4.08/4.12 MAYBE 4.08/4.12 4.08/4.12 DP problem for innermost termination. 4.08/4.12 P = 4.08/4.12 init#(x1, x2, x3) -> f3#(rnd1, rnd2, rnd3) 4.08/4.12 f8#(I0, I1, I2) -> f8#(I3, I4, I5) [-1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 0 <= I0 - 1 /\ I4 + 1 <= I1 /\ I4 + 1 <= I0 /\ I3 + 1 <= I1 /\ I3 + 1 <= I0] 4.08/4.12 f6#(I6, I7, I8) -> f8#(I9, I10, I11) [-1 <= y1 - 1 /\ -1 <= y2 - 1 /\ 0 <= 5 * y3 /\ 0 <= y1 + y2 /\ 0 <= y1 + y2 + 5 * y3 - 1 /\ y4 - 2 * y5 = 0 /\ I9 <= I7 /\ I10 <= I7 /\ -1 <= I6 - 1 /\ -1 <= I7 - 1 /\ -1 <= I8 - 1 /\ -1 <= I9 - 1 /\ -1 <= I10 - 1 /\ y4 - 2 * y5 <= 1 /\ 0 <= y4 - 2 * y5] 4.08/4.12 f5#(I12, I13, I14) -> f6#(I12, I13, I14) [-1 <= I15 - 1 /\ -1 <= I16 - 1 /\ 0 <= 5 * I17 /\ 0 <= I15 + I16 /\ 0 <= I15 + I16 + 5 * I17 - 1 /\ I18 - 2 * I19 = 0 /\ y6 <= I13 /\ y7 <= I13 /\ -1 <= I12 - 1 /\ -1 <= I13 - 1 /\ -1 <= I14 - 1 /\ -1 <= y6 - 1 /\ -1 <= y7 - 1] 4.08/4.12 f6#(I20, I21, I22) -> f8#(I23, I24, I25) [-1 <= I26 - 1 /\ -1 <= I27 - 1 /\ 0 <= 5 * I28 /\ 0 <= I26 + I27 /\ 0 <= I26 + I27 + 5 * I28 - 1 /\ I29 - 2 * I30 = 0 /\ I23 <= I20 /\ I24 <= I20 /\ -1 <= I20 - 1 /\ -1 <= I21 - 1 /\ -1 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I24 - 1 /\ I29 - 2 * I30 <= 1 /\ 0 <= I29 - 2 * I30] 4.08/4.12 f5#(I31, I32, I33) -> f6#(I31, I32, I33) [-1 <= I34 - 1 /\ -1 <= I35 - 1 /\ 0 <= 5 * I36 /\ 0 <= I34 + I35 /\ 0 <= I34 + I35 + 5 * I36 - 1 /\ I37 - 2 * I38 = 0 /\ I39 <= I31 /\ I40 <= I31 /\ -1 <= I31 - 1 /\ -1 <= I32 - 1 /\ -1 <= I33 - 1 /\ -1 <= I39 - 1 /\ -1 <= I40 - 1] 4.08/4.12 f5#(I41, I42, I43) -> f8#(I44, I45, I46) [-1 <= I47 - 1 /\ -1 <= I48 - 1 /\ 0 <= 5 * I49 /\ 0 <= I47 + I48 + 5 * I49 - 1 /\ 0 <= I47 + I48 /\ I44 <= I43 /\ I45 <= I43 /\ -1 <= I41 - 1 /\ -1 <= I42 - 1 /\ -1 <= I43 - 1 /\ -1 <= I44 - 1 /\ -1 <= I45 - 1] 4.08/4.12 f5#(I50, I51, I52) -> f8#(I53, I54, I55) [-1 <= I56 - 1 /\ -1 <= I57 - 1 /\ I53 <= I51 /\ I54 <= I51 /\ -1 <= I50 - 1 /\ -1 <= I51 - 1 /\ -1 <= I52 - 1 /\ -1 <= I53 - 1 /\ -1 <= I54 - 1] 4.08/4.12 f5#(I58, I59, I60) -> f8#(I61, I62, I63) [-1 <= I62 - 1 /\ -1 <= I61 - 1 /\ -1 <= I60 - 1 /\ -1 <= I59 - 1 /\ -1 <= I58 - 1 /\ I62 <= I58 /\ I61 <= I58] 4.08/4.12 f5#(I64, I65, I66) -> f8#(I67, I68, I69) [-1 <= I68 - 1 /\ -1 <= I67 - 1 /\ -1 <= I66 - 1 /\ -1 <= I65 - 1 /\ -1 <= I64 - 1 /\ I68 <= I66 /\ I67 <= I66] 4.08/4.12 f7#(I70, I71, I72) -> f7#(I70 - 1, I70, I73) [0 <= I71 - 1] 4.08/4.12 f4#(I74, I75, I76) -> f7#(I76 * I76 - 1, I76 * I76, I77) [I76 - 2 * I78 = 0 /\ -1 <= I76 - 1 /\ 0 <= I74 - 1 /\ -1 <= I75 - 1 /\ I76 - 2 * I78 <= 1 /\ 0 <= I76 - 2 * I78] 4.08/4.12 f2#(I79, I80, I81) -> f4#(I79, I80, I81) [I81 - 2 * I82 = 0 /\ -1 <= I81 - 1 /\ 0 <= I79 - 1 /\ -1 <= I80 - 1] 4.08/4.12 f2#(I83, I84, I85) -> f7#(I85 - 1, I85, I86) [-1 <= I84 - 1 /\ 0 <= I83 - 1] 4.08/4.12 f3#(I87, I88, I89) -> f7#(I88 - 1, I88, I90) [-1 <= I88 - 1 /\ 0 <= I87 - 1] 4.08/4.12 f6#(I91, I92, I93) -> f5#(I94, I95, I96) [-1 <= I97 - 1 /\ -1 <= I98 - 1 /\ 0 <= 5 * I99 /\ 0 <= I97 + I98 /\ I100 - 2 * I101 = 0 /\ I102 <= I103 /\ 0 <= I97 + I98 + 5 * I99 - 1 /\ I94 - 2 <= I91 /\ I95 + 1 <= I92 /\ I96 - 2 <= I93 /\ -1 <= I91 - 1 /\ 0 <= I92 - 1 /\ -1 <= I93 - 1 /\ 0 <= I94 - 1 /\ -1 <= I95 - 1 /\ 0 <= I96 - 1 /\ I100 - 2 * I101 <= 1 /\ 0 <= I100 - 2 * I101] 4.08/4.12 f5#(I104, I105, I106) -> f6#(I104, I105, I106) [-1 <= I107 - 1 /\ -1 <= I108 - 1 /\ 0 <= 5 * I109 /\ 0 <= I107 + I108 /\ I110 - 2 * I111 = 0 /\ I112 <= I113 /\ 0 <= I107 + I108 + 5 * I109 - 1 /\ y8 - 2 <= I104 /\ y9 + 1 <= I105 /\ y10 - 2 <= I106 /\ -1 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ 0 <= y8 - 1 /\ -1 <= y9 - 1 /\ 0 <= y10 - 1] 4.08/4.12 f6#(I114, I115, I116) -> f5#(I117, I118, I119) [-1 <= I120 - 1 /\ -1 <= I121 - 1 /\ 0 <= 5 * I122 /\ 0 <= I120 + I121 /\ I123 - 2 * I124 = 0 /\ I125 <= I126 - 1 /\ 0 <= I120 + I121 + 5 * I122 - 1 /\ I117 + 1 <= I114 /\ I118 <= I115 /\ I119 <= I116 /\ 0 <= I114 - 1 /\ -1 <= I115 - 1 /\ -1 <= I116 - 1 /\ -1 <= I117 - 1 /\ -1 <= I118 - 1 /\ -1 <= I119 - 1 /\ I123 - 2 * I124 <= 1 /\ 0 <= I123 - 2 * I124] 4.08/4.12 f5#(I127, I128, I129) -> f6#(I127, I128, I129) [-1 <= I130 - 1 /\ -1 <= I131 - 1 /\ 0 <= 5 * I132 /\ 0 <= I130 + I131 /\ I133 - 2 * I134 = 0 /\ I135 <= I136 - 1 /\ 0 <= I130 + I131 + 5 * I132 - 1 /\ I137 + 1 <= I127 /\ I138 <= I128 /\ I139 <= I129 /\ 0 <= I127 - 1 /\ -1 <= I128 - 1 /\ -1 <= I129 - 1 /\ -1 <= I137 - 1 /\ -1 <= I138 - 1 /\ -1 <= I139 - 1] 4.08/4.12 f6#(I140, I141, I142) -> f5#(I143, I144, I145) [-1 <= I146 - 1 /\ -1 <= I147 - 1 /\ 0 <= 5 * I148 /\ 0 <= I146 + I147 /\ 0 <= I146 + I147 + 5 * I148 - 1 /\ I149 - 2 * I150 = 1 /\ I143 <= I140 /\ I144 <= I141 /\ I145 + 1 <= I142 /\ -1 <= I140 - 1 /\ -1 <= I141 - 1 /\ 0 <= I142 - 1 /\ -1 <= I143 - 1 /\ -1 <= I144 - 1 /\ -1 <= I145 - 1 /\ I149 - 2 * I150 <= 1 /\ 0 <= I149 - 2 * I150] 4.08/4.12 f5#(I151, I152, I153) -> f6#(I151, I152, I153) [-1 <= I154 - 1 /\ -1 <= I155 - 1 /\ 0 <= 5 * I156 /\ 0 <= I154 + I155 /\ 0 <= I154 + I155 + 5 * I156 - 1 /\ I157 - 2 * I158 = 1 /\ I159 <= I151 /\ I160 <= I152 /\ I161 + 1 <= I153 /\ -1 <= I151 - 1 /\ -1 <= I152 - 1 /\ 0 <= I153 - 1 /\ -1 <= I159 - 1 /\ -1 <= I160 - 1 /\ -1 <= I161 - 1] 4.08/4.12 f4#(I162, I163, I164) -> f5#(I165, I166, I167) [I164 - 2 * I168 = 0 /\ -1 <= I164 - 1 /\ I167 <= I163 /\ 0 <= I162 - 1 /\ -1 <= I163 - 1 /\ -1 <= I165 - 1 /\ -1 <= I166 - 1 /\ -1 <= I167 - 1 /\ I164 - 2 * I168 <= 1 /\ 0 <= I164 - 2 * I168] 4.08/4.12 f2#(I169, I170, I171) -> f4#(I169, I170, I171) [I171 - 2 * I172 = 0 /\ -1 <= I171 - 1 /\ I173 <= I170 /\ 0 <= I169 - 1 /\ -1 <= I170 - 1 /\ -1 <= I174 - 1 /\ -1 <= I175 - 1 /\ -1 <= I173 - 1] 4.08/4.12 f4#(I176, I177, I178) -> f5#(I179, I180, I181) [-1 <= I178 - 1 /\ I178 - 2 * I182 = 1 /\ I181 <= I177 /\ 0 <= I176 - 1 /\ -1 <= I177 - 1 /\ -1 <= I179 - 1 /\ -1 <= I180 - 1 /\ -1 <= I181 - 1 /\ I178 - 2 * I182 <= 1 /\ 0 <= I178 - 2 * I182] 4.08/4.12 f2#(I183, I184, I185) -> f4#(I183, I184, I185) [-1 <= I185 - 1 /\ I185 - 2 * I186 = 1 /\ I187 <= I184 /\ 0 <= I183 - 1 /\ -1 <= I184 - 1 /\ -1 <= I188 - 1 /\ -1 <= I189 - 1 /\ -1 <= I187 - 1] 4.08/4.12 f3#(I190, I191, I192) -> f2#(I193, I194, I191) [-1 <= I194 - 1 /\ 0 <= I193 - 1 /\ 0 <= I190 - 1 /\ -1 <= I191 - 1 /\ I193 <= I190] 4.08/4.12 f1#(I195, I196, I197) -> f2#(I198, I199, I197) [-1 <= I199 - 1 /\ 0 <= I198 - 1 /\ -1 <= I196 - 1 /\ 0 <= I195 - 1 /\ I199 <= I196 /\ I198 - 1 <= I196 /\ -1 <= I197 - 1 /\ I198 <= I195] 4.08/4.12 R = 4.08/4.12 init(x1, x2, x3) -> f3(rnd1, rnd2, rnd3) 4.08/4.12 f8(I0, I1, I2) -> f8(I3, I4, I5) [-1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 0 <= I0 - 1 /\ I4 + 1 <= I1 /\ I4 + 1 <= I0 /\ I3 + 1 <= I1 /\ I3 + 1 <= I0] 4.08/4.12 f6(I6, I7, I8) -> f8(I9, I10, I11) [-1 <= y1 - 1 /\ -1 <= y2 - 1 /\ 0 <= 5 * y3 /\ 0 <= y1 + y2 /\ 0 <= y1 + y2 + 5 * y3 - 1 /\ y4 - 2 * y5 = 0 /\ I9 <= I7 /\ I10 <= I7 /\ -1 <= I6 - 1 /\ -1 <= I7 - 1 /\ -1 <= I8 - 1 /\ -1 <= I9 - 1 /\ -1 <= I10 - 1 /\ y4 - 2 * y5 <= 1 /\ 0 <= y4 - 2 * y5] 4.08/4.12 f5(I12, I13, I14) -> f6(I12, I13, I14) [-1 <= I15 - 1 /\ -1 <= I16 - 1 /\ 0 <= 5 * I17 /\ 0 <= I15 + I16 /\ 0 <= I15 + I16 + 5 * I17 - 1 /\ I18 - 2 * I19 = 0 /\ y6 <= I13 /\ y7 <= I13 /\ -1 <= I12 - 1 /\ -1 <= I13 - 1 /\ -1 <= I14 - 1 /\ -1 <= y6 - 1 /\ -1 <= y7 - 1] 4.08/4.12 f6(I20, I21, I22) -> f8(I23, I24, I25) [-1 <= I26 - 1 /\ -1 <= I27 - 1 /\ 0 <= 5 * I28 /\ 0 <= I26 + I27 /\ 0 <= I26 + I27 + 5 * I28 - 1 /\ I29 - 2 * I30 = 0 /\ I23 <= I20 /\ I24 <= I20 /\ -1 <= I20 - 1 /\ -1 <= I21 - 1 /\ -1 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I24 - 1 /\ I29 - 2 * I30 <= 1 /\ 0 <= I29 - 2 * I30] 4.08/4.12 f5(I31, I32, I33) -> f6(I31, I32, I33) [-1 <= I34 - 1 /\ -1 <= I35 - 1 /\ 0 <= 5 * I36 /\ 0 <= I34 + I35 /\ 0 <= I34 + I35 + 5 * I36 - 1 /\ I37 - 2 * I38 = 0 /\ I39 <= I31 /\ I40 <= I31 /\ -1 <= I31 - 1 /\ -1 <= I32 - 1 /\ -1 <= I33 - 1 /\ -1 <= I39 - 1 /\ -1 <= I40 - 1] 4.08/4.12 f5(I41, I42, I43) -> f8(I44, I45, I46) [-1 <= I47 - 1 /\ -1 <= I48 - 1 /\ 0 <= 5 * I49 /\ 0 <= I47 + I48 + 5 * I49 - 1 /\ 0 <= I47 + I48 /\ I44 <= I43 /\ I45 <= I43 /\ -1 <= I41 - 1 /\ -1 <= I42 - 1 /\ -1 <= I43 - 1 /\ -1 <= I44 - 1 /\ -1 <= I45 - 1] 4.08/4.12 f5(I50, I51, I52) -> f8(I53, I54, I55) [-1 <= I56 - 1 /\ -1 <= I57 - 1 /\ I53 <= I51 /\ I54 <= I51 /\ -1 <= I50 - 1 /\ -1 <= I51 - 1 /\ -1 <= I52 - 1 /\ -1 <= I53 - 1 /\ -1 <= I54 - 1] 4.08/4.12 f5(I58, I59, I60) -> f8(I61, I62, I63) [-1 <= I62 - 1 /\ -1 <= I61 - 1 /\ -1 <= I60 - 1 /\ -1 <= I59 - 1 /\ -1 <= I58 - 1 /\ I62 <= I58 /\ I61 <= I58] 4.08/4.12 f5(I64, I65, I66) -> f8(I67, I68, I69) [-1 <= I68 - 1 /\ -1 <= I67 - 1 /\ -1 <= I66 - 1 /\ -1 <= I65 - 1 /\ -1 <= I64 - 1 /\ I68 <= I66 /\ I67 <= I66] 4.08/4.12 f7(I70, I71, I72) -> f7(I70 - 1, I70, I73) [0 <= I71 - 1] 4.08/4.12 f4(I74, I75, I76) -> f7(I76 * I76 - 1, I76 * I76, I77) [I76 - 2 * I78 = 0 /\ -1 <= I76 - 1 /\ 0 <= I74 - 1 /\ -1 <= I75 - 1 /\ I76 - 2 * I78 <= 1 /\ 0 <= I76 - 2 * I78] 4.08/4.12 f2(I79, I80, I81) -> f4(I79, I80, I81) [I81 - 2 * I82 = 0 /\ -1 <= I81 - 1 /\ 0 <= I79 - 1 /\ -1 <= I80 - 1] 4.08/4.12 f2(I83, I84, I85) -> f7(I85 - 1, I85, I86) [-1 <= I84 - 1 /\ 0 <= I83 - 1] 4.08/4.12 f3(I87, I88, I89) -> f7(I88 - 1, I88, I90) [-1 <= I88 - 1 /\ 0 <= I87 - 1] 4.08/4.12 f6(I91, I92, I93) -> f5(I94, I95, I96) [-1 <= I97 - 1 /\ -1 <= I98 - 1 /\ 0 <= 5 * I99 /\ 0 <= I97 + I98 /\ I100 - 2 * I101 = 0 /\ I102 <= I103 /\ 0 <= I97 + I98 + 5 * I99 - 1 /\ I94 - 2 <= I91 /\ I95 + 1 <= I92 /\ I96 - 2 <= I93 /\ -1 <= I91 - 1 /\ 0 <= I92 - 1 /\ -1 <= I93 - 1 /\ 0 <= I94 - 1 /\ -1 <= I95 - 1 /\ 0 <= I96 - 1 /\ I100 - 2 * I101 <= 1 /\ 0 <= I100 - 2 * I101] 4.08/4.12 f5(I104, I105, I106) -> f6(I104, I105, I106) [-1 <= I107 - 1 /\ -1 <= I108 - 1 /\ 0 <= 5 * I109 /\ 0 <= I107 + I108 /\ I110 - 2 * I111 = 0 /\ I112 <= I113 /\ 0 <= I107 + I108 + 5 * I109 - 1 /\ y8 - 2 <= I104 /\ y9 + 1 <= I105 /\ y10 - 2 <= I106 /\ -1 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ 0 <= y8 - 1 /\ -1 <= y9 - 1 /\ 0 <= y10 - 1] 4.08/4.12 f6(I114, I115, I116) -> f5(I117, I118, I119) [-1 <= I120 - 1 /\ -1 <= I121 - 1 /\ 0 <= 5 * I122 /\ 0 <= I120 + I121 /\ I123 - 2 * I124 = 0 /\ I125 <= I126 - 1 /\ 0 <= I120 + I121 + 5 * I122 - 1 /\ I117 + 1 <= I114 /\ I118 <= I115 /\ I119 <= I116 /\ 0 <= I114 - 1 /\ -1 <= I115 - 1 /\ -1 <= I116 - 1 /\ -1 <= I117 - 1 /\ -1 <= I118 - 1 /\ -1 <= I119 - 1 /\ I123 - 2 * I124 <= 1 /\ 0 <= I123 - 2 * I124] 4.08/4.12 f5(I127, I128, I129) -> f6(I127, I128, I129) [-1 <= I130 - 1 /\ -1 <= I131 - 1 /\ 0 <= 5 * I132 /\ 0 <= I130 + I131 /\ I133 - 2 * I134 = 0 /\ I135 <= I136 - 1 /\ 0 <= I130 + I131 + 5 * I132 - 1 /\ I137 + 1 <= I127 /\ I138 <= I128 /\ I139 <= I129 /\ 0 <= I127 - 1 /\ -1 <= I128 - 1 /\ -1 <= I129 - 1 /\ -1 <= I137 - 1 /\ -1 <= I138 - 1 /\ -1 <= I139 - 1] 4.08/4.12 f6(I140, I141, I142) -> f5(I143, I144, I145) [-1 <= I146 - 1 /\ -1 <= I147 - 1 /\ 0 <= 5 * I148 /\ 0 <= I146 + I147 /\ 0 <= I146 + I147 + 5 * I148 - 1 /\ I149 - 2 * I150 = 1 /\ I143 <= I140 /\ I144 <= I141 /\ I145 + 1 <= I142 /\ -1 <= I140 - 1 /\ -1 <= I141 - 1 /\ 0 <= I142 - 1 /\ -1 <= I143 - 1 /\ -1 <= I144 - 1 /\ -1 <= I145 - 1 /\ I149 - 2 * I150 <= 1 /\ 0 <= I149 - 2 * I150] 4.08/4.12 f5(I151, I152, I153) -> f6(I151, I152, I153) [-1 <= I154 - 1 /\ -1 <= I155 - 1 /\ 0 <= 5 * I156 /\ 0 <= I154 + I155 /\ 0 <= I154 + I155 + 5 * I156 - 1 /\ I157 - 2 * I158 = 1 /\ I159 <= I151 /\ I160 <= I152 /\ I161 + 1 <= I153 /\ -1 <= I151 - 1 /\ -1 <= I152 - 1 /\ 0 <= I153 - 1 /\ -1 <= I159 - 1 /\ -1 <= I160 - 1 /\ -1 <= I161 - 1] 4.08/4.12 f4(I162, I163, I164) -> f5(I165, I166, I167) [I164 - 2 * I168 = 0 /\ -1 <= I164 - 1 /\ I167 <= I163 /\ 0 <= I162 - 1 /\ -1 <= I163 - 1 /\ -1 <= I165 - 1 /\ -1 <= I166 - 1 /\ -1 <= I167 - 1 /\ I164 - 2 * I168 <= 1 /\ 0 <= I164 - 2 * I168] 4.08/4.12 f2(I169, I170, I171) -> f4(I169, I170, I171) [I171 - 2 * I172 = 0 /\ -1 <= I171 - 1 /\ I173 <= I170 /\ 0 <= I169 - 1 /\ -1 <= I170 - 1 /\ -1 <= I174 - 1 /\ -1 <= I175 - 1 /\ -1 <= I173 - 1] 4.08/4.12 f4(I176, I177, I178) -> f5(I179, I180, I181) [-1 <= I178 - 1 /\ I178 - 2 * I182 = 1 /\ I181 <= I177 /\ 0 <= I176 - 1 /\ -1 <= I177 - 1 /\ -1 <= I179 - 1 /\ -1 <= I180 - 1 /\ -1 <= I181 - 1 /\ I178 - 2 * I182 <= 1 /\ 0 <= I178 - 2 * I182] 4.08/4.12 f2(I183, I184, I185) -> f4(I183, I184, I185) [-1 <= I185 - 1 /\ I185 - 2 * I186 = 1 /\ I187 <= I184 /\ 0 <= I183 - 1 /\ -1 <= I184 - 1 /\ -1 <= I188 - 1 /\ -1 <= I189 - 1 /\ -1 <= I187 - 1] 4.08/4.12 f3(I190, I191, I192) -> f2(I193, I194, I191) [-1 <= I194 - 1 /\ 0 <= I193 - 1 /\ 0 <= I190 - 1 /\ -1 <= I191 - 1 /\ I193 <= I190] 4.08/4.12 f1(I195, I196, I197) -> f2(I198, I199, I197) [-1 <= I199 - 1 /\ 0 <= I198 - 1 /\ -1 <= I196 - 1 /\ 0 <= I195 - 1 /\ I199 <= I196 /\ I198 - 1 <= I196 /\ -1 <= I197 - 1 /\ I198 <= I195] 4.08/4.12 4.08/4.12 The dependency graph for this problem is: 4.08/4.12 0 -> 14, 25 4.08/4.12 1 -> 1 4.08/4.12 2 -> 1 4.08/4.12 3 -> 2, 4, 15, 17, 19 4.08/4.12 4 -> 1 4.08/4.12 5 -> 2, 4, 15, 17, 19 4.08/4.12 6 -> 1 4.08/4.12 7 -> 1 4.08/4.12 8 -> 1 4.08/4.12 9 -> 1 4.08/4.12 10 -> 10 4.08/4.12 11 -> 10 4.08/4.12 12 -> 11, 21 4.08/4.12 13 -> 10 4.08/4.12 14 -> 10 4.08/4.12 15 -> 3, 5, 6, 7, 8, 9, 16, 18, 20 4.08/4.12 16 -> 2, 4, 15, 17, 19 4.08/4.12 17 -> 3, 5, 6, 7, 8, 9, 16, 18, 20 4.08/4.12 18 -> 2, 4, 15, 17, 19 4.08/4.12 19 -> 3, 