56, I57, I58) -> f6(I52, I53, I59, I52, I52, I54, I56) [0 <= I59 - 1 /\ 0 <= I55 - 1 /\ -1 <= I56 - 1 /\ I59 <= I55] 56.69/56.51 f4(I60, I61, I62, I63, I64, I65, I66) -> f6(I62, I63, I67, I62, I62, I68, I64) [0 <= I62 + I63 - 2 * I68 /\ I62 + I63 - 2 * I68 <= 1 /\ 0 <= I67 - 1 /\ 0 <= I61 - 1 /\ 0 <= I60 - 1 /\ I67 <= I61 /\ I67 <= I60 /\ -1 <= I64 - 1 /\ I68 <= I68 + 1 - 1 /\ I63 - (I68 + 1) <= I63 - I62 - 1 /\ I63 - I62 <= I68 - I62 /\ I62 <= I63 - 1] 56.69/56.51 f3(I69, I70, I71, I72, I73, I74, I75) -> f4(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 f4(I80, I81, I82, I83, I84, I85, I86) -> f6(I82, I83, I87, I82, I82, I88, I84) [0 <= I82 + I83 - 2 * I88 /\ I82 + I83 - 2 * I88 <= 1 /\ 0 <= I87 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I87 <= I81 /\ I87 <= I80 /\ -1 <= I84 - 1 /\ I83 - I82 <= I83 - (I88 + 1) /\ I83 - I82 <= I88 - I82 /\ I82 <= I83 - 1] 56.69/56.51 f3(I89, I90, I91, I92, I93, I94, I95) -> f4(I89, I90, I91, I92, I93, I96, I97) [I91 <= I92 - 1 /\ I92 - I91 <= I98 - I91 /\ I92 - I91 <= I92 - (I98 + 1) /\ -1 <= I93 - 1 /\ I99 <= I89 /\ I99 <= I90 /\ 0 <= I89 - 1 /\ 0 <= I90 - 1 /\ 0 <= I99 - 1] 56.69/56.51 f4(I100, I101, I102, I103, I104, I105, I106) -> f5(I102, I103, I107, I108, I104, I109, I110) [0 <= I102 + I103 - 2 * I107 /\ I102 + I103 - 2 * I107 <= 1 /\ 0 <= I108 - 1 /\ 0 <= I101 - 1 /\ 0 <= I100 - 1 /\ I108 <= I101 /\ I108 <= I100 /\ I103 - (I107 + 1) <= I103 - I102 - 1 /\ I107 <= I107 + 1 - 1 /\ I107 - I102 <= I103 - I102 - 1 /\ I102 <= I103 - 1] 56.69/56.51 f3(I111, I112, I113, I114, I115, I116, I117) -> f4(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 f4(I122, I123, I124, I125, I126, I127, I128) -> f5(I124, I125, I129, I130, I126, I131, I132) [0 <= I124 + I125 - 2 * I129 /\ I124 + I125 - 2 * I129 <= 1 /\ 0 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1 /\ I130 <= I123 /\ I130 <= I122 /\ I125 - I124 <= I125 - (I129 + 1) /\ I129 - I124 <= I125 - I124 - 1 /\ I124 <= I125 - 1] 56.69/56.51 f3(I133, I134, I135, I136, I137, I138, I139) -> f4(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 f4(I144, I145, I146, I147, I148, I149, I150) -> f3(I151, I152, I153, I147, I148, I154, I155) [I146 <= I147 - 1 /\ I156 - I146 <= I147 - I146 - 1 /\ I156 <= I156 + 1 - 1 /\ I147 - (I156 + 1) <= I147 - I146 - 1 /\ I151 <= I144 /\ I151 <= I145 /\ I152 <= I144 /\ I152 <= I145 /\ 0 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I151 - 1 /\ 0 <= I152 - 1 /\ I146 + I147 - 2 * I156 <= 1 /\ 0 <= I146 + I147 - 2 * I156 /\ I156 + 1 = I153] 56.69/56.51 f3(I157, I158, I159, I160, I161, I162, I163) -> f4(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 f4(I168, I169, I170, I171, I172, I173, I174) -> f3(I175, I176, I177, I171, I172, I178, I179) [I170 <= I171 - 1 /\ I171 - I170 <= I180 - I170 /\ I171 - (I180 + 1) <= I171 - I170 - 1 /\ I180 <= I180 + 1 - 1 /\ I175 <= I168 /\ I175 <= I169 /\ I176 <= I168 /\ I176 <= I169 /\ 0 <= I168 - 1 /\ 0 <= I169 - 1 /\ 0 <= I175 - 1 /\ 0 <= I176 - 1 /\ I170 + I171 - 2 * I180 <= 1 /\ 0 <= I170 + I171 - 2 * I180 /\ I180 + 1 = I177] 56.69/56.51 f3(I181, I182, I183, I184, I185, I186, I187) -> f4(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 f4(I193, I194, I195, I196, I197, I198, I199) -> f3(I200, I201, I195, I202, I197, I203, I204) [0 <= I195 + I196 - 2 * I202 /\ I195 + I196 - 2 * I202 <= 1 /\ 0 <= I201 - 1 /\ 0 <= I200 - 1 /\ 0 <= I194 - 1 /\ 0 <= I193 - 1 /\ I201 <= I194 /\ I201 <= I193 /\ I200 <= I194 /\ I200 <= I193 /\ I202 - I195 <= I196 - I195 - 1 /\ I195 <= I196 - 1] 56.69/56.51 f3(I205, I206, I207, I208, I209, I210, I211) -> f4(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 f2(I217, I218, I219, I220, I221, I222, I223) -> f3(I224, I225, 0, I219 - 1, I219, I226, I227) [0 <= I225 - 1 /\ 0 <= I224 - 1 /\ 0 <= I217 - 1 /\ I225 <= I217 /\ I224 <= I217 /\ I219 <= I218 /\ -1 <= I219 - 1 /\ I219 - 1 <= I219 - 1] 56.69/56.51 f2(I228, I229, I230, I231, I232, I233, I234) -> f2(I235, I229 + 1, I230, I236, I237, I238, I239) [0 <= I235 - 1 /\ 0 <= I228 - 1 /\ I229 <= I230 - 1 /\ I235 <= I228] 56.69/56.51 f1(I240, I241, I242, I243, I244, I245, I246) -> f2(I247, 0, I241, I248, I249, I250, I251) [0 <= I247 - 1 /\ 0 <= I240 - 1 /\ -1 <= I241 - 1 /\ I247 <= I240] 56.69/56.51 56.69/56.51 We use the reverse value criterion with the projection function NU: 56.69/56.51 NU[f8#(z1,z2,z3,z4,z5,z6,z7)] = z6 + -1 * z4 56.69/56.51 56.69/56.51 This gives the following inequalities: 56.69/56.51 I3 <= I5 /\ I1 <= I6 - 1 /\ I2 <= I6 - 1 /\ y2 <= y1 - 1 /\ I3 <= I6 - 1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I3 = I4 ==> I5 + -1 * I3 > I5 + -1 * (I3 + 1) with I5 + -1 * I3 >= 0 56.69/56.51 I11 <= I13 /\ I9 <= I14 - 1 /\ I10 <= I14 - 1 /\ I16 <= I17 /\ I11 <= I14 - 1 /\ I15 <= I8 /\ 0 <= I8 - 1 /\ 0 <= I15 - 1 /\ I11 = I12 ==> I13 + -1 * I11 > I13 + -1 * (I11 + 1) with I13 + -1 * I11 >= 0 56.69/56.51 56.69/56.51 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 56.69/56.51 56.69/56.51 DP problem for innermost termination. 