34.75/34.27 MAYBE 34.75/34.27 34.75/34.27 DP problem for innermost termination. 34.75/34.27 P = 34.75/34.27 init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 34.75/34.27 f10#(I0, I1, I2, I3) -> f5#(I4, I5, I6, I7) [-1 <= I4 - 1 /\ -1 <= I3 - 1 /\ -1 <= I1 - 1 /\ 3 <= I0 - 1 /\ I4 <= I3 /\ I4 <= I1 /\ I4 + 2 <= I0] 34.75/34.27 f5#(I8, I9, I10, I11) -> f10#(I12, I13, I14, I15) [-1 <= I15 - 1 /\ -1 <= I13 - 1 /\ 3 <= I12 - 1 /\ 3 <= I8 - 1 /\ I15 + 2 <= I8 /\ I13 + 2 <= I8 /\ I12 <= I8] 34.75/34.27 f5#(I16, I17, I18, I19) -> f10#(I20, I21, I22, I23) [-1 <= I23 - 1 /\ -1 <= I21 - 1 /\ 5 <= I20 - 1 /\ 1 <= I16 - 1 /\ I23 + 2 <= I16 /\ I21 + 2 <= I16] 34.75/34.27 f5#(I24, I25, I26, I27) -> f10#(I28, I29, I30, I31) [-1 <= I31 - 1 /\ -1 <= I29 - 1 /\ 5 <= I28 - 1 /\ 1 <= I24 - 1 /\ I31 + 2 <= I24 /\ I29 + 2 <= I24] 34.75/34.27 f5#(I32, I33, I34, I35) -> f10#(I36, I37, I38, I39) [-1 <= I39 - 1 /\ -1 <= I37 - 1 /\ 5 <= I36 - 1 /\ 1 <= I32 - 1 /\ I39 + 2 <= I32 /\ I37 + 2 <= I32] 34.75/34.27 f5#(I40, I41, I42, I43) -> f10#(I44, I45, I46, I47) [-1 <= I47 - 1 /\ -1 <= I45 - 1 /\ 5 <= I44 - 1 /\ 1 <= I40 - 1 /\ I47 + 2 <= I40 /\ I45 + 2 <= I40] 34.75/34.27 f5#(I48, I49, I50, I51) -> f10#(I52, I53, I54, I55) [-1 <= I55 - 1 /\ -1 <= I53 - 1 /\ 5 <= I52 - 1 /\ 1 <= I48 - 1 /\ I55 + 2 <= I48 /\ I53 + 2 <= I48] 34.75/34.27 f5#(I56, I57, I58, I59) -> f10#(I60, I61, I62, I63) [-1 <= I63 - 1 /\ -1 <= I61 - 1 /\ 5 <= I60 - 1 /\ 1 <= I56 - 1 /\ I63 + 2 <= I56 /\ I61 + 2 <= I56 /\ I60 - 4 <= I56] 34.75/34.27 f5#(I64, I65, I66, I67) -> f10#(I68, I69, I70, I71) [-1 <= I71 - 1 /\ -1 <= I69 - 1 /\ 5 <= I68 - 1 /\ 1 <= I64 - 1 /\ I71 + 2 <= I64 /\ I69 + 2 <= I64 /\ I68 - 4 <= I64] 34.75/34.27 f5#(I72, I73, I74, I75) -> f10#(I76, I77, I78, I79) [-1 <= I79 - 1 /\ -1 <= I77 - 1 /\ 5 <= I76 - 1 /\ 1 <= I72 - 1 /\ I79 + 2 <= I72 /\ I77 + 2 <= I72 /\ I76 - 4 <= I72] 34.75/34.27 f5#(I80, I81, I82, I83) -> f5#(I84, I85, I86, I87) [-1 <= I84 - 1 /\ 1 <= I80 - 1 /\ I84 + 2 <= I80] 34.75/34.27 f5#(I88, I89, I90, I91) -> f5#(I92, I93, I94, I95) [2 <= I92 - 1 /\ 2 <= I88 - 1 /\ I92 - 2 <= I88] 34.75/34.27 f5#(I96, I97, I98, I99) -> f5#(I100, I101, I102, I103) [-1 <= I100 - 1 /\ 1 <= I96 - 1 /\ I100 + 2 <= I96] 34.75/34.27 f5#(I104, I105, I106, I107) -> f5#(I108, I109, I110, I111) [-1 <= I108 - 1 /\ 1 <= I104 - 1 /\ I108 + 2 <= I104] 34.75/34.27 f2#(I112, I113, I114, I115) -> f2#(I112 - 1, I113, I116, I117) [0 <= I112 - 1 /\ -1 <= I113 - 1 /\ 0 <= I114 - 1 /\ I114 <= I113 - 1 /\ -1 <= y1 - 1 /\ y1 <= 42 /\ I112 - 1 <= I112 - 1 /\ 1 <= I116 - 1 /\ 1 <= y2 - 1] 34.75/34.27 f9#(I118, I119, I120, I121) -> f2#(I119, I120, I121, I122) [1 <= I121 - 1 /\ 0 <= I118 - 1 /\ I119 <= I118 - 1] 34.75/34.27 f2#(I123, I124, I125, I126) -> f9#(I123, I123 - 1, I124, I127) [0 <= I123 - 1 /\ -1 <= I124 - 1 /\ 0 <= I125 - 1 /\ I125 <= I124 - 1 /\ -1 <= I128 - 1 /\ I128 <= 42 /\ 1 <= I129 - 1 /\ I123 - 1 <= I123 - 1] 34.75/34.27 f2#(I130, I131, I132, I133) -> f9#(1, 0, I131, I134) [0 <= I132 - 1 /\ -1 <= I131 - 1 /\ I132 <= I131 - 1 /\ -1 <= I135 - 1 /\ 1 <= I134 - 1 /\ I135 <= 42 /\ 1 = I130] 34.75/34.27 f7#(I136, I137, I138, I139) -> f2#(I136 - 1, I138, I140, I141) [I136 - 1 <= I136 - 1 /\ I137 <= I136 - 1 /\ 1 <= I140 - 1 /\ 1 <= I139 - 1 /\ 0 <= I136 - 1] 34.75/34.27 f2#(I142, I143, I144, I145) -> f2#(I142 - 1, I143, I146, I147) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ 0 <= I144 - 1 /\ I144 <= I143 - 1 /\ -1 <= I148 - 1 /\ I148 <= 42 /\ 1 <= I146 - 1 /\ I142 - 1 <= I142 - 1] 34.75/34.27 f8#(I149, I150, I151, I152) -> f2#(I150, I151, I152, I153) [1 <= I152 - 1 /\ 0 <= I149 - 1 /\ I150 <= I149 - 1] 34.75/34.27 f7#(I154, I155, I156, I157) -> f8#(I154, I154 - 1, I156, I158) [1 <= I157 - 1 /\ I155 <= I154 - 1 /\ 0 <= I154 - 1] 34.75/34.27 f7#(I159, I160, I161, I162) -> f8#(I159, I159 - 1, I161, I162) [0 = I160 /\ 0 <= I159 - 1 /\ 1 <= I162 - 1] 34.75/34.27 f7#(I163, I164, I165, I166) -> f2#(I164, I165, I166, I167) [1 <= I166 - 1 /\ 0 <= I163 - 1 /\ I164 <= I163 - 1] 34.75/34.27 