28.81/28.87 MAYBE 28.81/28.87 28.81/28.87 DP problem for innermost termination. 28.81/28.87 P = 28.81/28.87 init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 28.81/28.87 f9#(I0, I1, I2, I3, I4) -> f9#(I5, I6, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 + 1 <= I1 /\ I6 + 3 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0] 28.81/28.87 f8#(I10, I11, I12, I13, I14) -> f9#(I15, I16, I17, I18, I19) [-1 <= I16 - 1 /\ 0 <= I15 - 1 /\ -1 <= I12 - 1 /\ 1 <= I11 - 1 /\ 0 <= I10 - 1 /\ I16 + 1 <= I10 /\ I15 <= I10] 28.81/28.87 f8#(I20, I21, I22, I23, I24) -> f8#(I25, I26, I27, I28, I29) [-1 <= I27 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I22 - 1 /\ 2 <= I21 - 1 /\ 2 <= I20 - 1 /\ I27 + 1 <= I22 /\ I27 + 3 <= I21 /\ I26 <= I22 /\ I26 + 2 <= I21 /\ I25 + 2 <= I20] 28.81/28.87 f5#(I30, I31, I32, I33, I34) -> f8#(I35, I36, I37, I38, I39) [-1 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 0 <= I32 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 1 <= I32 /\ I37 + 3 <= I31 /\ I36 <= I32 /\ I36 + 2 <= I31 /\ I35 + 2 <= I30] 28.81/28.87 f7#(I40, I41, I42, I43, I44) -> f5#(I45, I46, I47, I48, I49) [2 <= I47 - 1 /\ 4 <= I46 - 1 /\ 0 <= I45 - 1 /\ 4 <= I41 - 1 /\ 0 <= I40 - 1 /\ I47 + 2 <= I41 /\ I46 <= I41 /\ I45 <= I40] 28.81/28.87 f5#(I50, I51, I52, I53, I54) -> f7#(I55, I56, I57, I58, I59) [6 <= I56 - 1 /\ 1 <= I55 - 1 /\ 4 <= I52 - 1 /\ 6 <= I51 - 1 /\ 2 <= I50 - 1 /\ I56 - 2 <= I52 /\ I56 <= I51 /\ I55 + 3 <= I52 /\ I55 + 5 <= I51 /\ I55 + 1 <= I50] 28.81/28.87 f5#(I60, I61, I62, I63, I64) -> f7#(I65, I66, I67, I68, I69) [6 <= I66 - 1 /\ 0 <= I65 - 1 /\ 4 <= I62 - 1 /\ 6 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I62 /\ I66 <= I61] 28.81/28.87 f5#(I70, I71, I72, I73, I74) -> f7#(I75, I76, I77, I78, I79) [5 <= I76 - 1 /\ 0 <= I75 - 1 /\ 3 <= I72 - 1 /\ 5 <= I71 - 1 /\ 2 <= I70 - 1 /\ I76 - 2 <= I72 /\ I76 <= I71 /\ I76 - 3 <= I70] 28.81/28.87 f6#(I80, I81, I82, I83, I84) -> f5#(I85, I86, I87, I88, I89) [1 <= I87 - 1 /\ 3 <= I86 - 1 /\ 0 <= I85 - 1 /\ 0 <= I80 - 1 /\ I87 - 1 <= I80 /\ I86 - 3 <= I80 /\ I85 <= I80] 28.81/28.87 f5#(I90, I91, I92, I93, I94) -> f6#(I95, I96, I97, I98, I99) [1 <= I95 - 1 /\ 1 <= I92 - 1 /\ 3 <= I91 - 1 /\ 2 <= I90 - 1 /\ I95 <= I92 /\ I95 + 2 <= I91 /\ I95 + 1 <= I90] 28.81/28.87 f5#(I100, I101, I102, I103, I104) -> f6#(I105, I106, I107, I108, I109) [2 <= I105 - 1 /\ 1 <= I102 - 1 /\ 3 <= I101 - 1 /\ 2 <= I100 - 1] 28.81/28.87 f5#(I110, I111, I112, I113, I114) -> f5#(I115, I116, I117, I118, I119) [2 <= I117 - 1 /\ 4 <= I116 - 1 /\ 1 <= I115 - 1 /\ 2 <= I112 - 1 /\ 4 <= I111 - 1 /\ 2 <= I110 - 1 /\ I117 <= I112 /\ I117 + 2 <= I111 /\ I116 - 2 <= I112 /\ I116 <= I111 /\ I115 + 1 <= I112 /\ I115 + 3 <= I111 /\ I115 + 1 <= I110] 28.81/28.87 f3#(I120, I121, I122, I123, I124) -> f5#(I125, I126, I127, I128, I129) [I124 + 2 <= I121 /\ -1 <= I127 - 1 /\ 0 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I122 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ I127 + 1 <= I122 /\ I126 <= I122 /\ 1 <= I123 - 1 /\ I125 <= I121] 28.81/28.87 f4#(I130, I131, I132, I133, I134) -> f4#(I130 - 1, I135, I136, I137, I138) [I130 - 1 <= I130 - 1 /\ 0 <= I130 - 1] 28.81/28.87 f2#(I139, I140, I141, I142, I143) -> f4#(I144, I145, I146, I147, I148) [0 <= I140 - 1 /\ 0 <= I139 - 1 /\ 1 <= I141 - 1 /\ -1 <= I144 - 1] 28.81/28.87 f1#(I149, I150, I151, I152, I153) -> f4#(I154, I155, I156, I157, I158) [0 <= I149 - 1 /\ 0 <= I150 - 1 /\ -1 <= I154 - 1] 28.81/28.87 f2#(I159, I160, I161, I162, I163) -> f3#(I164, I165, I166, I161, I167) [-1 <= y1 - 1 /\ 1 <= I161 - 1 /\ I164 <= I159 /\ I164 <= I160 /\ I165 <= I159 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 2 <= I166 - 1 /\ I167 + 2 <= I159] 28.81/28.87 f2#(I168, I169, I170, I171, I172) -> f3#(I173, I174, I175, I170, I176) [I176 + 2 <= I168 /\ 1 <= I175 - 1 /\ 0 <= I174 - 1 /\ 0 <= I173 - 1 /\ 0 <= I169 - 1 /\ 0 <= I168 - 1 /\ I175 - 1 <= I169 /\ I175 - 1 <= I168 /\ I174 <= I168 /\ I173 <= I169 /\ 1 <= I170 - 1 /\ I173 <= I168] 28.81/28.87 f1#(I177, I178, I179, I180, I181) -> f2#(I182, I183, I178, I184, I185) [0 <= I183 - 1 /\ 1 <= I182 - 1 /\ 0 <= I177 - 1 /\ I183 <= I177 /\ 0 <= I178 - 1 /\ I182 - 1 <= I177] 28.81/28.87 f1#(I186, I187, I188, I189, I190) -> f2#(I191, I192, I187, I193, I194) [-1 <= I195 - 1 /\ 0 <= I187 - 1 /\ I192 <= I186 /\ 0 <= I186 - 1 /\ 2 <= I191 - 1 /\ 0 <= I192 - 1] 28.81/28.87 R = 28.81/28.87 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 28.81/28.87 f9(I0, I1, I2, I3, I4) -> f9(I5, I6, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 + 1 <= I1 /\ I6 + 3 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0] 28.81/28.87 f8(I10, I11, I12, I13, I14) -> f9(I15, I16, I17, I18, I19) [-1 <= I16 - 1 /\ 0 <= I15 - 1 /\ -1 <= I12 - 1 /\ 1 <= I11 - 1 /\ 0 <= I10 - 1 /\ I16 + 1 <= I10 /\ I15 <= I10] 28.81/28.87 f8(I20, I21, I22, I23, I24) -> f8(I25, I26, I27, I28, I29) [-1 <= I27 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I22 - 1 /\ 2 <= I21 - 1 /\ 2 <= I20 - 1 /\ I27 + 1 <= I22 /\ I27 + 3 <= I21 /\ I26 <= I22 /\ I26 + 2 <= I21 /\ I25 + 2 <= I20] 28.81/28.87 f5(I30, I31, I32, I33, I34) -> f8(I35, I36, I37, I38, I39) [-1 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 0 <= I32 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 1 <= I32 /\ I37 + 3 <= I31 /\ I36 <= I32 /\ I36 + 2 <= I31 /\ I35 + 2 <= I30] 28.81/28.87 f7(I40, I41, I42, I43, I44) -> f5(I45, I46, I47, I48, I49) [2 <= I47 - 1 /\ 4 <= I46 - 1 /\ 0 <= I45 - 1 /\ 4 <= I41 - 1 /\ 0 <= I40 - 1 /\ I47 + 2 <= I41 /\ I46 <= I41 /\ I45 <= I40] 28.81/28.87 f5(I50, I51, I52, I53, I54) -> f7(I55, I56, I57, I58, I59) [6 <= I56 - 1 /\ 1 <= I55 - 1 /\ 4 <= I52 - 1 /\ 6 <= I51 - 1 /\ 2 <= I50 - 1 /\ I56 - 2 <= I52 /\ I56 <= I51 /\ I55 + 3 <= I52 /\ I55 + 5 <= I51 /\ I55 + 1 <= I50] 28.81/28.87 f5(I60, I61, I62, I63, I64) -> f7(I65, I66, I67, I68, I69) [6 <= I66 - 1 /\ 0 <= I65 - 1 /\ 4 <= I62 - 1 /\ 6 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I62 /\ I66 <= I61] 28.81/28.87 f5(I70, I71, I72, I73, I74) -> f7(I75, I76, I77, I78, I79) [5 <= I76 - 1 /\ 0 <= I75 - 1 /\ 3 <= I72 - 1 /\ 5 <= I71 - 1 /\ 2 <= I70 - 1 /\ I76 - 2 <= I72 /\ I76 <= I71 /\ I76 - 3 <= I70] 28.81/28.87 f6(I80, I81, I82, I83, I84) -> f5(I85, I86, I87, I88, I89) [1 <= I87 - 1 /\ 3 <= I86 - 1 /\ 0 <= I85 - 1 /\ 0 <= I80 - 1 /\ I87 - 1 <= I80 /\ I86 - 3 <= I80 /\ I85 <= I80] 28.81/28.87 f5(I90, I91, I92, I93, I94) -> f6(I95, I96, I97, I98, I99) [1 <= I95 - 1 /\ 1 <= I92 - 1 /\ 3 <= I91 - 1 /\ 2 <= I90 - 1 /\ I95 <= I92 /\ I95 + 2 <= I91 /\ I95 + 1 <= I90] 28.81/28.87 f5(I100, I101, I102, I103, I104) -> f6(I105, I106, I107, I108, I109) [2 <= I105 - 1 /\ 1 <= I102 - 1 /\ 3 <= I101 - 1 /\ 2 <= I100 - 1] 28.81/28.87 f5(I110, I111, I112, I113, I114) -> f5(I115, I116, I117, I118, I119) [2 <= I117 - 1 /\ 4 <= I116 - 1 /\ 1 <= I115 - 1 /\ 2 <= I112 - 1 /\ 4 <= I111 - 1 /\ 2 <= I110 - 1 /\ I117 <= I112 /\ I117 + 2 <= I111 /\ I116 - 2 <= I112 /\ I116 <= I111 /\ I115 + 1 <= I112 /\ I115 + 3 <= I111 /\ I115 + 1 <= I110] 28.81/28.87 f3(I120, I121, I122, I123, I124) -> f5(I125, I126, I127, I128, I129) [I124 + 2 <= I121 /\ -1 <= I127 - 1 /\ 0 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I122 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ I127 + 1 <= I122 /\ I126 <= I122 /\ 1 <= I123 - 1 /\ I125 <= I121] 28.81/28.87 f4(I130, I131, I132, I133, I134) -> f4(I130 - 1, I135, I136, I137, I138) [I130 - 1 <= I130 - 1 /\ 0 <= I130 - 1] 28.81/28.87 f2(I139, I140, I141, I142, I143) -> f4(I144, I145, I146, I147, I148) [0 <= I140 - 1 /\ 0 <= I139 - 1 /\ 1 <= I141 - 1 /\ -1 <= I144 - 1] 28.81/28.87 f1(I149, I150, I151, I152, I153) -> f4(I154, I155, I156, I157, I158) [0 <= I149 - 1 /\ 0 <= I150 - 1 /\ -1 <= I154 - 1] 28.81/28.87 f2(I159, I160, I161, I162, I163) -> f3(I164, I165, I166, I161, I167) [-1 <= y1 - 1 /\ 1 <= I161 - 1 /\ I164 <= I159 /\ I164 <= I160 /\ I165 <= I159 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 2 <= I166 - 1 /\ I167 + 2 <= I159] 28.81/28.87 f2(I168, I169, I170, I171, I172) -> f3(I173, I174, I175, I170, I176) [I176 + 2 <= I168 /\ 1 <= I175 - 1 /\ 0 <= I174 - 1 /\ 0 <= I173 - 1 /\ 0 <= I169 - 1 /\ 0 <= I168 - 1 /\ I175 - 1 <= I169 /\ I175 - 1 <= I168 /\ I174 <= I168 /\ I173 <= I169 /\ 1 <= I170 - 1 /\ I173 <= I168] 28.81/28.87 f1(I177, I178, I179, I180, I181) -> f2(I182, I183, I178, I184, I185) [0 <= I183 - 1 /\ 1 <= I182 - 1 /\ 0 <= I177 - 1 /\ I183 <= I177 /\ 0 <= I178 - 1 /\ I182 - 1 <= I177] 28.81/28.87 f1(I186, I187, I188, I189, I190) -> f2(I191, I192, I187, I193, I194) [-1 <= I195 - 1 /\ 0 <= I187 - 1 /\ I192 <= I186 /\ 0 <= I186 - 1 /\ 2 <= I191 - 1 /\ 0 <= I192 - 1] 28.81/28.87 28.81/28.87 The