18.35/18.37 YES 18.35/18.37 18.35/18.37 DP problem for innermost termination. 18.35/18.37 P = 18.35/18.37 init#(x1, x2, x3, x4, x5, x6, x7) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 18.35/18.37 f10#(I0, I1, I2, I3, I4, I5, I6) -> f10#(I7, I8, I2, I3, I9, I10, I11) [-1 <= I8 - 1 /\ -1 <= I7 - 1 /\ 2 <= I1 - 1 /\ 1 <= I0 - 1 /\ I8 + 2 <= I1 /\ 1 <= I3 - 1 /\ I7 + 2 <= I0] 18.35/18.37 f10#(I12, I13, I14, I15, I16, I17, I18) -> f10#(I19, I20, I14, I15, I21, I22, I23) [-1 <= I20 - 1 /\ -1 <= I19 - 1 /\ 2 <= I13 - 1 /\ 2 <= I12 - 1 /\ I20 + 2 <= I13 /\ 1 <= I15 - 1 /\ I19 + 2 <= I12] 18.35/18.37 f10#(I24, I25, I26, I27, I28, I29, I30) -> f6#(I31, I32, I33, I27, I34, I35, I36) [0 <= I33 - 1 /\ 0 <= I32 - 1 /\ 0 <= I31 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1 /\ I33 + 2 <= I24 /\ I32 + 2 <= I24 /\ 1 <= I27 - 1 /\ I31 + 2 <= I25] 18.35/18.37 f10#(I37, I38, I39, I40, I41, I42, I43) -> f6#(I44, I45, I46, I40, I47, I48, I49) [-1 <= I46 - 1 /\ -1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 2 <= I38 - 1 /\ 1 <= I37 - 1 /\ I46 + 3 <= I38 /\ I46 + 2 <= I37 /\ I45 + 3 <= I38 /\ I45 + 2 <= I37 /\ 1 <= I40 - 1 /\ I44 + 2 <= I38] 18.35/18.37 f9#(I50, I51, I52, I53, I54, I55, I56) -> f10#(I57, I58, I53, I54, I59, I60, I61) [1 = I52 /\ -1 <= I58 - 1 /\ -1 <= I57 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I50 - 1 /\ I58 <= I55 /\ I58 + 1 <= I50 /\ I57 <= I56 /\ I57 + 1 <= I51] 18.35/18.37 f6#(I62, I63, I64, I65, I66, I67, I68) -> f9#(I69, I70, 1, I71, I65, I72, I73) [-1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62] 18.35/18.37 f6#(I74, I75, I76, I77, I78, I79, I80) -> f9#(I81, I82, 0, I83, I77, I84, I85) [-1 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I76 - 1 /\ 0 <= I75 - 1 /\ 0 <= I74 - 1 /\ I85 + 1 <= I76 /\ I85 + 1 <= I75 /\ I84 + 1 <= I74 /\ I82 <= I76 /\ I82 <= I75 /\ 1 <= I77 - 1 /\ I81 <= I74] 18.35/18.37 f8#(I86, I87, I88, I89, I90, I91, I92) -> f8#(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 f8#(I96, I97, I98, I99, I100, I101, I102) -> f7#(I96 - 1, I99, I100, I103, I104, I105, I106) [I96 - 1 <= I96 - 1 /\ 1 <= I100 - 1 /\ 0 <= I98 - 1 /\ 1 <= I96 - 1 /\ I97 <= I98 - 1] 18.35/18.37 f7#(I107, I108, I109, I110, I111, I112, I113) -> f8#(I107, 0, I114, I108, I109 + 1, I115, I116) [-1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1] 18.35/18.37 f2#(I117, I118, I119, I120, I121, I122, I123) -> f7#(I124, I118, I125, I126, I127, I128, I129) [y1 <= I118 - 1 /\ 0 <= y1 - 1 /\ 0 <= I118 - 1 /\ -1 <= I124 - 1 /\ 3 <= I117 - 1 /\ I120 + 5 <= I117 /\ I119 + 5 <= I117 /\ y1 + 1 = I125] 18.35/18.37 f1#(I130, I131, I132, I133, I134, I135, I136) -> f7#(I137, I131, I138, I139, I140, I141, I142) [-1 <= y2 - 1 /\ 0 <= I131 - 1 /\ 0 <= I143 - 1 /\ I143 <= I131 - 1 /\ -1 <= I137 - 1 /\ 0 <= I130 - 1 /\ I143 + 1 = I138] 18.35/18.37 f1#(I144, I145, I146, I147, I148, I149, I150) -> f7#(I151, I145, 1, I152, I153, I154, I155) [0 <= I144 - 1 /\ 0 <= I145 - 1 /\ -1 <= I151 - 1] 18.35/18.37 f2#(I156, I157, I158, I159, I160, I161, I162) -> f6#(I163, I164, I165, I166, I167, I168, I169) [I170 <= I157 - 1 /\ 0 <= I170 - 1 /\ 0 <= I157 - 1 /\ -1 <= I171 - 1 /\ 1 <= I166 - 1 /\ I163 <= I156 /\ 3 <= I156 - 1 /\ 3 <= I163 - 1 /\ 3 <= I164 - 1 /\ 3 <= I165 - 1 /\ I159 + 5 <= I156 /\ I158 + 5 <= I156] 18.35/18.37 f2#(I172, I173, I174, I175, I176, I177, I178) -> f6#(I179, I180, I181, I182, I183, I184, I185) [I186 <= I173 - 1 /\ 0 <= I186 - 1 /\ 0 <= I173 - 1 /\ -1 <= I187 - 1 /\ 1 <= I182 - 1 /\ I179 <= I172 /\ I180 + 3 <= I172 /\ I181 + 3 <= I172 /\ 3 <= I172 - 1 /\ 3 <= I179 - 1 /\ 0 <= I180 - 1 /\ 0 <= I181 - 1 /\ I175 + 5 <= I172 /\ I174 + 5 <= I172] 18.35/18.37 f3#(I218, I219, I220, I221, I222, I223, I224) -> f2#(I225, I226, I221, I222, I227, I228, I229) [I221 + 5 <= I219 /\ I222 + 5 <= I219 /\ 3 <= I225 - 1 /\ 3 <= I219 - 1 /\ 0 <= I218 - 1 /\ I225 <= I219] 18.35/18.37 f1#(I230, I231, I232, I233, I234, I235, I236) -> f2#(I237, I231, I238, I239, I240, I241, I242) [-1 <= I243 - 1 /\ 0 <= I231 - 1 /\ 0 <= I230 - 1 /\ 3 <= I237 - 1] 18.35/18.37 R = 18.35/18.37 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 18.35/18.37 f10(I0, I1, I2, I3, I4, I5, I6) -> f10(I7, I8, I2, I3, I9, I10, I11) [-1 <= I8 - 1 /\ -1 <= I7 - 1 /\ 2 <= I1 - 1 /\ 1 <= I0 - 1 /\ I8 + 2 <= I1 /\ 1 <= I3 - 1 /\ I7 + 2 <= I0] 18.35/18.37 f10(I12, I13, I14, I15, I16, I17, I18) -> f10(I19, I20, I14, I15, I21, I22, I23) [-1 <= I20 - 1 /\ -1 <= I19 - 1 /\ 2 <= I13 - 1 /\ 2 <= I12 - 1 /\ I20 + 2 <= I13 /\ 1 <= I15 - 1 /\ I19 + 2 <= I12] 18.35/18.37 f10(I24, I25, I26, I27, I28, I29, I30) -> f6(I31, I32, I33, I27, I34, I35, I36) [0 <= I33 - 1 /\ 0 <= I32 - 1 /\ 0 <= I31 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1 /\ I33 + 2 <= I24 /\ I32 + 2 <= I24 /\ 1 <= I27 - 1 /\ I31 + 2 <= I25] 18.35/18.37 f10(I37, I38, I39, I40, I41, I42, I43) -> f6(I44, I45, I46, I40, I47, I48, I49) [-1 <= I46 - 1 /\ -1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 2 <= I38 - 1 /\ 1 <= I37 - 1 /\ I46 + 3 <= I38 /\ I46 + 2 <= I37 /\ I45 + 3 <= I38 /\ I45 + 2 <= I37 /\ 1 <= I40 - 1 /\ I44 + 2 <= I38] 18.35/18.37 