f2#(I168, I169, I170, I171) -> f7#(I168, I168 - 1, I169, I172) [0 <= I168 - 1 /\ -1 <= I169 - 1 /\ 0 <= I170 - 1 /\ I170 <= I169 - 1 /\ -1 <= I173 - 1 /\ I168 - 1 <= I168 - 1 /\ I173 <= 42] 34.75/34.27 f2#(I174, I175, I176, I177) -> f7#(1, 0, I175, I176 + 1) [0 <= I176 - 1 /\ -1 <= I175 - 1 /\ I176 <= I175 - 1 /\ I178 <= 42 /\ -1 <= I178 - 1 /\ 1 = I174] 34.75/34.27 f2#(I179, I180, I181, I182) -> f2#(I179 - 1, I180, I181 + 1, I183) [0 <= I179 - 1 /\ -1 <= I180 - 1 /\ 0 <= I181 - 1 /\ I181 <= I180 - 1 /\ -1 <= I184 - 1 /\ I179 - 1 <= I179 - 1 /\ I184 <= 42] 34.75/34.27 f6#(I185, I186, I187, I188) -> f5#(I189, I190, I191, I192) [0 <= I193 - 1 /\ 1 <= I187 - 1 /\ I189 <= I186 /\ 0 <= I185 - 1 /\ 0 <= I186 - 1 /\ 0 <= I189 - 1] 34.75/34.27 f1#(I194, I195, I196, I197) -> f6#(I198, I199, I200, I201) [-1 <= I202 - 1 /\ 0 <= I195 - 1 /\ I198 <= I194 /\ I199 - 1 <= I194 /\ 0 <= I194 - 1 /\ 0 <= I198 - 1 /\ 1 <= I199 - 1] 34.75/34.27 f1#(I203, I204, I205, I206) -> f6#(I207, I208, I209, I210) [-1 <= I211 - 1 /\ 0 <= I204 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 2 <= I208 - 1] 34.75/34.27 f1#(I212, I213, I214, I215) -> f6#(I216, I217, I218, I219) [-1 <= I220 - 1 /\ 0 <= I213 - 1 /\ I216 <= I212 /\ 0 <= I212 - 1 /\ 0 <= I216 - 1 /\ 2 <= I217 - 1] 34.75/34.27 f1#(I221, I222, I223, I224) -> f6#(I225, I226, I227, I228) [-1 <= I229 - 1 /\ 0 <= I222 - 1 /\ I225 <= I221 /\ 0 <= I221 - 1 /\ 0 <= I225 - 1 /\ 2 <= I226 - 1] 34.75/34.27 f1#(I230, I231, I232, I233) -> f6#(I234, I235, I236, I237) [-1 <= I238 - 1 /\ 0 <= I231 - 1 /\ I234 <= I230 /\ 0 <= I230 - 1 /\ 0 <= I234 - 1 /\ 2 <= I235 - 1] 34.75/34.27 f1#(I239, I240, I241, I242) -> f6#(I243, I244, I245, I246) [-1 <= I247 - 1 /\ 0 <= I240 - 1 /\ I243 <= I239 /\ 0 <= I239 - 1 /\ 0 <= I243 - 1 /\ 2 <= I244 - 1] 34.75/34.27 f1#(I248, I249, I250, I251) -> f6#(I252, I253, I254, I255) [-1 <= I256 - 1 /\ 0 <= I249 - 1 /\ I252 <= I248 /\ 0 <= I248 - 1 /\ 0 <= I252 - 1 /\ 2 <= I253 - 1] 34.75/34.27 f1#(I257, I258, I259, I260) -> f6#(I261, I262, I263, I264) [-1 <= I265 - 1 /\ 0 <= I258 - 1 /\ I261 <= I257 /\ 0 <= I257 - 1 /\ 0 <= I261 - 1 /\ 2 <= I262 - 1] 34.75/34.27 f3#(I266, I267, I268, I269) -> f5#(I270, I271, I272, I273) [I270 + 1 <= I266 /\ 0 <= I274 - 1 /\ 0 <= I266 - 1 /\ -1 <= I270 - 1] 34.75/34.27 f4#(I275, I276, I277, I278) -> f3#(I279, I280, I281, I282) [0 <= I279 - 1 /\ 0 <= I275 - 1 /\ I279 <= I275] 34.75/34.27 f1#(I283, I284, I285, I286) -> f3#(I287, I288, I289, I290) [-1 <= I291 - 1 /\ 0 <= I284 - 1 /\ I287 <= I283 /\ 0 <= I283 - 1 /\ 0 <= I287 - 1] 34.75/34.27 f1#(I292, I293, I294, I295) -> f3#(I296, I297, I298, I299) [0 <= I296 - 1 /\ 0 <= I292 - 1 /\ 0 <= I293 - 1 /\ I296 <= I292] 34.75/34.27 f1#(I300, I301, I302, I303) -> f2#(I304, I301, 1, I305) [0 <= I300 - 1 /\ 0 <= I301 - 1 /\ -1 <= I304 - 1] 34.75/34.27 R = 34.75/34.27 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 34.75/34.27 f10(I0, I1, I2, I3) -> f5(I4, I5, I6, I7) [-1 <= I4 - 1 /\ -1 <= I3 - 1 /\ -1 <= I1 - 1 /\ 3 <= I0 - 1 /\ I4 <= I3 /\ I4 <= I1 /\ I4 + 2 <= I0] 34.75/34.27 f5(I8, I9, I10, I11) -> f10(I12, I13, I14, I15) [-1 <= I15 - 1 /\ -1 <= I13 - 1 /\ 3 <= I12 - 1 /\ 3 <= I8 - 1 /\ I15 + 2 <= I8 /\ I13 + 2 <= I8 /\ I12 <= I8] 34.75/34.27 f5(I16, I17, I18, I19) -> f10(I20, I21, I22, I23) [-1 <= I23 - 1 /\ -1 <= I21 - 1 /\ 5 <= I20 - 1 /\ 1 <= I16 - 1 /\ I23 + 2 <= I16 /\ I21 + 2 <= I16] 34.75/34.27 f5(I24, I25, I26, I27) -> f10(I28, I29, I30, I31) [-1 <= I31 - 1 /\ -1 <= I29 - 1 /\ 5 <= I28 - 1 /\ 1 <= I24 - 1 /\ I31 + 2 <= I24 /\ I29 + 2 <= I24] 34.75/34.27 f5(I32, I33, I34, I35) -> f10(I36, I37, I38, I39) [-1 <= I39 - 1 /\ -1 <= I37 - 1 /\ 5 <= I36 - 1 /\ 1 <= I32 - 1 /\ I39 + 2 <= I32 /\ I37 + 2 <= I32] 34.75/34.27 f5(I40, I41, I42, I43) -> f10(I44, I45, I46, I47) [-1 <= I47 - 1 /\ -1 <= I45 - 1 /\ 5 <= I44 - 1 /\ 1 <= I40 - 1 /\ I47 + 2 <= I40 /\ I45 + 2 <= I40] 34.75/34.27 f5(I48, I49, I50, I51) -> f10(I52, I53, I54, I55) [-1 <= I55 - 1 /\ -1 <= I53 - 1 /\ 5 <= I52 - 1 /\ 1 <= I48 - 1 /\ I55 + 2 <= I48 /\ I53 + 2 <= I48] 