/export/starexec/sandbox2/solver/bin/starexec_run_Transition /export/starexec/sandbox2/benchmark/theBenchmark.smt2 /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES DP problem for innermost termination. P = init#(x1, x2, x3, x4, x5, x6, x7) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) f5#(I0, I1, I2, I3, I4, I5, I6) -> f5#(I0 - 1, I7, I8, I9, I10, I11, I12) [0 <= I0 - 1] f1#(I13, I14, I15, I16, I17, I18, I19) -> f5#(I20, I21, I22, I23, I24, I25, I26) [-1 <= y2 - 1 /\ 1 <= I14 - 1 /\ -1 <= y1 - 1 /\ 0 <= I13 - 1 /\ y1 - 1 = I20] f4#(I27, I28, I29, I30, I31, I32, I33) -> f3#(I34, I35, I36, I37, I38, I39, I40) [I41 <= I29 - 1 /\ 0 <= I29 - 1 /\ I40 <= I32 - 1 /\ -1 <= I32 - 1 /\ I42 <= y3 - 1 /\ -1 <= y3 - 1 /\ I27 - 2 * y4 = 1 /\ I34 <= I27 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ I37 <= I41 /\ 0 <= I27 - 2 * y4 /\ I27 - 2 * y4 <= 1 /\ I27 - 2 * I34 <= 1 /\ 0 <= I27 - 2 * I34 /\ I29 = I30 /\ I32 = I33] f3#(I43, I44, I45, I46, I47, I48, I49) -> f4#(I43, I44, I45, I45, I47, I48, I48) [I50 <= I45 - 1 /\ 0 <= I45 - 1 /\ I51 <= I48 - 1 /\ -1 <= I48 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1 /\ I43 - 2 * y5 = 1 /\ y6 <= I43 /\ -1 <= I50 - 1 /\ y7 <= I50 /\ 0 <= I51 - 1 /\ I45 = I46 /\ I48 = I49] f4#(I54, I55, I56, I57, I58, I59, I60) -> f3#(I61, I62, I63, I64, I65, I59, I66) [0 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I60 - 1 /\ I66 <= I60 - 1 /\ I67 <= I57 - 1 /\ I68 <= I58 - 1 /\ 0 <= I55 - 1 /\ I54 - 2 * I69 = 1 /\ -1 <= I56 - 1 /\ I63 <= I56 /\ I64 <= I67 /\ -1 <= I67 - 1 /\ I65 <= I68 /\ 0 <= I59 - 1 /\ I61 <= I54 /\ 0 <= I66 - 1 /\ -1 <= I68 - 1 /\ 0 <= I54 - 2 * I69 /\ I54 - 2 * I69 <= 1 /\ I54 - 2 * I61 <= 1 /\ 0 <= I54 - 2 * I61] f3#(I70, I71, I72, I73, I74, I75, I76) -> f4#(I70, I71, I72, I73, I74, I75, I76) [0 <= I73 - 1 /\ 0 <= I74 - 1 /\ -1 <= I76 - 1 /\ I77 <= I76 - 1 /\ I78 <= I73 - 1 /\ I79 <= I74 - 1 /\ 0 <= I71 - 1 /\ I70 - 2 * I80 = 1 /\ -1 <= I72 - 1 /\ I81 <= I72 /\ I82 <= I78 /\ -1 <= I78 - 1 /\ I83 <= I79 /\ 0 <= I75 - 1 /\ y8 <= I70 /\ -1 <= I79 - 1 /\ 0 <= I77 - 1] f4#(I84, I85, I86, I87, I88, I89, I90) -> f3#(I91, I92, I86, I93, I94, I85, I95) [0 <= I87 - 1 /\ 0 <= I88 - 1 /\ -1 <= I89 - 1 /\ I89 <= I85 - 1 /\ I89 <= I96 - 1 /\ I89 <= I86 - 1 /\ I89 <= I97 - 1 /\ -1 <= I90 - 1 /\ I98 <= I90 - 1 /\ I98 <= I95 - 1 /\ I93 <= I87 - 1 /\ -1 <= I98 - 1 /\ I98 <= I99 - 1 /\ I94 <= I88 - 1 /\ 0 <= I85 - 1 /\ I98 <= I93 - 1 /\ I98 <= I94 - 1 /\ I84 - 2 * I100 = 0 /\ I91 <= I84 /\ 0 <= I84 - 2 * I100 /\ I84 - 2 * I100 <= 1 /\ I84 - 2 * I91 <= 1 /\ 0 <= I84 - 2 * I91] f3#(I101, I102, I103, I104, I105, I106, I107) -> f4#(I101, I102, I103, I104, I105, I106, I107) [0 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ I106 <= I102 - 1 /\ I106 <= I108 - 1 /\ I106 <= I103 - 1 /\ I106 <= I109 - 1 /\ -1 <= I107 - 1 /\ I110 <= I107 - 1 /\ I110 <= I111 - 1 /\ I112 <= I104 - 1 /\ -1 <= I110 - 1 /\ I110 <= I113 - 1 /\ I114 <= I105 - 1 /\ 0 <= I102 - 1 /\ I110 <= I112 - 1 /\ I110 <= I114 - 1 /\ I115 <= I101 /\ I101 - 2 * y9 = 0] f4#(I116, I117, I118, I119, I120, I121, I122) -> f3#(I123, 0, I124, I125, 0, I126, I127) [I124 <= I118 - 1 /\ 0 <= I118 - 1 /\ I124 <= I121 - 1 /\ -1 <= I121 - 1 /\ I128 <= I129 - 1 /\ -1 <= I129 - 1 /\ I116 - 2 * I130 = 1 /\ I123 <= I116 /\ 0 <= I124 - 1 /\ 0 <= I116 - 2 * I130 /\ I116 - 2 * I130 <= 1 /\ I116 - 2 * I123 <= 1 /\ 0 <= I116 - 2 * I123 /\ I118 = I119 /\ I121 = I122 /\ I124 = I125 /\ I124 = I126 /\ I124 = I127] f3#(I131, I132, I133, I134, I135, I136, I137) -> f4#(I131, I132, I133, I133, I135, I136, I136) [I138 <= I133 - 1 /\ 0 <= I133 - 1 /\ I138 <= I136 - 1 /\ -1 <= I136 - 1 /\ I139 <= I140 - 1 /\ -1 <= I140 - 1 /\ I131 - 2 * I141 = 1 /\ 0 <= I138 - 1 /\ I142 <= I131 /\ I133 = I134 /\ I136 = I137] f4#(I143, I144, I145, I146, I147, I148, I149) -> f3#(I150, 1, I151, I152, I153, 0, I154) [0 <= I146 - 1 /\ 0 <= I147 - 1 /\ -1 <= I149 - 1 /\ I153 <= I149 - 1 /\ I155 <= I146 - 1 /\ I153 <= I147 - 1 /\ 0 <= I144 - 1 /\ I143 - 2 * I156 = 1 /\ -1 <= I157 - 1 /\ I155 <= I157 - 1 /\ I150 <= I143 /\ -1 <= I155 - 1 /\ 0 <= I153 - 1 /\ I152 <= I155 /\ 0 <= I143 - 2 * I156 /\ I143 - 2 * I156 <= 1 /\ I143 - 2 * I150 <= 1 /\ 0 <= I143 - 2 * I150 /\ I153 = I154] f3#(I158, I159, I160, I161, I162, I163, I164) -> f4#(I158, I159, I160, I161, I162, I163, I164) [0 <= I161 - 1 /\ 0 <= I162 - 1 /\ -1 <= I164 - 1 /\ I165 <= I164 - 1 /\ I166 <= I161 - 1 /\ I165 <= I162 - 1 /\ 0 <= I159 - 1 /\ I158 - 2 * I167 = 1 /\ -1 <= I168 - 1 /\ I166 <= I168 - 1 /\ I169 <= I158 /\ -1 <= I166 - 1 /\ I170 <= I166 /\ 0 <= I165 - 1] f4#(I171, I172, I173, I174, I175, I176, I177) -> f3#(I178, 1, I179, I180, I181, 0, I182) [I180 <= I173 - 1 /\ 0 <= I173 - 1 /\ I183 <= I176 - 1 /\ -1 <= I176 - 1 /\ I181 <= I184 - 1 /\ -1 <= I183 - 1 /\ I183 <= I181 - 1 /\ -1 <= I184 - 1 /\ I183 <= I185 - 1 /\ I183 <= I180 - 1 /\ I171 - 2 * I186 = 0 /\ I178 <= I171 /\ 0 <= I171 - 2 * I186 /\ I171 - 2 * I186 <= 1 /\ I171 - 2 * I178 <= 1 /\ 0 <= I171 - 2 * I178 /\ I173 = I174 /\ I176 = I177 /\ I181 = I182] f3#(I187, I188, I189, I190, I191, I192, I193) -> f4#(I187, I188, I189, I189, I191, I192, I192) [I194 <= I189 - 1 /\ 0 <= I189 - 1 /\ I195 <= I192 - 1 /\ -1 <= I192 - 1 /\ I196 <= I197 - 1 /\ -1 <= I195 - 1 /\ I195 <= I196 - 1 /\ -1 <= I197 - 1 /\ I195 <= I198 - 1 /\ I195 <= I194 - 1 /\ I199 <= I187 /\ I187 - 2 * I200 = 0 /\ I189 = I190 /\ I192 = I193] f2#(I201, I202, I203, I204, I205, I206, I207) -> f3#(I201, 0, I202, I202, 0, I202, I202) [0 <= I202 - 1] f1#(I208, I209, I210, I211, I212, I213, I214) -> f2#(I215, I216, I217, I218, I219, I220, I221) [-1 <= I222 - 1 /\ 1 <= I209 - 1 /\ I216 <= 0 /\ -1 <= I215 - 1 /\ 0 <= I208 - 1] f1#(I223, I224, I225, I226, I227, I228, I229) -> f2#(I230, I231, I232, I233, I234, I235, I236) [-1 <= I237 - 1 /\ 1 <= I224 - 1 /\ -1 <= I230 - 1 /\ I231 <= I238 - 1 /\ -1 <= I238 - 1 /\ 0 <= I223 - 1] R = init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) f5(I0, I1, I2, I3, I4, I5, I6) -> f5(I0 - 1, I7, I8, I9, I10, I11, I12) [0 <= I0 - 