dependency graph for this problem is: 28.81/28.87 0 -> 16, 19, 20 28.81/28.87 1 -> 1 28.81/28.87 2 -> 1 28.81/28.87 3 -> 2, 3 28.81/28.87 4 -> 2, 3 28.81/28.87 5 -> 4, 6, 7, 8, 10, 11, 12 28.81/28.87 6 -> 5 28.81/28.87 7 -> 5 28.81/28.87 8 -> 5 28.81/28.87 9 -> 4, 6, 7, 8, 10, 11, 12 28.81/28.87 10 -> 9 28.81/28.87 11 -> 9 28.81/28.87 12 -> 4, 6, 7, 8, 10, 11, 12 28.81/28.87 13 -> 4, 6, 7, 8, 10, 11, 12 28.81/28.87 14 -> 14 28.81/28.87 15 -> 14 28.81/28.87 16 -> 14 28.81/28.87 17 -> 13 28.81/28.87 18 -> 13 28.81/28.87 19 -> 15, 17, 18 28.81/28.87 20 -> 15, 17, 18 28.81/28.87 Where: 28.81/28.87 0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 28.81/28.87 1) f9#(I0, I1, I2, I3, I4) -> f9#(I5, I6, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 + 1 <= I1 /\ I6 + 3 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0] 28.81/28.87 2) f8#(I10, I11, I12, I13, I14) -> f9#(I15, I16, I17, I18, I19) [-1 <= I16 - 1 /\ 0 <= I15 - 1 /\ -1 <= I12 - 1 /\ 1 <= I11 - 1 /\ 0 <= I10 - 1 /\ I16 + 1 <= I10 /\ I15 <= I10] 28.81/28.87 3) f8#(I20, I21, I22, I23, I24) -> f8#(I25, I26, I27, I28, I29) [-1 <= I27 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I22 - 1 /\ 2 <= I21 - 1 /\ 2 <= I20 - 1 /\ I27 + 1 <= I22 /\ I27 + 3 <= I21 /\ I26 <= I22 /\ I26 + 2 <= I21 /\ I25 + 2 <= I20] 28.81/28.87 4) f5#(I30, I31, I32, I33, I34) -> f8#(I35, I36, I37, I38, I39) [-1 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 0 <= I32 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 1 <= I32 /\ I37 + 3 <= I31 /\ I36 <= I32 /\ I36 + 2 <= I31 /\ I35 + 2 <= I30] 28.81/28.87 5) f7#(I40, I41, I42, I43, I44) -> f5#(I45, I46, I47, I48, I49) [2 <= I47 - 1 /\ 4 <= I46 - 1 /\ 0 <= I45 - 1 /\ 4 <= I41 - 1 /\ 0 <= I40 - 1 /\ I47 + 2 <= I41 /\ I46 <= I41 /\ I45 <= I40] 28.81/28.87 6) f5#(I50, I51, I52, I53, I54) -> f7#(I55, I56, I57, I58, I59) [6 <= I56 - 1 /\ 1 <= I55 - 1 /\ 4 <= I52 - 1 /\ 6 <= I51 - 1 /\ 2 <= I50 - 1 /\ I56 - 2 <= I52 /\ I56 <= I51 /\ I55 + 3 <= I52 /\ I55 + 5 <= I51 /\ I55 + 1 <= I50] 28.81/28.87 7) f5#(I60, I61, I62, I63, I64) -> f7#(I65, I66, I67, I68, I69) [6 <= I66 - 1 /\ 0 <= I65 - 1 /\ 4 <= I62 - 1 /\ 6 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I62 /\ I66 <= I61] 28.81/28.87 8) f5#(I70, I71, I72, I73, I74) -> f7#(I75, I76, I77, I78, I79) [5 <= I76 - 1 /\ 0 <= I75 - 1 /\ 3 <= I72 - 1 /\ 5 <= I71 - 1 /\ 2 <= I70 - 1 /\ I76 - 2 <= I72 /\ I76 <= I71 /\ I76 - 3 <= I70] 28.81/28.87 9) f6#(I80, I81, I82, I83, I84) -> f5#(I85, I86, I87, I88, I89) [1 <= I87 - 1 /\ 3 <= I86 - 1 /\ 0 <= I85 - 1 /\ 0 <= I80 - 1 /\ I87 - 1 <= I80 /\ I86 - 3 <= I80 /\ I85 <= I80] 28.81/28.87 10) f5#(I90, I91, I92, I93, I94) -> f6#(I95, I96, I97, I98, I99) [1 <= I95 - 1 /\ 1 <= I92 - 1 /\ 3 <= I91 - 1 /\ 2 <= I90 - 1 /\ I95 <= I92 /\ I95 + 2 <= I91 /\ I95 + 1 <= I90] 28.81/28.87 11) f5#(I100, I101, I102, I103, I104) -> f6#(I105, I106, I107, I108, I109) [2 <= I105 - 1 /\ 1 <= I102 - 1 /\ 3 <= I101 - 1 /\ 2 <= I100 - 1] 28.81/28.87 12) f5#(I110, I111, I112, I113, I114) -> f5#(I115, I116, I117, I118, I119) [2 <= I117 - 1 /\ 4 <= I116 - 1 /\ 1 <= I115 - 1 /\ 2 <= I112 - 1 /\ 4 <= I111 - 1 /\ 2 <= I110 - 1 /\ I117 <= I112 /\ I117 + 2 <= I111 /\ I116 - 2 <= I112 /\ I116 <= I111 /\ I115 + 1 <= I112 /\ I115 + 3 <= I111 /\ I115 + 1 <= I110] 28.81/28.87 13) f3#(I120, I121, I122, I123, I124) -> f5#(I125, I126, I127, I128, I129) [I124 + 2 <= I121 /\ -1 <= I127 - 1 /\ 0 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I122 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ I127 + 1 <= I122 /\ I126 <= I122 /\ 1 <= I123 - 1 /\ I125 <= I121] 28.81/28.87 14) f4#(I130, I131, I132, I133, I134) -> f4#(I130 - 1, I135, I136, I137, I138) [I130 - 1 <= I130 - 1 /\ 0 <= I130 - 1] 28.81/28.87 15) f2#(I139, I140, I141, I142, I143) -> f4#(I144, I145, I146, I147, I148) [0 <= I140 - 1 /\ 0 <= I139 - 1 /\ 1 <= I141 - 1 /\ -1 <= I144 - 1] 28.81/28.87 16) f1#(I149, I150, I151, I152, I153) -> f4#(I154, I155, I156, I157, I158) [0 <= I149 - 1 /\ 0 <= I150 - 1 /\ -1 <= I154 - 1] 28.81/28.87 17) f2#(I159, I160, I161, I162, I163) -> f3#(I164, I165, I166, I161, I167) [-1 <= y1 - 1 /\ 1 <= I161 - 1 /\ I164 <= I159 /\ I164 <= I160 /\ I165 <= I159 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 2 <= I166 - 1 /\ I167 + 2 <= I159] 28.81/28.87 18) f2#(I168, I169, I170, I171, I172) -> f3#(I173, I174, I175, I170, I176) [I176 + 2 <= I168 /\ 1 <= I175 - 1 /\ 0 <= I174 - 1 /\ 0 <= I173 - 1 /\ 0 <= I169 - 1 /\ 0 <= I168 - 1 /\ I175 - 1 <= I169 /\ I175 - 1 <= I168 /\ I174 <= I168 /\ I173 <= I169 /\ 1 <= I170 - 1 /\ I173 <= I168] 28.81/28.87 19) f1#(I177, I178, I179, I180, I181) -> f2#(I182, I183, I178, I184, I185) [0 <= I183 - 1 /\ 1 <= I182 - 1 /\ 0 <= I177 - 1 /\ I183 <= I177 /\ 0 <= I178 - 1 /\ I182 - 1 <= I177] 28.81/28.87 20) f1#(I186, I187, I188, I189, I190) -> f2#(I191, I192, I187, I193, I194) [-1 <= I195 - 1 /\ 0 <= I187 - 1 /\ I192 <= I186 /\ 0 <= I186 - 1 /\ 2 <= I191 - 1 /\ 0 <= I192 - 1] 28.81/28.87 28.81/28.87 We have the following SCCs. 28.81/28.87 { 5, 6, 7, 8, 9, 10, 11, 12 } 28.81/28.87 { 3 } 28.81/28.87 { 1 } 28.81/28.87 { 14 } 28.81/28.87 28.81/28.87 DP problem for innermost termination. 28.81/28.87 P = 28.81/28.87 f4#(I130, I131, I132, I133, I134) -> f4#(I130 - 1, I135, I136, I137, I138) [I130 - 1 <= I130 - 1 /\ 0 <= I130 - 1] 28.81/28.87 R = 28.81/28.87 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 28.81/28.87 f9(I0, I1, I2, I3, I4) -> f9(I5, I6, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 + 1 <= I1 /\ I6 + 3 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0] 28.81/28.87 f8(I10, I11, I12, I13, I14) -> f9(I15, I16, I17, I18, I19) [-1 <= I16 - 1 /\ 0 <= I15 - 1 /\ -1 <= I12 - 1 /\ 1 <= I11 - 1 /\ 0 <= I10 - 1 /\ I16 + 1 <= I10 /\ I15 <= I10] 28.81/28.87 f8(I20, I21, I22, I23, I24) -> f8(I25, I26, I27, I28, I29) [-1 <= I27 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I22 - 1 /\ 2 <= I21 - 1 /\ 2 <= I20 - 1 /\ I27 + 1 <= I22 /\ I27 + 3 <= I21 /\ I26 <= I22 /\ I26 + 2 <= I21 /\ I25 + 2 <= I20] 28.81/28.87 f5(I30, I31, I32, I33, I34) -> f8(I35, I36, I37, I38, I39) [-1 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 0 <= I32 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 1 <= I32 /\ I37 + 3 <= I31 /\ I36 <= I32 /\ I36 + 2 <= I31 /\ I35 + 2 <= I30] 28.81/28.87 f7(I40, I41, I42, I43, I44) -> f5(I45, I46, I47, I48, I49) [2 <= I47 - 1 /\ 4 <= I46 - 1 /\ 0 <= I45 - 1 /\ 4 <= I41 - 1 /\ 0 <= I40 - 1 /\ I47 + 2 <= I41 /\ I46 <= I41 /\ I45 <= I40] 28.81/28.87 f5(I50, I51, I52, I53, I54) -> f7(I55, I56, I57, I58, I59) [6 <= I56 - 1 /\ 1 <= I55 - 1 /\ 4 <= I52 - 1 /\ 6 <= I51 - 1 /\ 2 <= I50 - 1 /\ I56 - 2 <= I52 /\ I56 <= I51 /\ I55 + 3 <= I52 /\ I55 + 5 <= I51 /\ I55 + 1 <= I50] 28.81/28.87 f5(I60, I61, I62, I63, I64) -> f7(I65, I66, I67, I68, I69) [6 <= I66 - 1 /\ 0 <= I65 - 1 /\ 4 <= I62 - 1 /\ 6 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I62 /\ I66 <= I61] 28.81/28.87 f5(I70, I71, I72, I73, I74) -> f7(I75, I76, I77, I78, I79) [5 <= I76 - 1 /\ 0 <= I75 - 1 /\ 3 <= I72 - 1 /\ 5 <= I71 - 1 /\ 2 <= I70 - 1 /\ I76 - 2 <= I72 /\ I76 <= I71 /\ I76 - 3 <= I70] 28.81/28.87 f6(I80, I81, I82, I83, I84) -> f5(I85, I86, I87, I88, I89) [1 <= I87 - 1 /\ 3 <= I86 - 1 /\ 0 <= I85 - 1 /\ 0 <= I80 - 1 /\ I87 - 1 <= I80 /\ I86 - 3 <= I80 /\ I85 <= I80] 28.81/28.87 f5(I90, I91, I92, I93, I94) -> f6(I95, I96, I97, I98, I99) [1 <= I95 - 1 /\ 1 <= I92 - 1 /\ 3 <= I91 - 1 /\ 2 <= I90 - 1 /\ I95 <= I92 /\ I95 + 2 <= I91 /\ I95 + 1 <= I90] 28.81/28.87 f5(I100, I101, I102, I103, I104) -> f6(I105, I106, I107, I108, I109) [2 <= I105 - 1 /\ 1 <= I102 - 1 /\ 3 <= I101 - 1 /\ 2 <= I100 - 1] 28.81/28.87 f5(I110, I111, I112, I113, I114) -> f5(I115, I116, I117, I118, I119) [2 <= I117 - 1 /\ 4 <= I116 - 1 /\ 1 <= I115 - 1 /\ 2 <= I112 - 1 /\ 4 <= I111 - 1 /\ 2 <= I110 - 1 /\ I117 <= I112 /\ I117 + 2 <= I111 /\ I116 - 2 <= I112 /\ I116 <= I111 /\ I115 + 1 <= I112 /\ I115 + 3 <= I111 /\ I115 + 1 <= I110] 28.81/28.87 f3(I120, I121, I122, I123, I124) -> f5(I125, I126, I127, I128, I129) [I124 + 2 <= I121 /\ -1 <= I127 - 1 /\ 0 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I122 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ I127 + 1 <= I122 /\ I126 <= I122 /\ 1 <= I123 - 1 /\ I125 <= I121] 28.81/28.87 f4(I130, I131, I132, I133, I134) -> f4(I130 - 1, I135, I136, I137, I138) [I130 - 1 <= I130 - 1 /\ 0 <= I130 - 1] 28.81/28.87 f2(I139, I140, I141, I142, I143) -> f4(I144, I145, I146, I147, I148) [0 <= I140 - 1 /\ 0 <= I139 - 1 /\ 1 <= I141 - 1 /\ -1 <= I144 - 1] 28.81/28.87 f1(I149, I150, I151, I152, I153) -> f4(I154, I155, I156, I157, I158) [0 <= I149 - 1 /\ 0 <= I150 - 1 /\ -1 <= I154 - 1] 28.81/28.87 