56.69/56.51 P = 56.69/56.51 f7#(I26, I27, I28, I29, I30, I31, I32) -> f7#(I26, I27, I33, I29 + 1, I30, I31, I34) [0 <= I33 - 1 /\ 0 <= I28 - 1 /\ I33 <= I28 /\ I29 <= I31 - 1 /\ I29 <= I30 /\ I30 + I27 + 1 - I29 <= I31 - 1] 56.69/56.51 R = 56.69/56.51 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 56.69/56.51 f8(I0, I1, I2, I3, I4, I5, I6) -> f8(I7, I1 + 1, I2, I3 + 1, I3 + 1, I5, I6) [I3 <= I5 /\ I1 <= I6 - 1 /\ I2 <= I6 - 1 /\ y2 <= y1 - 1 /\ I3 <= I6 - 1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I3 = I4] 56.69/56.51 f8(I8, I9, I10, I11, I12, I13, I14) -> f8(I15, I9, I10 - 1, I11 + 1, I11 + 1, I13, I14) [I11 <= I13 /\ I9 <= I14 - 1 /\ I10 <= I14 - 1 /\ I16 <= I17 /\ I11 <= I14 - 1 /\ I15 <= I8 /\ 0 <= I8 - 1 /\ 0 <= I15 - 1 /\ I11 = I12] 56.69/56.51 f7(I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I18, I22, I18, I18, I22, I23) [0 <= I25 - 1 /\ 0 <= I20 - 1 /\ I22 <= I21 - 1 /\ I25 <= I20] 56.69/56.51 f7(I26, I27, I28, I29, I30, I31, I32) -> f7(I26, I27, I33, I29 + 1, I30, I31, I34) [0 <= I33 - 1 /\ 0 <= I28 - 1 /\ I33 <= I28 /\ I29 <= I31 - 1 /\ I29 <= I30 /\ I30 + I27 + 1 - I29 <= I31 - 1] 56.69/56.51 f6(I35, I36, I37, I38, I39, I40, I41) -> f6(I35, I36, I42, I38 + 1, I38 + 1, I40, I41) [I38 = I39 /\ 0 <= I42 - 1 /\ 0 <= I37 - 1 /\ I42 <= I37 /\ I38 <= I41 - 1 /\ I38 <= I40] 56.69/56.51 f6(I43, I44, I45, I46, I47, I48, I49) -> f7(I43, I48, I50, I48 + 1, I44, I49, I51) [I46 = I47 /\ 0 <= I50 - 1 /\ 0 <= I45 - 1 /\ I48 <= I46 - 1 /\ I50 <= I45] 56.69/56.51 f5(I52, I53, I54, I55, I56, I57, I58) -> f6(I52, I53, I59, I52, I52, I54, I56) [0 <= I59 - 1 /\ 0 <= I55 - 1 /\ -1 <= I56 - 1 /\ I59 <= I55] 56.69/56.51 f4(I60, I61, I62, I63, I64, I65, I66) -> f6(I62, I63, I67, I62, I62, I68, I64) [0 <= I62 + I63 - 2 * I68 /\ I62 + I63 - 2 * I68 <= 1 /\ 0 <= I67 - 1 /\ 0 <= I61 - 1 /\ 0 <= I60 - 1 /\ I67 <= I61 /\ I67 <= I60 /\ -1 <= I64 - 1 /\ I68 <= I68 + 1 - 1 /\ I63 - (I68 + 1) <= I63 - I62 - 1 /\ I63 - I62 <= I68 - I62 /\ I62 <= I63 - 1] 56.69/56.51 f3(I69, I70, I71, I72, I73, I74, I75) -> f4(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 f4(I80, I81, I82, I83, I84, I85, I86) -> f6(I82, I83, I87, I82, I82, I88, I84) [0 <= I82 + I83 - 2 * I88 /\ I82 + I83 - 2 * I88 <= 1 /\ 0 <= I87 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I87 <= I81 /\ I87 <= I80 /\ -1 <= I84 - 1 /\ I83 - I82 <= I83 - (I88 + 1) /\ I83 - I82 <= I88 - I82 /\ I82 <= I83 - 1] 56.69/56.51 f3(I89, I90, I91, I92, I93, I94, I95) -> f4(I89, I90, I91, I92, I93, I96, I97) [I91 <= I92 - 1 /\ I92 - I91 <= I98 - I91 /\ I92 - I91 <= I92 - (I98 + 1) /\ -1 <= I93 - 1 /\ I99 <= I89 /\ I99 <= I90 /\ 0 <= I89 - 1 /\ 0 <= I90 - 1 /\ 0 <= I99 - 1] 56.69/56.51 f4(I100, I101, I102, I103, I104, I105, I106) -> f5(I102, I103, I107, I108, I104, I109, I110) [0 <= I102 + I103 - 2 * I107 /\ I102 + I103 - 2 * I107 <= 1 /\ 0 <= I108 - 1 /\ 0 <= I101 - 1 /\ 0 <= I100 - 1 /\ I108 <= I101 /\ I108 <= I100 /\ I103 - (I107 + 1) <= I103 - I102 - 1 /\ I107 <= I107 + 1 - 1 /\ I107 - I102 <= I103 - I102 - 1 /\ I102 <= I103 - 1] 56.69/56.51 f3(I111, I112, I113, I114, I115, I116, I117) -> f4(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 f4(I122, I123, I124, I125, I126, I127, I128) -> f5(I124, I125, I129, I130, I126, I131, I132) [0 <= I124 + I125 - 2 * I129 /\ I124 + I125 - 2 * I129 <= 1 /\ 0 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1 /\ I130 <= I123 /\ I130 <= I122 /\ I125 - I124 <= I125 - (I129 + 1) /\ I129 - I124 <= I125 - I124 - 1 /\ I124 <= I125 - 1] 56.69/56.51 f3(I133, I134, I135, I136, I137, I138, I139) -> f4(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 f4(I144, I145, I146, I147, I148, I149, I150) -> f3(I151, I152, I153, I147, I148, I154, I155) [I146 <= I147 - 1 /\ I156 - I146 <= I147 - I146 - 1 /\ I156 <= I156 + 1 - 1 /\ I147 - (I156 + 1) <= I147 - I146 - 1 /\ I151 <= I144 /\ I151 <= I145 /\ I152 <= I144 /\ I152 <= I145 /\ 0 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I151 - 1 /\ 0 <= I152 - 1 /\ I146 + I147 - 2 * I156 <= 1 /\ 0 <= I146 + I147 - 2 * I156 /\ I156 + 1 = I153] 56.69/56.51 f3(I157, I158, I159, I160, I161, I162, I163) -> f4(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 f4(I168, I169, I170, I171, I172, I173, I174) -> f3(I175, I176, I177, I171, I172, I178, I179) [I170 <= I171 - 1 /\ I171 - I170 <= I180 - I170 /\ I171 - (I180 + 1) <= I171 - I170 - 1 /\ I180 <= I180 + 1 - 1 /\ I175 <= I168 /\ I175 <= I169 /\ I176 <= I168 /\ I176 <= I169 /\ 0 <= I168 - 1 /\ 0 <= I169 - 1 /\ 0 <= I175 - 1 /\ 0 <= I176 - 1 /\ I170 + I171 - 2 * I180 <= 1 /\ 0 <= I170 + I171 - 2 * I180 /\ I180 + 1 = I177] 56.69/56.51 f3(I181, I182, I183, I184, I185, I186, I187) -> f4(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 f4(I193, I194, I195, I196, I197, I198, I199) -> f3(I200, I201, I195, I202, I197, I203, I204) [0 <= I195 + I196 - 2 * I202 /\ I195 + I196 - 2 * I202 <= 1 /\ 0 <= I201 - 1 /\ 0 <= I200 - 1 /\ 0 <= I194 - 1 /\ 0 <= I193 - 1 /\ I201 <= I194 /\ I201 <= I193 /\ I200 <= I194 /\ I200 <= I193 /\ I202 - I195 <= I196 - I195 - 1 /\ I195 <= I196 - 1] 56.69/56.51 f3(I205, I206, I207, I208, I209, I210, I211) -> f4(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 f2(I217, I218, I219, I220, I221, I222, I223) -> f3(I224, I225, 0, I219 - 1, I219, I226, I227) [0 <= I225 - 1 /\ 0 <= I224 - 1 /\ 0 <= I217 - 1 /\ I225 <= I217 /\ I224 <= I217 /\ I219 <= I218 /\ -1 <= I219 - 1 /\ I219 - 1 <= I219 - 1] 56.69/56.51 f2(I228, I229, I230, I231, I232, I233, I234) -> f2(I235, I229 + 1, I230, I236, I237, I238, I239) [0 <= I235 - 1 /\ 0 <= I228 - 1 /\ I229 <= I230 - 1 /\ I235 <= I228] 56.69/56.51 f1(I240, I241, I242, I243, I244, I245, I246) -> f2(I247, 0, I241, I248, I249, I250, I251) [0 <= I247 - 1 /\ 0 <= I240 - 1 /\ -1 <= I241 - 1 /\ I247 <= I240] 56.69/56.51 56.69/56.51 We use the reverse value criterion with the projection function NU: 56.69/56.51 NU[f7#(z1,z2,z3,z4,z5,z6,z7)] = z6 - 1 + -1 * z4 56.69/56.51 56.69/56.51 This gives the following inequalities: 56.69/56.51 0 <= I33 - 1 /\ 0 <= I28 - 1 /\ I33 <= I28 /\ I29 <= I31 - 1 /\ I29 <= I30 /\ I30 + I27 + 1 - I29 <= I31 - 1 ==> I31 - 1 + -1 * I29 > I31 - 1 + -1 * (I29 + 1) with I31 - 1 + -1 * I29 >= 0 56.69/56.51 56.69/56.51 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 56.69/56.51 56.69/56.51 DP problem for innermost termination. 56.69/56.51 P = 56.69/56.51 f6#(I35, I36, I37, I38, I39, I40, I41) -> f6#(I35, I36, I42, I38 + 1, I38 + 1, I40, I41) [I38 = I39 /\ 0 <= I42 - 1 /\ 0 <= I37 - 1 /\ I42 <= I37 /\ I38 <= I41 - 1 /\ I38 <= I40] 56.69/56.51 R = 56.69/56.51 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 56.69/56.51 f8(I0, I1, I2, I3, I4, I5, I6) -> f8(I7, I1 + 1, I2, I3 + 1, I3 + 1, I5, I6) [I3 <= I5 /\ I1 <= I6 - 1 /\ I2 <= I6 - 1 /\ y2 <= y1 - 1 /\ I3 <= I6 - 1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I3 = I4] 56.69/56.51 f8(I8, I9, I10, I11, I12, I13, I14) -> f8(I15, I9, I10 - 1, I11 + 1, I11 + 1, I13, I14) [I11 <= I13 /\ I9 <= I14 - 1 /\ I10 <= I14 - 1 /\ I16 <= I17 /\ I11 <= I14 - 1 /\ I15 <= I8 /\ 0 <= I8 - 1 /\ 0 <= I15 - 1 /\ I11 = I12] 56.69/56.51 f7(I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I18, I22, I18, I18, I22, I23) [0 <= I25 - 1 /\ 0 <= I20 - 1 /\ I22 <= I21 - 1 /\ I25 <= I20] 56.69/56.51 f7(I26, I27, I28, I29, I30, I31, I32) -> f7(I26, I27, I33, I29 + 1, I30, I31, I34) [0 <= I33 - 1 /\ 0 <= I28 - 1 /\ I33 <= I28 /\ I29 <= I31 - 1 /\ I29 <= I30 /\ I30 + I27 + 1 - I29 <= I31 - 1] 56.69/56.51 f6(I35, I36, I37, I38, I39, I40, I41) -> f6(I35, I36, I42, I38 + 1, I38 + 1, I40, I41) [I38 = I39 /\ 0 <= I42 - 1 /\ 0 <= I37 - 1 /\ I42 <= I37 /\ I38 <= I41 - 1 /\ I38 <= I40] 56.69/56.51 f6(I43, I44, I45, I46, I47, I48, I49) -> f7(I43, I48, I50, I48 + 1, I44, I49, I51) [I46 = I47 /\ 0 <= I50 - 1 /\ 0 <= I45 - 1 /\ I48 <= I46 - 1 /\ I50 <= I45] 56.69/56.51 f5(I52, I53, I54, I55, I56, I57, I58) -> f6(I52, I53, I59, I52, I52, I54, I56) [0 <= I59 - 1 /\ 0 <= I55 - 1 /\ -1 <= I56 - 1 /\ I59 <= I55] 56.69/56.51 f4(I60, I61, I62, I63, I64, I65, I66) -> f6(I62, I63, I67, I62, I62, I68, I64) [0 <= I62 + I63 - 2 * I68 /\ I62 + I63 - 2 * I68 <= 1 /\ 0 <= I67 - 1 /\ 0 <= I61 - 1 /\ 0 <= I60 - 1 /\ I67 <= I61 /\ I67 <= I60 /\ -1 <= I64 - 1 /\ I68 <= I68 + 1 - 1 /\ I63 - (I68 + 1) <= I63 - I62 - 1 /\ I63 - I62 <= I68 - I62 /\ I62 <= I63 - 1] 56.69/56.51 f3(I69, I70, I71, I72, I73, I74, I75) -> f4(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 f4(I80, I81, I82, I83, I84, I85, I86) -> f6(I82, I83, I87, I82, I82, I88, I84) [0 <= I82 + I83 - 2 * I88 /\ I82 + I83 - 2 * I88 <= 1 /\ 0 <= I87 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I87 <= I81 /\ I87 <= I80 /\ -1 <= I84 - 1 /\ I83 - I82 <= I83 - (I88 + 1) /\ I83 - I82 <= I88 - I82 /\ I82 <= I83 - 1] 56.69/56.51 f3(I89, I90, I91, I92, I93, I94, I95) -> f4(I89, I90, I91, I92, I93, I96, I97) [I91 <= I92 - 1 /\ I92 - I91 <= I98 - I91 /\ I92 - I91 <= I92 - (I98 + 1) /\ -1 <= I93 - 1 /\ I99 <= I89 /\ I99 <= I90 /\ 0 <= I89 - 1 /\ 0 <= I90 - 1 /\ 0 <= I99 - 1] 56.69/56.51 f4(I100, I101, I102, I103, I104, I105, I106) -> f5(I102, I103, I107, I108, I104, I109, I110) [0 <= I102 + I103 - 2 * I107 /\ I102 + I103 - 2 * I107 <= 1 /\ 0 <= I108 - 1 /\ 0 <= I101 - 1 /\ 0 <= I100 - 1 /\ I108 <= I101 /\ I108 <= I100 /\ I103 - (I107 + 1) <= I103 - I102 - 1 /\ I107 <= I107 + 1 - 1 /\ I107 - I102 <= I103 - I102 - 1 /\ I102 <= I103 - 1] 56.69/56.51 f3(I111, I112, I113, I114, I115, I116, I117) -> f4(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 f4(I122, I123, I124, I125, I126, I127, I128) -> f5(I124, I125, I129, I130, I126, I131, I132) [0 <= I124 + I125 - 2 * I129 /\ I124 + I125 - 2 * I129 <= 1 /\ 0 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1 /\ I130 <= I123 /\ I130 <= I122 /\ I125 - I124 <= I125 - (I129 + 1) /\ I129 - I124 <= I125 - I124 - 1 /\ I124 <= I125 - 1] 56.69/56.51 f3(I133, I134, I135, I136, I137, I138, I139) -> f4(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 f4(I144, I145, I146, I147, I148, I149, I150) -> f3(I151, I152, I153, I147, I148, I154, I155) [I146 <= I147 - 1 /\ I156 - I146 <= I147 - I146 - 1 /\ I156 <= I156 + 1 - 1 /\ I147 - (I156 + 1) <= I147 - I146 - 1 /\ I151 <= I144 /\ I151 <= I145 /\ I152 <= I144 /\ I152 <= I145 /\ 0 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I151 - 1 /\ 0 <= I152 - 1 /\ I146 + I147 - 2 * I156 <= 1 /\ 0 <= I146 + I147 - 2 * I156 /\ I156 + 1 = I153] 56.69/56.51 