34.75/34.27 f5(I56, I57, I58, I59) -> f10(I60, I61, I62, I63) [-1 <= I63 - 1 /\ -1 <= I61 - 1 /\ 5 <= I60 - 1 /\ 1 <= I56 - 1 /\ I63 + 2 <= I56 /\ I61 + 2 <= I56 /\ I60 - 4 <= I56] 34.75/34.27 f5(I64, I65, I66, I67) -> f10(I68, I69, I70, I71) [-1 <= I71 - 1 /\ -1 <= I69 - 1 /\ 5 <= I68 - 1 /\ 1 <= I64 - 1 /\ I71 + 2 <= I64 /\ I69 + 2 <= I64 /\ I68 - 4 <= I64] 34.75/34.27 f5(I72, I73, I74, I75) -> f10(I76, I77, I78, I79) [-1 <= I79 - 1 /\ -1 <= I77 - 1 /\ 5 <= I76 - 1 /\ 1 <= I72 - 1 /\ I79 + 2 <= I72 /\ I77 + 2 <= I72 /\ I76 - 4 <= I72] 34.75/34.27 f5(I80, I81, I82, I83) -> f5(I84, I85, I86, I87) [-1 <= I84 - 1 /\ 1 <= I80 - 1 /\ I84 + 2 <= I80] 34.75/34.27 f5(I88, I89, I90, I91) -> f5(I92, I93, I94, I95) [2 <= I92 - 1 /\ 2 <= I88 - 1 /\ I92 - 2 <= I88] 34.75/34.27 f5(I96, I97, I98, I99) -> f5(I100, I101, I102, I103) [-1 <= I100 - 1 /\ 1 <= I96 - 1 /\ I100 + 2 <= I96] 34.75/34.27 f5(I104, I105, I106, I107) -> f5(I108, I109, I110, I111) [-1 <= I108 - 1 /\ 1 <= I104 - 1 /\ I108 + 2 <= I104] 34.75/34.27 f2(I112, I113, I114, I115) -> f2(I112 - 1, I113, I116, I117) [0 <= I112 - 1 /\ -1 <= I113 - 1 /\ 0 <= I114 - 1 /\ I114 <= I113 - 1 /\ -1 <= y1 - 1 /\ y1 <= 42 /\ I112 - 1 <= I112 - 1 /\ 1 <= I116 - 1 /\ 1 <= y2 - 1] 34.75/34.27 f9(I118, I119, I120, I121) -> f2(I119, I120, I121, I122) [1 <= I121 - 1 /\ 0 <= I118 - 1 /\ I119 <= I118 - 1] 34.75/34.27 f2(I123, I124, I125, I126) -> f9(I123, I123 - 1, I124, I127) [0 <= I123 - 1 /\ -1 <= I124 - 1 /\ 0 <= I125 - 1 /\ I125 <= I124 - 1 /\ -1 <= I128 - 1 /\ I128 <= 42 /\ 1 <= I129 - 1 /\ I123 - 1 <= I123 - 1] 34.75/34.27 f2(I130, I131, I132, I133) -> f9(1, 0, I131, I134) [0 <= I132 - 1 /\ -1 <= I131 - 1 /\ I132 <= I131 - 1 /\ -1 <= I135 - 1 /\ 1 <= I134 - 1 /\ I135 <= 42 /\ 1 = I130] 34.75/34.27 f7(I136, I137, I138, I139) -> f2(I136 - 1, I138, I140, I141) [I136 - 1 <= I136 - 1 /\ I137 <= I136 - 1 /\ 1 <= I140 - 1 /\ 1 <= I139 - 1 /\ 0 <= I136 - 1] 34.75/34.27 f2(I142, I143, I144, I145) -> f2(I142 - 1, I143, I146, I147) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ 0 <= I144 - 1 /\ I144 <= I143 - 1 /\ -1 <= I148 - 1 /\ I148 <= 42 /\ 1 <= I146 - 1 /\ I142 - 1 <= I142 - 1] 34.75/34.27 f8(I149, I150, I151, I152) -> f2(I150, I151, I152, I153) [1 <= I152 - 1 /\ 0 <= I149 - 1 /\ I150 <= I149 - 1] 34.75/34.27 f7(I154, I155, I156, I157) -> f8(I154, I154 - 1, I156, I158) [1 <= I157 - 1 /\ I155 <= I154 - 1 /\ 0 <= I154 - 1] 34.75/34.27 f7(I159, I160, I161, I162) -> f8(I159, I159 - 1, I161, I162) [0 = I160 /\ 0 <= I159 - 1 /\ 1 <= I162 - 1] 34.75/34.27 f7(I163, I164, I165, I166) -> f2(I164, I165, I166, I167) [1 <= I166 - 1 /\ 0 <= I163 - 1 /\ I164 <= I163 - 1] 34.75/34.27 f2(I168, I169, I170, I171) -> f7(I168, I168 - 1, I169, I172) [0 <= I168 - 1 /\ -1 <= I169 - 1 /\ 0 <= I170 - 1 /\ I170 <= I169 - 1 /\ -1 <= I173 - 1 /\ I168 - 1 <= I168 - 1 /\ I173 <= 42] 34.75/34.27 f2(I174, I175, I176, I177) -> f7(1, 0, I175, I176 + 1) [0 <= I176 - 1 /\ -1 <= I175 - 1 /\ I176 <= I175 - 1 /\ I178 <= 42 /\ -1 <= I178 - 1 /\ 1 = I174] 34.75/34.27 f2(I179, I180, I181, I182) -> f2(I179 - 1, I180, I181 + 1, I183) [0 <= I179 - 1 /\ -1 <= I180 - 1 /\ 0 <= I181 - 1 /\ I181 <= I180 - 1 /\ -1 <= I184 - 1 /\ I179 - 1 <= I179 - 1 /\ I184 <= 42] 34.75/34.27 f6(I185, I186, I187, I188) -> f5(I189, I190, I191, I192) [0 <= I193 - 1 /\ 1 <= I187 - 1 /\ I189 <= I186 /\ 0 <= I185 - 1 /\ 0 <= I186 - 1 /\ 0 <= I189 - 1] 34.75/34.27 f1(I194, I195, I196, I197) -> f6(I198, I199, I200, I201) [-1 <= I202 - 1 /\ 0 <= I195 - 1 /\ I198 <= I194 /\ I199 - 1 <= I194 /\ 0 <= I194 - 1 /\ 0 <= I198 - 1 /\ 1 <= I199 - 1] 34.75/34.27 f1(I203, I204, I205, I206) -> f6(I207, I208, I209, I210) [-1 <= I211 - 1 /\ 0 <= I204 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 2 <= I208 - 1] 34.75/34.27 f1(I212, I213, I214, I215) -> f6(I216, I217, I218, I219) [-1 <= I220 - 1 /\ 0 <= I213 - 1 /\ I216 <= I212 /\ 0 <= I212 - 1 /\ 0 <= I216 - 1 /\ 2 <= I217 - 1] 34.75/34.27 f1(I221, I222, I223, I224) -> f6(I225, I226, I227, I228) [-1 <= I229 - 1 /\ 0 <= I222 - 1 /\ I225 <= I221 /\ 0 <= I221 - 1 /\ 0 <= I225 - 1 /\ 2 <= I226 - 1] 34.75/34.27 f1(I230, I231, I232, I233) -> f6(I234, I235, I236, I237) [-1 <= I238 - 1 /\ 0 <= I231 - 1 /\ I234 <= I230 /\ 0 <= I230 - 1 /\ 0 <= I234 - 1 /\ 2 <= I235 - 1] 34.75/34.27 f1(I239, I240, I241, I242) -> f6(I243, I244, I245, I246) [-1 <= I247 - 1 /\ 0 <= I240 - 1 /\ I243 <= I239 /\ 0 <= I239 - 1 /\ 0 <= I243 - 1 /\ 2 <= I244 - 1] 34.75/34.27 f1(I248, I249, I250, I251) -> f6(I252, I253, I254, I255) [-1 <= I256 - 1 /\ 0 <= I249 - 1 /\ I252 <= I248 /\ 0 <= I248 - 1 /\ 0 <= I252 - 1 /\ 2 <= I253 - 1] 34.75/34.27 f1(I257, I258, I259, I260) -> f6(I261, I262, I263, I264) [-1 <= I265 - 1 /\ 0 <= I258 - 1 /\ I261 <= I257 /\ 0 <= I257 - 1 /\ 0 <= I261 - 1 /\ 2 <= I262 - 1] 34.75/34.27 f3(I266, I267, I268, I269) -> f5(I270, I271, I272, I273) [I270 + 1 <= I266 /\ 0 <= I274 - 1 /\ 0 <= I266 - 1 /\ -1 <= I270 - 1] 34.75/34.27 f4(I275, I276, I277, I278) -> f3(I279, I280, I281, I282) [0 <= I279 - 1 /\ 0 <= I275 - 1 /\ I279 <= I275] 34.75/34.27 f1(I283, I284, I285, I286) -> f3(I287, I288, I289, I290) [-1 <= I291 - 1 /\ 0 <= I284 - 1 /\ I287 <= I283 /\ 0 <= I283 - 1 /\ 0 <= I287 - 1] 34.75/34.27 f1(I292, I293, I294, I295) -> f3(I296, I297, I298, I299) [0 <= I296 - 1 /\ 0 <= I292 - 1 /\ 0 <= I293 - 1 /\ I296 <= I292] 34.75/34.27 f1(I300, I301, I302, I303) -> f2(I304, I301, 1, I305) [0 <= I300 - 1 /\ 0 <= I301 - 1 /\ -1 <= I304 - 1] 34.75/34.27 34.75/34.27 The dependency graph for this problem is: 34.75/34.27 0 -> 29, 30, 31, 32, 33, 34, 35, 36, 39, 40, 41 34.75/34.27 1 -> 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 34.75/34.27 2 -> 1 34.75/34.27 3 -> 1 34.75/34.27 4 -> 1 34.75/34.27 5 -> 1 34.75/34.27 6 -> 1 34.75/34.27 7 -> 1 34.75/34.27 8 -> 1 34.75/34.27 9 -> 1 34.75/34.27 10 -> 1 34.75/34.27 11 -> 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 34.75/34.27 12 -> 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 34.75/34.27 13 -> 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 34.75/34.27 14 -> 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 34.75/34.27 15 -> 15, 17, 18, 20, 25, 26, 27 34.75/34.27 16 -> 15, 17, 18, 20, 25, 26, 27 34.75/34.27 17 -> 16 34.75/34.27 18 -> 16 34.75/34.27 19 -> 15, 17, 18, 20, 25, 26, 27 34.75/34.27 20 -> 15, 17, 18, 20, 25, 26, 27 34.75/34.27 21 -> 15, 17, 18, 20, 25, 26, 27 34.75/34.27 22 -> 21 34.75/34.27 23 -> 21 34.75/34.27 24 -> 15, 17, 18, 20, 25, 26, 27 34.75/34.27 25 -> 19, 22, 23, 24 34.75/34.27 26 -> 19, 22, 23, 24 34.75/34.27 27 -> 15, 17, 18, 20, 25, 26, 27 34.75/34.27 28 -> 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 34.75/34.27 29 -> 28 34.75/34.27 30 -> 28 34.75/34.27 31 -> 28 34.75/34.27 32 -> 28 34.75/34.27 33 -> 28 34.75/34.27 34 -> 28 34.75/34.27 35 -> 28 34.75/34.27 36 -> 28 34.75/34.27 37 -> 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 34.75/34.27 38 -> 37 34.75/34.27 39 -> 37 34.75/34.27 40 -> 37 34.75/34.27 41 -> 15, 17, 18, 20, 25, 26, 27 34.75/34.27 Where: 34.75/34.27 0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 34.75/34.27 1) f10#(I0, I1, I2, I3) -> f5#(I4, I5, I6, I7) [-1 <= I4 - 1 /\ -1 <= I3 - 1 /\ -1 <= I1 - 1 /\ 3 <= I0 - 1 /\ I4 <= I3 /\ I4 <= I1 /\ I4 + 2 <= I0] 34.75/34.27 2) f5#(I8, I9, I10, I11) -> f10#(I12, I13, I14, I15) [-1 <= I15 - 1 /\ -1 <= I13 - 1 /\ 3 <= I12 - 1 /\ 3 <= I8 - 1 /\ I15 + 2 <= I8 /\ I13 + 2 <= I8 /\ I12 <= I8] 34.75/34.27 3) f5#(I16, I17, I18, I19) -> f10#(I20, I21, I22, I23) [-1 <= I23 - 1 /\ -1 <= I21 - 1 /\ 5 <= I20 - 1 /\ 1 <= I16 - 1 /\ I23 + 2 <= I16 /\ I21 + 2 <= I16] 34.75/34.27 4) f5#(I24, I25, I26, I27) -> f10#(I28, I29, I30, I31) [-1 <= I31 - 1 /\ -1 <= I29 - 1 /\ 5 <= I28 - 1 /\ 1 <= I24 - 1 /\ I31 + 2 <= I24 /\ I29 + 2 <= I24] 34.75/34.27 5) f5#(I32, I33, I34, I35) -> f10#(I36, I37, I38, I39) [-1 <= I39 - 1 /\ -1 <= I37 - 1 /\ 5 <= I36 - 1 /\ 1 <= I32 - 1 /\ I39 + 2 <= I32 /\ I37 + 2 <= I32] 34.75/34.27 6) f5#(I40, I41, I42, I43) -> f10#(I44, I45, I46, I47) [-1 <= I47 - 1 /\ -1 <= I45 - 1 /\ 5 <= I44 - 1 /\ 1 <= I40 - 1 /\ I47 + 