1] f1(I13, I14, I15, I16, I17, I18, I19) -> f5(I20, I21, I22, I23, I24, I25, I26) [-1 <= y2 - 1 /\ 1 <= I14 - 1 /\ -1 <= y1 - 1 /\ 0 <= I13 - 1 /\ y1 - 1 = I20] f4(I27, I28, I29, I30, I31, I32, I33) -> f3(I34, I35, I36, I37, I38, I39, I40) [I41 <= I29 - 1 /\ 0 <= I29 - 1 /\ I40 <= I32 - 1 /\ -1 <= I32 - 1 /\ I42 <= y3 - 1 /\ -1 <= y3 - 1 /\ I27 - 2 * y4 = 1 /\ I34 <= I27 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ I37 <= I41 /\ 0 <= I27 - 2 * y4 /\ I27 - 2 * y4 <= 1 /\ I27 - 2 * I34 <= 1 /\ 0 <= I27 - 2 * I34 /\ I29 = I30 /\ I32 = I33] f3(I43, I44, I45, I46, I47, I48, I49) -> f4(I43, I44, I45, I45, I47, I48, I48) [I50 <= I45 - 1 /\ 0 <= I45 - 1 /\ I51 <= I48 - 1 /\ -1 <= I48 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1 /\ I43 - 2 * y5 = 1 /\ y6 <= I43 /\ -1 <= I50 - 1 /\ y7 <= I50 /\ 0 <= I51 - 1 /\ I45 = I46 /\ I48 = I49] f4(I54, I55, I56, I57, I58, I59, I60) -> f3(I61, I62, I63, I64, I65, I59, I66) [0 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I60 - 1 /\ I66 <= I60 - 1 /\ I67 <= I57 - 1 /\ I68 <= I58 - 1 /\ 0 <= I55 - 1 /\ I54 - 2 * I69 = 1 /\ -1 <= I56 - 1 /\ I63 <= I56 /\ I64 <= I67 /\ -1 <= I67 - 1 /\ I65 <= I68 /\ 0 <= I59 - 1 /\ I61 <= I54 /\ 0 <= I66 - 1 /\ -1 <= I68 - 1 /\ 0 <= I54 - 2 * I69 /\ I54 - 2 * I69 <= 1 /\ I54 - 2 * I61 <= 1 /\ 0 <= I54 - 2 * I61] f3(I70, I71, I72, I73, I74, I75, I76) -> f4(I70, I71, I72, I73, I74, I75, I76) [0 <= I73 - 1 /\ 0 <= I74 - 1 /\ -1 <= I76 - 1 /\ I77 <= I76 - 1 /\ I78 <= I73 - 1 /\ I79 <= I74 - 1 /\ 0 <= I71 - 1 /\ I70 - 2 * I80 = 1 /\ -1 <= I72 - 1 /\ I81 <= I72 /\ I82 <= I78 /\ -1 <= I78 - 1 /\ I83 <= I79 /\ 0 <= I75 - 1 /\ y8 <= I70 /\ -1 <= I79 - 1 /\ 0 <= I77 - 1] f4(I84, I85, I86, I87, I88, I89, I90) -> f3(I91, I92, I86, I93, I94, I85, I95) [0 <= I87 - 1 /\ 0 <= I88 - 1 /\ -1 <= I89 - 1 /\ I89 <= I85 - 1 /\ I89 <= I96 - 1 /\ I89 <= I86 - 1 /\ I89 <= I97 - 1 /\ -1 <= I90 - 1 /\ I98 <= I90 - 1 /\ I98 <= I95 - 1 /\ I93 <= I87 - 1 /\ -1 <= I98 - 1 /\ I98 <= I99 - 1 /\ I94 <= I88 - 1 /\ 0 <= I85 - 1 /\ I98 <= I93 - 1 /\ I98 <= I94 - 1 /\ I84 - 2 * I100 = 0 /\ I91 <= I84 /\ 0 <= I84 - 2 * I100 /\ I84 - 2 * I100 <= 1 /\ I84 - 2 * I91 <= 1 /\ 0 <= I84 - 2 * I91] f3(I101, I102, I103, I104, I105, I106, I107) -> f4(I101, I102, I103, I104, I105, I106, I107) [0 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ I106 <= I102 - 1 /\ I106 <= I108 - 1 /\ I106 <= I103 - 1 /\ I106 <= I109 - 1 /\ -1 <= I107 - 1 /\ I110 <= I107 - 1 /\ I110 <= I111 - 1 /\ I112 <= I104 - 1 /\ -1 <= I110 - 1 /\ I110 <= I113 - 1 /\ I114 <= I105 - 1 /\ 0 <= I102 - 1 /\ I110 <= I112 - 1 /\ I110 <= I114 - 1 /\ I115 <= I101 /\ I101 - 2 * y9 = 0] f4(I116, I117, I118, I119, I120, I121, I122) -> f3(I123, 0, I124, I125, 0, I126, I127) [I124 <= I118 - 1 /\ 0 <= I118 - 1 /\ I124 <= I121 - 1 /\ -1 <= I121 - 1 /\ I128 <= I129 - 1 /\ -1 <= I129 - 1 /\ I116 - 2 * I130 = 1 /\ I123 <= I116 /\ 0 <= I124 - 1 /\ 0 <= I116 - 2 * I130 /\ I116 - 2 * I130 <= 1 /\ I116 - 2 * I123 <= 1 /\ 0 <= I116 - 2 * I123 /\ I118 = I119 /\ I121 = I122 /\ I124 = I125 /\ I124 = I126 /\ I124 = I127] f3(I131, I132, I133, I134, I135, I136, I137) -> f4(I131, I132, I133, I133, I135, I136, I136) [I138 <= I133 - 1 /\ 0 <= I133 - 1 /\ I138 <= I136 - 1 /\ -1 <= I136 - 1 /\ I139 <= I140 - 1 /\ -1 <= I140 - 1 /\ I131 - 2 * I141 = 1 /\ 0 <= I138 - 1 /\ I142 <= I131 /\ I133 = I134 /\ I136 = I137] f4(I143, I144, I145, I146, I147, I148, I149) -> f3(I150, 1, I151, I152, I153, 0, I154) [0 <= I146 - 1 /\ 0 <= I147 - 1 /\ -1 <= I149 - 1 /\ I153 <= I149 - 1 /\ I155 <= I146 - 1 /\ I153 <= I147 - 1 /\ 0 <= I144 - 1 /\ I143 - 2 * I156 = 1 /\ -1 <= I157 - 1 /\ I155 <= I157 - 1 /\ I150 <= I143 /\ -1 <= I155 - 1 /\ 0 <= I153 - 1 /\ I152 <= I155 /\ 0 <= I143 - 2 * I156 /\ I143 - 2 * I156 <= 1 /\ I143 - 2 * I150 <= 1 /\ 0 <= I143 - 2 * I150 /\ I153 = I154] f3(I158, I159, I160, I161, I162, I163, I164) -> f4(I158, I159, I160, I161, I162, I163, I164) [0 <= I161 - 1 /\ 0 <= I162 - 1 /\ -1 <= I164 - 1 /\ I165 <= I164 - 1 /\ I166 <= I161 - 1 /\ I165 <= I162 - 1 /\ 0 <= I159 - 1 /\ I158 - 2 * I167 = 1 /\ -1 <= I168 - 1 /\ I166 <= I168 - 1 /\ I169 <= I158 /\ -1 <= I166 - 1 /\ I170 <= I166 /\ 0 <= I165 - 1] f4(I171, I172, I173, I174, I175, I176, I177) -> f3(I178, 1, I179, I180, I181, 0, I182) [I180 <= I173 - 1 /\ 0 <= I173 - 1 /\ I183 <= I176 - 1 /\ -1 <= I176 - 1 /\ I181 <= I184 - 1 /\ -1 <= I183 - 1 /\ I183 <= I181 - 1 /\ -1 <= I184 - 1 /\ I183 <= I185 - 1 /\ I183 <= I180 - 1 /\ I171 - 2 * I186 = 0 /\ I178 <= I171 /\ 0 <= I171 - 2 * I186 /\ I171 - 2 * I186 <= 1 /\ I171 - 2 * I178 <= 1 /\ 0 <= I171 - 2 * I178 /\ I173 = I174 /\ I176 = I177 /\ I181 = I182] f3(I187, I188, I189, I190, I191, I192, I193) -> f4(I187, I188, I189, I189, I191, I192, I192) [I194 <= I189 - 1 /\ 0 <= I189 - 1 /\ I195 <= I192 - 1 /\ -1 <= I192 - 1 /\ I196 <= I197 - 1 /\ -1 <= I195 - 1 /\ I195 <= I196 - 1 /\ -1 <= I197 - 1 /\ I195 <= I198 - 1 /\ I195 <= I194 - 1 /\ I199 <= I187 /\ I187 - 2 * I200 = 0 /\ I189 = I190 /\ I192 = I193] f2(I201, I202, I203, I204, I205, I206, I207) -> f3(I201, 0, I202, I202, 0, I202, I202) [0 <= I202 - 1] f1(I208, I209, I210, I211, I212, I213, I214) -> f2(I215, I216, I217, I218, I219, I220, I221) [-1 <= I222 - 1 /\ 1 <= I209 - 1 /\ I216 <= 0 /\ -1 <= I215 - 1 /\ 0 <= I208 - 1] f1(I223, I224, I225, I226, I227, I228, I229) -> f2(I230, I231, I232, I233, I234, I235, I236) [-1 <= I237 - 1 /\ 1 <= I224 - 1 /\ -1 <= I230 - 1 /\ I231 <= I238 - 1 /\ -1 <= I238 - 1 /\ 0 <= I223 - 1] The dependency graph for this problem is: 0 -> 2, 16, 17 1 -> 1 2 -> 1 3 -> 4, 6, 8, 10, 12, 14 4 -> 3, 5, 9, 11 5 -> 4, 6, 8, 10, 12, 14 6 -> 3, 5, 9, 11 7 -> 4, 6, 8, 10, 12, 14 8 -> 7, 13 9 -> 4, 10, 14 10 -> 3, 5, 9, 11 11 -> 8, 12 12 -> 3, 5, 9, 11 13 -> 8, 12 14 -> 7, 13 15 -> 4, 10, 14 16 -> 17 -> 15 Where: 0) init#(x1, x2, x3, x4, x5, x6, x7) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 1) f5#(I0, I1, I2, I3, I4, I5, I6) -> f5#(I0 - 1, I7, I8, I9, I10, I11, I12) [0 <= I0 - 1] 2) f1#(I13, I14, I15, I16, I17, I18, I19) -> f5#(I20, I21, I22, I23, I24, I25, I26) [-1 <= y2 - 1 /\ 1 <= I14 - 1 /\ -1 <= y1 - 1 /\ 0 <= I13 - 1 /\ y1 - 1 = I20] 3) f4#(I27, I28, I29, I30, I31, I32, I33) -> f3#(I34, I35, I36, I37, I38, I39, I40) [I41 <= I29 - 1 /\ 0 <= I29 - 1 /\ I40 <= I32 - 1 /\ -1 <= I32 - 1 /\ I42 <= y3 - 1 /\ -1 <= y3 - 1 /\ I27 - 2 * y4 = 1 /\ I34 <= I27 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ I37 <= I41 /\ 0 <= I27 - 2 * y4 /\ I27 - 2 * y4 <= 1 /\ I27 - 2 * I34 <= 1 /\ 0 <= I27 - 2 * I34 /\ I29 = I30 /\ I32 = I33] 4) f3#(I43, I44, I45, I46, I47, I48, I49) -> f4#(I43, I44, I45, I45, I47, I48, I48) [I50 <= I45 - 1 /\ 0 <= I45 - 1 /\ I51 <= I48 - 1 /\ -1 <= I48 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1 /\ I43 - 2 * y5 = 1 /\ y6 <= I43 /\ -1 <= I50 - 1 /\ y7 <= I50 /\ 0 <= I51 - 1 /\ I45 = I46 /\ I48 = I49] 5) f4#(I54, I55, I56, I57, I58, I59, I60) -> f3#(I61, I62, I63, I64, I65, I59, I66) [0 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I60 - 1 /\ I66 <= I60 - 1 /\ I67 <= I57 - 1 /\ I68 <= I58 - 1 /\ 0 <= I55 - 1 /\ I54 - 2 * I69 = 1 /\ -1 <= I56 - 1 /\ I63 <= I56 /\ I64 <= I67 /\ -1 <= I67 - 1 /\ I65 <= I68 /\ 0 <= I59 - 1 /\ I61 <= I54 /\ 0 <= I66 - 1 /\ -1 <= I68 - 1 /\ 0 <= I54 - 2 * I69 /\ I54 - 2 * I69 <= 1 /\ I54 - 2 * I61 <= 1 /\ 0 <= I54 - 2 * I61] 6) f3#(I70, I71, I72, I73, I74, I75, I76) -> f4#(I70, I71, I72, I73, I74, I75, I76) [0 <= I73 - 1 /\ 0 <= I74 - 1 /\ -1 <= I76 - 1 /\ I77 <= I76 - 1 /\ I78 <= I73 - 1 /\ I79 <= I74 - 1 /\ 0 <= I71 - 1 /\ I70 - 2 * I80 = 1 /\ -1 <= I72 - 1 /\ I81 <= I72 /\ I82 <= I78 /\ -1 <= I78 - 1 /\ I83 <= I79 /\ 0 <= I75 - 1 /\ y8 <= I70 /\ -1 <= I79 - 1 /\ 0 <= I77 - 1] 7) f4#(I84, I85, I86, I87, I88, I89, I90) -> f3#(I91, I92, I86, I93, I94, I85, I95) [0 <= I87 - 1 /\ 0 <= I88 - 1 /\ -1 <= I89 - 1 /\ I89 <= I85 - 1 /\ I89 <= I96 - 1 /\ I89 <= I86 - 1 /\ I89 <= I97 - 1 /\ -1 <= I90 - 1 /\ I98 <= I90 - 1 /\ I98 <= I95 - 1 /\ I93 <= I87 - 1 /\ -1 <= I98 - 1 /\ I98 <= I99 - 1 /\ I94 <= I88 - 1 /\ 0 <= I85 - 1 /\ I98 <= I93 - 1 /\ I98 <= I94 - 1 /\ I84 - 2 * I100 = 0 /\ I91 <= I84 /\ 0 <= I84 - 2 * I100 /\ I84 - 2 * I100 <= 1 /\ I84 - 2 * I91 <= 1 /\ 0 <= I84 - 2 * I91] 8) f3#(I101, I102, I103, I104, I105, I106, I107) -> f4#(I101, I102, I103, I104, I105, I106, I107) [0 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ I106 <= I102 - 1 /\ I106 <= I108 - 1 /\ I106 <= I103 - 1 /\ I106 <= I109 - 1 /\ -1 <= I107 - 1 /\ I110 <= I107 - 1 /\ I110 <= I111 - 1 /\ I112 <= I104 - 1 /\ -1 <= I110 - 1 /\ I110 <= I113 - 1 /\ I114 <= I105 - 1 /\ 0 <= I102 - 1 /\ I110 <= I112 - 1 /\ I110 <= I114 - 1 /\ I115 <= I101 /\ I101 - 2 * y9 = 0] 9) f4#(I116, I117, I118, I119, I120, I121, I122) -> f3#(I123, 0, I124, I125, 0, I126, I127) [I124 <= I118 - 1 /\ 0 <= I118 - 1 /\ I124 <= I121 - 1 /\ -1 <= I121 - 1 /\ I128 <= I129 - 1 /\ -1 <= I129 - 1 /\ I116 - 2 * I130 = 1 /\ I123 <= I116 /\ 0 <= I124 - 1 /\ 0 <= I116 - 2 * I130 /\ I116 - 2 * I130 <= 1 /\ I116 - 2 * I123 <= 1 /\ 0 <= I116 - 2 * I123 /\ I118 = I119 /\ I121 = I122 /\ I124 = I125 /\ I124 = I126 /\ I124 = I127] 10) f3#(I131, I132, I133, I134, I135, I136, I137) -> f4#(I131, I132, I133, I133, I135, I136, I136) [I138 <= I133 - 1 /\ 0 <= I133 - 1 /\ I138 <= I136 - 1 /\ -1 <= I136 - 1 /\ I139 <= I140 - 1 /\ -1 <= I140 - 1 /\ I131 - 2 * I141 = 1 /\ 0 <= I138 - 1 /\ I142 <= I131 /\ I133 = I134 /\ I136 = I137] 11) f4#(I143, I144, I145, I146, I147, I148, I149) -> f3#(I150, 1, I151, I152, I153, 0, I154) [0 <= I146 - 1 /\ 0 <= I147 - 1 /\ -1 <= I149 - 1 /\ I153 <= I149 - 1 /\ I155 <= I146 - 1 /\ I153 <= I147 - 1 /\ 0 <= I144 - 1 /\ I143 - 2 * I156 = 1 /\ -1 <= I157 - 1 /\ I155 <= I157 - 1 /\ I150 <= I143 /\ -1 <= I155 - 1 /\ 0 <= I153 - 1 /\ I152 <= I155 /\ 0 <= I143 - 2 * I156 /\ I143 - 2 * I156 <= 1 /\ I143 - 2 * I150 <= 1 /\ 0 <= I143 - 2 * I150 /\ I153 = I154] 12) f3#(I158, I159, I160, I161, I162, I163, I164) -> f4#(I158, I159, I160, I161, I162, I163, I164) [0 <= I161 - 1 /\ 0 <= I162 - 1 /\ -1 <= I164 - 1 /\ I165 <= I164 - 1 /\ I166 <= I161 - 1 /\ I165 <= I162 - 1 /\ 0 <= I159 - 1 /\ I158 - 2 * I167 = 1 /\ -1 <= I168 - 1 /\ I166 <= I168 - 1 /\ I169 <= I158 /\ -1 <= I166 - 1 /\ I170 <= I166 /\ 0 <= I165 - 1] 13) f4#(I171, I172, I173, I174, I175, I176, I177) -> f3#(I178, 1, I179, I180, I181, 0, I182) [I180 <= I173 - 1 /\ 0 <= I173 - 1 /\ I183 <= I176 - 1 /\ -1 <= I176 - 1 /\ I181 <= I184 - 1 /\ -1 <= I183 - 1 /\ I183 <= I181 - 1 /\ -1 <= I184 - 1 /\ I183 <= I185 - 1 /\ I183 <= I180 - 1 /\ I171 - 2 * I186 = 0 /\ I178 <= I171 /\ 0 <= I171 - 2 * I186 /\ I171 - 2 * I186 <= 1 /\ I171 - 2 * I178 <= 1 /\ 0 <= I171 - 2 * I178 /\ I173 = I174 /\ I176 = I177 /\ I181 = I182] 14) f3#(I187, I188, I189, I190, I191, I192, I193) -> f4#(I187, I188, I189, I189, I191, I192, I192) [I194 <= I189 - 1 /\ 0 <= I189 - 1 /\ I195 <= I192 - 1 /\ -1 <= I192 - 1 /\ I196 <= I197 - 1 /\ -1 <= I195 - 1 /\ I195 <= I196 - 1 /\ -1 <= I197 - 1 /\ I195 <= I198 - 1 /\ I195 <= I194 - 1 /\ I199 <= I187 /\ I187 - 2 * I200 = 0 /\ I189 = I190 /\ I192 = I193] 15) f2#(I201, I202, I203, I204, I205, I206, I207) -> f3#(I201, 0, I202, I202, 0, I202, I202) [0 <= I202 - 1] 16) f1#(I208, I209, I210, I211, I212, I213, I214) -> f2#(I215, I216, I217, I218, I219, I220, I221) [-1 <= I222 - 1 /\ 1 <= I209 - 1 /\ I216 <= 0 /\ -1 <= I215 - 1 /\ 0 <= I208 - 1] 17) f1#(I223, I224, I225, I226, I227, I228, I229) -> f2#(I230, I231, I232, I233, I234, I235, I236) [-1 <= I237 - 1 /\ 1 <= I224 - 1 /\ -1 <= I230 - 1 /\ I231 <= I238 - 1 /\ -1 <= I238 - 1 /\ 0 <= I223 - 1] We have the following SCCs. { 1 } { 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 } DP problem for innermost termination. P = f4#(I27, I28, I29, I30, I31, I32, I33) -> f3#(I34, I35, I36, I37, I38, I39, I40) [I41 <= I29 - 1 /\ 0 <= I29 - 1 /\ I40 <= I32 - 1 /\ -1 <= I32 - 1 /\ I42 <= y3 - 1 /\ -1 <= y3 - 1 /\ I27 - 2 * y4 = 1 /\ I34 <= I27 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ I37 <= I41 /\ 0 <= I27 - 2 * y4 /\ I27 - 2 * y4 <= 1 /\ I27 - 2 * I34 <= 1 /\ 0 <= I27 - 2 * I34 /\ I29 = I30 /\ I32 = I33] f3#(I43, I44, I45, I46, I47, I48, I49) -> f4#(I43, I44, I45, I45, I47, I48, I48) [I50 <= I45 - 1 /\ 0 <= I45 - 1 /\ I51 <= I48 - 1 /\ -1 <= I48 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1 /\ I43 - 2 * y5 = 1 /\ y6 <= I43 /\ -1 <= I50 - 1 /\ y7 <= I50 /\ 0 <= I51 - 1 /\ I45 = I46 /\ I48 = I49] f4#(I54, I55, I56, I57, I58, I59, I60) -> f3#(I61, I62, I63, I64, I65, I59, I66) [0 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I60 - 1 /\ I66 <= I60 - 1 /\ I67 <= I57 - 1 /\ I68 <= I58 - 1 /\ 0 <= I55 - 1 /\ I54 - 2 * I69 = 1 /\ -1 <= I56 - 1 /\ I63 <= I56 /\ I64 <= I67 /\ -1 <= I67 - 1 /\ I65 <= I68 /\ 0 <= I59 - 1 /\ I61 <= I54 /\ 0 <= I66 - 1 /\ -1 <= I68 - 1 /\ 0 <= I54 - 2 * I69 /\ I54 - 2 * I69 <= 1 /\ I54 - 2 * I61 <= 1 /\ 0 <= I54 - 2 * I61] f3#(I70, I71, I72, I73, I74, I75, I76) -> f4#(I70, I71, I72, I73, I74, I75, I76) [0 <= I73 - 1 /\ 0 <= I74 - 1 /\ -1 <= I76 - 1 /\ I77 <= I76 - 1 /\ I78 <= I73 - 1 /\ I79 <= I74 - 1 /\ 0 <= I71 - 1 /\ I70 - 2 * I80 = 1 /\ -1 <= I72 - 1 /\ I81 <= I72 /\ I82 <= I78 /\ -1 <= I78 - 1 /\ I83 <= I79 /\ 0 <= I75 - 1 /\ y8 <= I70 /\ -1 <= I79 - 1 /\ 0 <= I77 - 1] f4#(I84, I85, I86, I87, I88, I89, I90) -> f3#(I91, I92, I86, I93, I94, I85, I95) [0 <= I87 - 1 /\ 0 <= I88 - 1 /\ -1 <= I89 - 1 /\ I89 <= I85 - 1 /\ I89 <= I96 - 1 /\ I89 <= I86 - 1 /\ I89 <= I97 - 1 /\ -1 <= I90 - 1 /\ I98 <= I90 - 1 /\ I98 <= I95 - 1 /\ I93 <= I87 - 1 /\ -1 <= I98 - 1 /\ I98 <= I99 - 1 /\ I94 <= I88 - 1 /\ 0 <= I85 - 1 /\ I98 <= I93 - 1 /\ I98 <= I94 - 1 /\ I84 - 2 * I100 = 0 /\ I91 <= I84 /\ 0 <= I84 - 2 * I100 /\ I84 - 2 * I100 <= 1 /\ I84 - 2 * I91 <= 1 /\ 0 <= I84 - 2 * I91] f3#(I101, I102, I103, I104, I105, I106, I107) -> f4#(I101, I102, I103, I104, I105, I106, I107) [0 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ I106 <= I102 - 1 /\ I106 <= I108 - 1 /\ I106 <= I103 - 1 /\ I106 <= I109 - 1 /\ -1 <= I107 - 1 /\ I110 <= I107 - 1 /\ I110 <= I111 - 1 /\ I112 <= I104 - 1 /\ -1 <= I110 - 1 /\ I110 <= I113 - 1 /\ I114 <= I105 - 1 /\ 0 <= I102 - 1 /\ I110 <= I112 - 1 /\ I110 <= I114 - 1 /\ I115 <= I101 /\ I101 - 2 * y9 = 0] f4#(I116, I117, I118, I119, I120, I121, I122) -> f3#(I123, 0, I124, I125, 0, I126, I127) [I124 <= I118 - 1 /\ 0 <= I118 - 1 /\ I124 <= I121 - 1 /\ -1 <= I121 - 1 /\ I128 <= I129 - 1 /\ -1 <= I129 - 1 /\ I116 - 2 * I130 = 1 /\ I123 <= I116 /\ 0 <= I124 - 1 /\ 0 <= I116 - 2 * I130 /\ I116 - 2 * I130 <= 1 /\ I116 - 2 * I123 <= 1 /\ 0 <= I116 - 2 * I123 /\ I118 = I119 /\ I121 = I122 /\ I124 = I125 /\ I124 = I126 /\ I124 = I127] f3#(I131, I132, I133, I134, I135, I136, I137) -> f4#(I131, I132, I133, I133, I135, I136, I136) [I138 <= I133 - 1 /\ 0 <= I133 - 1 /\ I138 <= I136 - 1 /\ -1 <= I136 - 1 /\ I139 <= I140 - 1 /\ -1 <= I140 - 1 /\ I131 - 2 * I141 = 1 /\ 0 <= I138 - 1 /\ I142 <= I131 /\ I133 = I134 /\ I136 = I137] f4#(I143, I144, I145, I146, I147, I148, I149) -> f3#(I150, 1, I151, I152, I153, 0, I154) [0 <= I146 - 1 /\ 0 <= I147 - 1 /\ -1 <= I149 - 1 /\ I153 <= I149 - 1 /\ I155 <= I146 - 1 /\ I153 <= I147 - 1 /\ 0 <= I144 - 1 /\ I143 - 2 * I156 = 1 /\ -1 <= I157 - 1 /\ I155 <= I157 - 1 /\ I150 <= I143 /\ -1 <= I155 - 1 /\ 0 <= I153 - 1 /\ I152 <= I155 /\ 0 <= I143 - 2 * I156 /\ I143 - 2 * I156 <= 1 /\ I143 - 2 * I150 <= 1 /\ 0 <= I143 - 2 * I150 /\ I153 = I154] f3#(I158, I159, I160, I161, I162, I163, I164) -> f4#(I158, I159, I160, I161, I162, I163, I164) [0 <= I161 - 1 /\ 0 <= I162 - 1 /\ -1 <= I164 - 1 /\ I165 <= I164 - 1 /\ I166 <= I161 - 1 /\ I165 <= I162 - 1 /\ 0 <= I159 - 1 /\ I158 - 2 * I167 = 1 /\ -1 <= I168 - 1 /\ I166 <= I168 - 1 /\ I169 <= I158 /\ -1 <= I166 - 1 /\ I170 <= I166 /\ 0 <= I165 - 1] f4#(I171, I172, I173, I174, I175, I176, I177) -> f3#(I178, 1, I179, I180, I181, 0, I182) [I180 <= I173 - 1 /\ 0 <= I173 - 1 /\ I183 <= I176 - 1 /\ -1 <= I176 - 1 /\ I181 <= I184 - 1 /\ -1 <= I183 - 1 /\ I183 <= I181 - 1 /\ -1 <= I184 - 1 /\ I183 <= I185 - 1 /\ I183 <= I180 - 1 /\ I171 - 2 * I186 = 0 /\ I178 <= I171 /\ 0 <= I171 - 2 * I186 /\ I171 - 2 * I186 <= 1 /\ I171 - 2 * I178 <= 1 /\ 0 <= I171 - 2 * I178 /\ I173 = I174 /\ I176 = I177 /\ I181 = I182] f3#(I187, I188, I189, I190, I191, I192, I193) -> f4#(I187, I188, I189, I189, I191, I192, I192) [I194 <= I189 - 1 /\ 0 <= I189 - 1 /\ I195 <= I192 - 1 /\ -1 <= I192 - 1 /\ I196 <= I197 - 1 /\ -1 <= I195 - 1 /\ I195 <= I196 - 1 /\ -1 <= I197 - 1 /\ I195 <= I198 - 1 /\ I195 <= I194 - 1 /\ I199 <= I187 /\ I187 - 2 * I200 = 0 /\ I189 = I190 /\ I192 = I193] R = init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) f5(I0, I1, I2, I3, I4, I5, I6) -> f5(I0 - 1, I7, I8, I9, I10, I11, I12) [0 <= I0 - 1] f1(I13, I14, I15, I16, I17, I18, I19) -> f5(I20, I21, I22, I23, I24, I25, I26) [-1 <= y2 - 1 /\ 1 <= I14 - 1 /\ -1 <= y1 - 1 /\ 0 <= I13 - 1 /\ y1 - 1 = I20] f4(I27, I28, I29, I30, I31, I32, I33) -> f3(I34, I35, I36, I37, I38, I39, I40) [I41 <= I29 - 1 /\ 0 <= I29 - 1 /\ I40 <= I32 - 1 /\ -1 <= I32 - 1 /\ I42 <= y3 - 1 /\ -1 <= y3 - 1 /\ I27 - 2 * y4 = 1 /\ I34 <= I27 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ I37 <= I41 /\ 0 <= I27 - 2 * y4 /\ I27 - 2 * y4 <= 1 /\ I27 - 2 * I34 <= 1 /\ 0 <= I27 - 2 * I34 /\ I29 = I30 /\ I32 = I33] f3(I43, I44, I45, I46, I47, I48, I49) -> f4(I43, I44, I45, I45, I47, I48, I48) [I50 <= I45 - 1 /\ 0 <= I45 - 1 /\ I51 <= I48 - 1 /\ -1 <= I48 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1 /\ I43 - 2 * y5 = 1 /\ y6 <= I43 /\ -1 <= I50 - 1 /\ y7 <= I50 /\ 0 <= I51 - 1 /\ I45 = I46 /\ I48 = I49] f4(I54, I55, I56, I57, I58, I59, I60) -> f3(I61, I62, I63, I64, I65, I59, I66) [0 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I60 - 1 /\ I66 <= I60 - 1 /\ I67 <= I57 - 1 /\ I68 <= I58 - 1 /\ 0 <= I55 - 1 /\ I54 - 2 * I69 = 1 /\ -1 <= I56 - 1 /\ I63 <= I56 /\ I64 <= I67 /\ -1 <= I67 - 1 /\ I65 <= I68 /\ 0 <= I59 - 1 /\ I61 <= I54 /\ 0 <= I66 - 1 /\ -1 <= I68 - 1 /\ 0 <= I54 - 2 * I69 /\ I54 - 2 * I69 <= 1 /\ I54 - 2 * I61 <= 1 /\ 0 <= I54 - 2 * I61] f3(I70, I71, I72, I73, I74, I75, I76) -> f4(I70, I71, I72, I73, I74, I75, I76) [0 <= I73 - 1 /\ 0 <= I74 - 1 /\ -1 <= I76 - 1 /\ I77 <= I76 - 1 /\ I78 <= I73 - 1 /\ I79 <= I74 - 1 /\ 0 <= I71 - 1 /\ I70 - 2 * I80 = 1 /\ -1 <= I72 - 1 /\ I81 <= I72 /\ I82 <= I78 /\ -1 <= I78 - 1 /\ I83 <= I79 /\ 0 <= I75 - 1 /\ y8 <= I70 /\ -1 <= I79 - 1 /\ 0 <= I77 - 1] f4(I84, I85, I86, I87, I88, I89, I90) -> f3(I91, I92, I86, I93, I94, I85, I95) [0 <= I87 - 1 /\ 0 <= I88 - 1 /\ -1 <= I89 - 1 /\ I89 <= I85 - 1 /\ I89 <= I96 - 1 /\ I89 <= I86 - 1 /\ I89 <= I97 - 1 /\ -1 <= I90 - 1 /\ I98 <= I90 - 1 /\ I98 <= I95 - 1 /\ I93 <= I87 - 1 /\ -1 <= I98 - 1 /\ I98 <= I99 - 1 /\ I94 <= I88 - 1 /\ 0 <= I85 - 1 /\ I98 <= I93 - 1 /\ I98 <= I94 - 1 /\ I84 - 2 * I100 = 0 /\ I91 <= I84 /\ 0 <= I84 - 2 * I100 /\ I84 - 2 * I100 <= 1 /\ I84 - 2 * I91 <= 1 /\ 0 <= I84 - 2 * I91] f3(I101, I102, I103, I104, I105, I106, I107) -> f4(I101, I102, I103, I104, I105, I106, I107) [0 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ I106 <= I102 - 1 /\ I106 <= I108 - 1 /\ I106 <= I103 - 1 /\ I106 <= I109 - 1 /\ -1 <= I107 - 1 /\ I110 <= I107 - 1 /\ I110 <= I111 - 1 /\ I112 <= I104 - 1 /\ -1 <= I110 - 1 /\ I110 <= I113 - 1 /\ I114 <= I105 - 1 /\ 0 <= I102 - 1 /\ I110 <= I112 - 1 /\ I110 <= I114 - 1 /\ I115 <= I101 /\ I101 - 2 * y9 = 0] f4(I116, I117, I118, I119, I120, I121, I122) -> f3(I123, 0, I124, I125, 0, I126, I127) [I124 <= I118 - 1 /\ 0 <= I118 - 1 /\ I124 <= I121 - 1 /\ -1 <= I121 - 1 /\ I128 <= I129 - 1 /\ -1 <= I129 - 1 /\ I116 - 2 * I130 = 1 /\ I123 <= I116 /\ 0 <= I124 - 1 /\ 0 <= I116 - 2 * I130 /\ I116 - 2 * I130 <= 1 /\ I116 - 2 * I123 <= 1 /\ 0 <= I116 - 2 * I123 /\ I118 = I119 /\ I121 = I122 /\ I124 = I125 /\ I124 = I126 /\ I124 = I127] f3(I131, I132, I133, I134, I135, I136, I137) -> f4(I131, I132, I133, I133, I135, I136, I136) [I138 <= I133 - 1 /\ 0 <= I133 - 1 /\ I138 <= I136 - 1 /\ -1 <= I136 - 1 /\ I139 <= I140 - 1 /\ -1 <= I140 - 1 /\ I131 - 2 * I141 = 1 /\ 0 <= I138 - 1 /\ I142 <= I131 /\ I133 = I134 /\ I136 = I137] f4(I143, I144, I145, I146, I147, I148, I149) -> f3(I150, 1, I151, I152, I153, 0, I154) [0 <= I146 - 1 /\ 0 <= I147 - 1 /\ -1 <= I149 - 1 /\ I153 <= I149 - 1 /\ I155 <= I146 - 1 /\ I153 <= I147 - 1 /\ 0 <= I144 - 1 /\ I143 - 2 * I156 = 1 /\ -1 <= I157 - 1 /\ I155 <= I157 - 1 /\ I150 <= I143 /\ -1 <= I155 - 1 /\ 0 <= I153 - 1 /\ I152 <= I155 /\ 0 <= I143 - 2 * I156 /\ I143 - 2 * I156 <= 1 /\ I143 - 2 * I150 <= 1 /\ 0 <= I143 - 2 * I150 /\ I153 = I154] f3(I158, I159, I160, I161, I162, I163, I164) -> f4(I158, I159, I160, I161, I162, I163, I164) [0 <= I161 - 1 /\ 0 <= I162 - 1 /\ -1 <= I164 - 1 /\ I165 <= I164 - 1 /\ I166 <= I161 - 1 /\ I165 <= I162 - 1 /\ 0 <= I159 - 1 /\ I158 - 2 * I167 = 1 /\ -1 <= I168 - 1 /\ I166 <= I168 - 1 /\ I169 <= I158 /\ -1 <= I166 - 1 /\ I170 <= I166 /\ 0 <= I165 - 1] f4(I171, I172, I173, I174, I175, I176, I177) -> f3(I178, 1, I179, I180, I181, 0, I182) [I180 <= I173 - 1 /\ 0 <= I173 - 1 /\ I183 <= I176 - 1 /\ -1 <= I176 - 1 /\ I181 <= I184 - 1 /\ -1 <= I183 - 1 /\ I183 <= I181 - 1 /\ -1 <= I184 - 1 /\ I183 <= I185 - 1 /\ I183 <= I180 - 1 /\ I171 - 2 * I186 = 0 /\ I178 <= I171 /\ 0 <= I171 - 2 * I186 /\ I171 - 2 * I186 <= 1 /\ I171 - 2 * I178 <= 1 /\ 0 <= I171 - 2 * I178 /\ I173 = I174 /\ I176 = I177 /\ I181 = I182] f3(I187, I188, I189, I190, I191, I192, I193) -> f4(I187, I188, I189, I189, I191, I192, I192) [I194 <= I189 - 1 /\ 0 <= I189 - 1 /\ I195 <= I192 - 1 /\ -1 <= I192 - 1 /\ I196 <= I197 - 1 /\ -1 <= I195 - 1 /\ I195 <= I196 - 1 /\ -1 <= I197 - 1 /\ I195 <= I198 - 1 /\ I195 <= I194 - 1 /\ I199 <= I187 /\ I187 - 2 * I200 = 0 /\ I189 = I190 /\ I192 = I193] f2(I201, I202, I203, I204, I205, I206, I207) -> f3(I201, 0, I202, I202, 0, I202, I202) [0 <= I202 - 1] f1(I208, I209, I210, I211, I212, I213, I214) -> f2(I215, I216, I217, I218, I219, I220, I221) [-1 <= I222 - 1 /\ 1 <= I209 - 1 /\ I216 <= 0 /\ -1 <= I215 - 1 /\ 0 <= I208 - 1] f1(I223, I224, I225, I226, I227, I228, I229) -> f2(I230, I231, I232, I233, I234, I235, I236) [-1 <= I237 - 1 /\ 1 <= I224 - 1 /\ -1 <= I230 - 1 /\ I231 <= I238 - 1 /\ -1 <= I238 - 1 /\ 0 <= I223 - 1] We use the basic value criterion with the projection function NU: NU[f3#(z1,z2,z3,z4,z5,z6,z7)] = z4 NU[f4#(z1,z2,z3,z4,z5,z6,z7)] = z4 This gives the following inequalities: I41 <= I29 - 1 /\ 0 <= I29 - 1 /\ I40 <= I32 - 1 /\ -1 <= I32 - 1 /\ I42 <= y3 - 1 /\ -1 <= y3 - 1 /\ I27 - 2 * y4 = 1 /\ I34 <= I27 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ I37 <= I41 /\ 0 <= I27 - 2 * y4 /\ I27 - 2 * y4 <= 1 /\ I27 - 2 * I34 <= 1 /\ 0 <= I27 - 2 * I34 /\ I29 = I30 /\ I32 = I33 ==> I30 >! I37 I50 <= I45 - 1 /\ 0 <= I45 - 1 /\ I51 <= I48 - 1 /\ -1 <= I48 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1 /\ I43 - 2 * y5 = 1 /\ y6 <= I43 /\ -1 <= I50 - 1 /\ y7 <= I50 /\ 0 <= I51 - 1 /\ I45 = I46 /\ I48 = I49 ==> I46 (>! \union =) I45 0 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I60 - 1 /\ I66 <= I60 - 1 /\ I67 <= I57 - 1 /\ I68 <= I58 - 1 /\ 0 <= I55 - 1 /\ I54 - 2 * I69 = 1 /\ -1 <= I56 - 1 /\ I63 <= I56 /\ I64 <= I67 /\ -1 <= I67 - 1 /\ I65 <= I68 /\ 0 <= I59 - 1 /\ I61 <= I54 /\ 0 <= I66 - 1 /\ -1 <= I68 - 1 /\ 0 <= I54 - 2 * I69 /\ I54 - 2 * I69 <= 1 /\ I54 - 2 * I61 <= 1 /\ 0 <= I54 - 2 * I61 ==> I57 >! I64 0 <= I73 - 1 /\ 0 <= I74 - 1 /\ -1 <= I76 - 1 /\ I77 <= I76 - 1 /\ I78 <= I73 - 1 /\ I79 <= I74 - 1 /\ 0 <= I71 - 1 /\ I70 - 2 * I80 = 1 /\ -1 <= I72 - 1 /\ I81 <= I72 /\ I82 <= I78 /\ -1 <= I78 - 1 /\ I83 <= I79 /\ 0 <= I75 - 1 /\ y8 <= I70 /\ -1 <= I79 - 1 /\ 0 <= I77 - 1 ==> I73 (>! \union =) I73 0 <= I87 - 1 /\ 0 <= I88 - 1 /\ -1 <= I89 - 1 /\ I89 <= I85 - 1 /\ I89 <= I96 - 1 /\ I89 <= I86 - 1 /\ I89 <= I97 - 1 /\ -1 <= I90 - 1 /\ I98 <= I90 - 1 /\ I98 <= I95 - 1 /\ I93 <= I87 - 1 /\ -1 <= I98 - 1 /\ I98 <= I99 - 1 /\ I94 <= I88 - 1 /\ 0 <= I85 - 1 /\ I98 <= I93 - 1 /\ I98 <= I94 - 1 /\ I84 - 2 * I100 = 0 /\ I91 <= I84 /\ 0 <= I84 - 2 * I100 /\ I84 - 2 * I100 <= 1 /\ I84 - 2 * I91 <= 1 /\ 0 <= I84 - 2 * I91 ==> I87 >! I93 0 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ I106 <= I102 - 1 /\ I106 <= I108 - 1 /\ I106 <= I103 - 1 /\ I106 <= I109 - 1 /\ -1 <= I107 - 1 /\ I110 <= I107 - 1 /\ I110 <= I111 - 1 /\ I112 <= I104 - 1 /\ -1 <= I110 - 1 /\ I110 <= I113 - 1 /\ I114 <= I105 - 1 /\ 0 <= I102 - 1 /\ I110 <= I112 - 1 /\ I110 <= I114 - 1 /\ I115 <= I101 /\ I101 - 2 * y9 = 0 ==> I104 (>! \union =) I104 I124 <= I118 - 1 /\ 0 <= I118 - 1 /\ I124 <= I121 - 1 /\ -1 <= I121 - 1 /\ I128 <= I129 - 1 /\ -1 <= I129 - 1 /\ I116 - 2 * I130 = 1 /\ I123 <= I116 /\ 0 <= I124 - 1 /\ 0 <= I116 - 2 * I130 /\ I116 - 2 * I130 <= 1 /\ I116 - 2 * I123 <= 1 /\ 0 <= I116 - 2 * I123 /\ I118 = I119 /\ I121 = I122 /\ I124 = I125 /\ I124 = I126 /\ I124 = I127 ==> I119 >! I125 I138 <= I133 - 1 /\ 0 <= I133 - 1 /\ I138 <= I136 - 1 /\ -1 <= I136 - 1 /\ I139 <= I140 - 1 /\ -1 <= I140 - 1 /\ I131 - 2 * I141 = 1 /\ 0 <= I138 - 1 /\ I142 <= I131 /\ I133 = I134 /\ I136 = I137 ==> I134 (>! \union =) I133 0 <= I146 - 1 /\ 0 <= I147 - 1 /\ -1 <= I149 - 1 /\ I153 <= I149 - 1 /\ I155 <= I146 - 1 /\ I153 <= I147 - 1 /\ 0 <= I144 - 1 /\ I143 - 2 * I156 = 1 /\ -1 <= I157 - 1 /\ I155 <= I157 - 1 /\ I150 <= I143 /\ -1 <= I155 - 1 /\ 0 <= I153 - 1 /\ I152 <= I155 /\ 0 <= I143 - 2 * I156 /\ I143 - 2 * I156 <= 1 /\ I143 - 2 * I150 <= 1 /\ 0 <= I143 - 2 * I150 /\ I153 = I154 ==> I146 >! I152 0 <= I161 - 1 /\ 0 <= I162 - 1 /\ -1 <= I164 - 1 /\ I165 <= I164 - 1 /\ I166 <= I161 - 1 /\ I165 <= I162 - 1 /\ 0 <= I159 - 1 /\ I158 - 2 * I167 = 1 /\ -1 <= I168 - 1 /\ I166 <= I168 - 1 /\ I169 <= I158 /\ -1 <= I166 - 1 /\ I170 <= I166 /\ 0 <= I165 - 1 ==> I161 (>! \union =) I161 I180 <= I173 - 1 /\ 0 <= I173 - 1 /\ I183 <= I176 - 1 /\ -1 <= I176 - 1 /\ I181 <= I184 - 1 /\ -1 <= I183 - 1 /\ I183 <= I181 - 1 /\ -1 <= I184 - 1 /\ I183 <= I185 - 1 /\ I183 <= I180 - 1 /\ I171 - 2 * I186 = 0 /\ I178 <= I171 /\ 0 <= I171 - 2 * I186 /\ I171 - 2 * I186 <= 1 /\ I171 - 2 * I178 <= 1 /\ 0 <= I171 - 2 * I178 /\ I173 = I174 /\ I176 = I177 /\ I181 = I182 ==> I174 >! I180 I194 <= I189 - 1 /\ 0 <= I189 - 1 /\ I195 <= I192 - 1 /\ -1 <= I192 - 1 /\ I196 <= I197 - 1 /\ -1 <= I195 - 1 /\ I195 <= I196 - 1 /\ -1 <= I197 - 1 /\ I195 <= I198 - 1 /\ I195 <= I194 - 1 /\ I199 <= I187 /\ I187 - 2 * I200 = 0 /\ I189 = I190 /\ I192 = I193 ==> I190 (>! \union =) I189 We remove all the strictly oriented dependency pairs. DP problem for innermost termination. P = f3#(I43, I44, I45, I46, I47, I48, I49) -> f4#(I43, I44, I45, I45, I47, I48, I48) [I50 <= I45 - 1 /\ 0 <= I45 - 1 /\ I51 <= I48 - 1 /\ -1 <= I48 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1 /\ I43 - 2 * y5 = 1 /\ y6 <= I43 /\ -1 <= I50 - 1 /\ y7 <= I50 /\ 0 <= I51 - 1 /\ I45 = I46 /\ I48 = I49] f3#(I70, I71, I72, I73, I74, I75, I76) -> f4#(I70, I71, I72, I73, I74, I75, I76) [0 <= I73 - 1 /\ 0 <= I74 - 1 /\ -1 <= I76 - 1 /\ I77 <= I76 - 1 /\ I78 <= I73 - 1 /\ I79 <= I74 - 1 /\ 0 <= I71 - 1 /\ I70 - 2 * I80 = 1 /\ -1 <= I72 - 1 /\ I81 <= I72 /\ I82 <= I78 /\ -1 <= I78 - 1 /\ I83 <= I79 /\ 0 <= I75 - 1 /\ y8 <= I70 /\ -1 <= I79 - 1 /\ 0 <= I77 - 1] f3#(I101, I102, I103, I104, I105, I106, I107) -> f4#(I101, I102, I103, I104, I105, I106, I107) [0 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ I106 <= I102 - 1 /\ I106 <= I108 - 1 /\ I106 <= I103 - 1 /\ I106 <= I109 - 1 /\ -1 <= I107 - 1 /\ I110 <= I107 - 1 /\ I110 <= I111 - 1 /\ I112 <= I104 - 1 /\ -1 <= I110 - 1 /\ I110 <= I113 - 1 /\ I114 <= I105 - 1 /\ 0 <= I102 - 1 /\ I110 <= I112 - 1 /\ I110 <= I114 - 1 /\ I115 <= I101 /\ I101 - 2 * y9 = 0] f3#(I131, I132, I133, I134, I135, I136, I137) -> f4#(I131, I132, I133, I133, I135, I136, I136) [I138 <= I133 - 1 /\ 0 <= I133 - 1 /\ I138 <= I136 - 1 /\ -1 <= I136 - 1 /\ I139 <= I140 - 1 /\ -1 <= I140 - 1 /\ I131 - 2 * I141 = 1 /\ 0 <= I138 - 1 /\ I142 <= I131 /\ I133 = I134 /\ I136 = I137] f3#(I158, I159, I160, I161, I162, I163, I164) -> f4#(I158, I159, I160, I161, I162, I163, I164) [0 <= I161 - 1 /\ 0 <= I162 - 1 /\ -1 <= I164 - 1 /\ I165 <= I164 - 1 /\ I166 <= I161 - 1 /\ I165 <= I162 - 1 /\ 0 <= I159 - 1 /\ I158 - 2 * I167 = 1 /\ -1 <= I168 - 1 /\ I166 <= I168 - 1 /\ I169 <= I158 /\ -1 <= I166 - 1 /\ I170 <= I166 /\ 0 <= I165 - 1] f3#(I187, I188, I189, I190, I191, I192, I193) -> f4#(I187, I188, I189, I189, I191, I192, I192) [I194 <= I189 - 1 /\ 0 <= I189 - 1 /\ I195 <= I192 - 1 /\ -1 <= I192 - 1 /\ I196 <= I197 - 1 /\ -1 <= I195 - 1 /\ I195 <= I196 - 1 /\ -1 <= I197 - 1 /\ I195 <= I198 - 1 /\ I195 <= I194 - 1 /\ I199 <= I187 /\ I187 - 2 * I200 = 0 /\ I189 = I190 /\ I192 = I193] R = init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) f5(I0, I1, I2, I3, I4, I5, I6) -> f5(I0 - 1, I7, I8, I9, I10, I11, I12) [0 <= I0 - 1] f1(I13, I14, I15, I16, I17, I18, I19) -> f5(I20, I21, I22, I23, I24, I25, I26) [-1 <= y2 - 1 /\ 1 <= I14 - 1 /\ -1 <= y1 - 1 /\ 0 <= I13 - 1 /\ y1 - 1 = I20] f4(I27, I28, I29, I30, I31, I32, I33) -> f3(I34, I35, I36, I37, I38, I39, I40) [I41 <= I29 - 1 /\ 0 <= I29 - 1 /\ I40 <= I32 - 1 /\ -1 <= I32 - 1 /\ I42 <= y3 - 1 /\ -1 <= y3 - 1 /\ I27 - 2 * y4 = 1 /\ I34 <= I27 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ I37 <= I41 /\ 0 <= I27 - 2 * y4 /\ I27 - 2 * y4 <= 1 /\ I27 - 2 * I34 <= 1 /\ 0 <= I27 - 2 * I34 /\ I29 = I30 /\ I32 = I33] f3(I43, I44, I45, I46, I47, I48, I49) -> f4(I43, I44, I45, I45, I47, I48, I48) [I50 <= I45 - 1 /\ 0 <= I45 - 1 /\ I51 <= I48 - 1 /\ -1 <= I48 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1 /\ I43 - 2 * y5 = 1 /\ y6 <= I43 /\ -1 <= I50 - 1 /\ y7 <= I50 /\ 0 <= I51 - 1 /\ I45 = I46 /\ I48 = I49] f4(I54, I55, I56, I57, I58, I59, I60) -> f3(I61, I62, I63, I64, I65, I59, I66) [0 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I60 - 1 /\ I66 <= I60 - 1 /\ I67 <= I57 - 1 /\ I68 <= I58 - 1 /\ 0 <= I55 - 1 /\ I54 - 2 * I69 = 1 /\ -1 <= I56 - 1 /\ I63 <= I56 /\ I64 <= I67 /\ -1 <= I67 - 1 /\ I65 <= I68 /\ 0 <= I59 - 1 /\ I61 <= I54 /\ 0 <= I66 - 1 /\ -1 <= I68 - 1 /\ 0 <= I54 - 2 * I69 /\ I54 - 2 * I69 <= 1 /\ I54 - 2 * I61 <= 1 /\ 0 <= I54 - 2 * I61] f3(I70, I71, I72, I73, I74, I75, I76) -> f4(I70, I71, I72, I73, I74, I75, I76) [0 <= I73 - 1 /\ 0 <= I74 - 1 /\ -1 <= I76 - 1 /\ I77 <= I76 - 1 /\ I78 <= I73 - 1 /\ I79 <= I74 - 1 /\ 0 <= I71 - 1 /\ I70 - 2 * I80 = 1 /\ -1 <= I72 - 1 /\ I81 <= I72 /\ I82 <= I78 /\ -1 <= I78 - 1 /\ I83 <= I79 /\ 0 <= I75 - 1 /\ y8 <= I70 /\ -1 <= I79 - 1 /\ 0 <= I77 - 1] f4(I84, I85, I86, I87, I88, I89, I90) -> f3(I91, I92, I86, I93, I94, I85, I95) [0 <= I87 - 1 /\ 0 <= I88 - 1 /\ -1 <= I89 - 1 /\ I89 <= I85 - 1 /\ I89 <= I96 - 1 /\ I89 <= I86 - 1 /\ I89 <= I97 - 1 /\ -1 <= I90 - 1 /\ I98 <= I90 - 1 /\ I98 <= I95 - 1 /\ I93 <= I87 - 1 /\ -1 <= I98 - 1 /\ I98 <= I99 - 1 /\ I94 <= I88 - 1 /\ 0 <= I85 - 1 /\ I98 <= I93 - 1 /\ I98 <= I94 - 1 /\ I84 - 2 * I100 = 0 /\ I91 <= I84 /\ 0 <= I84 - 2 * I100 /\ I84 - 2 * I100 <= 1 /\ I84 - 2 * I91 <= 1 /\ 0 <= I84 - 2 * I91] f3(I101, I102, I103, I104, I105, I106, I107) -> f4(I101, I102, I103, I104, I105, I106, I107) [0 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ I106 <= I102 - 1 /\ I106 <= I108 - 1 /\ I106 <= I103 - 1 /\ I106 <= I109 - 1 /\ -1 <= I107 - 1 /\ I110 <= I107 - 1 /\ I110 <= I111 - 1 /\ I112 <= I104 - 1 /\ -1 <= I110 - 1 /\ I110 <= I113 - 1 /\ I114 <= I105 - 1 /\ 0 <= I102 - 1 /\ I110 <= I112 - 1 /\ I110 <= I114 - 1 /\ I115 <= I101 /\ I101 - 2 * y9 = 0] f4(I116, I117, I118, I119, I120, I121, I122) -> f3(I123, 0, I124, I125, 0, I126, I127) [I124 <= I118 - 1 /\ 0 <= I118 - 1 /\ I124 <= I121 - 1 /\ -1 <= I121 - 1 /\ I128 <= I129 - 1 /\ -1 <= I129 - 1 /\ I116 - 2 * I130 = 1 /\ I123 <= I116 /\ 0 <= I124 - 1 /\ 0 <= I116 - 2 * I130 /\ I116 - 2 * I130 <= 1 /\ I116 - 2 * I123 <= 1 /\ 0 <= I116 - 2 * I123 /\ I118 = I119 /\ I121 = I122 /\ I124 = I125 /\ I124 = I126 /\ I124 = I127] f3(I131, I132, I133, I134, I135, I136, I137) -> f4(I131, I132, I133, I133, I135, I136, I136) [I138 <= I133 - 1 /\ 0 <= I133 - 1 /\ I138 <= I136 - 1 /\ -1 <= I136 - 1 /\ I139 <= I140 - 1 /\ -1 <= I140 - 1 /\ I131 - 2 * I141 = 1 /\ 0 <= I138 - 1 /\ I142 <= I131 /\ I133 = I134 /\ I136 = I137] f4(I143, I144, I145, I146, I147, I148, I149) -> f3(I150, 1, I151, I152, I153, 0, I154) [0 <= I146 - 1 /\ 0 <= I147 - 1 /\ -1 <= I149 - 1 /\ I153 <= I149 - 1 /\ I155 <= I146 - 1 /\ I153 <= I147 - 1 /\ 0 <= I144 - 1 /\ I143 - 2 * I156 = 1 /\ -1 <= I157 - 1 /\ I155 <= I157 - 1 /\ I150 <= I143 /\ -1 <= I155 - 1 /\ 0 <= I153 - 1 /\ I152 <= I155 /\ 0 <= I143 - 2 * I156 /\ I143 - 2 * I156 <= 1 /\ I143 - 2 * I150 <= 1 /\ 0 <= I143 - 2 * I150 /\ I153 = I154] f3(I158, I159, I160, I161, I162, I163, I164) -> f4(I158, I159, I160, I161, I162, I163, I164) [0 <= I161 - 1 /\ 0 <= I162 - 1 /\ -1 <= I164 - 1 /\ I165 <= I164 - 1 /\ I166 <= I161 - 1 /\ I165 <= I162 - 1 /\ 0 <= I159 - 1 /\ I158 - 2 * I167 = 1 /\ -1 <= I168 - 1 /\ I166 <= I168 - 1 /\ I169 <= I158 /\ -1 <= I166 - 1 /\ I170 <= I166 /\ 0 <= I165 - 1] f4(I171, I172, I173, I174, I175, I176, I177) -> f3(I178, 1, I179, I180, I181, 0, I182) [I180 <= I173 - 1 /\ 0 <= I173 - 1 /\ I183 <= I176 - 1 /\ -1 <= I176 - 1 /\ I181 <= I184 - 1 /\ -1 <= I183 - 1 /\ I183 <= I181 - 1 /\ -1 <= I184 - 1 /\ I183 <= I185 - 1 /\ I183 <= I180 - 1 /\ I171 - 2 * I186 = 0 /\ I178 <= I171 /\ 0 <= I171 - 2 * I186 /\ I171 - 2 * I186 <= 1 /\ I171 - 2 * I178 <= 1 /\ 0 <= I171 - 2 * I178 /\ I173 = I174 /\ I176 = I177 /\ I181 = I182] f3(I187, I188, I189, I190, I191, I192, I193) -> f4(I187, I188, I189, I189, I191, I192, I192) [I194 <= I189 - 1 /\ 0 <= I189 - 1 /\ I195 <= I192 - 1 /\ -1 <= I192 - 1 /\ I196 <= I197 - 1 /\ -1 <= I195 - 1 /\ I195 <= I196 - 1 /\ -1 <= I197 - 1 /\ I195 <= I198 - 1 /\ I195 <= I194 - 1 /\ I199 <= I187 /\ I187 - 2 * I200 = 0 /\ I189 = I190 /\ I192 = I193] f2(I201, I202, I203, I204, I205, I206, I207) -> f3(I201, 0, I202, I202, 0, I202, I202) [0 <= I202 - 1] f1(I208, I209, I210, I211, I212, I213, I214) -> f2(I215, I216, I217, I218, I219, I220, I221) [-1 <= I222 - 1 /\ 1 <= I209 - 1 /\ I216 <= 0 /\ -1 <= I215 - 1 /\ 0 <= I208 - 1] f1(I223, I224, I225, I226, I227, I228, I229) -> f2(I230, I231, I232, I233, I234, I235, I236) [-1 <= I237 - 1 /\ 1 <= I224 - 1 /\ -1 <= I230 - 1 /\ I231 <= I238 - 1 /\ -1 <= I238 - 1 /\ 0 <= I223 - 1] The dependency graph for this problem is: 4 -> 6 -> 8 -> 10 -> 12 -> 14 -> Where: 4) f3#(I43, I44, I45, I46, I47, I48, I49) -> f4#(I43, I44, I45, I45, I47, I48, I48) [I50 <= I45 - 1 /\ 0 <= I45 - 1 /\ I51 <= I48 - 1 /\ -1 <= I48 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1 /\ I43 - 2 * y5 = 1 /\ y6 <= I43 /\ -1 <= I50 - 1 /\ y7 <= I50 /\ 0 <= I51 - 1 /\ I45 = I46 /\ I48 = I49] 6) f3#(I70, I71, I72, I73, I74, I75, I76) -> f4#(I70, I71, I72, I73, I74, I75, I76) [0 <= I73 - 1 /\ 0 <= I74 - 1 /\ -1 <= I76 - 1 /\ I77 <= I76 - 1 /\ I78 <= I73 - 1 /\ I79 <= I74 - 1 /\ 0 <= I71 - 1 /\ I70 - 2 * I80 = 1 /\ -1 <= I72 - 1 /\ I81 <= I72 /\ I82 <= I78 /\ -1 <= I78 - 1 /\ I83 <= I79 /\ 0 <= I75 - 1 /\ y8 <= I70 /\ -1 <= I79 - 1 /\ 0 <= I77 - 1] 8) f3#(I101, I102, I103, I104, I105, I106, I107) -> f4#(I101, I102, I103, I104, I105, I106, I107) [0 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ I106 <= I102 - 1 /\ I106 <= I108 - 1 /\ I106 <= I103 - 1 /\ I106 <= I109 - 1 /\ -1 <= I107 - 1 /\ I110 <= I107 - 1 /\ I110 <= I111 - 1 /\ I112 <= I104 - 1 /\ -1 <= I110 - 1 /\ I110 <= I113 - 1 /\ I114 <= I105 - 1 /\ 0 <= I102 - 1 /\ I110 <= I112 - 1 /\ I110 <= I114 - 1 /\ I115 <= I101 /\ I101 - 2 * y9 = 0] 10) f3#(I131, I132, I133, I134, I135, I136, I137) -> f4#(I131, I132, I133, I133, I135, I136, I136) [I138 <= I133 - 1 /\ 0 <= I133 - 1 /\ I138 <= I136 - 1 /\ -1 <= I136 - 1 /\ I139 <= I140 - 1 /\ -1 <= I140 - 1 /\ I131 - 2 * I141 = 1 /\ 0 <= I138 - 1 /\ I142 <= I131 /\ I133 = I134 /\ I136 = I137] 12) f3#(I158, I159, I160, I161, I162, I163, I164) -> f4#(I158, I159, I160, I161, I162, I163, I164) [0 <= I161 - 1 /\ 0 <= I162 - 1 /\ -1 <= I164 - 1 /\ I165 <= I164 - 1 /\ I166 <= I161 - 1 /\ I165 <= I162 - 1 /\ 0 <= I159 - 1 /\ I158 - 2 * I167 = 1 /\ -1 <= I168 - 1 /\ I166 <= I168 - 1 /\ I169 <= I158 /\ -1 <= I166 - 1 /\ I170 <= I166 /\ 0 <= I165 - 1] 14) f3#(I187, I188, I189, I190, I191, I192, I193) -> f4#(I187, I188, I189, I189, I191, I192, I192) [I194 <= I189 - 1 /\ 0 <= I189 - 1 /\ I195 <= I192 - 1 /\ -1 <= I192 - 1 /\ I196 <= I197 - 1 /\ -1 <= I195 - 1 /\ I195 <= I196 - 1 /\ -1 <= I197 - 1 /\ I195 <= I198 - 1 /\ I195 <= I194 - 1 /\ I199 <= I187 /\ I187 - 2 * I200 = 0 /\ I189 = I190 /\ I192 = I193] We have the following SCCs. DP problem for innermost termination. P = f5#(I0, I1, I2, I3, I4, I5, I6) -> f5#(I0 - 1, I7, I8, I9, I10, I11, I12) [0 <= I0 - 1] R = init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) f5(I0, I1, I2, I3, I4, I5, I6) -> f5(I0 - 1, I7, I8, I9, I10, I11, I12) [0 <= I0 - 1] f1(I13, I14, I15, I16, I17, I18, I19) -> f5(I20, I21, I22, I23, I24, I25, I26) [-1 <= y2 - 1 /\ 1 <= I14 - 1 /\ -1 <= y1 - 1 /\ 0 <= I13 - 1 /\ y1 - 1 = I20] f4(I27, I28, I29, I30, I31, I32, I33) -> f3(I34, I35, I36, I37, I38, I39, I40) [I41 <= I29 - 1 /\ 0 <= I29 - 1 /\ I40 <= I32 - 1 /\ -1 <= I32 - 1 /\ I42 <= y3 - 1 /\ -1 <= y3 - 1 /\ I27 - 2 * y4 = 1 /\ I34 <= I27 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ I37 <= I41 /\ 0 <= I27 - 2 * y4 /\ I27 - 2 * y4 <= 1 /\ I27 - 2 * I34 <= 1 /\ 0 <= I27 - 2 * I34 /\ I29 = I30 /\ I32 = I33] f3(I43, I44, I45, I46, I47, I48, I49) -> f4(I43, I44, I45, I45, I47, I48, I48) [I50 <= I45 - 1 /\ 0 <= I45 - 1 /\ I51 <= I48 - 1 /\ -1 <= I48 - 1 /\ I52 <= I53 - 1 /\ -1 <= I53 - 1 /\ I43 - 2 * y5 = 1 /\ y6 <= I43 /\ -1 <= I50 - 1 /\ y7 <= I50 /\ 0 <= I51 - 1 /\ I45 = I46 /\ I48 = I49] f4(I54, I55, I56, I57, I58, I59, I60) -> f3(I61, I62, I63, I64, I65, I59, I66) [0 <= I57 - 1 /\ 0 <= I58 - 1 /\ -1 <= I60 - 1 /\ I66 <= I60 - 1 /\ I67 <= I57 - 1 /\ I68 <= I58 - 1 /\ 0 <= I55 - 1 /\ I54 - 2 * I69 = 1 /\ -1 <= I56 - 1 /\ I63 <= I56 /\ I64 <= I67 /\ -1 <= I67 - 1 /\ I65 <= I68 /\ 0 <= I59 - 1 /\ I61 <= I54 /\ 0 <= I66 - 1 /\ -1 <= I68 - 1 /\ 0 <= I54 - 2 * I69 /\ I54 - 2 * I69 <= 1 /\ I54 - 2 * I61 <= 1 /\ 0 <= I54 - 2 * I61] f3(I70, I71, I72, I73, I74, I75, I76) -> f4(I70, I71, I72, I73, I74, I75, I76) [0 <= I73 - 1 /\ 0 <= I74 - 1 /\ -1 <= I76 - 1 /\ I77 <= I76 - 1 /\ I78 <= I73 - 1 /\ I79 <= I74 - 1 /\ 0 <= I71 - 1 /\ I70 - 2 * I80 = 1 /\ -1 <= I72 - 1 /\ I81 <= I72 /\ I82 <= I78 /\ -1 <= I78 - 1 /\ I83 <= I79 /\ 0 <= I75 - 1 /\ y8 <= I70 /\ -1 <= I79 - 1 /\ 0 <= I77 - 1] f4(I84, I85, I86, I87, I88, I89, I90) -> f3(I91, I92, I86, I93, I94, I85, I95) [0 <= I87 - 1 /\ 0 <= I88 - 1 /\ -1 <= I89 - 1 /\ I89 <= I85 - 1 /\ I89 <= I96 - 1 /\ I89 <= I86 - 1 /\ I89 <= I97 - 1 /\ -1 <= I90 - 1 /\ I98 <= I90 - 1 /\ I98 <= I95 - 1 /\ I93 <= I87 - 1 /\ -1 <= I98 - 1 /\ I98 <= I99 - 1 /\ I94 <= I88 - 1 /\ 0 <= I85 - 1 /\ I98 <= I93 - 1 /\ I98 <= I94 - 1 /\ I84 - 2 * I100 = 0 /\ I91 <= I84 /\ 0 <= I84 - 2 * I100 /\ I84 - 2 * I100 <= 1 /\ I84 - 2 * I91 <= 1 /\ 0 <= I84 - 2 * I91] f3(I101, I102, I103, I104, I105, I106, I107) -> f4(I101, I102, I103, I104, I105, I106, I107) [0 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ I106 <= I102 - 1 /\ I106 <= I108 - 1 /\ I106 <= I103 - 1 /\ I106 <= I109 - 1 /\ -1 <= I107 - 1 /\ I110 <= I107 - 1 /\ I110 <= I111 - 1 /\ I112 <= I104 - 1 /\ -1 <= I110 - 1 /\ I110 <= I113 - 1 /\ I114 <= I105 - 1 /\ 0 <= I102 - 1 /\ I110 <= I112 - 1 /\ I110 <= I114 - 1 /\ I115 <= I101 /\ I101 - 2 * y9 = 0] f4(I116, I117, I118, I119, I120, I121, I122) -> f3(I123, 0, I124, I125, 0, I126, I127) [I124 <= I118 - 1 /\ 0 <= I118 - 1 /\ I124 <= I121 - 1 /\ -1 <= I121 - 1 /\ I128 <= I129 - 1 /\ -1 <= I129 - 1 /\ I116 - 2 * I130 = 1 /\ I123 <= I116 /\ 0 <= I124 - 1 /\ 0 <= I116 - 2 * I130 /\ I116 - 2 * I130 <= 1 /\ I116 - 2 * I123 <= 1 /\ 0 <= I116 - 2 * I123 /\ I118 = I119 /\ I121 = I122 /\ I124 = I125 /\ I124 = I126 /\ I124 = I127] f3(I131, I132, I133, I134, I135, I136, I137) -> f4(I131, I132, I133, I133, I135, I136, I136) [I138 <= I133 - 1 /\ 0 <= I133 - 1 /\ I138 <= I136 - 1 /\ -1 <= I136 - 1 /\ I139 <= I140 - 1 /\ -1 <= I140 - 1 /\ I131 - 2 * I141 = 1 /\ 0 <= I138 - 1 /\ I142 <= I131 /\ I133 = I134 /\ I136 = I137] f4(I143, I144, I145, I146, I147, I148, I149) -> f3(I150, 1, I151, I152, I153, 0, I154) [0 <= I146 - 1 /\ 0 <= I147 - 1 /\ -1 <= I149 - 1 /\ I153 <= I149 - 1 /\ I155 <= I146 - 1 /\ I153 <= I147 - 1 /\ 0 <= I144 - 1 /\ I143 - 2 * I156 = 1 /\ -1 <= I157 - 1 /\ I155 <= I157 - 1 /\ I150 <= I143 /\ -1 <= I155 - 1 /\ 0 <= I153 - 1 /\ I152 <= I155 /\ 0 <= I143 - 2 * I156 /\ I143 - 2 * I156 <= 1 /\ I143 - 2 * I150 <= 1 /\ 0 <= I143 - 2 * I150 /\ I153 = I154] f3(I158, I159, I160, I161, I162, I163, I164) -> f4(I158, I159, I160, I161, I162, I163, I164) [0 <= I161 - 1 /\ 0 <= I162 - 1 /\ -1 <= I164 - 1 /\ I165 <= I164 - 1 /\ I166 <= I161 - 1 /\ I165 <= I162 - 1 /\ 0 <= I159 - 1 /\ I158 - 2 * I167 = 1 /\ -1 <= I168 - 1 /\ I166 <= I168 - 1 /\ I169 <= I158 /\ -1 <= I166 - 1 /\ I170 <= I166 /\ 0 <= I165 - 1] f4(I171, I172, I173, I174, I175, I176, I177) -> f3(I178, 1, I179, I180, I181, 0, I182) [I180 <= I173 - 1 /\ 0 <= I173 - 1 /\ I183 <= I176 - 1 /\ -1 <= I176 - 1 /\ I181 <= I184 - 1 /\ -1 <= I183 - 1 /\ I183 <= I181 - 1 /\ -1 <= I184 - 1 /\ I183 <= I185 - 1 /\ I183 <= I180 - 1 /\ I171 - 2 * I186 = 0 /\ I178 <= I171 /\ 0 <= I171 - 2 * I186 /\ I171 - 2 * I186 <= 1 /\ I171 - 2 * I178 <= 1 /\ 0 <= I171 - 2 * I178 /\ I173 = I174 /\ I176 = I177 /\ I181 = I182] f3(I187, I188, I189, I190, I191, I192, I193) -> f4(I187, I188, I189, I189, I191, I192, I192) [I194 <= I189 - 1 /\ 0 <= I189 - 1 /\ I195 <= I192 - 1 /\ -1 <= I192 - 1 /\ I196 <= I197 - 1 /\ -1 <= I195 - 1 /\ I195 <= I196 - 1 /\ -1 <= I197 - 1 /\ I195 <= I198 - 1 /\ I195 <= I194 - 1 /\ I199 <= I187 /\ I187 - 2 * I200 = 0 /\ I189 = I190 /\ I192 = I193] f2(I201, I202, I203, I204, I205, I206, I207) -> f3(I201, 0, I202, I202, 0, I202, I202) [0 <= I202 - 1] f1(I208, I209, I210, I211, I212, I213, I214) -> f2(I215, I216, I217, I218, I219, I220, I221) [-1 <= I222 - 1 /\ 1 <= I209 - 1 /\ I216 <= 0 /\ -1 <= I215 - 1 /\ 0 <= I208 - 1] f1(I223, I224, I225, I226, I227, I228, I229) -> f2(I230, I231, I232, I233, I234, I235, I236) [-1 <= I237 - 1 /\ 1 <= I224 - 1 /\ -1 <= I230 - 1 /\ I231 <= I238 - 1 /\ -1 <= I238 - 1 /\ 0 <= I223 - 1] We use the basic value criterion with the projection function NU: NU[f5#(z1,z2,z3,z4,z5,z6,z7)] = z1 This gives the following inequalities: 0 <= I0 - 1 ==> I0 >! I0 - 1 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.