f3(I157, I158, I159, I160, I161, I162, I163) -> f4(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 f4(I168, I169, I170, I171, I172, I173, I174) -> f3(I175, I176, I177, I171, I172, I178, I179) [I170 <= I171 - 1 /\ I171 - I170 <= I180 - I170 /\ I171 - (I180 + 1) <= I171 - I170 - 1 /\ I180 <= I180 + 1 - 1 /\ I175 <= I168 /\ I175 <= I169 /\ I176 <= I168 /\ I176 <= I169 /\ 0 <= I168 - 1 /\ 0 <= I169 - 1 /\ 0 <= I175 - 1 /\ 0 <= I176 - 1 /\ I170 + I171 - 2 * I180 <= 1 /\ 0 <= I170 + I171 - 2 * I180 /\ I180 + 1 = I177] 56.69/56.51 f3(I181, I182, I183, I184, I185, I186, I187) -> f4(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 f4(I193, I194, I195, I196, I197, I198, I199) -> f3(I200, I201, I195, I202, I197, I203, I204) [0 <= I195 + I196 - 2 * I202 /\ I195 + I196 - 2 * I202 <= 1 /\ 0 <= I201 - 1 /\ 0 <= I200 - 1 /\ 0 <= I194 - 1 /\ 0 <= I193 - 1 /\ I201 <= I194 /\ I201 <= I193 /\ I200 <= I194 /\ I200 <= I193 /\ I202 - I195 <= I196 - I195 - 1 /\ I195 <= I196 - 1] 56.69/56.51 f3(I205, I206, I207, I208, I209, I210, I211) -> f4(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 f2(I217, I218, I219, I220, I221, I222, I223) -> f3(I224, I225, 0, I219 - 1, I219, I226, I227) [0 <= I225 - 1 /\ 0 <= I224 - 1 /\ 0 <= I217 - 1 /\ I225 <= I217 /\ I224 <= I217 /\ I219 <= I218 /\ -1 <= I219 - 1 /\ I219 - 1 <= I219 - 1] 56.69/56.51 f2(I228, I229, I230, I231, I232, I233, I234) -> f2(I235, I229 + 1, I230, I236, I237, I238, I239) [0 <= I235 - 1 /\ 0 <= I228 - 1 /\ I229 <= I230 - 1 /\ I235 <= I228] 56.69/56.51 f1(I240, I241, I242, I243, I244, I245, I246) -> f2(I247, 0, I241, I248, I249, I250, I251) [0 <= I247 - 1 /\ 0 <= I240 - 1 /\ -1 <= I241 - 1 /\ I247 <= I240] 56.69/56.51 56.69/56.51 We use the reverse value criterion with the projection function NU: 56.69/56.51 NU[f6#(z1,z2,z3,z4,z5,z6,z7)] = z7 - 1 + -1 * z4 56.69/56.51 56.69/56.51 This gives the following inequalities: 56.69/56.51 I38 = I39 /\ 0 <= I42 - 1 /\ 0 <= I37 - 1 /\ I42 <= I37 /\ I38 <= I41 - 1 /\ I38 <= I40 ==> I41 - 1 + -1 * I38 > I41 - 1 + -1 * (I38 + 1) with I41 - 1 + -1 * I38 >= 0 56.69/56.51 56.69/56.51 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 56.69/56.51 56.69/56.51 DP problem for innermost termination. 56.69/56.51 P = 56.69/56.51 f3#(I69, I70, I71, I72, I73, I74, I75) -> f4#(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 f3#(I111, I112, I113, I114, I115, I116, I117) -> f4#(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 f3#(I133, I134, I135, I136, I137, I138, I139) -> f4#(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 f4#(I144, I145, I146, I147, I148, I149, I150) -> f3#(I151, I152, I153, I147, I148, I154, I155) [I146 <= I147 - 1 /\ I156 - I146 <= I147 - I146 - 1 /\ I156 <= I156 + 1 - 1 /\ I147 - (I156 + 1) <= I147 - I146 - 1 /\ I151 <= I144 /\ I151 <= I145 /\ I152 <= I144 /\ I152 <= I145 /\ 0 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I151 - 1 /\ 0 <= I152 - 1 /\ I146 + I147 - 2 * I156 <= 1 /\ 0 <= I146 + I147 - 2 * I156 /\ I156 + 1 = I153] 56.69/56.51 f3#(I157, I158, I159, I160, I161, I162, I163) -> f4#(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 f3#(I181, I182, I183, I184, I185, I186, I187) -> f4#(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 f4#(I193, I194, I195, I196, I197, I198, I199) -> f3#(I200, I201, I195, I202, I197, I203, I204) [0 <= I195 + I196 - 2 * I202 /\ I195 + I196 - 2 * I202 <= 1 /\ 0 <= I201 - 1 /\ 0 <= I200 - 1 /\ 0 <= I194 - 1 /\ 0 <= I193 - 1 /\ I201 <= I194 /\ I201 <= I193 /\ I200 <= I194 /\ I200 <= I193 /\ I202 - I195 <= I196 - I195 - 1 /\ I195 <= I196 - 1] 56.69/56.51 f3#(I205, I206, I207, I208, I209, I210, I211) -> f4#(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 R = 56.69/56.51 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 56.69/56.51 f8(I0, I1, I2, I3, I4, I5, I6) -> f8(I7, I1 + 1, I2, I3 + 1, I3 + 1, I5, I6) [I3 <= I5 /\ I1 <= I6 - 1 /\ I2 <= I6 - 1 /\ y2 <= y1 - 1 /\ I3 <= I6 - 1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I3 = I4] 56.69/56.51 f8(I8, I9, I10, I11, I12, I13, I14) -> f8(I15, I9, I10 - 1, I11 + 1, I11 + 1, I13, I14) [I11 <= I13 /\ I9 <= I14 - 1 /\ I10 <= I14 - 1 /\ I16 <= I17 /\ I11 <= I14 - 1 /\ I15 <= I8 /\ 0 <= I8 - 1 /\ 0 <= I15 - 1 /\ I11 = I12] 56.69/56.51 f7(I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I18, I22, I18, I18, I22, I23) [0 <= I25 - 1 /\ 0 <= I20 - 1 /\ I22 <= I21 - 1 /\ I25 <= I20] 56.69/56.51 f7(I26, I27, I28, I29, I30, I31, I32) -> f7(I26, I27, I33, I29 + 1, I30, I31, I34) [0 <= I33 - 1 /\ 0 <= I28 - 1 /\ I33 <= I28 /\ I29 <= I31 - 1 /\ I29 <= I30 /\ I30 + I27 + 1 - I29 <= I31 - 1] 56.69/56.51 f6(I35, I36, I37, I38, I39, I40, I41) -> f6(I35, I36, I42, I38 + 1, I38 + 1, I40, I41) [I38 = I39 /\ 0 <= I42 - 1 /\ 0 <= I37 - 1 /\ I42 <= I37 /\ I38 <= I41 - 1 /\ I38 <= I40] 56.69/56.51 f6(I43, I44, I45, I46, I47, I48, I49) -> f7(I43, I48, I50, I48 + 1, I44, I49, I51) [I46 = I47 /\ 0 <= I50 - 1 /\ 0 <= I45 - 1 /\ I48 <= I46 - 1 /\ I50 <= I45] 56.69/56.51 f5(I52, I53, I54, I55, I56, I57, I58) -> f6(I52, I53, I59, I52, I52, I54, I56) [0 <= I59 - 1 /\ 0 <= I55 - 1 /\ -1 <= I56 - 1 /\ I59 <= I55] 56.69/56.51 f4(I60, I61, I62, I63, I64, I65, I66) -> f6(I62, I63, I67, I62, I62, I68, I64) [0 <= I62 + I63 - 2 * I68 /\ I62 + I63 - 2 * I68 <= 1 /\ 0 <= I67 - 1 /\ 0 <= I61 - 1 /\ 0 <= I60 - 1 /\ I67 <= I61 /\ I67 <= I60 /\ -1 <= I64 - 1 /\ I68 <= I68 + 1 - 1 /\ I63 - (I68 + 1) <= I63 - I62 - 1 /\ I63 - I62 <= I68 - I62 /\ I62 <= I63 - 1] 56.69/56.51 f3(I69, I70, I71, I72, I73, I74, I75) -> f4(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 f4(I80, I81, I82, I83, I84, I85, I86) -> f6(I82, I83, I87, I82, I82, I88, I84) [0 <= I82 + I83 - 2 * I88 /\ I82 + I83 - 2 * I88 <= 1 /\ 0 <= I87 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I87 <= I81 /\ I87 <= I80 /\ -1 <= I84 - 1 /\ I83 - I82 <= I83 - (I88 + 1) /\ I83 - I82 <= I88 - I82 /\ I82 <= I83 - 1] 56.69/56.51 f3(I89, I90, I91, I92, I93, I94, I95) -> f4(I89, I90, I91, I92, I93, I96, I97) [I91 <= I92 - 1 /\ I92 - I91 <= I98 - I91 /\ I92 - I91 <= I92 - (I98 + 1) /\ -1 <= I93 - 1 /\ I99 <= I89 /\ I99 <= I90 /\ 0 <= I89 - 1 /\ 0 <= I90 - 1 /\ 0 <= I99 - 1] 56.69/56.51 f4(I100, I101, I102, I103, I104, I105, I106) -> f5(I102, I103, I107, I108, I104, I109, I110) [0 <= I102 + I103 - 2 * I107 /\ I102 + I103 - 2 * I107 <= 1 /\ 0 <= I108 - 1 /\ 0 <= I101 - 1 /\ 0 <= I100 - 1 /\ I108 <= I101 /\ I108 <= I100 /\ I103 - (I107 + 1) <= I103 - I102 - 1 /\ I107 <= I107 + 1 - 1 /\ I107 - I102 <= I103 - I102 - 1 /\ I102 <= I103 - 1] 56.69/56.51 f3(I111, I112, I113, I114, I115, I116, I117) -> f4(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 f4(I122, I123, I124, I125, I126, I127, I128) -> f5(I124, I125, I129, I130, I126, I131, I132) [0 <= I124 + I125 - 2 * I129 /\ I124 + I125 - 2 * I129 <= 1 /\ 0 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1 /\ I130 <= I123 /\ I130 <= I122 /\ I125 - I124 <= I125 - (I129 + 1) /\ I129 - I124 <= I125 - I124 - 1 /\ I124 <= I125 - 1] 56.69/56.51 f3(I133, I134, I135, I136, I137, I138, I139) -> f4(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 f4(I144, I145, I146, I147, I148, I149, I150) -> f3(I151, I152, I153, I147, I148, I154, I155) [I146 <= I147 - 1 /\ I156 - I146 <= I147 - I146 - 1 /\ I156 <= I156 + 1 - 1 /\ I147 - (I156 + 1) <= I147 - I146 - 1 /\ I151 <= I144 /\ I151 <= I145 /\ I152 <= I144 /\ I152 <= I145 /\ 0 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I151 - 1 /\ 0 <= I152 - 1 /\ I146 + I147 - 2 * I156 <= 1 /\ 0 <= I146 + I147 - 2 * I156 /\ I156 + 1 = I153] 56.69/56.51 f3(I157, I158, I159, I160, I161, I162, I163) -> f4(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 f4(I168, I169, I170, I171, I172, I173, I174) -> f3(I175, I176, I177, I171, I172, I178, I179) [I170 <= I171 - 1 /\ I171 - I170 <= I180 - I170 /\ I171 - (I180 + 1) <= I171 - I170 - 1 /\ I180 <= I180 + 1 - 1 /\ I175 <= I168 /\ I175 <= I169 /\ I176 <= I168 /\ I176 <= I169 /\ 0 <= I168 - 1 /\ 0 <= I169 - 1 /\ 0 <= I175 - 1 /\ 0 <= I176 - 1 /\ I170 + I171 - 2 * I180 <= 1 /\ 0 <= I170 + I171 - 2 * I180 /\ I180 + 1 = I177] 56.69/56.51 f3(I181, I182, I183, I184, I185, I186, I187) -> f4(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 f4(I193, I194, I195, I196, I197, I198, I199) -> f3(I200, I201, I195, I202, I197, I203, I204) [0 <= I195 + I196 - 2 * I202 /\ I195 + I196 - 2 * I202 <= 1 /\ 0 <= I201 - 1 /\ 0 <= I200 - 1 /\ 0 <= I194 - 1 /\ 0 <= I193 - 1 /\ I201 <= I194 /\ I201 <= I193 /\ I200 <= I194 /\ I200 <= I193 /\ I202 - I195 <= I196 - I195 - 1 /\ I195 <= I196 - 1] 56.69/56.51 f3(I205, I206, I207, I208, I209, I210, I211) -> f4(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 f2(I217, I218, I219, I220, I221, I222, I223) -> f3(I224, I225, 0, I219 - 1, I219, I226, I227) [0 <= I225 - 1 /\ 0 <= I224 - 1 /\ 0 <= I217 - 1 /\ I225 <= I217 /\ I224 <= I217 /\ I219 <= I218 /\ -1 <= I219 - 1 /\ I219 - 1 <= I219 - 1] 56.69/56.51 f2(I228, I229, I230, I231, I232, I233, I234) -> f2(I235, I229 + 1, I230, I236, I237, I238, I239) [0 <= I235 - 1 /\ 0 <= I228 - 1 /\ I229 <= I230 - 1 /\ I235 <= I228] 56.69/56.51 f1(I240, I241, I242, I243, I244, I245, I246) -> f2(I247, 0, I241, I248, I249, I250, I251) [0 <= I247 - 1 /\ 0 <= I240 - 1 /\ -1 <= I241 - 1 /\ I247 <= I240] 56.69/56.51 56.69/56.51 We use the reverse value criterion with the projection function NU: 56.69/56.51 NU[f4#(z1,z2,z3,z4,z5,z6,z7)] = z4 - 1 + -1 * z3 56.69/56.51 NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = z4 - 1 + -1 * z3 56.69/56.51 56.69/56.51 This gives the following inequalities: 56.69/56.51 I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1 ==> I72 - 1 + -1 * I71 >= I72 - 1 + -1 * I71 56.69/56.51 I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1 ==> I114 - 1 + -1 * I113 >= I114 - 1 + -1 * I113 56.69/56.51 I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1 ==> I136 - 1 + -1 * I135 >= I136 - 1 + -1 * I135 56.69/56.51 I146 <= I147 - 1 /\ I156 - I146 <= I147 - I146 - 1 /\ I156 <= I156 + 1 - 1 /\ I147 - (I156 + 1) <= I147 - I146 - 1 /\ I151 <= I144 /\ I151 <= I145 /\ I152 <= I144 /\ I152 <= I145 /\ 0 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I151 - 1 /\ 0 <= I152 - 1 /\ I146 + I147 - 2 * I156 <= 1 /\ 0 <= I146 + I147 - 2 * I156 /\ I156 + 1 = I153 ==> I147 - 1 + -1 * I146 > I147 - 1 + -1 * I153 with I147 - 1 + -1 * I146 >= 0 56.69/56.51 I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1 ==> I160 - 1 + -1 * I159 >= I160 - 1 + -1 * I159 56.69/56.51 I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1 ==> I184 - 1 + -1 * I183 >= I184 - 1 + -1 * I183 56.69/56.51 0 <= I195 + I196 - 2 * I202 /\ I195 + I196 - 2 * I202 <= 1 /\ 0 <= I201 - 1 /\ 0 <= I200 - 1 /\ 0 <= I194 - 1 /\ 0 <= I193 - 1 /\ I201 <= I194 /\ I201 <= I193 /\ I200 <= I194 /\ I200 <= I193 /\ I202 - I195 <= I196 - I195 - 1 /\ I195 <= I196 - 1 ==> I196 - 1 + -1 * I195 > I202 - 1 + -1 * I195 with I196 - 1 + -1 * I195 >= 0 56.69/56.51 I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1 ==> I208 - 1 + -1 * I207 >= I208 - 1 + -1 * I207 56.69/56.51 56.69/56.51 We remove all the strictly oriented dependency pairs. 