2 <= I40 /\ I45 + 2 <= I40] 34.75/34.27 7) f5#(I48, I49, I50, I51) -> f10#(I52, I53, I54, I55) [-1 <= I55 - 1 /\ -1 <= I53 - 1 /\ 5 <= I52 - 1 /\ 1 <= I48 - 1 /\ I55 + 2 <= I48 /\ I53 + 2 <= I48] 34.75/34.27 8) f5#(I56, I57, I58, I59) -> f10#(I60, I61, I62, I63) [-1 <= I63 - 1 /\ -1 <= I61 - 1 /\ 5 <= I60 - 1 /\ 1 <= I56 - 1 /\ I63 + 2 <= I56 /\ I61 + 2 <= I56 /\ I60 - 4 <= I56] 34.75/34.27 9) f5#(I64, I65, I66, I67) -> f10#(I68, I69, I70, I71) [-1 <= I71 - 1 /\ -1 <= I69 - 1 /\ 5 <= I68 - 1 /\ 1 <= I64 - 1 /\ I71 + 2 <= I64 /\ I69 + 2 <= I64 /\ I68 - 4 <= I64] 34.75/34.27 10) f5#(I72, I73, I74, I75) -> f10#(I76, I77, I78, I79) [-1 <= I79 - 1 /\ -1 <= I77 - 1 /\ 5 <= I76 - 1 /\ 1 <= I72 - 1 /\ I79 + 2 <= I72 /\ I77 + 2 <= I72 /\ I76 - 4 <= I72] 34.75/34.27 11) f5#(I80, I81, I82, I83) -> f5#(I84, I85, I86, I87) [-1 <= I84 - 1 /\ 1 <= I80 - 1 /\ I84 + 2 <= I80] 34.75/34.27 12) f5#(I88, I89, I90, I91) -> f5#(I92, I93, I94, I95) [2 <= I92 - 1 /\ 2 <= I88 - 1 /\ I92 - 2 <= I88] 34.75/34.27 13) f5#(I96, I97, I98, I99) -> f5#(I100, I101, I102, I103) [-1 <= I100 - 1 /\ 1 <= I96 - 1 /\ I100 + 2 <= I96] 34.75/34.27 14) f5#(I104, I105, I106, I107) -> f5#(I108, I109, I110, I111) [-1 <= I108 - 1 /\ 1 <= I104 - 1 /\ I108 + 2 <= I104] 34.75/34.27 15) f2#(I112, I113, I114, I115) -> f2#(I112 - 1, I113, I116, I117) [0 <= I112 - 1 /\ -1 <= I113 - 1 /\ 0 <= I114 - 1 /\ I114 <= I113 - 1 /\ -1 <= y1 - 1 /\ y1 <= 42 /\ I112 - 1 <= I112 - 1 /\ 1 <= I116 - 1 /\ 1 <= y2 - 1] 34.75/34.27 16) f9#(I118, I119, I120, I121) -> f2#(I119, I120, I121, I122) [1 <= I121 - 1 /\ 0 <= I118 - 1 /\ I119 <= I118 - 1] 34.75/34.27 17) f2#(I123, I124, I125, I126) -> f9#(I123, I123 - 1, I124, I127) [0 <= I123 - 1 /\ -1 <= I124 - 1 /\ 0 <= I125 - 1 /\ I125 <= I124 - 1 /\ -1 <= I128 - 1 /\ I128 <= 42 /\ 1 <= I129 - 1 /\ I123 - 1 <= I123 - 1] 34.75/34.27 18) f2#(I130, I131, I132, I133) -> f9#(1, 0, I131, I134) [0 <= I132 - 1 /\ -1 <= I131 - 1 /\ I132 <= I131 - 1 /\ -1 <= I135 - 1 /\ 1 <= I134 - 1 /\ I135 <= 42 /\ 1 = I130] 34.75/34.27 19) f7#(I136, I137, I138, I139) -> f2#(I136 - 1, I138, I140, I141) [I136 - 1 <= I136 - 1 /\ I137 <= I136 - 1 /\ 1 <= I140 - 1 /\ 1 <= I139 - 1 /\ 0 <= I136 - 1] 34.75/34.27 20) f2#(I142, I143, I144, I145) -> f2#(I142 - 1, I143, I146, I147) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ 0 <= I144 - 1 /\ I144 <= I143 - 1 /\ -1 <= I148 - 1 /\ I148 <= 42 /\ 1 <= I146 - 1 /\ I142 - 1 <= I142 - 1] 34.75/34.27 21) f8#(I149, I150, I151, I152) -> f2#(I150, I151, I152, I153) [1 <= I152 - 1 /\ 0 <= I149 - 1 /\ I150 <= I149 - 1] 34.75/34.27 22) f7#(I154, I155, I156, I157) -> f8#(I154, I154 - 1, I156, I158) [1 <= I157 - 1 /\ I155 <= I154 - 1 /\ 0 <= I154 - 1] 34.75/34.27 23) f7#(I159, I160, I161, I162) -> f8#(I159, I159 - 1, I161, I162) [0 = I160 /\ 0 <= I159 - 1 /\ 1 <= I162 - 1] 34.75/34.27 24) f7#(I163, I164, I165, I166) -> f2#(I164, I165, I166, I167) [1 <= I166 - 1 /\ 0 <= I163 - 1 /\ I164 <= I163 - 1] 34.75/34.27 25) f2#(I168, I169, I170, I171) -> f7#(I168, I168 - 1, I169, I172) [0 <= I168 - 1 /\ -1 <= I169 - 1 /\ 0 <= I170 - 1 /\ I170 <= I169 - 1 /\ -1 <= I173 - 1 /\ I168 - 1 <= I168 - 1 /\ I173 <= 42] 34.75/34.27 26) f2#(I174, I175, I176, I177) -> f7#(1, 0, I175, I176 + 1) [0 <= I176 - 1 /\ -1 <= I175 - 1 /\ I176 <= I175 - 1 /\ I178 <= 42 /\ -1 <= I178 - 1 /\ 1 = I174] 34.75/34.27 27) f2#(I179, I180, I181, I182) -> f2#(I179 - 1, I180, I181 + 1, I183) [0 <= I179 - 1 /\ -1 <= I180 - 1 /\ 0 <= I181 - 1 /\ I181 <= I180 - 1 /\ -1 <= I184 - 1 /\ I179 - 1 <= I179 - 1 /\ I184 <= 42] 34.75/34.27 28) f6#(I185, I186, I187, I188) -> f5#(I189, I190, I191, I192) [0 <= I193 - 1 /\ 1 <= I187 - 1 /\ I189 <= I186 /\ 0 <= I185 - 1 /\ 0 <= I186 - 1 /\ 0 <= I189 - 1] 34.75/34.27 29) f1#(I194, I195, I196, I197) -> f6#(I198, I199, I200, I201) [-1 <= I202 - 1 /\ 0 <= I195 - 1 /\ I198 <= I194 /\ I199 - 1 <= I194 /\ 0 <= I194 - 1 /\ 0 <= I198 - 1 /\ 1 <= I199 - 1] 34.75/34.27 30) f1#(I203, I204, I205, I206) -> f6#(I207, I208, I209, I210) [-1 <= I211 - 1 /\ 0 <= I204 