f9(I50, I51, I52, I53, I54, I55, I56) -> f10(I57, I58, I53, I54, I59, I60, I61) [1 = I52 /\ -1 <= I58 - 1 /\ -1 <= I57 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I50 - 1 /\ I58 <= I55 /\ I58 + 1 <= I50 /\ I57 <= I56 /\ I57 + 1 <= I51] 18.35/18.37 f6(I62, I63, I64, I65, I66, I67, I68) -> f9(I69, I70, 1, I71, I65, I72, I73) [-1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62] 18.35/18.37 f6(I74, I75, I76, I77, I78, I79, I80) -> f9(I81, I82, 0, I83, I77, I84, I85) [-1 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I76 - 1 /\ 0 <= I75 - 1 /\ 0 <= I74 - 1 /\ I85 + 1 <= I76 /\ I85 + 1 <= I75 /\ I84 + 1 <= I74 /\ I82 <= I76 /\ I82 <= I75 /\ 1 <= I77 - 1 /\ I81 <= I74] 18.35/18.37 f8(I86, I87, I88, I89, I90, I91, I92) -> f8(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 f8(I96, I97, I98, I99, I100, I101, I102) -> f7(I96 - 1, I99, I100, I103, I104, I105, I106) [I96 - 1 <= I96 - 1 /\ 1 <= I100 - 1 /\ 0 <= I98 - 1 /\ 1 <= I96 - 1 /\ I97 <= I98 - 1] 18.35/18.37 f7(I107, I108, I109, I110, I111, I112, I113) -> f8(I107, 0, I114, I108, I109 + 1, I115, I116) [-1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1] 18.35/18.37 f2(I117, I118, I119, I120, I121, I122, I123) -> f7(I124, I118, I125, I126, I127, I128, I129) [y1 <= I118 - 1 /\ 0 <= y1 - 1 /\ 0 <= I118 - 1 /\ -1 <= I124 - 1 /\ 3 <= I117 - 1 /\ I120 + 5 <= I117 /\ I119 + 5 <= I117 /\ y1 + 1 = I125] 18.35/18.37 f1(I130, I131, I132, I133, I134, I135, I136) -> f7(I137, I131, I138, I139, I140, I141, I142) [-1 <= y2 - 1 /\ 0 <= I131 - 1 /\ 0 <= I143 - 1 /\ I143 <= I131 - 1 /\ -1 <= I137 - 1 /\ 0 <= I130 - 1 /\ I143 + 1 = I138] 18.35/18.37 f1(I144, I145, I146, I147, I148, I149, I150) -> f7(I151, I145, 1, I152, I153, I154, I155) [0 <= I144 - 1 /\ 0 <= I145 - 1 /\ -1 <= I151 - 1] 18.35/18.37 f2(I156, I157, I158, I159, I160, I161, I162) -> f6(I163, I164, I165, I166, I167, I168, I169) [I170 <= I157 - 1 /\ 0 <= I170 - 1 /\ 0 <= I157 - 1 /\ -1 <= I171 - 1 /\ 1 <= I166 - 1 /\ I163 <= I156 /\ 3 <= I156 - 1 /\ 3 <= I163 - 1 /\ 3 <= I164 - 1 /\ 3 <= I165 - 1 /\ I159 + 5 <= I156 /\ I158 + 5 <= I156] 18.35/18.37 f2(I172, I173, I174, I175, I176, I177, I178) -> f6(I179, I180, I181, I182, I183, I184, I185) [I186 <= I173 - 1 /\ 0 <= I186 - 1 /\ 0 <= I173 - 1 /\ -1 <= I187 - 1 /\ 1 <= I182 - 1 /\ I179 <= I172 /\ I180 + 3 <= I172 /\ I181 + 3 <= I172 /\ 3 <= I172 - 1 /\ 3 <= I179 - 1 /\ 0 <= I180 - 1 /\ 0 <= I181 - 1 /\ I175 + 5 <= I172 /\ I174 + 5 <= I172] 18.35/18.37 f5(I188, I189, I190, I191, I192, I193, I194) -> f4(I195, I196, I197, I198, I199, I200, I201) [0 <= I195 - 1 /\ 0 <= I188 - 1 /\ I195 <= I188] 18.35/18.37 f1(I202, I203, I204, I205, I206, I207, I208) -> f4(I209, I210, I211, I212, I213, I214, I215) [-1 <= I216 - 1 /\ 0 <= I203 - 1 /\ 0 <= I217 - 1 /\ I217 <= I203 - 1 /\ -1 <= y3 - 1 /\ I209 <= I202 /\ 0 <= I202 - 1 /\ 0 <= I209 - 1] 18.35/18.37 f3(I218, I219, I220, I221, I222, I223, I224) -> f2(I225, I226, I221, I222, I227, I228, I229) [I221 + 5 <= I219 /\ I222 + 5 <= I219 /\ 3 <= I225 - 1 /\ 3 <= I219 - 1 /\ 0 <= I218 - 1 /\ I225 <= I219] 18.35/18.37 f1(I230, I231, I232, I233, I234, I235, I236) -> f2(I237, I231, I238, I239, I240, I241, I242) [-1 <= I243 - 1 /\ 0 <= I231 - 1 /\ 0 <= I230 - 1 /\ 3 <= I237 - 1] 18.35/18.37 18.35/18.37 The dependency graph for this problem is: 18.35/18.37 0 -> 12, 13, 17 18.35/18.37 1 -> 1, 2, 3, 4 18.35/18.37 2 -> 1, 2, 3, 4 18.35/18.37 3 -> 6, 7 18.35/18.37 4 -> 6, 7 18.35/18.37 5 -> 1, 2, 3, 4 18.35/18.37 6 -> 5 18.35/18.37 7 -> 18.35/18.37 8 -> 8, 9 18.35/18.37 9 -> 10 18.35/18.37 10 -> 8, 9 18.35/18.37 11 -> 10 18.35/18.37 12 -> 10 18.35/18.37 13 -> 10 18.35/18.37 14 -> 6, 7 18.35/18.37 15 -> 6, 7 18.35/18.37 16 -> 11, 14, 15 18.35/18.37 17 -> 11, 14, 15 18.35/18.37 Where: 18.35/18.37 0) init#(x1, x2, x3, x4, x5, x6, x7) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 18.35/18.37 1) f10#(I0, I1, I2, I3, I4, I5, I6) -> f10#(I7, I8, I2, I3, I9, I10, I11) [-1 <= I8 - 1 /\ -1 <= I7 - 1 /\ 2 <= I1 - 1 /\ 1 <= I0 - 1 /\ I8 + 2 <= I1 /\ 1 <= I3 - 1 /\ I7 + 2 <= I0] 18.35/18.37 2) f10#(I12, I13, I14, I15, I16, I17, I18) -> f10#(I19, I20, I14, I15, I21, I22, I23) [-1 <= I20 - 1 /\ -1 <= I19 - 1 /\ 2 <= I13 - 1 /\ 2 <= I12 - 1 /\ I20 + 2 <= I13 /\ 1 <= I15 - 1 /\ I19 + 2 <= I12] 18.35/18.37 3) f10#(I24, I25, I26, I27, I28, I29, I30) -> f6#(I31, I32, I33, I27, I34, I35, I36) [0 <= I33 - 1 /\ 0 <= I32 - 1 /\ 0 <= I31 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1 /\ I33 + 2 <= I24 /\ I32 + 2 <= I24 /\ 1 <= I27 - 1 /\ I31 + 2 <= I25] 18.35/18.37 4) f10#(I37, I38, I39, I40, I41, I42, I43) -> f6#(I44, I45, I46, I40, I47, I48, I49) [-1 <= I46 - 1 /\ -1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 2 <= I38 - 1 /\ 1 <= I37 - 1 /\ I46 + 3 <= I38 /\ I46 + 2 <= I37 /\ I45 + 3 <= I38 /\ I45 + 2 <= I37 /\ 1 <= I40 - 1 /\ I44 + 2 <= I38] 18.35/18.37 5) f9#(I50, I51, I52, I53, I54, I55, I56) -> f10#(I57, I58, I53, I54, I59, I60, I61) [1 = I52 /\ -1 <= I58 - 1 /\ -1 <= I57 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I50 - 1 /\ I58 <= I55 /\ I58 + 1 <= I50 /\ I57 <= I56 /\ I57 + 1 <= I51] 