5, 6, 7, 8, 9, 16, 18, 20 4.08/4.12 20 -> 2, 4, 15, 17, 19 4.08/4.12 21 -> 3, 5, 6, 7, 8, 9, 16, 18, 20 4.08/4.12 22 -> 11, 21 4.08/4.12 23 -> 3, 5, 6, 7, 8, 9, 16, 18, 20 4.08/4.12 24 -> 23 4.08/4.12 25 -> 12, 13, 22, 24 4.08/4.12 26 -> 12, 13, 22, 24 4.08/4.12 Where: 4.08/4.12 0) init#(x1, x2, x3) -> f3#(rnd1, rnd2, rnd3) 4.08/4.12 1) f8#(I0, I1, I2) -> f8#(I3, I4, I5) [-1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 0 <= I0 - 1 /\ I4 + 1 <= I1 /\ I4 + 1 <= I0 /\ I3 + 1 <= I1 /\ I3 + 1 <= I0] 4.08/4.12 2) f6#(I6, I7, I8) -> f8#(I9, I10, I11) [-1 <= y1 - 1 /\ -1 <= y2 - 1 /\ 0 <= 5 * y3 /\ 0 <= y1 + y2 /\ 0 <= y1 + y2 + 5 * y3 - 1 /\ y4 - 2 * y5 = 0 /\ I9 <= I7 /\ I10 <= I7 /\ -1 <= I6 - 1 /\ -1 <= I7 - 1 /\ -1 <= I8 - 1 /\ -1 <= I9 - 1 /\ -1 <= I10 - 1 /\ y4 - 2 * y5 <= 1 /\ 0 <= y4 - 2 * y5] 4.08/4.12 3) f5#(I12, I13, I14) -> f6#(I12, I13, I14) [-1 <= I15 - 1 /\ -1 <= I16 - 1 /\ 0 <= 5 * I17 /\ 0 <= I15 + I16 /\ 0 <= I15 + I16 + 5 * I17 - 1 /\ I18 - 2 * I19 = 0 /\ y6 <= I13 /\ y7 <= I13 /\ -1 <= I12 - 1 /\ -1 <= I13 - 1 /\ -1 <= I14 - 1 /\ -1 <= y6 - 1 /\ -1 <= y7 - 1] 4.08/4.12 4) f6#(I20, I21, I22) -> f8#(I23, I24, I25) [-1 <= I26 - 1 /\ -1 <= I27 - 1 /\ 0 <= 5 * I28 /\ 0 <= I26 + I27 /\ 0 <= I26 + I27 + 5 * I28 - 1 /\ I29 - 2 * I30 = 0 /\ I23 <= I20 /\ I24 <= I20 /\ -1 <= I20 - 1 /\ -1 <= I21 - 1 /\ -1 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I24 - 1 /\ I29 - 2 * I30 <= 1 /\ 0 <= I29 - 2 * I30] 4.08/4.12 5) f5#(I31, I32, I33) -> f6#(I31, I32, I33) [-1 <= I34 - 1 /\ -1 <= I35 - 1 /\ 0 <= 5 * I36 /\ 0 <= I34 + I35 /\ 0 <= I34 + I35 + 5 * I36 - 1 /\ I37 - 2 * I38 = 0 /\ I39 <= I31 /\ I40 <= I31 /\ -1 <= I31 - 1 /\ -1 <= I32 - 1 /\ -1 <= I33 - 1 /\ -1 <= I39 - 1 /\ -1 <= I40 - 1] 4.08/4.12 6) f5#(I41, I42, I43) -> f8#(I44, I45, I46) [-1 <= I47 - 1 /\ -1 <= I48 - 1 /\ 0 <= 5 * I49 /\ 0 <= I47 + I48 + 5 * I49 - 1 /\ 0 <= I47 + I48 /\ I44 <= I43 /\ I45 <= I43 /\ -1 <= I41 - 1 /\ -1 <= I42 - 1 /\ -1 <= I43 - 1 /\ -1 <= I44 - 1 /\ -1 <= I45 - 1] 4.08/4.12 7) f5#(I50, I51, I52) -> f8#(I53, I54, I55) [-1 <= I56 - 1 /\ -1 <= I57 - 1 /\ I53 <= I51 /\ I54 <= I51 /\ -1 <= I50 - 1 /\ -1 <= I51 - 1 /\ -1 <= I52 - 1 /\ -1 <= I53 - 1 /\ -1 <= I54 - 1] 4.08/4.12 8) f5#(I58, I59, I60) -> f8#(I61, I62, I63) [-1 <= I62 - 1 /\ -1 <= I61 - 1 /\ -1 <= I60 - 1 /\ -1 <= I59 - 1 /\ -1 <= I58 - 1 /\ I62 <= I58 /\ I61 <= I58] 4.08/4.12 9) f5#(I64, I65, I66) -> f8#(I67, I68, I69) [-1 <= I68 - 1 /\ -1 <= I67 - 1 /\ -1 <= I66 - 1 /\ -1 <= I65 - 1 /\ -1 <= I64 - 1 /\ I68 <= I66 /\ I67 <= I66] 4.08/4.12 10) f7#(I70, I71, I72) -> f7#(I70 - 1, I70, I73) [0 <= I71 - 1] 4.08/4.12 11) f4#(I74, I75, I76) -> f7#(I76 * I76 - 1, I76 * I76, I77) [I76 - 2 * I78 = 0 /\ -1 <= I76 - 1 /\ 0 <= I74 - 1 /\ -1 <= I75 - 1 /\ I76 - 2 * I78 <= 1 /\ 0 <= I76 - 2 * I78] 4.08/4.12 12) f2#(I79, I80, I81) -> f4#(I79, I80, I81) [I81 - 2 * I82 = 0 /\ -1 <= I81 - 1 /\ 0 <= I79 - 1 /\ -1 <= I80 - 1] 4.08/4.12 13) f2#(I83, I84, I85) -> f7#(I85 - 1, I85, I86) [-1 <= I84 - 1 /\ 0 <= I83 - 1] 4.08/4.12 14) f3#(I87, I88, I89) -> f7#(I88 - 1, I88, I90) [-1 <= I88 - 1 /\ 0 <= I87 - 1] 4.08/4.12 15) f6#(I91, I92, I93) -> f5#(I94, I95, I96) [-1 <= I97 - 1 /\ -1 <= I98 - 1 /\ 0 <= 5 * I99 /\ 0 <= I97 + I98 /\ I100 - 2 * I101 = 0 /\ I102 <= I103 /\ 0 <= I97 + I98 + 5 * I99 - 1 /\ I94 - 2 <= I91 /\ I95 + 1 <= I92 /\ I96 - 2 <= I93 /\ -1 <= I91 - 1 /\ 0 <= I92 - 1 /\ -1 <= I93 - 1 /\ 0 <= I94 - 1 /\ -1 <= I95 - 1 /\ 0 <= I96 - 1 /\ I100 - 2 * I101 <= 1 /\ 0 <= I100 - 2 * I101] 4.08/4.12 16) f5#(I104, I105, I106) -> f6#(I104, I105, I106) [-1 <= I107 - 1 /\ -1 <= I108 - 1 /\ 0 <= 5 * I109 /\ 0 <= I107 + I108 /\ I110 - 2 * I111 = 0 /\ I112 <= I113 /\ 0 <= I107 + I108 + 5 * I109 - 1 /\ y8 - 2 <= I104 /\ y9 + 1 <= I105 /\ y10 - 2 <= I106 /\ -1 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ 0 <= y8 - 1 /\ -1 <= y9 - 1 /\ 0 <= y10 - 1] 4.08/4.12 17) f6#(I114, I115, I116) -> f5#(I117, I118, I119) [-1 <= I120 - 1 /\ -1 <= I121 - 1 /\ 0 <= 5 * I122 /\ 0 <= I120 + I121 /\ I123 - 2 * I124 = 0 /\ I125 <= I126 - 1 /\ 0 <= I120 + I121 + 5 * I122 - 1 /\ I117 + 1 <= I114 /\ I118 <= I115 /\ I119 <= I116 /\ 0 <= I114 - 1 /\ -1 <= I115 - 1 /\ -1 <= I116 - 1 /\ -1 <= I117 - 1 /\ -1 <= I118 - 1 /\ -1 <= I119 - 1 /\ I123 - 2 * I124 <= 1 /\ 0 <= I123 - 2 * I124] 4.08/4.12 18) f5#(I127, I128, I129) -> f6#(I127, I128, I129) [-1 <= I130 - 1 /\ -1 <= I131 - 1 /\ 0 <= 5 * I132 /\ 0 <= I130 + I131 /\ I133 - 2 * I134 = 0 /\ I135 <= I136 - 1 /\ 0 <= I130 + I131 + 5 * I132 - 1 /\ I137 + 1 <= I127 /\ I138 <= I128 /\ I139 <= I129 /\ 0 <= I127 - 1 /\ -1 <= I128 - 1 /\ -1 <= I129 - 1 /\ -1 <= I137 - 1 /\ -1 <= I138 - 1 /\ -1 <= I139 - 1] 4.08/4.12 19) f6#(I140, I141, I142) -> f5#(I143, I144, I145) [-1 <= I146 - 1 /\ -1 <= I147 - 1 /\ 0 <= 5 * I148 /\ 0 <= I146 + I147 /\ 0 <= I146 + I147 + 5 * I148 - 1 /\ I149 - 2 * I150 = 1 /\ I143 <= I140 /\ I144 <= I141 /\ I145 + 1 <= I142 /\ -1 <= I140 - 1 /\ -1 <= I141 - 1 /\ 0 <= I142 - 1 /\ -1 <= I143 - 1 /\ -1 <= I144 - 1 /\ -1 <= I145 - 1 /\ I149 - 2 * I150 <= 1 /\ 0 <= I149 - 2 * I150] 4.08/4.12 20) f5#(I151, I152, I153) -> f6#(I151, I152, I153) [-1 <= I154 - 1 /\ -1 <= I155 - 1 /\ 0 <= 5 * I156 /\ 0 <= I154 + I155 /\ 0 <= I154 + I155 + 5 * I156 - 1 /\ I157 - 2 * I158 = 1 /\ I159 <= I151 /\ I160 <= I152 /\ I161 + 1 <= I153 /\ -1 <= I151 - 1 /\ -1 <= I152 - 1 /\ 0 <= I153 - 1 /\ -1 <= I159 - 1 /\ -1 <= I160 - 1 /\ -1 <= I161 - 1] 4.08/4.12 21) f4#(I162, I163, I164) -> f5#(I165, I166, I167) [I164 - 2 * I168 = 0 /\ -1 <= I164 - 1 /\ I167 <= I163 /\ 0 <= I162 - 1 /\ -1 <= I163 - 1 /\ -1 <= I165 - 1 /\ -1 <= I166 - 1 /\ -1 <= I167 - 1 /\ I164 - 2 * I168 <= 1 /\ 0 <= I164 - 2 * I168] 4.08/4.12 22) f2#(I169, I170, I171) -> f4#(I169, I170, I171) [I171 - 2 * I172 = 0 /\ -1 <= I171 - 1 /\ I173 <= I170 /\ 0 <= I169 - 1 /\ -1 <= I170 - 1 /\ -1 <= I174 - 1 /\ -1 <= I175 - 1 /\ -1 <= I173 - 1] 4.08/4.12 23) f4#(I176, I177, I178) -> f5#(I179, I180, I181) [-1 <= I178 - 1 /\ I178 - 2 * I182 = 1 /\ I181 <= I177 /\ 0 <= I176 - 1 /\ -1 <= I177 - 1 /\ -1 <= I179 - 1 /\ -1 <= I180 - 1 /\ -1 <= I181 - 1 /\ I178 - 2 * I182 <= 1 /\ 0 <= I178 - 2 * I182] 4.08/4.12 24) f2#(I183, I184, I185) -> f4#(I183, I184, I185) [-1 <= I185 - 1 /\ I185 - 2 * I186 = 1 /\ I187 <= I184 /\ 0 <= I183 - 1 /\ -1 <= I184 - 1 /\ -1 <= I188 - 1 /\ -1 <= I189 - 1 /\ -1 <= I187 - 1] 4.08/4.12 25) f3#(I190, I191, I192) -> f2#(I193, I194, I191) [-1 <= I194 - 1 /\ 0 <= I193 - 1 /\ 0 <= I190 - 1 /\ -1 <= I191 - 1 /\ I193 <= I190] 4.08/4.12 26) f1#(I195, I196, I197) -> f2#(I198, I199, I197) [-1 <= I199 - 1 /\ 0 <= I198 - 1 /\ -1 <= I196 - 1 /\ 0 <= I195 - 1 /\ I199 <= I196 /\ I198 - 1 <= I196 /\ -1 <= I197 - 1 /\ I198 <= I195] 4.08/4.12 4.08/4.12 We have the following SCCs. 4.08/4.12 { 3, 5, 15, 16, 17, 18, 19, 20 } 4.08/4.12 { 1 } 4.08/4.12 { 10 } 4.08/4.12 4.08/4.12 DP problem for innermost termination. 