f2(I159, I160, I161, I162, I163) -> f3(I164, I165, I166, I161, I167) [-1 <= y1 - 1 /\ 1 <= I161 - 1 /\ I164 <= I159 /\ I164 <= I160 /\ I165 <= I159 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 2 <= I166 - 1 /\ I167 + 2 <= I159] 28.81/28.87 f2(I168, I169, I170, I171, I172) -> f3(I173, I174, I175, I170, I176) [I176 + 2 <= I168 /\ 1 <= I175 - 1 /\ 0 <= I174 - 1 /\ 0 <= I173 - 1 /\ 0 <= I169 - 1 /\ 0 <= I168 - 1 /\ I175 - 1 <= I169 /\ I175 - 1 <= I168 /\ I174 <= I168 /\ I173 <= I169 /\ 1 <= I170 - 1 /\ I173 <= I168] 28.81/28.87 f1(I177, I178, I179, I180, I181) -> f2(I182, I183, I178, I184, I185) [0 <= I183 - 1 /\ 1 <= I182 - 1 /\ 0 <= I177 - 1 /\ I183 <= I177 /\ 0 <= I178 - 1 /\ I182 - 1 <= I177] 28.81/28.87 f1(I186, I187, I188, I189, I190) -> f2(I191, I192, I187, I193, I194) [-1 <= I195 - 1 /\ 0 <= I187 - 1 /\ I192 <= I186 /\ 0 <= I186 - 1 /\ 2 <= I191 - 1 /\ 0 <= I192 - 1] 28.81/28.87 28.81/28.87 We use the basic value criterion with the projection function NU: 28.81/28.87 NU[f4#(z1,z2,z3,z4,z5)] = z1 28.81/28.87 28.81/28.87 This gives the following inequalities: 28.81/28.87 I130 - 1 <= I130 - 1 /\ 0 <= I130 - 1 ==> I130 >! I130 - 1 28.81/28.87 28.81/28.87 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 28.81/28.87 28.81/28.87 DP problem for innermost termination. 28.81/28.87 P = 28.81/28.87 f9#(I0, I1, I2, I3, I4) -> f9#(I5, I6, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 + 1 <= I1 /\ I6 + 3 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0] 28.81/28.87 R = 28.81/28.87 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 28.81/28.87 f9(I0, I1, I2, I3, I4) -> f9(I5, I6, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 + 1 <= I1 /\ I6 + 3 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0] 28.81/28.87 f8(I10, I11, I12, I13, I14) -> f9(I15, I16, I17, I18, I19) [-1 <= I16 - 1 /\ 0 <= I15 - 1 /\ -1 <= I12 - 1 /\ 1 <= I11 - 1 /\ 0 <= I10 - 1 /\ I16 + 1 <= I10 /\ I15 <= I10] 28.81/28.87 f8(I20, I21, I22, I23, I24) -> f8(I25, I26, I27, I28, I29) [-1 <= I27 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I22 - 1 /\ 2 <= I21 - 1 /\ 2 <= I20 - 1 /\ I27 + 1 <= I22 /\ I27 + 3 <= I21 /\ I26 <= I22 /\ I26 + 2 <= I21 /\ I25 + 2 <= I20] 28.81/28.87 f5(I30, I31, I32, I33, I34) -> f8(I35, I36, I37, I38, I39) [-1 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 0 <= I32 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 1 <= I32 /\ I37 + 3 <= I31 /\ I36 <= I32 /\ I36 + 2 <= I31 /\ I35 + 2 <= I30] 28.81/28.87 f7(I40, I41, I42, I43, I44) -> f5(I45, I46, I47, I48, I49) [2 <= I47 - 1 /\ 4 <= I46 - 1 /\ 0 <= I45 - 1 /\ 4 <= I41 - 1 /\ 0 <= I40 - 1 /\ I47 + 2 <= I41 /\ I46 <= I41 /\ I45 <= I40] 28.81/28.87 f5(I50, I51, I52, I53, I54) -> f7(I55, I56, I57, I58, I59) [6 <= I56 - 1 /\ 1 <= I55 - 1 /\ 4 <= I52 - 1 /\ 6 <= I51 - 1 /\ 2 <= I50 - 1 /\ I56 - 2 <= I52 /\ I56 <= I51 /\ I55 + 3 <= I52 /\ I55 + 5 <= I51 /\ I55 + 1 <= I50] 28.81/28.87 f5(I60, I61, I62, I63, I64) -> f7(I65, I66, I67, I68, I69) [6 <= I66 - 1 /\ 0 <= I65 - 1 /\ 4 <= I62 - 1 /\ 6 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I62 /\ I66 <= I61] 28.81/28.87 f5(I70, I71, I72, I73, I74) -> f7(I75, I76, I77, I78, I79) [5 <= I76 - 1 /\ 0 <= I75 - 1 /\ 3 <= I72 - 1 /\ 5 <= I71 - 1 /\ 2 <= I70 - 1 /\ I76 - 2 <= I72 /\ I76 <= I71 /\ I76 - 3 <= I70] 28.81/28.87 f6(I80, I81, I82, I83, I84) -> f5(I85, I86, I87, I88, I89) [1 <= I87 - 1 /\ 3 <= I86 - 1 /\ 0 <= I85 - 1 /\ 0 <= I80 - 1 /\ I87 - 1 <= I80 /\ I86 - 3 <= I80 /\ I85 <= I80] 28.81/28.87 f5(I90, I91, I92, I93, I94) -> f6(I95, I96, I97, I98, I99) [1 <= I95 - 1 /\ 1 <= I92 - 1 /\ 3 <= I91 - 1 /\ 2 <= I90 - 1 /\ I95 <= I92 /\ I95 + 2 <= I91 /\ I95 + 1 <= I90] 28.81/28.87 f5(I100, I101, I102, I103, I104) -> f6(I105, I106, I107, I108, I109) [2 <= I105 - 1 /\ 1 <= I102 - 1 /\ 3 <= I101 - 1 /\ 2 <= I100 - 1] 28.81/28.87 f5(I110, I111, I112, I113, I114) -> f5(I115, I116, I117, I118, I119) [2 <= I117 - 1 /\ 4 <= I116 - 1 /\ 1 <= I115 - 1 /\ 2 <= I112 - 1 /\ 4 <= I111 - 1 /\ 2 <= I110 - 1 /\ I117 <= I112 /\ I117 + 2 <= I111 /\ I116 - 2 <= I112 /\ I116 <= I111 /\ I115 + 1 <= I112 /\ I115 + 3 <= I111 /\ I115 + 1 <= I110] 28.81/28.87 f3(I120, I121, I122, I123, I124) -> f5(I125, I126, I127, I128, I129) [I124 + 2 <= I121 /\ -1 <= I127 - 1 /\ 0 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I122 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ I127 + 1 <= I122 /\ I126 <= I122 /\ 1 <= I123 - 1 /\ I125 <= I121] 28.81/28.87 f4(I130, I131, I132, I133, I134) -> f4(I130 - 1, I135, I136, I137, I138) [I130 - 1 <= I130 - 1 /\ 0 <= I130 - 1] 28.81/28.87 f2(I139, I140, I141, I142, I143) -> f4(I144, I145, I146, I147, I148) [0 <= I140 - 1 /\ 0 <= I139 - 1 /\ 1 <= I141 - 1 /\ -1 <= I144 - 1] 28.81/28.87 f1(I149, I150, I151, I152, I153) -> f4(I154, I155, I156, I157, I158) [0 <= I149 - 1 /\ 0 <= I150 - 1 /\ -1 <= I154 - 1] 28.81/28.87 f2(I159, I160, I161, I162, I163) -> f3(I164, I165, I166, I161, I167) [-1 <= y1 - 1 /\ 1 <= I161 - 1 /\ I164 <= I159 /\ I164 <= I160 /\ I165 <= I159 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 2 <= I166 - 1 /\ I167 + 2 <= I159] 28.81/28.87 f2(I168, I169, I170, I171, I172) -> f3(I173, I174, I175, I170, I176) [I176 + 2 <= I168 /\ 1 <= I175 - 1 /\ 0 <= I174 - 1 /\ 0 <= I173 - 1 /\ 0 <= I169 - 1 /\ 0 <= I168 - 1 /\ I175 - 1 <= I169 /\ I175 - 1 <= I168 /\ I174 <= I168 /\ I173 <= I169 /\ 1 <= I170 - 1 /\ I173 <= I168] 28.81/28.87 f1(I177, I178, I179, I180, I181) -> f2(I182, I183, I178, I184, I185) [0 <= I183 - 1 /\ 1 <= I182 - 1 /\ 0 <= I177 - 1 /\ I183 <= I177 /\ 0 <= I178 - 1 /\ I182 - 1 <= I177] 28.81/28.87 f1(I186, I187, I188, I189, I190) -> f2(I191, I192, I187, I193, I194) [-1 <= I195 - 1 /\ 0 <= I187 - 1 /\ I192 <= I186 /\ 0 <= I186 - 1 /\ 2 <= I191 - 1 /\ 0 <= I192 - 1] 28.81/28.87 28.81/28.87 We use the basic value criterion with the projection function NU: 28.81/28.87 NU[f9#(z1,z2,z3,z4,z5)] = z2 28.81/28.87 28.81/28.87 This gives the following inequalities: 28.81/28.87 -1 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 + 1 <= I1 /\ I6 + 3 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0 ==> I1 >! I6 28.81/28.87 28.81/28.87 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 28.81/28.87 28.81/28.87 DP problem for innermost termination. 28.81/28.87 P = 28.81/28.87 f8#(I20, I21, I22, I23, I24) -> f8#(I25, I26, I27, I28, I29) [-1 <= I27 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I22 - 1 /\ 2 <= I21 - 1 /\ 2 <= I20 - 1 /\ I27 + 1 <= I22 /\ I27 + 3 <= I21 /\ I26 <= I22 /\ I26 + 2 <= I21 /\ I25 + 2 <= I20] 28.81/28.87 R = 28.81/28.87 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 28.81/28.87 f9(I0, I1, I2, I3, I4) -> f9(I5, I6, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 + 1 <= I1 /\ I6 + 3 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0] 28.81/28.87 f8(I10, I11, I12, I13, I14) -> f9(I15, I16, I17, I18, I19) [-1 <= I16 - 1 /\ 0 <= I15 - 1 /\ -1 <= I12 - 1 /\ 1 <= I11 - 1 /\ 0 <= I10 - 1 /\ I16 + 1 <= I10 /\ I15 <= I10] 28.81/28.87 f8(I20, I21, I22, I23, I24) -> f8(I25, I26, I27, I28, I29) [-1 <= I27 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I22 - 1 /\ 2 <= I21 - 1 /\ 2 <= I20 - 1 /\ I27 + 1 <= I22 /\ I27 + 3 <= I21 /\ I26 <= I22 /\ I26 + 2 <= I21 /\ I25 + 2 <= I20] 28.81/28.87 f5(I30, I31, I32, I33, I34) -> f8(I35, I36, I37, I38, I39) [-1 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 0 <= I32 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 1 <= I32 /\ I37 + 3 <= I31 /\ I36 <= I32 /\ I36 + 2 <= I31 /\ I35 + 2 <= I30] 28.81/28.87 f7(I40, I41, I42, I43, I44) -> f5(I45, I46, I47, I48, I49) [2 <= I47 - 1 /\ 4 <= I46 - 1 /\ 0 <= I45 - 1 /\ 4 <= I41 - 1 /\ 0 <= I40 - 1 /\ I47 + 2 <= I41 /\ I46 <= I41 /\ I45 <= I40] 28.81/28.87 f5(I50, I51, I52, I53, I54) -> f7(I55, I56, I57, I58, I59) [6 <= I56 - 1 /\ 1 <= I55 - 1 /\ 4 <= I52 - 1 /\ 6 <= I51 - 1 /\ 2 <= I50 - 1 /\ I56 - 2 <= I52 /\ I56 <= I51 /\ I55 + 3 <= I52 /\ I55 + 5 <= I51 /\ I55 + 1 <= I50] 28.81/28.87 f5(I60, I61, I62, I63, I64) -> f7(I65, I66, I67, I68, I69) [6 <= I66 - 1 /\ 0 <= I65 - 1 /\ 4 <= I62 - 1 /\ 6 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I62 /\ I66 <= I61] 28.81/28.87 f5(I70, I71, I72, I73, I74) -> f7(I75, I76, I77, I78, I79) [5 <= I76 - 1 /\ 0 <= I75 - 1 /\ 3 <= I72 - 1 /\ 5 <= I71 - 1 /\ 2 <= I70 - 1 /\ I76 - 2 <= I72 /\ I76 <= I71 /\ I76 - 3 <= I70] 28.81/28.87 f6(I80, I81, I82, I83, I84) -> f5(I85, I86, I87, I88, I89) [1 <= I87 - 1 /\ 3 <= I86 - 1 /\ 0 <= I85 - 1 /\ 0 <= I80 - 1 /\ I87 - 1 <= I80 /\ I86 - 3 <= I80 /\ I85 <= I80] 28.81/28.87 f5(I90, I91, I92, I93, I94) -> f6(I95, I96, I97, I98, I99) [1 <= I95 - 1 /\ 1 <= I92 - 1 /\ 3 <= I91 - 1 /\ 2 <= I90 - 1 /\ I95 <= I92 /\ I95 + 2 <= I91 /\ I95 + 1 <= I90] 28.81/28.87 f5(I100, I101, I102, I103, I104) -> f6(I105, I106, I107, I108, I109) [2 <= I105 - 1 /\ 1 <= I102 - 1 /\ 3 <= I101 - 1 /\ 2 <= I100 - 1] 28.81/28.87 f5(I110, I111, I112, I113, I114) -> f5(I115, I116, I117, I118, I119) [2 <= I117 - 1 /\ 4 <= I116 - 1 /\ 1 <= I115 - 1 /\ 2 <= I112 - 1 /\ 4 <= I111 - 1 /\ 2 <= I110 - 1 /\ I117 <= I112 /\ I117 + 2 <= I111 /\ I116 - 2 <= I112 /\ I116 <= I111 /\ I115 + 1 <= I112 /\ I115 + 3 <= I111 /\ I115 + 1 <= I110] 28.81/28.87 f3(I120, I121, I122, I123, I124) -> f5(I125, I126, I127, I128, I129) [I124 + 2 <= I121 /\ -1 <= I127 - 1 /\ 0 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I122 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ I127 + 1 <= I122 /\ I126 <= I122 /\ 1 <= I123 - 1 /\ I125 <= I121] 28.81/28.87 f4(I130, I131, I132, I133, I134) -> f4(I130 - 1, I135, I136, I137, I138) [I130 - 1 <= I130 - 1 /\ 0 <= I130 - 1] 28.81/28.87 f2(I139, I140, I141, I142, I143) -> f4(I144, I145, I146, I147, I148) [0 <= I140 - 1 /\ 0 <= I139 - 1 /\ 1 <= I141 - 1 /\ -1 <= I144 - 1] 28.81/28.87 f1(I149, I150, I151, I152, I153) -> f4(I154, I155, I156, I157, I158) [0 <= I149 - 1 /\ 0 <= I150 - 1 /\ -1 <= I154 - 1] 28.81/28.87 f2(I159, I160, I161, I162, I163) -> f3(I164, I165, I166, I161, I167) [-1 <= y1 - 1 /\ 1 <= I161 - 1 /\ I164 <= I159 /\ I164 <= I160 /\ I165 <= I159 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 2 <= I166 - 1 /\ I167 + 2 <= I159] 28.81/28.87 f2(I168, I169, I170, I171, I172) -> f3(I173, I174, I175, I170, I176) [I176 + 2 <= I168 /\ 1 <= I175 - 1 /\ 0 <= I174 - 1 /\ 0 <= I173 - 1 /\ 0 <= I169 - 1 /\ 0 <= I168 - 1 /\ I175 - 1 <= I169 /\ I175 - 1 <= I168 /\ I174 <= I168 /\ I173 <= I169 /\ 1 <= I170 - 1 /\ I173 <= I168] 28.81/28.87 f1(I177, I178, I179, I180, I181) -> f2(I182, I183, I178, I184, I185) [0 <= I183 - 1 /\ 1 <= I182 - 1 /\ 0 <= I177 - 1 /\ I183 <= I177 /\ 0 <= I178 - 1 /\ I182 - 1 <= I177] 28.81/28.87 f1(I186, I187, I188, I189, I190) -> f2(I191, I192, I187, I193, I194) [-1 <= I195 - 1 /\ 0 <= I187 - 1 /\ I192 <= I186 /\ 0 <= I186 - 1 /\ 2 <= I191 - 1 /\ 0 <= I192 - 1] 28.81/28.87 28.81/28.87 We use the basic value criterion with the projection function NU: 28.81/28.87 NU[f8#(z1,z2,z3,z4,z5)] = z2 28.81/28.87 28.81/28.87 This gives the following inequalities: 28.81/28.87 -1 <= I27 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I22 - 1 /\ 2 <= I21 - 1 /\ 2 <= I20 - 1 /\ I27 + 1 <= I22 /\ I27 + 3 <= I21 /\ I26 <= I22 /\ I26 + 2 <= I21 /\ I25 + 2 <= I20 ==> I21 >! I26 28.81/28.87 28.81/28.87 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 28.81/28.87 28.81/28.87 DP problem for innermost termination. 28.81/28.87 P = 28.81/28.87 f7#(I40, I41, I42, I43, I44) -> f5#(I45, I46, I47, I48, I49) [2 <= I47 - 1 /\ 4 <= I46 - 1 /\ 0 <= I45 - 1 /\ 4 <= I41 - 1 /\ 0 <= I40 - 1 /\ I47 + 2 <= I41 /\ I46 <= I41 /\ I45 <= I40] 28.81/28.87 f5#(I50, I51, I52, I53, I54) -> f7#(I55, I56, I57, I58, I59) [6 <= I56 - 1 /\ 1 <= I55 - 1 /\ 4 <= I52 - 1 /\ 6 <= I51 - 1 /\ 2 <= I50 - 1 /\ I56 - 2 <= I52 /\ I56 <= I51 /\ I55 + 3 <= I52 /\ I55 + 5 <= I51 /\ I55 + 1 <= I50] 28.81/28.87 f5#(I60, I61, I62, I63, I64) -> f7#(I65, I66, I67, I68, I69) [6 <= I66 - 1 /\ 0 <= I65 - 1 /\ 4 <= I62 - 1 /\ 6 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I62 /\ I66 <= I61] 28.81/28.87 f5#(I70, I71, I72, I73, I74) -> f7#(I75, I76, I77, I78, I79) [5 <= I76 - 1 /\ 0 <= I75 - 1 /\ 3 <= I72 - 1 /\ 5 <= I71 - 1 /\ 2 <= I70 - 1 /\ I76 - 2 <= I72 /\ I76 <= I71 /\ I76 - 3 <= I70] 28.81/28.87 f6#(I80, I81, I82, I83, I84) -> f5#(I85, I86, I87, I88, I89) [1 <= I87 - 1 /\ 3 <= I86 - 1 /\ 0 <= I85 - 1 /\ 0 <= I80 - 1 /\ I87 - 1 <= I80 /\ I86 - 3 <= I80 /\ I85 <= I80] 28.81/28.87 f5#(I90, I91, I92, I93, I94) -> f6#(I95, I96, I97, I98, I99) [1 <= I95 - 1 /\ 1 <= I92 - 1 /\ 3 <= I91 - 1 /\ 2 <= I90 - 1 /\ I95 <= I92 /\ I95 + 2 <= I91 /\ I95 + 1 <= I90] 28.81/28.87 f5#(I100, I101, I102, I103, I104) -> f6#(I105, I106, I107, I108, I109) [2 <= I105 - 1 /\ 1 <= I102 - 1 /\ 3 <= I101 - 1 /\ 2 <= I100 - 1] 28.81/28.87 f5#(I110, I111, I112, I113, I114) -> f5#(I115, I116, I117, I118, I119) [2 <= I117 - 1 /\ 4 <= I116 - 1 /\ 1 <= I115 - 1 /\ 2 <= I112 - 1 /\ 4 <= I111 - 1 /\ 2 <= I110 - 1 /\ I117 <= I112 /\ I117 + 2 <= I111 /\ I116 - 2 <= I112 /\ I116 <= I111 /\ I115 + 1 <= I112 /\ I115 + 3 <= I111 /\ I115 + 