18.35/18.37 6) f6#(I62, I63, I64, I65, I66, I67, I68) -> f9#(I69, I70, 1, I71, I65, I72, I73) [-1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62] 18.35/18.37 7) f6#(I74, I75, I76, I77, I78, I79, I80) -> f9#(I81, I82, 0, I83, I77, I84, I85) [-1 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I76 - 1 /\ 0 <= I75 - 1 /\ 0 <= I74 - 1 /\ I85 + 1 <= I76 /\ I85 + 1 <= I75 /\ I84 + 1 <= I74 /\ I82 <= I76 /\ I82 <= I75 /\ 1 <= I77 - 1 /\ I81 <= I74] 18.35/18.37 8) f8#(I86, I87, I88, I89, I90, I91, I92) -> f8#(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 9) f8#(I96, I97, I98, I99, I100, I101, I102) -> f7#(I96 - 1, I99, I100, I103, I104, I105, I106) [I96 - 1 <= I96 - 1 /\ 1 <= I100 - 1 /\ 0 <= I98 - 1 /\ 1 <= I96 - 1 /\ I97 <= I98 - 1] 18.35/18.37 10) f7#(I107, I108, I109, I110, I111, I112, I113) -> f8#(I107, 0, I114, I108, I109 + 1, I115, I116) [-1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1] 18.35/18.37 11) f2#(I117, I118, I119, I120, I121, I122, I123) -> f7#(I124, I118, I125, I126, I127, I128, I129) [y1 <= I118 - 1 /\ 0 <= y1 - 1 /\ 0 <= I118 - 1 /\ -1 <= I124 - 1 /\ 3 <= I117 - 1 /\ I120 + 5 <= I117 /\ I119 + 5 <= I117 /\ y1 + 1 = I125] 18.35/18.37 12) f1#(I130, I131, I132, I133, I134, I135, I136) -> f7#(I137, I131, I138, I139, I140, I141, I142) [-1 <= y2 - 1 /\ 0 <= I131 - 1 /\ 0 <= I143 - 1 /\ I143 <= I131 - 1 /\ -1 <= I137 - 1 /\ 0 <= I130 - 1 /\ I143 + 1 = I138] 18.35/18.37 13) f1#(I144, I145, I146, I147, I148, I149, I150) -> f7#(I151, I145, 1, I152, I153, I154, I155) [0 <= I144 - 1 /\ 0 <= I145 - 1 /\ -1 <= I151 - 1] 18.35/18.37 14) f2#(I156, I157, I158, I159, I160, I161, I162) -> f6#(I163, I164, I165, I166, I167, I168, I169) [I170 <= I157 - 1 /\ 0 <= I170 - 1 /\ 0 <= I157 - 1 /\ -1 <= I171 - 1 /\ 1 <= I166 - 1 /\ I163 <= I156 /\ 3 <= I156 - 1 /\ 3 <= I163 - 1 /\ 3 <= I164 - 1 /\ 3 <= I165 - 1 /\ I159 + 5 <= I156 /\ I158 + 5 <= I156] 18.35/18.37 15) f2#(I172, I173, I174, I175, I176, I177, I178) -> f6#(I179, I180, I181, I182, I183, I184, I185) [I186 <= I173 - 1 /\ 0 <= I186 - 1 /\ 0 <= I173 - 1 /\ -1 <= I187 - 1 /\ 1 <= I182 - 1 /\ I179 <= I172 /\ I180 + 3 <= I172 /\ I181 + 3 <= I172 /\ 3 <= I172 - 1 /\ 3 <= I179 - 1 /\ 0 <= I180 - 1 /\ 0 <= I181 - 1 /\ I175 + 5 <= I172 /\ I174 + 5 <= I172] 18.35/18.37 16) f3#(I218, I219, I220, I221, I222, I223, I224) -> f2#(I225, I226, I221, I222, I227, I228, I229) [I221 + 5 <= I219 /\ I222 + 5 <= I219 /\ 3 <= I225 - 1 /\ 3 <= I219 - 1 /\ 0 <= I218 - 1 /\ I225 <= I219] 18.35/18.37 17) f1#(I230, I231, I232, I233, I234, I235, I236) -> f2#(I237, I231, I238, I239, I240, I241, I242) [-1 <= I243 - 1 /\ 0 <= I231 - 1 /\ 0 <= I230 - 1 /\ 3 <= I237 - 1] 18.35/18.37 18.35/18.37 We have the following SCCs. 18.35/18.37 { 1, 2, 3, 4, 5, 6 } 18.35/18.37 { 8, 9, 10 } 18.35/18.37 18.35/18.37 DP problem for innermost termination. 18.35/18.37 P = 18.35/18.37 f8#(I86, I87, I88, I89, I90, I91, I92) -> f8#(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 f8#(I96, I97, I98, I99, I100, I101, I102) -> f7#(I96 - 1, I99, I100, I103, I104, I105, I106) [I96 - 1 <= I96 - 1 /\ 1 <= I100 - 1 /\ 0 <= I98 - 1 /\ 1 <= I96 - 1 /\ I97 <= I98 - 1] 18.35/18.37 f7#(I107, I108, I109, I110, I111, I112, I113) -> f8#(I107, 0, I114, I108, I109 + 1, I115, I116) [-1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1] 18.35/18.37 R = 18.35/18.37 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 18.35/18.37 f10(I0, I1, I2, I3, I4, I5, I6) -> f10(I7, I8, I2, I3, I9, I10, I11) [-1 <= I8 - 1 /\ -1 <= I7 - 1 /\ 2 <= I1 - 1 /\ 1 <= I0 - 1 /\ I8 + 2 <= I1 /\ 1 <= I3 - 1 /\ I7 + 2 <= I0] 18.35/18.37 f10(I12, I13, I14, I15, I16, I17, I18) -> f10(I19, I20, I14, I15, I21, I22, I23) [-1 <= I20 - 1 /\ -1 <= I19 - 1 /\ 2 <= I13 - 1 /\ 2 <= I12 - 1 /\ I20 + 2 <= I13 /\ 1 <= I15 - 1 /\ I19 + 2 <= I12] 18.35/18.37 f10(I24, I25, I26, I27, I28, I29, I30) -> f6(I31, I32, I33, I27, I34, I35, I36) [0 <= I33 - 1 /\ 0 <= I32 - 1 /\ 0 <= I31 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1 /\ I33 + 2 <= I24 /\ I32 + 2 <= I24 /\ 1 <= I27 - 1 /\ I31 + 2 <= I25] 18.35/18.37 f10(I37, I38, I39, I40, I41, I42, I43) -> f6(I44, I45, I46, I40, I47, I48, I49) [-1 <= I46 - 1 /\ -1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 2 <= I38 - 1 /\ 1 <= I37 - 1 /\ I46 + 3 <= I38 /\ I46 + 2 <= I37 /\ I45 + 3 <= I38 /\ I45 + 2 <= I37 /\ 1 <= I40 - 1 /\ I44 + 2 <= I38] 18.35/18.37 f9(I50, I51, I52, I53, I54, I55, I56) -> f10(I57, I58, I53, I54, I59, I60, I61) [1 = I52 /\ -1 <= I58 - 1 /\ -1 <= I57 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I50 - 1 /\ I58 <= I55 /\ I58 + 1 <= I50 /\ I57 <= I56 /\ I57 + 1 <= I51] 18.35/18.37 f6(I62, I63, I64, I65, I66, I67, I68) -> f9(I69, I70, 1, I71, I65, I72, I73) [-1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62] 18.35/18.37 f6(I74, I75, I76, I77, I78, I79, I80) -> f9(I81, I82, 0, I83, I77, I84, I85) [-1 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I76 - 1 /\ 0 <= I75 - 1 /\ 0 <= I74 - 1 /\ I85 + 1 <= I76 /\ I85 + 1 <= I75 /\ I84 + 1 <= I74 /\ I82 <= I76 /\ I82 <= I75 /\ 1 <= I77 - 1 /\ I81 <= I74] 18.35/18.37 