56.69/56.51 56.69/56.51 DP problem for innermost termination. 56.69/56.51 P = 56.69/56.51 f3#(I69, I70, I71, I72, I73, I74, I75) -> f4#(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 f3#(I111, I112, I113, I114, I115, I116, I117) -> f4#(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 f3#(I133, I134, I135, I136, I137, I138, I139) -> f4#(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 f3#(I157, I158, I159, I160, I161, I162, I163) -> f4#(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 f3#(I181, I182, I183, I184, I185, I186, I187) -> f4#(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 f3#(I205, I206, I207, I208, I209, I210, I211) -> f4#(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 R = 56.69/56.51 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 56.69/56.51 f8(I0, I1, I2, I3, I4, I5, I6) -> f8(I7, I1 + 1, I2, I3 + 1, I3 + 1, I5, I6) [I3 <= I5 /\ I1 <= I6 - 1 /\ I2 <= I6 - 1 /\ y2 <= y1 - 1 /\ I3 <= I6 - 1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I3 = I4] 56.69/56.51 f8(I8, I9, I10, I11, I12, I13, I14) -> f8(I15, I9, I10 - 1, I11 + 1, I11 + 1, I13, I14) [I11 <= I13 /\ I9 <= I14 - 1 /\ I10 <= I14 - 1 /\ I16 <= I17 /\ I11 <= I14 - 1 /\ I15 <= I8 /\ 0 <= I8 - 1 /\ 0 <= I15 - 1 /\ I11 = I12] 56.69/56.51 f7(I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I18, I22, I18, I18, I22, I23) [0 <= I25 - 1 /\ 0 <= I20 - 1 /\ I22 <= I21 - 1 /\ I25 <= I20] 56.69/56.51 f7(I26, I27, I28, I29, I30, I31, I32) -> f7(I26, I27, I33, I29 + 1, I30, I31, I34) [0 <= I33 - 1 /\ 0 <= I28 - 1 /\ I33 <= I28 /\ I29 <= I31 - 1 /\ I29 <= I30 /\ I30 + I27 + 1 - I29 <= I31 - 1] 56.69/56.51 f6(I35, I36, I37, I38, I39, I40, I41) -> f6(I35, I36, I42, I38 + 1, I38 + 1, I40, I41) [I38 = I39 /\ 0 <= I42 - 1 /\ 0 <= I37 - 1 /\ I42 <= I37 /\ I38 <= I41 - 1 /\ I38 <= I40] 56.69/56.51 f6(I43, I44, I45, I46, I47, I48, I49) -> f7(I43, I48, I50, I48 + 1, I44, I49, I51) [I46 = I47 /\ 0 <= I50 - 1 /\ 0 <= I45 - 1 /\ I48 <= I46 - 1 /\ I50 <= I45] 56.69/56.51 f5(I52, I53, I54, I55, I56, I57, I58) -> f6(I52, I53, I59, I52, I52, I54, I56) [0 <= I59 - 1 /\ 0 <= I55 - 1 /\ -1 <= I56 - 1 /\ I59 <= I55] 56.69/56.51 f4(I60, I61, I62, I63, I64, I65, I66) -> f6(I62, I63, I67, I62, I62, I68, I64) [0 <= I62 + I63 - 2 * I68 /\ I62 + I63 - 2 * I68 <= 1 /\ 0 <= I67 - 1 /\ 0 <= I61 - 1 /\ 0 <= I60 - 1 /\ I67 <= I61 /\ I67 <= I60 /\ -1 <= I64 - 1 /\ I68 <= I68 + 1 - 1 /\ I63 - (I68 + 1) <= I63 - I62 - 1 /\ I63 - I62 <= I68 - I62 /\ I62 <= I63 - 1] 56.69/56.51 f3(I69, I70, I71, I72, I73, I74, I75) -> f4(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 f4(I80, I81, I82, I83, I84, I85, I86) -> f6(I82, I83, I87, I82, I82, I88, I84) [0 <= I82 + I83 - 2 * I88 /\ I82 + I83 - 2 * I88 <= 1 /\ 0 <= I87 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I87 <= I81 /\ I87 <= I80 /\ -1 <= I84 - 1 /\ I83 - I82 <= I83 - (I88 + 1) /\ I83 - I82 <= I88 - I82 /\ I82 <= I83 - 1] 56.69/56.51 f3(I89, I90, I91, I92, I93, I94, I95) -> f4(I89, I90, I91, I92, I93, I96, I97) [I91 <= I92 - 1 /\ I92 - I91 <= I98 - I91 /\ I92 - I91 <= I92 - (I98 + 1) /\ -1 <= I93 - 1 /\ I99 <= I89 /\ I99 <= I90 /\ 0 <= I89 - 1 /\ 0 <= I90 - 1 /\ 0 <= I99 - 1] 56.69/56.51 f4(I100, I101, I102, I103, I104, I105, I106) -> f5(I102, I103, I107, I108, I104, I109, I110) [0 <= I102 + I103 - 2 * I107 /\ I102 + I103 - 2 * I107 <= 1 /\ 0 <= I108 - 1 /\ 0 <= I101 - 1 /\ 0 <= I100 - 1 /\ I108 <= I101 /\ I108 <= I100 /\ I103 - (I107 + 1) <= I103 - I102 - 1 /\ I107 <= I107 + 1 - 1 /\ I107 - I102 <= I103 - I102 - 1 /\ I102 <= I103 - 1] 56.69/56.51 f3(I111, I112, I113, I114, I115, I116, I117) -> f4(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 f4(I122, I123, I124, I125, I126, I127, I128) -> f5(I124, I125, I129, I130, I126, I131, I132) [0 <= I124 + I125 - 2 * I129 /\ I124 + I125 - 2 * I129 <= 1 /\ 0 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1 /\ I130 <= I123 /\ I130 <= I122 /\ I125 - I124 <= I125 - (I129 + 1) /\ I129 - I124 <= I125 - I124 - 1 /\ I124 <= I125 - 1] 56.69/56.51 f3(I133, I134, I135, I136, I137, I138, I139) -> f4(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 f4(I144, I145, I146, I147, I148, I149, I150) -> f3(I151, I152, I153, I147, I148, I154, I155) [I146 <= I147 - 1 /\ I156 - I146 <= I147 - I146 - 1 /\ I156 <= I156 + 1 - 1 /\ I147 - (I156 + 1) <= I147 - I146 - 1 /\ I151 <= I144 /\ I151 <= I145 /\ I152 <= I144 /\ I152 <= I145 /\ 0 