1 <= I110] 28.81/28.87 R = 28.81/28.87 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 28.81/28.87 f9(I0, I1, I2, I3, I4) -> f9(I5, I6, I7, I8, I9) [-1 <= I6 - 1 /\ 0 <= I5 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 + 1 <= I1 /\ I6 + 3 <= I0 /\ I5 <= I1 /\ I5 + 2 <= I0] 28.81/28.87 f8(I10, I11, I12, I13, I14) -> f9(I15, I16, I17, I18, I19) [-1 <= I16 - 1 /\ 0 <= I15 - 1 /\ -1 <= I12 - 1 /\ 1 <= I11 - 1 /\ 0 <= I10 - 1 /\ I16 + 1 <= I10 /\ I15 <= I10] 28.81/28.87 f8(I20, I21, I22, I23, I24) -> f8(I25, I26, I27, I28, I29) [-1 <= I27 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I22 - 1 /\ 2 <= I21 - 1 /\ 2 <= I20 - 1 /\ I27 + 1 <= I22 /\ I27 + 3 <= I21 /\ I26 <= I22 /\ I26 + 2 <= I21 /\ I25 + 2 <= I20] 28.81/28.87 f5(I30, I31, I32, I33, I34) -> f8(I35, I36, I37, I38, I39) [-1 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I35 - 1 /\ 0 <= I32 - 1 /\ 2 <= I31 - 1 /\ 2 <= I30 - 1 /\ I37 + 1 <= I32 /\ I37 + 3 <= I31 /\ I36 <= I32 /\ I36 + 2 <= I31 /\ I35 + 2 <= I30] 28.81/28.87 f7(I40, I41, I42, I43, I44) -> f5(I45, I46, I47, I48, I49) [2 <= I47 - 1 /\ 4 <= I46 - 1 /\ 0 <= I45 - 1 /\ 4 <= I41 - 1 /\ 0 <= I40 - 1 /\ I47 + 2 <= I41 /\ I46 <= I41 /\ I45 <= I40] 28.81/28.87 f5(I50, I51, I52, I53, I54) -> f7(I55, I56, I57, I58, I59) [6 <= I56 - 1 /\ 1 <= I55 - 1 /\ 4 <= I52 - 1 /\ 6 <= I51 - 1 /\ 2 <= I50 - 1 /\ I56 - 2 <= I52 /\ I56 <= I51 /\ I55 + 3 <= I52 /\ I55 + 5 <= I51 /\ I55 + 1 <= I50] 28.81/28.87 f5(I60, I61, I62, I63, I64) -> f7(I65, I66, I67, I68, I69) [6 <= I66 - 1 /\ 0 <= I65 - 1 /\ 4 <= I62 - 1 /\ 6 <= I61 - 1 /\ 2 <= I60 - 1 /\ I66 - 2 <= I62 /\ I66 <= I61] 28.81/28.87 f5(I70, I71, I72, I73, I74) -> f7(I75, I76, I77, I78, I79) [5 <= I76 - 1 /\ 0 <= I75 - 1 /\ 3 <= I72 - 1 /\ 5 <= I71 - 1 /\ 2 <= I70 - 1 /\ I76 - 2 <= I72 /\ I76 <= I71 /\ I76 - 3 <= I70] 28.81/28.87 f6(I80, I81, I82, I83, I84) -> f5(I85, I86, I87, I88, I89) [1 <= I87 - 1 /\ 3 <= I86 - 1 /\ 0 <= I85 - 1 /\ 0 <= I80 - 1 /\ I87 - 1 <= I80 /\ I86 - 3 <= I80 /\ I85 <= I80] 28.81/28.87 f5(I90, I91, I92, I93, I94) -> f6(I95, I96, I97, I98, I99) [1 <= I95 - 1 /\ 1 <= I92 - 1 /\ 3 <= I91 - 1 /\ 2 <= I90 - 1 /\ I95 <= I92 /\ I95 + 2 <= I91 /\ I95 + 1 <= I90] 28.81/28.87 f5(I100, I101, I102, I103, I104) -> f6(I105, I106, I107, I108, I109) [2 <= I105 - 1 /\ 1 <= I102 - 1 /\ 3 <= I101 - 1 /\ 2 <= I100 - 1] 28.81/28.87 f5(I110, I111, I112, I113, I114) -> f5(I115, I116, I117, I118, I119) [2 <= I117 - 1 /\ 4 <= I116 - 1 /\ 1 <= I115 - 1 /\ 2 <= I112 - 1 /\ 4 <= I111 - 1 /\ 2 <= I110 - 1 /\ I117 <= I112 /\ I117 + 2 <= I111 /\ I116 - 2 <= I112 /\ I116 <= I111 /\ I115 + 1 <= I112 /\ I115 + 3 <= I111 /\ I115 + 1 <= I110] 28.81/28.87 f3(I120, I121, I122, I123, I124) -> f5(I125, I126, I127, I128, I129) [I124 + 2 <= I121 /\ -1 <= I127 - 1 /\ 0 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I122 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ I127 + 1 <= I122 /\ I126 <= I122 /\ 1 <= I123 - 1 /\ I125 <= I121] 28.81/28.87 f4(I130, I131, I132, I133, I134) -> f4(I130 - 1, I135, I136, I137, I138) [I130 - 1 <= I130 - 1 /\ 0 <= I130 - 1] 28.81/28.87 f2(I139, I140, I141, I142, I143) -> f4(I144, I145, I146, I147, I148) [0 <= I140 - 1 /\ 0 <= I139 - 1 /\ 1 <= I141 - 1 /\ -1 <= I144 - 1] 28.81/28.87 f1(I149, I150, I151, I152, I153) -> f4(I154, I155, I156, I157, I158) [0 <= I149 - 1 /\ 0 <= I150 - 1 /\ -1 <= I154 - 1] 28.81/28.87 f2(I159, I160, I161, I162, I163) -> f3(I164, I165, I166, I161, I167) [-1 <= y1 - 1 /\ 1 <= I161 - 1 /\ I164 <= I159 /\ I164 <= I160 /\ I165 <= I159 /\ 0 <= I159 - 1 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 0 <= I165 - 1 /\ 2 <= I166 - 1 /\ I167 + 2 <= I159] 28.81/28.87 f2(I168, I169, I170, I171, I172) -> f3(I173, I174, I175, I170, I176) [I176 + 2 <= I168 /\ 1 <= I175 - 1 /\ 0 <= I174 - 1 /\ 0 <= I173 - 1 /\ 0 <= I169 - 1 /\ 0 <= I168 - 1 /\ I175 - 1 <= I169 /\ I175 - 1 <= I168 /\ I174 <= I168 /\ I173 <= I169 /\ 1 <= I170 - 1 /\ I173 <= I168] 28.81/28.87 f1(I177, I178, I179, I180, I181) -> f2(I182, I183, I178, I184, I185) [0 <= I183 - 1 /\ 1 <= I182 - 1 /\ 0 <= I177 - 1 /\ I183 <= I177 /\ 0 <= I178 - 1 /\ I182 - 1 <= I177] 28.81/28.87 f1(I186, I187, I188, I189, I190) -> f2(I191, I192, I187, I193, I194) [-1 <= I195 - 1 /\ 0 <= I187 - 1 /\ I192 <= I186 /\ 0 <= I186 - 1 /\ 2 <= I191 - 1 /\ 0 <= I192 - 1] 28.81/28.87 28.81/31.84 EOF