f8(I86, I87, I88, I89, I90, I91, I92) -> f8(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 f8(I96, I97, I98, I99, I100, I101, I102) -> f7(I96 - 1, I99, I100, I103, I104, I105, I106) [I96 - 1 <= I96 - 1 /\ 1 <= I100 - 1 /\ 0 <= I98 - 1 /\ 1 <= I96 - 1 /\ I97 <= I98 - 1] 18.35/18.37 f7(I107, I108, I109, I110, I111, I112, I113) -> f8(I107, 0, I114, I108, I109 + 1, I115, I116) [-1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1] 18.35/18.37 f2(I117, I118, I119, I120, I121, I122, I123) -> f7(I124, I118, I125, I126, I127, I128, I129) [y1 <= I118 - 1 /\ 0 <= y1 - 1 /\ 0 <= I118 - 1 /\ -1 <= I124 - 1 /\ 3 <= I117 - 1 /\ I120 + 5 <= I117 /\ I119 + 5 <= I117 /\ y1 + 1 = I125] 18.35/18.37 f1(I130, I131, I132, I133, I134, I135, I136) -> f7(I137, I131, I138, I139, I140, I141, I142) [-1 <= y2 - 1 /\ 0 <= I131 - 1 /\ 0 <= I143 - 1 /\ I143 <= I131 - 1 /\ -1 <= I137 - 1 /\ 0 <= I130 - 1 /\ I143 + 1 = I138] 18.35/18.37 f1(I144, I145, I146, I147, I148, I149, I150) -> f7(I151, I145, 1, I152, I153, I154, I155) [0 <= I144 - 1 /\ 0 <= I145 - 1 /\ -1 <= I151 - 1] 18.35/18.37 f2(I156, I157, I158, I159, I160, I161, I162) -> f6(I163, I164, I165, I166, I167, I168, I169) [I170 <= I157 - 1 /\ 0 <= I170 - 1 /\ 0 <= I157 - 1 /\ -1 <= I171 - 1 /\ 1 <= I166 - 1 /\ I163 <= I156 /\ 3 <= I156 - 1 /\ 3 <= I163 - 1 /\ 3 <= I164 - 1 /\ 3 <= I165 - 1 /\ I159 + 5 <= I156 /\ I158 + 5 <= I156] 18.35/18.37 f2(I172, I173, I174, I175, I176, I177, I178) -> f6(I179, I180, I181, I182, I183, I184, I185) [I186 <= I173 - 1 /\ 0 <= I186 - 1 /\ 0 <= I173 - 1 /\ -1 <= I187 - 1 /\ 1 <= I182 - 1 /\ I179 <= I172 /\ I180 + 3 <= I172 /\ I181 + 3 <= I172 /\ 3 <= I172 - 1 /\ 3 <= I179 - 1 /\ 0 <= I180 - 1 /\ 0 <= I181 - 1 /\ I175 + 5 <= I172 /\ I174 + 5 <= I172] 18.35/18.37 f5(I188, I189, I190, I191, I192, I193, I194) -> f4(I195, I196, I197, I198, I199, I200, I201) [0 <= I195 - 1 /\ 0 <= I188 - 1 /\ I195 <= I188] 18.35/18.37 f1(I202, I203, I204, I205, I206, I207, I208) -> f4(I209, I210, I211, I212, I213, I214, I215) [-1 <= I216 - 1 /\ 0 <= I203 - 1 /\ 0 <= I217 - 1 /\ I217 <= I203 - 1 /\ -1 <= y3 - 1 /\ I209 <= I202 /\ 0 <= I202 - 1 /\ 0 <= I209 - 1] 18.35/18.37 f3(I218, I219, I220, I221, I222, I223, I224) -> f2(I225, I226, I221, I222, I227, I228, I229) [I221 + 5 <= I219 /\ I222 + 5 <= I219 /\ 3 <= I225 - 1 /\ 3 <= I219 - 1 /\ 0 <= I218 - 1 /\ I225 <= I219] 18.35/18.37 f1(I230, I231, I232, I233, I234, I235, I236) -> f2(I237, I231, I238, I239, I240, I241, I242) [-1 <= I243 - 1 /\ 0 <= I231 - 1 /\ 0 <= I230 - 1 /\ 3 <= I237 - 1] 18.35/18.37 18.35/18.37 We use the basic value criterion with the projection function NU: 18.35/18.37 NU[f7#(z1,z2,z3,z4,z5,z6,z7)] = z1 18.35/18.37 NU[f8#(z1,z2,z3,z4,z5,z6,z7)] = z1 18.35/18.37 18.35/18.37 This gives the following inequalities: 18.35/18.37 I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1 ==> I86 (>! \union =) I86 18.35/18.37 I96 - 1 <= I96 - 1 /\ 1 <= I100 - 1 /\ 0 <= I98 - 1 /\ 1 <= I96 - 1 /\ I97 <= I98 - 1 ==> I96 >! I96 - 1 18.35/18.37 -1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1 ==> I107 (>! \union =) I107 18.35/18.37 18.35/18.37 We remove all the strictly oriented dependency pairs. 18.35/18.37 18.35/18.37 DP problem for innermost termination. 18.35/18.37 P = 18.35/18.37 f8#(I86, I87, I88, I89, I90, I91, I92) -> f8#(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 f7#(I107, I108, I109, I110, I111, I112, I113) -> f8#(I107, 0, I114, I108, I109 + 1, I115, I116) [-1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1] 18.35/18.37 R = 18.35/18.37 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 18.35/18.37 f10(I0, I1, I2, I3, I4, I5, I6) -> f10(I7, I8, I2, I3, I9, I10, I11) [-1 <= I8 - 1 /\ -1 <= I7 - 1 /\ 2 <= I1 - 1 /\ 1 <= I0 - 1 /\ I8 + 2 <= I1 /\ 1 <= I3 - 1 /\ I7 + 2 <= I0] 18.35/18.37 f10(I12, I13, I14, I15, I16, I17, I18) -> f10(I19, I20, I14, I15, I21, I22, I23) [-1 <= I20 - 1 /\ -1 <= I19 - 1 /\ 2 <= I13 - 1 /\ 2 <= I12 - 1 /\ I20 + 2 <= I13 /\ 1 <= I15 - 1 /\ I19 + 2 <= I12] 18.35/18.37 f10(I24, I25, I26, I27, I28, I29, I30) -> f6(I31, I32, I33, I27, I34, I35, I36) [0 <= I33 - 1 /\ 0 <= I32 - 1 /\ 0 <= I31 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1 /\ I33 + 2 <= I24 /\ I32 + 2 <= I24 /\ 1 <= I27 - 1 /\ I31 + 2 <= I25] 18.35/18.37 f10(I37, I38, I39, I40, I41, I42, I43) -> f6(I44, I45, I46, I40, I47, I48, I49) [-1 <= I46 - 1 /\ -1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 2 <= I38 - 1 /\ 1 <= I37 - 1 /\ I46 + 3 <= I38 /\ I46 + 2 <= I37 /\ I45 + 3 <= I38 /\ I45 + 2 <= I37 /\ 1 <= I40 - 1 /\ I44 + 2 <= I38] 18.35/18.37 f9(I50, I51, I52, I53, I54, I55, I56) -> f10(I57, I58, I53, I54, I59, I60, I61) [1 = I52 /\ -1 <= I58 - 1 /\ -1 <= I57 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I50 - 1 /\ I58 <= I55 /\ I58 + 1 <= I50 /\ I57 <= I56 /\ I57 + 1 <= I51] 18.35/18.37 f6(I62, I63, I64, I65, I66, I67, I68) -> f9(I69, I70, 1, I71, I65, I72, I73) [-1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62] 18.35/18.37 f6(I74, I75, I76, I77, I78, I79, I80) -> f9(I81, I82, 0, I83, I77, I84, I85) [-1 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I76 - 1 /\ 0 <= I75 - 1 /\ 0 <= I74 - 1 /\ I85 + 1 <= I76 /\ I85 + 1 <= I75 /\ I84 + 1 <= I74 /\ I82 <= I76 /\ I82 <= I75 /\ 1 <= I77 - 1 /\ I81 <= I74] 18.35/18.37 f8(I86, I87, I88, I89, I90, I91, I92) -> f8(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 f8(I96, I97, I98, I99, I100, I101, I102) -> f7(I96 - 1, I99, I100, I103, I104, I105, I106) [I96 - 1 <= I96 - 1 /\ 1 <= I100 - 1 /\ 0 <= I98 - 1 /\ 1 <= I96 - 1 /\ I97 <= I98 - 1] 18.35/18.37 f7(I107, I108, I109, I110, I111, I112, I113) -> f8(I107, 0, I114, I108, I109 + 1, I115, I116) [-1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1] 18.35/18.37 f2(I117, I118, I119, I120, I121, I122, I123) -> f7(I124, I118, I125, I126, I127, I128, I129) [y1 <= I118 - 1 /\ 0 <= y1 - 1 /\ 0 <= I118 - 1 /\ -1 <= I124 - 1 /\ 3 <= I117 - 1 /\ I120 + 5 <= I117 /\ I119 + 5 <= I117 /\ y1 + 1 = I125] 18.35/18.37 f1(I130, I131, I132, I133, I134, I135, I136) -> f7(I137, I131, I138, I139, I140, I141, I142) [-1 <= y2 - 1 /\ 0 <= I131 - 1 /\ 0 <= I143 - 1 /\ I143 <= I131 - 1 /\ -1 <= I137 - 1 /\ 0 <= I130 - 1 /\ I143 + 1 = I138] 18.35/18.37 f1(I144, I145, I146, I147, I148, I149, I150) -> f7(I151, I145, 1, I152, I153, I154, I155) [0 <= I144 - 1 /\ 0 <= I145 - 1 /\ -1 <= I151 - 1] 18.35/18.37 f2(I156, I157, I158, I159, I160, I161, I162) -> f6(I163, I164, I165, I166, I167, I168, I169) [I170 <= I157 - 1 /\ 0 <= I170 - 1 /\ 0 <= I157 - 1 /\ -1 <= I171 - 1 /\ 1 <= I166 - 1 /\ I163 <= I156 /\ 3 <= I156 - 1 /\ 3 <= I163 - 1 /\ 3 <= I164 - 1 /\ 3 <= I165 - 1 /\ I159 + 5 <= I156 /\ I158 + 5 <= I156] 18.35/18.37 f2(I172, I173, I174, I175, I176, I177, I178) -> f6(I179, I180, I181, I182, I183, I184, I185) [I186 <= I173 - 1 /\ 0 <= I186 - 1 /\ 0 <= I173 - 1 /\ -1 <= I187 - 1 /\ 1 <= I182 - 1 /\ I179 <= I172 /\ I180 + 3 <= I172 /\ I181 + 3 <= I172 /\ 3 <= I172 - 1 /\ 3 <= I179 - 1 /\ 0 <= I180 - 1 /\ 0 <= I181 - 1 /\ I175 + 5 <= I172 /\ I174 + 5 <= I172] 18.35/18.37 f5(I188, I189, I190, I191, I192, I193, I194) -> f4(I195, I196, I197, I198, I199, I200, I201) [0 <= I195 - 1 /\ 0 <= I188 - 1 /\ I195 <= I188] 18.35/18.37 f1(I202, I203, I204, I205, I206, I207, I208) -> f4(I209, I210, I211, I212, I213, I214, I215) [-1 <= I216 - 1 /\ 0 <= I203 - 1 /\ 0 <= I217 - 1 /\ I217 <= I203 - 1 /\ -1 <= y3 - 1 /\ I209 <= I202 /\ 0 <= I202 - 1 /\ 0 <= I209 - 1] 18.35/18.37 f3(I218, I219, I220, I221, I222, I223, I224) -> f2(I225, I226, I221, I222, I227, I228, I229) [I221 + 5 <= I219 /\ I222 + 5 <= I219 /\ 3 <= I225 - 1 /\ 3 <= I219 - 1 /\ 0 <= I218 - 1 /\ I225 <= I219] 18.35/18.37 f1(I230, I231, I232, I233, I234, I235, I236) -> f2(I237, I231, I238, I239, I240, I241, I242) [-1 <= I243 - 1 /\ 0 <= I231 - 1 /\ 0 <= I230 - 1 /\ 3 <= I237 - 1] 18.35/18.37 18.35/18.37 The dependency graph for this problem is: 18.35/18.37 8 -> 8 18.35/18.37 10 -> 8 18.35/18.37 Where: 18.35/18.37 8) f8#(I86, I87, I88, I89, I90, I91, I92) -> f8#(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 10) f7#(I107, I108, I109, I110, I111, I112, I113) -> f8#(I107, 0, I114, I108, I109 + 1, I115, I116) [-1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1] 18.35/18.37 18.35/18.37 We have the following SCCs. 18.35/18.37 { 8 } 18.35/18.37 18.35/18.37 DP problem for innermost termination. 18.35/18.37 P = 18.35/18.37 f8#(I86, I87, I88, I89, I90, I91, I92) -> f8#(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 R = 18.35/18.37 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 18.35/18.37 f10(I0, I1, I2, I3, I4, I5, I6) -> f10(I7, I8, I2, I3, I9, I10, I11) [-1 <= I8 - 1 /\ -1 <= I7 - 1 /\ 2 <= I1 - 1 /\ 1 <= I0 - 1 /\ I8 + 2 <= I1 /\ 1 <= I3 - 1 /\ I7 + 2 <= I0] 18.35/18.37 f10(I12, I13, I14, I15, I16, I17, I18) -> f10(I19, I20, I14, I15, I21, I22, I23) [-1 <= I20 - 1 /\ -1 <= I19 - 1 /\ 2 <= I13 - 1 /\ 2 <= I12 - 1 /\ I20 + 2 <= I13 /\ 1 <= I15 - 1 /\ I19 + 2 <= I12] 18.35/18.37 f10(I24, I25, I26, I27, I28, I29, I30) -> f6(I31, I32, I33, I27, I34, I35, I36) [0 <= I33 - 1 /\ 0 <= I32 - 1 /\ 0 <= I31 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1 /\ I33 + 2 <= I24 /\ I32 + 2 <= I24 /\ 1 <= I27 - 1 /\ I31 + 2 <= I25] 18.35/18.37 f10(I37, I38, I39, I40, I41, I42, I43) -> f6(I44, I45, I46, I40, I47, I48, I49) [-1 <= I46 - 1 /\ -1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 2 <= I38 - 1 /\ 1 <= I37 - 1 /\ I46 + 3 <= I38 /\ I46 + 2 <= I37 /\ I45 + 3 <= I38 /\ I45 + 2 <= I37 /\ 1 <= I40 - 1 /\ I44 + 2 <= I38] 18.35/18.37 f9(I50, I51, I52, I53, I54, I55, I56) -> f10(I57, I58, I53, I54, I59, I60, I61) [1 = I52 /\ -1 <= I58 - 1 /\ -1 <= I57 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I50 - 1 /\ I58 <= I55 /\ I58 + 1 <= I50 /\ I57 <= I56 /\ I57 + 1 <= I51] 18.35/18.37 f6(I62, I63, I64, I65, I66, I67, I68) -> f9(I69, I70, 1, I71, I65, I72, I73) [-1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62] 18.35/18.37 f6(I74, I75, I76, I77, I78, I79, I80) -> f9(I81, I82, 0, I83, I77, I84, I85) [-1 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I76 - 1 /\ 0 <= I75 - 1 /\ 0 <= I74 - 1 /\ I85 + 1 <= I76 /\ I85 + 1 <= I75 /\ I84 + 1 <= I74 /\ I82 <= I76 /\ I82 <= I75 /\ 1 <= I77 - 1 /\ I81 <= I74] 18.35/18.37 