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I151 - 1 /\ 0 <= I152 - 1 /\ I146 + I147 - 2 * I156 <= 1 /\ 0 <= I146 + I147 - 2 * I156 /\ I156 + 1 = I153] 56.69/56.51 f3(I157, I158, I159, I160, I161, I162, I163) -> f4(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 f4(I168, I169, I170, I171, I172, I173, I174) -> f3(I175, I176, I177, I171, I172, I178, I179) [I170 <= I171 - 1 /\ I171 - I170 <= I180 - I170 /\ I171 - (I180 + 1) <= I171 - I170 - 1 /\ I180 <= I180 + 1 - 1 /\ I175 <= I168 /\ I175 <= I169 /\ I176 <= I168 /\ I176 <= I169 /\ 0 <= I168 - 1 /\ 0 <= I169 - 1 /\ 0 <= I175 - 1 /\ 0 <= I176 - 1 /\ I170 + I171 - 2 * I180 <= 1 /\ 0 <= I170 + I171 - 2 * I180 /\ I180 + 1 = I177] 56.69/56.51 f3(I181, I182, I183, I184, I185, I186, I187) -> f4(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 f4(I193, I194, I195, I196, I197, I198, I199) -> f3(I200, I201, I195, I202, I197, I203, I204) [0 <= I195 + I196 - 2 * I202 /\ I195 + I196 - 2 * I202 <= 1 /\ 0 <= I201 - 1 /\ 0 <= I200 - 1 /\ 0 <= I194 - 1 /\ 0 <= I193 - 1 /\ I201 <= I194 /\ I201 <= I193 /\ I200 <= I194 /\ I200 <= I193 /\ I202 - I195 <= I196 - I195 - 1 /\ I195 <= I196 - 1] 56.69/56.51 f3(I205, I206, I207, I208, I209, I210, I211) -> f4(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 f2(I217, I218, I219, I220, I221, I222, I223) -> f3(I224, I225, 0, I219 - 1, I219, I226, I227) [0 <= I225 - 1 /\ 0 <= I224 - 1 /\ 0 <= I217 - 1 /\ I225 <= I217 /\ I224 <= I217 /\ I219 <= I218 /\ -1 <= I219 - 1 /\ I219 - 1 <= I219 - 1] 56.69/56.51 f2(I228, I229, I230, I231, I232, I233, I234) -> f2(I235, I229 + 1, I230, I236, I237, I238, I239) [0 <= I235 - 1 /\ 0 <= I228 - 1 /\ I229 <= I230 - 1 /\ I235 <= I228] 56.69/56.51 f1(I240, I241, I242, I243, I244, I245, I246) -> f2(I247, 0, I241, I248, I249, I250, I251) [0 <= I247 - 1 /\ 0 <= I240 - 1 /\ -1 <= I241 - 1 /\ I247 <= I240] 56.69/56.51 56.69/56.51 The dependency graph for this problem is: 56.69/56.51 9 -> 56.69/56.51 13 -> 56.69/56.51 15 -> 56.69/56.51 17 -> 56.69/56.51 19 -> 56.69/56.51 21 -> 56.69/56.51 Where: 56.69/56.51 9) f3#(I69, I70, I71, I72, I73, I74, I75) -> f4#(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 13) f3#(I111, I112, I113, I114, I115, I116, I117) -> f4#(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 15) f3#(I133, I134, I135, I136, I137, I138, I139) -> f4#(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 17) f3#(I157, I158, I159, I160, I161, I162, I163) -> f4#(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 19) f3#(I181, I182, I183, I184, I185, I186, I187) -> f4#(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 21) f3#(I205, I206, I207, I208, I209, I210, I211) -> f4#(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 56.69/56.51 We have the following SCCs. 56.69/56.51 56.69/56.51 56.69/56.51 DP problem for innermost termination. 56.69/56.51 P = 56.69/56.51 f2#(I228, I229, I230, I231, I232, I233, I234) -> f2#(I235, I229 + 1, I230, I236, I237, I238, I239) [0 <= I235 - 1 /\ 0 <= I228 - 1 /\ I229 <= I230 - 1 /\ I235 <= I228] 56.69/56.51 R = 56.69/56.51 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 56.69/56.51 f8(I0, I1, I2, I3, I4, I5, I6) -> f8(I7, I1 + 1, I2, I3 + 1, I3 + 1, I5, I6) [I3 <= I5 /\ I1 <= I6 - 1 /\ I2 <= I6 - 1 /\ y2 <= y1 - 1 /\ I3 <= I6 - 1 /\ I7 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I7 - 1 /\ I3 = I4] 56.69/56.51 f8(I8, I9, I10, I11, I12, I13, I14) -> f8(I15, I9, I10 - 1, I11 + 1, I11 + 1, I13, I14) [I11 <= I13 /\ I9 <= I14 - 1 /\ I10 <= I14 - 1 /\ I16 <= I17 /\ I11 <= I14 - 1 /\ I15 <= I8 /\ 0 <= I8 - 1 /\ 0 <= I15 - 1 /\ I11 = I12] 56.69/56.51 f7(I18, I19, I20, I21, I22, I23, I24) -> f8(I25, I18, I22, I18, I18, I22, I23) [0 <= I25 - 1 /\ 0 <= I20 - 1 /\ I22 <= I21 - 1 /\ I25 <= I20] 56.69/56.51 f7(I26, I27, I28, I29, I30, I31, I32) -> f7(I26, I27, I33, I29 + 1, I30, I31, I34) [0 <= I33 - 1 /\ 0 <= I28 - 1 /\ I33 <= I28 /\ I29 <= I31 - 1 /\ I29 <= I30 /\ I30 + I27 + 1 - I29 <= I31 - 1] 56.69/56.51 f6(I35, I36, I37, I38, I39, I40, I41) -> f6(I35, I36, I42, I38 + 1, I38 + 1, I40, I41) [I38 = I39 /\ 0 <= I42 - 1 /\ 0 <= I37 - 1 /\ I42 <= I37 /\ I38 <= I41 - 1 /\ I38 <= I40] 56.69/56.51 f6(I43, I44, I45, I46, I47, I48, I49) -> f7(I43, I48, I50, I48 + 1, I44, I49, I51) [I46 = I47 /\ 0 <= I50 - 1 /\ 0 <= I45 - 1 /\ I48 <= I46 - 1 /\ I50 <= I45] 56.69/56.51 f5(I52, I53, I54, I55, I56, I57, I58) -> f6(I52, I53, I59, I52, I52, I54, I56) [0 <= I59 - 1 /\ 0 <= I55 - 1 /\ -1 <= I56 - 1 /\ I59 <= I55] 56.69/56.51 f4(I60, I61, I62, I63, I64, I65, I66) -> f6(I62, I63, I67, I62, I62, I68, I64) [0 <= I62 + I63 - 2 * I68 /\ I62 + I63 - 2 * I68 <= 1 /\ 0 <= I67 - 1 /\ 0 <= I61 - 1 /\ 0 <= I60 - 1 /\ I67 <= I61 /\ I67 <= I60 /\ -1 <= I64 - 1 /\ I68 <= I68 + 1 - 1 /\ I63 - (I68 + 1) <= I63 - I62 - 1 /\ I63 - I62 <= I68 - I62 /\ I62 <= I63 - 1] 56.69/56.51 f3(I69, I70, I71, I72, I73, I74, I75) -> f4(I69, I70, I71, I72, I73, I76, I77) [I71 <= I72 - 1 /\ I72 - I71 <= I78 - I71 /\ I72 - (I78 + 1) <= I72 - I71 - 1 /\ I78 <= I78 + 1 - 1 /\ -1 <= I73 - 1 /\ I79 <= I69 /\ I79 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I79 - 1] 56.69/56.51 