4.08/4.12 P = 4.08/4.12 f7#(I70, I71, I72) -> f7#(I70 - 1, I70, I73) [0 <= I71 - 1] 4.08/4.12 R = 4.08/4.12 init(x1, x2, x3) -> f3(rnd1, rnd2, rnd3) 4.08/4.12 f8(I0, I1, I2) -> f8(I3, I4, I5) [-1 <= I4 - 1 /\ -1 <= I3 - 1 /\ 0 <= I1 - 1 /\ 0 <= I0 - 1 /\ I4 + 1 <= I1 /\ I4 + 1 <= I0 /\ I3 + 1 <= I1 /\ I3 + 1 <= I0] 4.08/4.12 f6(I6, I7, I8) -> f8(I9, I10, I11) [-1 <= y1 - 1 /\ -1 <= y2 - 1 /\ 0 <= 5 * y3 /\ 0 <= y1 + y2 /\ 0 <= y1 + y2 + 5 * y3 - 1 /\ y4 - 2 * y5 = 0 /\ I9 <= I7 /\ I10 <= I7 /\ -1 <= I6 - 1 /\ -1 <= I7 - 1 /\ -1 <= I8 - 1 /\ -1 <= I9 - 1 /\ -1 <= I10 - 1 /\ y4 - 2 * y5 <= 1 /\ 0 <= y4 - 2 * y5] 4.08/4.12 f5(I12, I13, I14) -> f6(I12, I13, I14) [-1 <= I15 - 1 /\ -1 <= I16 - 1 /\ 0 <= 5 * I17 /\ 0 <= I15 + I16 /\ 0 <= I15 + I16 + 5 * I17 - 1 /\ I18 - 2 * I19 = 0 /\ y6 <= I13 /\ y7 <= I13 /\ -1 <= I12 - 1 /\ -1 <= I13 - 1 /\ -1 <= I14 - 1 /\ -1 <= y6 - 1 /\ -1 <= y7 - 1] 4.08/4.12 f6(I20, I21, I22) -> f8(I23, I24, I25) [-1 <= I26 - 1 /\ -1 <= I27 - 1 /\ 0 <= 5 * I28 /\ 0 <= I26 + I27 /\ 0 <= I26 + I27 + 5 * I28 - 1 /\ I29 - 2 * I30 = 0 /\ I23 <= I20 /\ I24 <= I20 /\ -1 <= I20 - 1 /\ -1 <= I21 - 1 /\ -1 <= I22 - 1 /\ -1 <= I23 - 1 /\ -1 <= I24 - 1 /\ I29 - 2 * I30 <= 1 /\ 0 <= I29 - 2 * I30] 4.08/4.12 f5(I31, I32, I33) -> f6(I31, I32, I33) [-1 <= I34 - 1 /\ -1 <= I35 - 1 /\ 0 <= 5 * I36 /\ 0 <= I34 + I35 /\ 0 <= I34 + I35 + 5 * I36 - 1 /\ I37 - 2 * I38 = 0 /\ I39 <= I31 /\ I40 <= I31 /\ -1 <= I31 - 1 /\ -1 <= I32 - 1 /\ -1 <= I33 - 1 /\ -1 <= I39 - 1 /\ -1 <= I40 - 1] 4.08/4.12 f5(I41, I42, I43) -> f8(I44, I45, I46) [-1 <= I47 - 1 /\ -1 <= I48 - 1 /\ 0 <= 5 * I49 /\ 0 <= I47 + I48 + 5 * I49 - 1 /\ 0 <= I47 + I48 /\ I44 <= I43 /\ I45 <= I43 /\ -1 <= I41 - 1 /\ -1 <= I42 - 1 /\ -1 <= I43 - 1 /\ -1 <= I44 - 1 /\ -1 <= I45 - 1] 4.08/4.12 f5(I50, I51, I52) -> f8(I53, I54, I55) [-1 <= I56 - 1 /\ -1 <= I57 - 1 /\ I53 <= I51 /\ I54 <= I51 /\ -1 <= I50 - 1 /\ -1 <= I51 - 1 /\ -1 <= I52 - 1 /\ -1 <= I53 - 1 /\ -1 <= I54 - 1] 4.08/4.12 f5(I58, I59, I60) -> f8(I61, I62, I63) [-1 <= I62 - 1 /\ -1 <= I61 - 1 /\ -1 <= I60 - 1 /\ -1 <= I59 - 1 /\ -1 <= I58 - 1 /\ I62 <= I58 /\ I61 <= I58] 4.08/4.12 f5(I64, I65, I66) -> f8(I67, I68, I69) [-1 <= I68 - 1 /\ -1 <= I67 - 1 /\ -1 <= I66 - 1 /\ -1 <= I65 - 1 /\ -1 <= I64 - 1 /\ I68 <= I66 /\ I67 <= I66] 4.08/4.12 f7(I70, I71, I72) -> f7(I70 - 1, I70, I73) [0 <= I71 - 1] 4.08/4.12 f4(I74, I75, I76) -> f7(I76 * I76 - 1, I76 * I76, I77) [I76 - 2 * I78 = 0 /\ -1 <= I76 - 1 /\ 0 <= I74 - 1 /\ -1 <= I75 - 1 /\ I76 - 2 * I78 <= 1 /\ 0 <= I76 - 2 * I78] 4.08/4.12 f2(I79, I80, I81) -> f4(I79, I80, I81) [I81 - 2 * I82 = 0 /\ -1 <= I81 - 1 /\ 0 <= I79 - 1 /\ -1 <= I80 - 1] 4.08/4.12 f2(I83, I84, I85) -> f7(I85 - 1, I85, I86) [-1 <= I84 - 1 /\ 0 <= I83 - 1] 4.08/4.12 f3(I87, I88, I89) -> f7(I88 - 1, I88, I90) [-1 <= I88 - 1 /\ 0 <= I87 - 1] 4.08/4.12 f6(I91, I92, I93) -> f5(I94, I95, I96) [-1 <= I97 - 1 /\ -1 <= I98 - 1 /\ 0 <= 5 * I99 /\ 0 <= I97 + I98 /\ I100 - 2 * I101 = 0 /\ I102 <= I103 /\ 0 <= I97 + I98 + 5 * I99 - 1 /\ I94 - 2 <= I91 /\ I95 + 1 <= I92 /\ I96 - 2 <= I93 /\ -1 <= I91 - 1 /\ 0 <= I92 - 1 /\ -1 <= I93 - 1 /\ 0 <= I94 - 1 /\ -1 <= I95 - 1 /\ 0 <= I96 - 1 /\ I100 - 2 * I101 <= 1 /\ 0 <= I100 - 2 * I101] 4.08/4.12 f5(I104, I105, I106) -> f6(I104, I105, I106) [-1 <= I107 - 1 /\ -1 <= I108 - 1 /\ 0 <= 5 * I109 /\ 0 <= I107 + I108 /\ I110 - 2 * I111 = 0 /\ I112 <= I113 /\ 0 <= I107 + I108 + 5 * I109 - 1 /\ y8 - 2 <= I104 /\ y9 + 1 <= I105 /\ y10 - 2 <= I106 /\ -1 <= I104 - 1 /\ 0 <= I105 - 1 /\ -1 <= I106 - 1 /\ 0 <= y8 - 1 /\ -1 <= y9 - 1 /\ 0 <= y10 - 1] 4.08/4.12 f6(I114, I115, I116) -> f5(I117, I118, I119) [-1 <= I120 - 1 /\ -1 <= I121 - 1 /\ 0 <= 5 * I122 /\ 0 <= I120 + I121 /\ I123 - 2 * I124 = 0 /\ I125 <= I126 - 1 /\ 0 <= I120 + I121 + 5 * I122 - 1 /\ I117 + 1 <= I114 /\ I118 <= I115 /\ I119 <= I116 /\ 0 <= I114 - 1 /\ -1 <= I115 - 1 /\ -1 <= I116 - 1 /\ -1 <= I117 - 1 /\ -1 <= I118 - 1 /\ -1 <= I119 - 1 /\ I123 - 2 * I124 <= 1 /\ 0 <= I123 - 2 * I124] 4.08/4.12 f5(I127, I128, I129) -> f6(I127, I128, I129) [-1 <= I130 - 1 /\ -1 <= I131 - 1 /\ 0 <= 5 * I132 /\ 0 <= I130 + I131 /\ I133 - 2 * I134 = 0 /\ I135 <= I136 - 1 /\ 0 <= I130 + I131 + 5 * I132 - 1 /\ I137 + 1 <= I127 /\ I138 <= I128 /\ I139 <= I129 /\ 0 <= I127 - 1 /\ -1 <= I128 - 1 /\ -1 <= I129 - 1 /\ -1 <= I137 - 1 /\ -1 <= I138 - 1 /\ -1 <= I139 - 1] 4.08/4.12 f6(I140, I141, I142) -> f5(I143, I144, I145) [-1 <= I146 - 1 /\ -1 <= I147 - 1 /\ 0 <= 5 * I148 /\ 0 <= I146 + I147 /\ 0 <= I146 + I147 + 5 * I148 - 1 /\ I149 - 2 * I150 = 1 /\ I143 <= I140 /\ I144 <= I141 /\ I145 + 1 <= I142 /\ -1 <= I140 - 1 /\ -1 <= I141 - 1 /\ 0 <= I142 - 1 /\ -1 <= I143 - 1 /\ -1 <= I144 - 1 /\ -1 <= I145 - 1 /\ I149 - 2 * I150 <= 1 /\ 0 <= I149 - 2 * I150] 4.08/4.12 f5(I151, I152, I153) -> f6(I151, I152, I153) [-1 <= I154 - 1 /\ -1 <= I155 - 1 /\ 0 <= 5 * I156 /\ 0 <= I154 + I155 /\ 0 <= I154 + I155 + 5 * I156 - 1 /\ I157 - 2 * I158 = 1 /\ I159 <= I151 /\ I160 <= I152 /\ I161 + 1 <= I153 /\ -1 <= I151 - 1 /\ -1 <= I152 - 1 /\ 0 <= I153 - 1 /\ -1 <= I159 - 1 /\ -1 <= I160 - 1 /\ -1 <= I161 - 1] 4.08/4.12 f4(I162, I163, I164) -> f5(I165, I166, I167) [I164 - 2 * I168 = 0 /\ -1 <= I164 - 1 /\ I167 <= I163 /\ 0 <= I162 - 1 /\ -1 <= I163 - 1 /\ -1 <= I165 - 1 /\ -1 <= I166 - 1 /\ -1 <= I167 - 1 /\ I164 - 2 * I168 <= 1 /\ 0 <= I164 - 2 * I168] 4.08/4.12 f2(I169, I170, I171) -> f4(I169, I170, I171) [I171 - 2 * I172 = 0 /\ -1 <= I171 - 1 /\ I173 <= I170 /\ 0 <= I169 - 1 /\ -1 <= I170 - 1 /\ -1 <= I174 - 1 /\ -1 <= I175 - 1 /\ -1 <= I173 - 1] 4.08/4.12 f4(I176, I177, I178) -> f5(I179, I180, I181) [-1 <= I178 - 1 /\ I178 - 2 * I182 = 1 /\ I181 <= I177 /\ 0 <= I176 - 1 /\ -1 <= I177 - 1 /\ -1 <= I179 - 1 /\ -1 <= I180 - 1 /\ -1 <= I181 - 1 /\ I178 - 2 * I182 <= 1 /\ 0 <= I178 - 2 * I182] 4.08/4.12 f2(I183, I184, I185) -> f4(I183, I184, I185) [-1 <= I185 - 1 /\ I185 - 2 * I186 = 1 /\ I187 <= I184 /\ 0 <= I183 - 1 /\ -1 <= I184 - 1 /\ -1 <= I188 - 1 /\ -1 <= I189 - 1 /\ -1 <= I187 - 1] 4.08/4.12 f3(I190, I191, I192) -> f2(I193, I194, I191) [-1 <= I194 - 1 /\ 0 <= I193 - 1 /\ 0 <= I190 - 1 /\ -1 <= I191 - 1 /\ I193 <= I190] 4.08/4.12 f1(I195, I196, I197) -> f2(I198, I199, I197) [-1 <= I199 - 1 /\ 0 <= I198 - 1 /\ -1 <= I196 - 1 /\ 0 <= I195 - 1 /\ I199 <= I196 /\ I198 - 1 <= I196 /\ -1 <= I197 - 1 /\ I198 <= I195] 4.08/4.12 4.08/7.10 EOF