f8(I86, I87, I88, I89, I90, I91, I92) -> f8(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 f8(I96, I97, I98, I99, I100, I101, I102) -> f7(I96 - 1, I99, I100, I103, I104, I105, I106) [I96 - 1 <= I96 - 1 /\ 1 <= I100 - 1 /\ 0 <= I98 - 1 /\ 1 <= I96 - 1 /\ I97 <= I98 - 1] 18.35/18.37 f7(I107, I108, I109, I110, I111, I112, I113) -> f8(I107, 0, I114, I108, I109 + 1, I115, I116) [-1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1] 18.35/18.37 f2(I117, I118, I119, I120, I121, I122, I123) -> f7(I124, I118, I125, I126, I127, I128, I129) [y1 <= I118 - 1 /\ 0 <= y1 - 1 /\ 0 <= I118 - 1 /\ -1 <= I124 - 1 /\ 3 <= I117 - 1 /\ I120 + 5 <= I117 /\ I119 + 5 <= I117 /\ y1 + 1 = I125] 18.35/18.37 f1(I130, I131, I132, I133, I134, I135, I136) -> f7(I137, I131, I138, I139, I140, I141, I142) [-1 <= y2 - 1 /\ 0 <= I131 - 1 /\ 0 <= I143 - 1 /\ I143 <= I131 - 1 /\ -1 <= I137 - 1 /\ 0 <= I130 - 1 /\ I143 + 1 = I138] 18.35/18.37 f1(I144, I145, I146, I147, I148, I149, I150) -> f7(I151, I145, 1, I152, I153, I154, I155) [0 <= I144 - 1 /\ 0 <= I145 - 1 /\ -1 <= I151 - 1] 18.35/18.37 f2(I156, I157, I158, I159, I160, I161, I162) -> f6(I163, I164, I165, I166, I167, I168, I169) [I170 <= I157 - 1 /\ 0 <= I170 - 1 /\ 0 <= I157 - 1 /\ -1 <= I171 - 1 /\ 1 <= I166 - 1 /\ I163 <= I156 /\ 3 <= I156 - 1 /\ 3 <= I163 - 1 /\ 3 <= I164 - 1 /\ 3 <= I165 - 1 /\ I159 + 5 <= I156 /\ I158 + 5 <= I156] 18.35/18.37 f2(I172, I173, I174, I175, I176, I177, I178) -> f6(I179, I180, I181, I182, I183, I184, I185) [I186 <= I173 - 1 /\ 0 <= I186 - 1 /\ 0 <= I173 - 1 /\ -1 <= I187 - 1 /\ 1 <= I182 - 1 /\ I179 <= I172 /\ I180 + 3 <= I172 /\ I181 + 3 <= I172 /\ 3 <= I172 - 1 /\ 3 <= I179 - 1 /\ 0 <= I180 - 1 /\ 0 <= I181 - 1 /\ I175 + 5 <= I172 /\ I174 + 5 <= I172] 18.35/18.37 f5(I188, I189, I190, I191, I192, I193, I194) -> f4(I195, I196, I197, I198, I199, I200, I201) [0 <= I195 - 1 /\ 0 <= I188 - 1 /\ I195 <= I188] 18.35/18.37 f1(I202, I203, I204, I205, I206, I207, I208) -> f4(I209, I210, I211, I212, I213, I214, I215) [-1 <= I216 - 1 /\ 0 <= I203 - 1 /\ 0 <= I217 - 1 /\ I217 <= I203 - 1 /\ -1 <= y3 - 1 /\ I209 <= I202 /\ 0 <= I202 - 1 /\ 0 <= I209 - 1] 18.35/18.37 f3(I218, I219, I220, I221, I222, I223, I224) -> f2(I225, I226, I221, I222, I227, I228, I229) [I221 + 5 <= I219 /\ I222 + 5 <= I219 /\ 3 <= I225 - 1 /\ 3 <= I219 - 1 /\ 0 <= I218 - 1 /\ I225 <= I219] 18.35/18.37 f1(I230, I231, I232, I233, I234, I235, I236) -> f2(I237, I231, I238, I239, I240, I241, I242) [-1 <= I243 - 1 /\ 0 <= I231 - 1 /\ 0 <= I230 - 1 /\ 3 <= I237 - 1] 18.35/18.37 18.35/18.37 We use the reverse value criterion with the projection function NU: 18.35/18.37 NU[f8#(z1,z2,z3,z4,z5,z6,z7)] = z3 - 1 + -1 * z2 18.35/18.37 18.35/18.37 This gives the following inequalities: 18.35/18.37 I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1 ==> I88 - 1 + -1 * I87 > I88 - 1 + -1 * (I87 + 1) with I88 - 1 + -1 * I87 >= 0 18.35/18.37 18.35/18.37 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 18.35/18.37 18.35/18.37 DP problem for innermost termination. 18.35/18.37 P = 18.35/18.37 f10#(I0, I1, I2, I3, I4, I5, I6) -> f10#(I7, I8, I2, I3, I9, I10, I11) [-1 <= I8 - 1 /\ -1 <= I7 - 1 /\ 2 <= I1 - 1 /\ 1 <= I0 - 1 /\ I8 + 2 <= I1 /\ 1 <= I3 - 1 /\ I7 + 2 <= I0] 18.35/18.37 f10#(I12, I13, I14, I15, I16, I17, I18) -> f10#(I19, I20, I14, I15, I21, I22, I23) [-1 <= I20 - 1 /\ -1 <= I19 - 1 /\ 2 <= I13 - 1 /\ 2 <= I12 - 1 /\ I20 + 2 <= I13 /\ 1 <= I15 - 1 /\ I19 + 2 <= I12] 18.35/18.37 f10#(I24, I25, I26, I27, I28, I29, I30) -> f6#(I31, I32, I33, I27, I34, I35, I36) [0 <= I33 - 1 /\ 0 <= I32 - 1 /\ 0 <= I31 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1 /\ I33 + 2 <= I24 /\ I32 + 2 <= I24 /\ 1 <= I27 - 1 /\ I31 + 2 <= I25] 18.35/18.37 f10#(I37, I38, I39, I40, I41, I42, I43) -> f6#(I44, I45, I46, I40, I47, I48, I49) [-1 <= I46 - 1 /\ -1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 2 <= I38 - 1 /\ 1 <= I37 - 1 /\ I46 + 3 <= I38 /\ I46 + 2 <= I37 /\ I45 + 3 <= I38 /\ I45 + 2 <= I37 /\ 1 <= I40 - 1 /\ I44 + 2 <= I38] 18.35/18.37 f9#(I50, I51, I52, I53, I54, I55, I56) -> f10#(I57, I58, I53, I54, I59, I60, I61) [1 = I52 /\ -1 <= I58 - 1 /\ -1 <= I57 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I50 - 1 /\ I58 <= I55 /\ I58 + 1 <= I50 /\ I57 <= I56 /\ I57 + 1 <= I51] 18.35/18.37 f6#(I62, I63, I64, I65, I66, I67, I68) -> f9#(I69, I70, 1, I71, I65, I72, I73) [-1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62] 18.35/18.37 R = 18.35/18.37 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 18.35/18.37 f10(I0, I1, I2, I3, I4, I5, I6) -> f10(I7, I8, I2, I3, I9, I10, I11) [-1 <= I8 - 1 /\ -1 <= I7 - 1 /\ 2 <= I1 - 1 /\ 1 <= I0 - 1 /\ I8 + 2 <= I1 /\ 1 <= I3 - 1 /\ I7 + 2 <= I0] 18.35/18.37 f10(I12, I13, I14, I15, I16, I17, I18) -> f10(I19, I20, I14, I15, I21, I22, I23) [-1 <= I20 - 1 /\ -1 <= I19 - 1 /\ 2 <= I13 - 1 /\ 2 <= I12 - 1 /\ I20 + 2 <= I13 /\ 1 <= I15 - 1 /\ I19 + 2 <= I12] 18.35/18.37 f10(I24, I25, I26, I27, I28, I29, I30) -> f6(I31, I32, I33, I27, I34, I35, I36) [0 <= I33 - 1 /\ 0 <= I32 - 1 /\ 0 <= I31 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1 /\ I33 + 2 <= I24 /\ I32 + 2 <= I24 /\ 1 <= I27 - 1 /\ I31 + 2 <= I25] 18.35/18.37 f10(I37, I38, I39, I40, I41, I42, I43) -> f6(I44, I45, I46, I40, I47, I48, I49) [-1 <= I46 - 1 /\ -1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 2 <= I38 - 1 /\ 1 <= I37 - 1 /\ I46 + 3 <= I38 /\ I46 + 2 <= I37 /\ I45 + 3 <= I38 /\ I45 + 2 <= I37 /\ 1 <= I40 - 1 /\ I44 + 2 <= I38] 18.35/18.37 f9(I50, I51, I52, I53, I54, I55, I56) -> f10(I57, I58, I53, I54, I59, I60, I61) [1 = I52 /\ -1 <= I58 - 1 /\ -1 <= I57 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I50 - 1 /\ I58 <= I55 /\ I58 + 1 <= I50 /\ I57 <= I56 /\ I57 + 1 <= I51] 18.35/18.37 f6(I62, I63, I64, I65, I66, I67, I68) -> f9(I69, I70, 1, I71, I65, I72, I73) [-1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62] 18.35/18.37 f6(I74, I75, I76, I77, I78, I79, I80) -> f9(I81, I82, 0, I83, I77, I84, I85) [-1 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I76 - 1 /\ 0 <= I75 - 1 /\ 0 <= I74 - 1 /\ I85 + 1 <= I76 /\ I85 + 1 <= I75 /\ I84 + 1 <= I74 /\ I82 <= I76 /\ I82 <= I75 /\ 1 <= I77 - 1 /\ I81 <= I74] 18.35/18.37 f8(I86, I87, I88, I89, I90, I91, I92) -> f8(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 f8(I96, I97, I98, I99, I100, I101, I102) -> f7(I96 - 1, I99, I100, I103, I104, I105, I106) [I96 - 1 <= I96 - 1 /\ 1 <= I100 - 1 /\ 0 <= I98 - 1 /\ 1 <= I96 - 1 /\ I97 <= I98 - 1] 18.35/18.37 f7(I107, I108, I109, I110, I111, I112, I113) -> f8(I107, 0, I114, I108, I109 + 1, I115, I116) [-1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1] 18.35/18.37 f2(I117, I118, I119, I120, I121, I122, I123) -> f7(I124, I118, I125, I126, I127, I128, I129) [y1 <= I118 - 1 /\ 0 <= y1 - 1 /\ 0 <= I118 - 1 /\ -1 <= I124 - 1 /\ 3 <= I117 - 1 /\ I120 + 5 <= I117 /\ I119 + 5 <= I117 /\ y1 + 1 = I125] 18.35/18.37 f1(I130, I131, I132, I133, I134, I135, I136) -> f7(I137, I131, I138, I139, I140, I141, I142) [-1 <= y2 - 1 /\ 0 <= I131 - 1 /\ 0 <= I143 - 1 /\ I143 <= I131 - 1 /\ -1 <= I137 - 1 /\ 0 <= I130 - 1 /\ I143 + 1 = I138] 18.35/18.37 f1(I144, I145, I146, I147, I148, I149, I150) -> f7(I151, I145, 1, I152, I153, I154, I155) [0 <= I144 - 1 /\ 0 <= I145 - 1 /\ -1 <= I151 - 1] 18.35/18.37 f2(I156, I157, I158, I159, I160, I161, I162) -> f6(I163, I164, I165, I166, I167, I168, I169) [I170 <= I157 - 1 /\ 0 <= I170 - 1 /\ 0 <= I157 - 1 /\ -1 <= I171 - 1 /\ 1 <= I166 - 1 /\ I163 <= I156 /\ 3 <= I156 - 1 /\ 3 <= I163 - 1 /\ 3 <= I164 - 1 /\ 3 <= I165 - 1 /\ I159 + 5 <= I156 /\ I158 + 5 <= I156] 18.35/18.37 f2(I172, I173, I174, I175, I176, I177, I178) -> f6(I179, I180, I181, I182, I183, I184, I185) [I186 <= I173 - 1 /\ 0 <= I186 - 1 /\ 0 <= I173 - 1 /\ -1 <= I187 - 1 /\ 1 <= I182 - 1 /\ I179 <= I172 /\ I180 + 3 <= I172 /\ I181 + 3 <= I172 /\ 3 <= I172 - 1 /\ 3 <= I179 - 1 /\ 0 <= I180 - 1 /\ 0 <= I181 - 1 /\ I175 + 5 <= I172 /\ I174 + 5 <= I172] 18.35/18.37 f5(I188, I189, I190, I191, I192, I193, I194) -> f4(I195, I196, I197, I198, I199, I200, I201) [0 <= I195 - 1 /\ 0 <= I188 - 1 /\ I195 <= I188] 18.35/18.37 f1(I202, I203, I204, I205, I206, I207, I208) -> f4(I209, I210, I211, I212, I213, I214, I215) [-1 <= I216 - 1 /\ 0 <= I203 - 1 /\ 0 <= I217 - 1 /\ I217 <= I203 - 1 /\ -1 <= y3 - 1 /\ I209 <= I202 /\ 0 <= I202 - 1 /\ 0 <= I209 - 1] 18.35/18.37 f3(I218, I219, I220, I221, I222, I223, I224) -> f2(I225, I226, I221, I222, I227, I228, I229) [I221 + 5 <= I219 /\ I222 + 5 <= I219 /\ 3 <= I225 - 1 /\ 3 <= I219 - 1 /\ 0 <= I218 - 1 /\ I225 <= I219] 18.35/18.37 f1(I230, I231, I232, I233, I234, I235, I236) -> f2(I237, I231, I238, I239, I240, I241, I242) [-1 <= I243 - 1 /\ 0 <= I231 - 1 /\ 0 <= I230 - 1 /\ 3 <= I237 - 1] 18.35/18.37 18.35/18.37 We use the basic value criterion with the projection function NU: 18.35/18.37 NU[f9#(z1,z2,z3,z4,z5,z6,z7)] = z2 18.35/18.37 NU[f6#(z1,z2,z3,z4,z5,z6,z7)] = z3 18.35/18.37 NU[f10#(z1,z2,z3,z4,z5,z6,z7)] = z1 18.35/18.37 18.35/18.37 This gives the following inequalities: 18.35/18.37 -1 <= I8 - 1 /\ -1 <= I7 - 1 /\ 2 <= I1 - 1 /\ 1 <= I0 - 1 /\ I8 + 2 <= I1 /\ 1 <= I3 - 1 /\ I7 + 2 <= I0 ==> I0 >! I7 18.35/18.37 -1 <= I20 - 1 /\ -1 <= I19 - 1 /\ 2 <= I13 - 1 /\ 2 <= I12 - 1 /\ I20 + 2 <= I13 /\ 1 <= I15 - 1 /\ I19 + 2 <= I12 ==> I12 >! I19 18.35/18.37 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ 0 <= I31 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1 /\ I33 + 2 <= I24 /\ I32 + 2 <= I24 /\ 1 <= I27 - 1 /\ I31 + 2 <= I25 ==> I24 >! I33 18.35/18.37 -1 <= I46 - 1 /\ -1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 2 <= I38 - 1 /\ 1 <= I37 - 1 /\ I46 + 3 <= I38 /\ I46 + 2 <= I37 /\ I45 + 3 <= I38 /\ I45 + 2 <= I37 /\ 1 <= I40 - 1 /\ I44 + 2 <= I38 ==> I37 >! I46 18.35/18.37 1 = I52 /\ -1 <= I58 - 1 /\ -1 <= I57 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I50 - 1 /\ I58 <= I55 /\ I58 + 1 <= I50 /\ I57 <= I56 /\ I57 + 1 <= I51 ==> I51 >! I57 18.35/18.37 -1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62 ==> I64 (>! \union =) I70 18.35/18.37 18.35/18.37 We remove all the strictly oriented dependency pairs. 18.35/18.37 18.35/18.37 DP problem for innermost termination. 