f4(I80, I81, I82, I83, I84, I85, I86) -> f6(I82, I83, I87, I82, I82, I88, I84) [0 <= I82 + I83 - 2 * I88 /\ I82 + I83 - 2 * I88 <= 1 /\ 0 <= I87 - 1 /\ 0 <= I81 - 1 /\ 0 <= I80 - 1 /\ I87 <= I81 /\ I87 <= I80 /\ -1 <= I84 - 1 /\ I83 - I82 <= I83 - (I88 + 1) /\ I83 - I82 <= I88 - I82 /\ I82 <= I83 - 1] 56.69/56.51 f3(I89, I90, I91, I92, I93, I94, I95) -> f4(I89, I90, I91, I92, I93, I96, I97) [I91 <= I92 - 1 /\ I92 - I91 <= I98 - I91 /\ I92 - I91 <= I92 - (I98 + 1) /\ -1 <= I93 - 1 /\ I99 <= I89 /\ I99 <= I90 /\ 0 <= I89 - 1 /\ 0 <= I90 - 1 /\ 0 <= I99 - 1] 56.69/56.51 f4(I100, I101, I102, I103, I104, I105, I106) -> f5(I102, I103, I107, I108, I104, I109, I110) [0 <= I102 + I103 - 2 * I107 /\ I102 + I103 - 2 * I107 <= 1 /\ 0 <= I108 - 1 /\ 0 <= I101 - 1 /\ 0 <= I100 - 1 /\ I108 <= I101 /\ I108 <= I100 /\ I103 - (I107 + 1) <= I103 - I102 - 1 /\ I107 <= I107 + 1 - 1 /\ I107 - I102 <= I103 - I102 - 1 /\ I102 <= I103 - 1] 56.69/56.51 f3(I111, I112, I113, I114, I115, I116, I117) -> f4(I111, I112, I113, I114, I115, I118, I119) [I113 <= I114 - 1 /\ I120 - I113 <= I114 - I113 - 1 /\ I120 <= I120 + 1 - 1 /\ I114 - (I120 + 1) <= I114 - I113 - 1 /\ I121 <= I111 /\ I121 <= I112 /\ 0 <= I111 - 1 /\ 0 <= I112 - 1 /\ 0 <= I121 - 1] 56.69/56.51 f4(I122, I123, I124, I125, I126, I127, I128) -> f5(I124, I125, I129, I130, I126, I131, I132) [0 <= I124 + I125 - 2 * I129 /\ I124 + I125 - 2 * I129 <= 1 /\ 0 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1 /\ I130 <= I123 /\ I130 <= I122 /\ I125 - I124 <= I125 - (I129 + 1) /\ I129 - I124 <= I125 - I124 - 1 /\ I124 <= I125 - 1] 56.69/56.51 f3(I133, I134, I135, I136, I137, I138, I139) -> f4(I133, I134, I135, I136, I137, I140, I141) [I135 <= I136 - 1 /\ I142 - I135 <= I136 - I135 - 1 /\ I136 - I135 <= I136 - (I142 + 1) /\ I143 <= I133 /\ I143 <= I134 /\ 0 <= I133 - 1 /\ 0 <= I134 - 1 /\ 0 <= I143 - 1] 56.69/56.51 f4(I144, I145, I146, I147, I148, I149, I150) -> f3(I151, I152, I153, I147, I148, I154, I155) [I146 <= I147 - 1 /\ I156 - I146 <= I147 - I146 - 1 /\ I156 <= I156 + 1 - 1 /\ I147 - (I156 + 1) <= I147 - I146 - 1 /\ I151 <= I144 /\ I151 <= I145 /\ I152 <= I144 /\ I152 <= I145 /\ 0 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I151 - 1 /\ 0 <= I152 - 1 /\ I146 + I147 - 2 * I156 <= 1 /\ 0 <= I146 + I147 - 2 * I156 /\ I156 + 1 = I153] 56.69/56.51 f3(I157, I158, I159, I160, I161, I162, I163) -> f4(I157, I158, I159, I160, I161, I164, I165) [I159 <= I160 - 1 /\ I166 - I159 <= I160 - I159 - 1 /\ I166 <= I166 + 1 - 1 /\ I160 - (I166 + 1) <= I160 - I159 - 1 /\ I167 <= I157 /\ I167 <= I158 /\ y3 <= I157 /\ y3 <= I158 /\ 0 <= I157 - 1 /\ 0 <= I158 - 1 /\ 0 <= I167 - 1 /\ 0 <= y3 - 1] 56.69/56.51 f4(I168, I169, I170, I171, I172, I173, I174) -> f3(I175, I176, I177, I171, I172, I178, I179) [I170 <= I171 - 1 /\ I171 - I170 <= I180 - I170 /\ I171 - (I180 + 1) <= I171 - I170 - 1 /\ I180 <= I180 + 1 - 1 /\ I175 <= I168 /\ I175 <= I169 /\ I176 <= I168 /\ I176 <= I169 /\ 0 <= I168 - 1 /\ 0 <= I169 - 1 /\ 0 <= I175 - 1 /\ 0 <= I176 - 1 /\ I170 + I171 - 2 * I180 <= 1 /\ 0 <= I170 + I171 - 2 * I180 /\ I180 + 1 = I177] 56.69/56.51 f3(I181, I182, I183, I184, I185, I186, I187) -> f4(I181, I182, I183, I184, I185, I188, I189) [I183 <= I184 - 1 /\ I184 - I183 <= I190 - I183 /\ I184 - (I190 + 1) <= I184 - I183 - 1 /\ I190 <= I190 + 1 - 1 /\ I191 <= I181 /\ I191 <= I182 /\ I192 <= I181 /\ I192 <= I182 /\ 0 <= I181 - 1 /\ 0 <= I182 - 1 /\ 0 <= I191 - 1 /\ 0 <= I192 - 1] 56.69/56.51 f4(I193, I194, I195, I196, I197, I198, I199) -> f3(I200, I201, I195, I202, I197, I203, I204) [0 <= I195 + I196 - 2 * I202 /\ I195 + I196 - 2 * I202 <= 1 /\ 0 <= I201 - 1 /\ 0 <= I200 - 1 /\ 0 <= I194 - 1 /\ 0 <= I193 - 1 /\ I201 <= I194 /\ I201 <= I193 /\ I200 <= I194 /\ I200 <= I193 /\ I202 - I195 <= I196 - I195 - 1 /\ I195 <= I196 - 1] 56.69/56.51 f3(I205, I206, I207, I208, I209, I210, I211) -> f4(I205, I206, I207, I208, I209, I212, I213) [I207 <= I208 - 1 /\ I214 - I207 <= I208 - I207 - 1 /\ I215 <= I205 /\ I215 <= I206 /\ I216 <= I205 /\ I216 <= I206 /\ 0 <= I205 - 1 /\ 0 <= I206 - 1 /\ 0 <= I215 - 1 /\ 0 <= I216 - 1] 56.69/56.51 f2(I217, I218, I219, I220, I221, I222, I223) -> f3(I224, I225, 0, I219 - 1, I219, I226, I227) [0 <= I225 - 1 /\ 0 <= I224 - 1 /\ 0 <= I217 - 1 /\ I225 <= I217 /\ I224 <= I217 /\ I219 <= I218 /\ -1 <= I219 - 1 /\ I219 - 1 <= I219 - 1] 56.69/56.51 f2(I228, I229, I230, I231, I232, I233, I234) -> f2(I235, I229 + 1, I230, I236, I237, I238, I239) [0 <= I235 - 1 /\ 0 <= I228 - 1 /\ I229 <= I230 - 1 /\ I235 <= I228] 56.69/56.51 f1(I240, I241, I242, I243, I244, I245, I246) -> f2(I247, 0, I241, I248, I249, I250, I251) [0 <= I247 - 1 /\ 0 <= I240 - 1 /\ -1 <= I241 - 1 /\ I247 <= I240] 56.69/56.51 56.69/56.51 We use the reverse value criterion with the projection function NU: 56.69/56.51 NU[f2#(z1,z2,z3,z4,z5,z6,z7)] = z3 - 1 + -1 * z2 56.69/56.51 56.69/56.51 This gives the following inequalities: 56.69/56.51 0 <= I235 - 1 /\ 0 <= I228 - 1 /\ I229 <= I230 - 1 /\ I235 <= I228 ==> I230 - 1 + -1 * I229 > I230 - 1 + -1 * (I229 + 1) with I230 - 1 + -1 * I229 >= 0 56.69/56.51 56.69/56.51 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 56.69/59.49 EOF