18.35/18.37 P = 18.35/18.37 f6#(I62, I63, I64, I65, I66, I67, I68) -> f9#(I69, I70, 1, I71, I65, I72, I73) [-1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62] 18.35/18.37 R = 18.35/18.37 init(x1, x2, x3, x4, x5, x6, x7) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6, rnd7) 18.35/18.37 f10(I0, I1, I2, I3, I4, I5, I6) -> f10(I7, I8, I2, I3, I9, I10, I11) [-1 <= I8 - 1 /\ -1 <= I7 - 1 /\ 2 <= I1 - 1 /\ 1 <= I0 - 1 /\ I8 + 2 <= I1 /\ 1 <= I3 - 1 /\ I7 + 2 <= I0] 18.35/18.37 f10(I12, I13, I14, I15, I16, I17, I18) -> f10(I19, I20, I14, I15, I21, I22, I23) [-1 <= I20 - 1 /\ -1 <= I19 - 1 /\ 2 <= I13 - 1 /\ 2 <= I12 - 1 /\ I20 + 2 <= I13 /\ 1 <= I15 - 1 /\ I19 + 2 <= I12] 18.35/18.37 f10(I24, I25, I26, I27, I28, I29, I30) -> f6(I31, I32, I33, I27, I34, I35, I36) [0 <= I33 - 1 /\ 0 <= I32 - 1 /\ 0 <= I31 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1 /\ I33 + 2 <= I24 /\ I32 + 2 <= I24 /\ 1 <= I27 - 1 /\ I31 + 2 <= I25] 18.35/18.37 f10(I37, I38, I39, I40, I41, I42, I43) -> f6(I44, I45, I46, I40, I47, I48, I49) [-1 <= I46 - 1 /\ -1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 2 <= I38 - 1 /\ 1 <= I37 - 1 /\ I46 + 3 <= I38 /\ I46 + 2 <= I37 /\ I45 + 3 <= I38 /\ I45 + 2 <= I37 /\ 1 <= I40 - 1 /\ I44 + 2 <= I38] 18.35/18.37 f9(I50, I51, I52, I53, I54, I55, I56) -> f10(I57, I58, I53, I54, I59, I60, I61) [1 = I52 /\ -1 <= I58 - 1 /\ -1 <= I57 - 1 /\ -1 <= I56 - 1 /\ -1 <= I55 - 1 /\ 0 <= I51 - 1 /\ 0 <= I50 - 1 /\ I58 <= I55 /\ I58 + 1 <= I50 /\ I57 <= I56 /\ I57 + 1 <= I51] 18.35/18.37 f6(I62, I63, I64, I65, I66, I67, I68) -> f9(I69, I70, 1, I71, I65, I72, I73) [-1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62] 18.35/18.37 f6(I74, I75, I76, I77, I78, I79, I80) -> f9(I81, I82, 0, I83, I77, I84, I85) [-1 <= I85 - 1 /\ -1 <= I84 - 1 /\ 0 <= I82 - 1 /\ 0 <= I81 - 1 /\ 0 <= I76 - 1 /\ 0 <= I75 - 1 /\ 0 <= I74 - 1 /\ I85 + 1 <= I76 /\ I85 + 1 <= I75 /\ I84 + 1 <= I74 /\ I82 <= I76 /\ I82 <= I75 /\ 1 <= I77 - 1 /\ I81 <= I74] 18.35/18.37 f8(I86, I87, I88, I89, I90, I91, I92) -> f8(I86, I87 + 1, I88, I89, I93, I94, I95) [I86 - 1 <= I86 - 1 /\ 1 <= I90 - 1 /\ 0 <= I88 - 1 /\ 1 <= I86 - 1 /\ I87 <= I88 - 1] 18.35/18.37 f8(I96, I97, I98, I99, I100, I101, I102) -> f7(I96 - 1, I99, I100, I103, I104, I105, I106) [I96 - 1 <= I96 - 1 /\ 1 <= I100 - 1 /\ 0 <= I98 - 1 /\ 1 <= I96 - 1 /\ I97 <= I98 - 1] 18.35/18.37 f7(I107, I108, I109, I110, I111, I112, I113) -> f8(I107, 0, I114, I108, I109 + 1, I115, I116) [-1 <= I114 - 1 /\ I109 <= I108 - 1 /\ 0 <= I109 - 1 /\ 1 <= I107 - 1 /\ -1 <= I108 - 1] 18.35/18.37 f2(I117, I118, I119, I120, I121, I122, I123) -> f7(I124, I118, I125, I126, I127, I128, I129) [y1 <= I118 - 1 /\ 0 <= y1 - 1 /\ 0 <= I118 - 1 /\ -1 <= I124 - 1 /\ 3 <= I117 - 1 /\ I120 + 5 <= I117 /\ I119 + 5 <= I117 /\ y1 + 1 = I125] 18.35/18.37 f1(I130, I131, I132, I133, I134, I135, I136) -> f7(I137, I131, I138, I139, I140, I141, I142) [-1 <= y2 - 1 /\ 0 <= I131 - 1 /\ 0 <= I143 - 1 /\ I143 <= I131 - 1 /\ -1 <= I137 - 1 /\ 0 <= I130 - 1 /\ I143 + 1 = I138] 18.35/18.37 f1(I144, I145, I146, I147, I148, I149, I150) -> f7(I151, I145, 1, I152, I153, I154, I155) [0 <= I144 - 1 /\ 0 <= I145 - 1 /\ -1 <= I151 - 1] 18.35/18.37 f2(I156, I157, I158, I159, I160, I161, I162) -> f6(I163, I164, I165, I166, I167, I168, I169) [I170 <= I157 - 1 /\ 0 <= I170 - 1 /\ 0 <= I157 - 1 /\ -1 <= I171 - 1 /\ 1 <= I166 - 1 /\ I163 <= I156 /\ 3 <= I156 - 1 /\ 3 <= I163 - 1 /\ 3 <= I164 - 1 /\ 3 <= I165 - 1 /\ I159 + 5 <= I156 /\ I158 + 5 <= I156] 18.35/18.37 f2(I172, I173, I174, I175, I176, I177, I178) -> f6(I179, I180, I181, I182, I183, I184, I185) [I186 <= I173 - 1 /\ 0 <= I186 - 1 /\ 0 <= I173 - 1 /\ -1 <= I187 - 1 /\ 1 <= I182 - 1 /\ I179 <= I172 /\ I180 + 3 <= I172 /\ I181 + 3 <= I172 /\ 3 <= I172 - 1 /\ 3 <= I179 - 1 /\ 0 <= I180 - 1 /\ 0 <= I181 - 1 /\ I175 + 5 <= I172 /\ I174 + 5 <= I172] 18.35/18.37 f5(I188, I189, I190, I191, I192, I193, I194) -> f4(I195, I196, I197, I198, I199, I200, I201) [0 <= I195 - 1 /\ 0 <= I188 - 1 /\ I195 <= I188] 18.35/18.37 f1(I202, I203, I204, I205, I206, I207, I208) -> f4(I209, I210, I211, I212, I213, I214, I215) [-1 <= I216 - 1 /\ 0 <= I203 - 1 /\ 0 <= I217 - 1 /\ I217 <= I203 - 1 /\ -1 <= y3 - 1 /\ I209 <= I202 /\ 0 <= I202 - 1 /\ 0 <= I209 - 1] 18.35/18.37 f3(I218, I219, I220, I221, I222, I223, I224) -> f2(I225, I226, I221, I222, I227, I228, I229) [I221 + 5 <= I219 /\ I222 + 5 <= I219 /\ 3 <= I225 - 1 /\ 3 <= I219 - 1 /\ 0 <= I218 - 1 /\ I225 <= I219] 18.35/18.37 f1(I230, I231, I232, I233, I234, I235, I236) -> f2(I237, I231, I238, I239, I240, I241, I242) [-1 <= I243 - 1 /\ 0 <= I231 - 1 /\ 0 <= I230 - 1 /\ 3 <= I237 - 1] 18.35/18.37 18.35/18.37 The dependency graph for this problem is: 18.35/18.37 6 -> 18.35/18.37 Where: 18.35/18.37 6) f6#(I62, I63, I64, I65, I66, I67, I68) -> f9#(I69, I70, 1, I71, I65, I72, I73) [-1 <= I73 - 1 /\ -1 <= I72 - 1 /\ 0 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 0 <= I62 - 1 /\ I73 + 1 <= I64 /\ I73 + 1 <= I63 /\ I72 + 1 <= I62 /\ I70 <= I64 /\ I70 <= I63 /\ 1 <= I65 - 1 /\ I69 <= I62] 18.35/18.37 18.35/18.37 We have the following SCCs. 18.35/18.37 18.35/21.35 EOF