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 2 <= I208 - 1] 34.75/34.27 31) f1#(I212, I213, I214, I215) -> f6#(I216, I217, I218, I219) [-1 <= I220 - 1 /\ 0 <= I213 - 1 /\ I216 <= I212 /\ 0 <= I212 - 1 /\ 0 <= I216 - 1 /\ 2 <= I217 - 1] 34.75/34.27 32) f1#(I221, I222, I223, I224) -> f6#(I225, I226, I227, I228) [-1 <= I229 - 1 /\ 0 <= I222 - 1 /\ I225 <= I221 /\ 0 <= I221 - 1 /\ 0 <= I225 - 1 /\ 2 <= I226 - 1] 34.75/34.27 33) f1#(I230, I231, I232, I233) -> f6#(I234, I235, I236, I237) [-1 <= I238 - 1 /\ 0 <= I231 - 1 /\ I234 <= I230 /\ 0 <= I230 - 1 /\ 0 <= I234 - 1 /\ 2 <= I235 - 1] 34.75/34.27 34) f1#(I239, I240, I241, I242) -> f6#(I243, I244, I245, I246) [-1 <= I247 - 1 /\ 0 <= I240 - 1 /\ I243 <= I239 /\ 0 <= I239 - 1 /\ 0 <= I243 - 1 /\ 2 <= I244 - 1] 34.75/34.27 35) f1#(I248, I249, I250, I251) -> f6#(I252, I253, I254, I255) [-1 <= I256 - 1 /\ 0 <= I249 - 1 /\ I252 <= I248 /\ 0 <= I248 - 1 /\ 0 <= I252 - 1 /\ 2 <= I253 - 1] 34.75/34.27 36) f1#(I257, I258, I259, I260) -> f6#(I261, I262, I263, I264) [-1 <= I265 - 1 /\ 0 <= I258 - 1 /\ I261 <= I257 /\ 0 <= I257 - 1 /\ 0 <= I261 - 1 /\ 2 <= I262 - 1] 34.75/34.27 37) f3#(I266, I267, I268, I269) -> f5#(I270, I271, I272, I273) [I270 + 1 <= I266 /\ 0 <= I274 - 1 /\ 0 <= I266 - 1 /\ -1 <= I270 - 1] 34.75/34.27 38) f4#(I275, I276, I277, I278) -> f3#(I279, I280, I281, I282) [0 <= I279 - 1 /\ 0 <= I275 - 1 /\ I279 <= I275] 34.75/34.27 39) f1#(I283, I284, I285, I286) -> f3#(I287, I288, I289, I290) [-1 <= I291 - 1 /\ 0 <= I284 - 1 /\ I287 <= I283 /\ 0 <= I283 - 1 /\ 0 <= I287 - 1] 34.75/34.27 40) f1#(I292, I293, I294, I295) -> f3#(I296, I297, I298, I299) [0 <= I296 - 1 /\ 0 <= I292 - 1 /\ 0 <= I293 - 1 /\ I296 <= I292] 34.75/34.27 41) f1#(I300, I301, I302, I303) -> f2#(I304, I301, 1, I305) [0 <= I300 - 1 /\ 0 <= I301 - 1 /\ -1 <= I304 - 1] 34.75/34.27 34.75/34.27 We have the following SCCs. 34.75/34.27 { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 } 34.75/34.27 { 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 } 34.75/34.27 34.75/34.27 DP problem for innermost termination. 34.75/34.27 P = 34.75/34.27 f2#(I112, I113, I114, I115) -> f2#(I112 - 1, I113, I116, I117) [0 <= I112 - 1 /\ -1 <= I113 - 1 /\ 0 <= I114 - 1 /\ I114 <= I113 - 1 /\ -1 <= y1 - 1 /\ y1 <= 42 /\ I112 - 1 <= I112 - 1 /\ 1 <= I116 - 1 /\ 1 <= y2 - 1] 34.75/34.27 f9#(I118, I119, I120, I121) -> f2#(I119, I120, I121, I122) [1 <= I121 - 1 /\ 0 <= I118 - 1 /\ I119 <= I118 - 1] 34.75/34.27 f2#(I123, I124, I125, I126) -> f9#(I123, I123 - 1, I124, I127) [0 <= I123 - 1 /\ -1 <= I124 - 1 /\ 0 <= I125 - 1 /\ I125 <= I124 - 1 /\ -1 <= I128 - 1 /\ I128 <= 42 /\ 1 <= I129 - 1 /\ I123 - 1 <= I123 - 1] 34.75/34.27 f2#(I130, I131, I132, I133) -> f9#(1, 0, I131, I134) [0 <= I132 - 1 /\ -1 <= I131 - 1 /\ I132 <= I131 - 1 /\ -1 <= I135 - 1 /\ 1 <= I134 - 1 /\ I135 <= 42 /\ 1 = I130] 34.75/34.27 f7#(I136, I137, I138, I139) -> f2#(I136 - 1, I138, I140, I141) [I136 - 1 <= I136 - 1 /\ I137 <= I136 - 1 /\ 1 <= I140 - 1 /\ 1 <= I139 - 1 /\ 0 <= I136 - 1] 34.75/34.27 f2#(I142, I143, I144, I145) -> f2#(I142 - 1, I143, I146, I147) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ 0 <= I144 - 1 /\ I144 <= I143 - 1 /\ -1 <= I148 - 1 /\ I148 <= 42 /\ 1 <= I146 - 1 /\ I142 - 1 <= I142 - 1] 34.75/34.27 f8#(I149, I150, I151, I152) -> f2#(I150, I151, I152, I153) [1 <= I152 - 1 /\ 0 <= I149 - 1 /\ I150 <= I149 - 1] 34.75/34.27 f7#(I154, I155, I156, I157) -> f8#(I154, I154 - 1, I156, I158) [1 <= I157 - 1 /\ I155 <= I154 - 1 /\ 0 <= I154 - 1] 34.75/34.27 f7#(I159, I160, I161, I162) -> f8#(I159, I159 - 1, I161, I162) [0 = I160 /\ 0 <= I159 - 1 /\ 1 <= I162 - 1] 34.75/34.27 f7#(I163, I164, I165, I166) -> f2#(I164, I165, I166, I167) [1 <= I166 - 1 /\ 0 <= I163 - 1 /\ I164 <= I163 - 1] 34.75/34.27 f2#(I168, I169, I170, I171) -> f7#(I168, I168 - 1, I169, I172) [0 <= I168 - 1 /\ -1 <= I169 - 1 /\ 0 <= I170 - 1 /\ I170 <= I169 - 1 /\ -1 <= I173 - 1 /\ I168 - 1 <= I168 - 1 /\ I173 <= 42] 34.75/34.27 f2#(I174, I175, I176, I177) -> f7#(1, 0, I175, I176 + 1) [0 <= I176 - 1 /\ -1 <= I175 - 1 /\ I176 <= I175 - 1 /\ I178 <= 42 /\ -1 <= I178 - 1 /\ 1 = I174] 34.75/34.27 f2#(I179, I180, I181, I182) -> f2#(I179 - 1, I180, I181 + 1, I183) [0 <= I179 - 1 /\ -1 <= I180 - 1 /\ 0 <= I181 - 1 /\ I181 <= I180 - 1 /\ -1 <= I184 - 1 /\ I179 - 1 <= I179 - 1 /\ I184 <= 42] 34.75/34.27 R = 34.75/34.27 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 34.75/34.27 f10(I0, I1, I2, I3) -> f5(I4, I5, I6, I7) [-1 <= I4 - 1 /\ -1 <= I3 - 1 /\ -1 <= I1 - 1 /\ 3 <= I0 - 1 /\ I4 <= I3 /\ I4 <= I1 /\ I4 + 2 <= I0] 34.75/34.27 f5(I8, I9, I10, I11) -> f10(I12, I13, I14, I15) [-1 <= I15 - 1 /\ -1 <= I13 - 1 /\ 3 <= I12 - 1 /\ 3 <= I8 - 1 /\ I15 + 2 <= I8 /\ I13 + 2 <= I8 /\ I12 <= I8] 34.75/34.27 f5(I16, I17, I18, I19) -> f10(I20, I21, I22, I23) [-1 <= I23 - 1 /\ -1 <= I21 - 1 /\ 5 <= I20 - 1 /\ 1 <= I16 - 1 /\ I23 + 2 <= I16 /\ I21 + 2 <= I16] 34.75/34.27 f5(I24, I25, I26, I27) -> f10(I28, I29, I30, I31) [-1 <= I31 - 1 /\ -1 <= I29 - 1 /\ 5 <= I28 - 1 /\ 1 <= I24 - 1 /\ I31 + 2 <= I24 /\ I29 + 2 <= I24] 34.75/34.27 f5(I32, I33, I34, I35) -> f10(I36, I37, I38, I39) [-1 <= I39 - 1 /\ -1 <= I37 - 1 /\ 5 <= I36 - 1 /\ 1 <= I32 - 1 /\ I39 + 2 <= I32 /\ I37 + 2 <= I32] 34.75/34.27 f5(I40, I41, I42, I43) -> f10(I44, I45, I46, I47) [-1 <= I47 - 1 /\ -1 <= I45 - 1 /\ 5 <= I44 - 1 /\ 1 <= I40 - 1 /\ I47 + 2 <= I40 /\ I45 + 2 <= I40] 34.75/34.27 f5(I48, I49, I50, I51) -> f10(I52, I53, I54, I55) [-1 <= I55 - 1 /\ -1 <= I53 - 1 /\ 5 <= I52 - 1 /\ 1 <= I48 - 1 /\ I55 + 2 <= I48 /\ I53 + 2 <= I48] 34.75/34.27 f5(I56, I57, I58, I59) -> f10(I60, I61, I62, I63) [-1 <= I63 - 1 /\ -1 <= I61 - 1 /\ 5 <= I60 - 1 /\ 1 <= I56 - 1 /\ I63 + 2 <= I56 /\ I61 + 2 <= I56 /\ I60 - 4 <= I56] 34.75/34.27 f5(I64, I65, I66, I67) -> f10(I68, I69, I70, I71) [-1 <= I71 - 1 /\ -1 <= I69 - 1 /\ 5 <= I68 - 1 /\ 1 <= I64 - 1 /\ I71 + 2 <= I64 /\ I69 + 2 <= I64 /\ I68 - 4 <= I64] 34.75/34.27 f5(I72, I73, I74, I75) -> f10(I76, I77, I78, I79) [-1 <= I79 - 1 /\ -1 <= I77 - 1 /\ 5 <= I76 - 1 /\ 1 <= I72 - 1 /\ I79 + 2 <= I72 /\ I77 + 2 <= I72 /\ I76 - 4 <= I72] 34.75/34.27 f5(I80, I81, I82, I83) -> f5(I84, I85, I86, I87) [-1 <= I84 - 1 /\ 1 <= I80 - 1 /\ I84 + 2 <= I80] 34.75/34.27 f5(I88, I89, I90, I91) -> f5(I92, I93, I94, I95) [2 <= I92 - 1 /\ 2 <= I88 - 1 /\ I92 - 2 <= I88] 34.75/34.27 f5(I96, I97, I98, I99) -> f5(I100, I101, I102, I103) [-1 <= I100 - 1 /\ 1 <= I96 - 1 /\ I100 + 2 <= I96] 34.75/34.27 f5(I104, I105, I106, I107) -> f5(I108, I109, I110, I111) [-1 <= I108 - 1 /\ 1 <= I104 - 1 /\ I108 + 2 <= I104] 34.75/34.27 f2(I112, I113, I114, I115) -> f2(I112 - 1, I113, I116, I117) [0 <= I112 - 1 /\ -1 <= I113 - 1 /\ 0 <= I114 - 1 /\ I114 <= I113 - 1 /\ -1 <= y1 - 1 /\ y1 <= 42 /\ I112 - 1 <= I112 - 1 /\ 1 <= I116 - 1 /\ 1 <= y2 - 1] 34.75/34.27 f9(I118, I119, I120, I121) -> f2(I119, I120, I121, I122) [1 <= I121 - 1 /\ 0 <= I118 - 1 /\ I119 <= I118 - 1] 34.75/34.27 f2(I123, I124, I125, I126) -> f9(I123, I123 - 1, I124, I127) [0 <= I123 - 1 /\ -1 <= I124 - 1 /\ 0 <= I125 - 1 /\ I125 <= I124 - 1 /\ -1 <= I128 - 1 /\ I128 <= 42 /\ 1 <= I129 - 1 /\ I123 - 1 <= I123 - 1] 34.75/34.27 f2(I130, I131, I132, I133) -> f9(1, 0, I131, I134) [0 <= I132 - 1 /\ -1 <= I131 - 1 /\ I132 <= I131 - 1 /\ -1 <= I135 - 1 /\ 1 <= I134 - 1 /\ I135 <= 42 /\ 1 = I130] 34.75/34.27 f7(I136, I137, I138, I139) -> f2(I136 - 1, I138, I140, I141) [I136 - 1 <= I136 - 1 /\ I137 <= I136 - 1 /\ 1 <= I140 - 1 /\ 1 <= I139 - 1 /\ 0 <= I136 - 1] 34.75/34.27 f2(I142, I143, I144, I145) -> f2(I142 - 1, I143, I146, I147) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ 0 <= I144 - 1 /\ I144 <= I143 - 1 /\ -1 <= I148 - 1 /\ I148 <= 42 /\ 1 <= I146 - 1 /\ I142 - 1 <= I142 - 1] 34.75/34.27 f8(I149, I150, I151, I152) -> f2(I150, I151, I152, I153) [1 <= I152 - 1 /\ 0 <= I149 - 1 /\ I150 <= I149 - 1] 34.75/34.27 f7(I154, I155, I156, I157) -> f8(I154, I154 - 1, I156, I158) [1 <= I157 - 1 /\ I155 <= I154 - 1 /\ 0 <= I154 - 1] 34.75/34.27 f7(I159, I160, I161, I162) -> f8(I159, I159 - 1, I161, I162) [0 = I160 /\ 0 <= I159 - 1 /\ 1 <= I162 - 1] 34.75/34.27 f7(I163, I164, I165, I166) -> f2(I164, I165, I166, I167) [1 <= I166 - 1 /\ 0 <= I163 - 1 /\ I164 <= I163 - 1] 34.75/34.27 f2(I168, I169, I170, I171) -> f7(I168, I168 - 1, I169, I172) [0 <= I168 - 1 /\ -1 <= I169 - 1 /\ 0 <= I170 - 1 /\ I170 <= I169 - 1 /\ -1 <= I173 - 1 /\ I168 - 1 <= I168 - 1 /\ I173 <= 42] 34.75/34.27 f2(I174, I175, I176, I177) -> f7(1, 0, I175, I176 + 1) [0 <= I176 - 1 /\ -1 <= I175 - 1 /\ I176 <= I175 - 1 /\ I178 <= 42 /\ -1 <= I178 - 1 /\ 1 = I174] 34.75/34.27 f2(I179, I180, I181, I182) -> f2(I179 - 1, I180, I181 + 1, I183) [0 <= I179 - 1 /\ -1 <= I180 - 1 /\ 0 <= I181 - 1 /\ I181 <= I180 - 1 /\ -1 <= I184 - 1 /\ I179 - 1 <= I179 - 1 /\ I184 <= 42] 34.75/34.27 f6(I185, I186, I187, I188) -> f5(I189, I190, I191, I192) [0 <= I193 - 1 /\ 1 <= I187 - 1 /\ I189 <= I186 /\ 0 <= I185 - 1 /\ 0 <= I186 - 1 /\ 0 <= I189 - 1] 34.75/34.27 f1(I194, I195, I196, I197) -> f6(I198, I199, I200, I201) [-1 <= I202 - 1 /\ 0 <= I195 - 1 /\ I198 <= I194 /\ I199 - 1 <= I194 /\ 0 <= I194 - 1 /\ 0 <= I198 - 1 /\ 1 <= I199 - 1] 34.75/34.27 f1(I203, I204, I205, I206) -> f6(I207, I208, I209, I210) [-1 <= I211 - 1 /\ 0 <= I204 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 2 <= I208 - 1] 34.75/34.27 f1(I212, I213, I214, I215) -> f6(I216, I217, I218, I219) [-1 <= I220 - 1 /\ 0 <= I213 - 1 /\ I216 <= I212 /\ 0 <= I212 - 1 /\ 0 <= I216 - 1 /\ 2 <= I217 - 1] 34.75/34.27 f1(I221, I222, I223, I224) -> f6(I225, I226, I227, I228) [-1 <= I229 - 1 /\ 0 <= I222 - 1 /\ I225 <= I221 /\ 0 <= I221 - 1 /\ 0 <= I225 - 1 /\ 2 <= I226 - 1] 34.75/34.27 f1(I230, I231, I232, I233) -> f6(I234, I235, I236, I237) [-1 <= I238 - 1 /\ 0 <= I231 - 1 /\ I234 <= I230 /\ 0 <= I230 - 1 /\ 0 <= I234 - 1 /\ 2 <= I235 - 1] 34.75/34.27 f1(I239, I240, I241, I242) -> f6(I243, I244, I245, I246) [-1 <= I247 - 1 /\ 0 <= I240 - 1 /\ I243 <= I239 /\ 0 <= I239 - 1 /\ 0 <= I243 - 1 /\ 2 <= I244 - 1] 34.75/34.27 f1(I248, I249, I250, I251) -> f6(I252, I253, I254, I255) [-1 <= I256 - 1 /\ 0 <= I249 - 1 /\ I252 <= I248 /\ 0 <= I248 - 1 /\ 0 <= I252 - 1 /\ 2 <= I253 - 1] 34.75/34.27 f1(I257, I258, I259, I260) -> f6(I261, I262, I263, I264) [-1 <= I265 - 1 /\ 0 <= I258 - 1 /\ I261 <= I257 /\ 0 <= I257 - 1 /\ 0 <= I261 - 1 /\ 2 <= I262 - 1] 34.75/34.27 f3(I266, I267, I268, I269) -> f5(I270, I271, I272, I273) [I270 + 1 <= I266 /\ 0 <= I274 - 1 /\ 0 <= I266 - 1 /\ -1 <= I270 - 1] 34.75/34.27 f4(I275, I276, I277, I278) -> f3(I279, I280, I281, I282) [0 <= I279 - 1 /\ 0 <= I275 - 1 /\ I279 <= I275] 34.75/34.27 f1(I283, I284, I285, I286) -> f3(I287, I288, I289, I290) [-1 <= I291 - 1 /\ 0 <= I284 - 1 /\ I287 <= I283 /\ 0 <= I283 - 1 /\ 0 <= I287 - 1] 34.75/34.27 f1(I292, I293, I294, I295) -> f3(I296, I297, I298, I299) [0 <= I296 - 1 /\ 0 <= I292 - 1 /\ 0 <= I293 - 1 /\ I296 <= I292] 34.75/34.27 f1(I300, I301, I302, I303) -> f2(I304, I301, 1, I305) [0 <= I300 - 1 /\ 0 <= I301 - 1 /\ -1 <= I304 - 1] 34.75/34.27 34.75/34.27 We use the basic value criterion with the projection function NU: 34.75/34.27 NU[f8#(z1,z2,z3,z4)] = z2 34.75/34.27 NU[f7#(z1,z2,z3,z4)] = z1 34.75/34.27 NU[f9#(z1,z2,z3,z4)] = z1 34.75/34.27 NU[f2#(z1,z2,z3,z4)] = z1 34.75/34.27 34.75/34.27 This gives the following inequalities: 34.75/34.27 0 <= I112 - 1 /\ -1 <= I113 - 1 /\ 0 <= I114 - 1 /\ I114 <= I113 - 1 /\ -1 <= y1 - 1 /\ y1 <= 42 /\ I112 - 1 <= I112 - 1 /\ 1 <= I116 - 1 /\ 1 <= y2 - 1 ==> I112 >! I112 - 1 34.75/34.27 1 <= I121 - 1 /\ 0 <= I118 - 1 /\ I119 <= I118 - 1 ==> I118 >! I119 34.75/34.27 0 <= I123 - 1 /\ -1 <= I124 - 1 /\ 0 <= I125 - 1 /\ I125 <= I124 - 1 /\ -1 <= I128 - 1 /\ I128 <= 42 /\ 1 <= I129 - 1 /\ I123 - 1 <= I123 - 1 ==> I123 (>! \union =) I123 34.75/34.27 0 <= I132 - 1 /\ -1 <= I131 - 1 /\ I132 <= I131 - 1 /\ -1 <= I135 - 1 /\ 1 <= I134 - 1 /\ I135 <= 42 /\ 1 = I130 ==> I130 (>! \union =) 1 34.75/34.27 I136 - 1 <= I136 - 1 /\ I137 <= I136 - 1 /\ 1 <= I140 - 1 /\ 1 <= I139 - 1 /\ 0 <= I136 - 1 ==> I136 >! I136 - 1 34.75/34.27 0 <= I142 - 1 /\ -1 <= I143 - 1 /\ 0 <= I144 - 1 /\ I144 <= I143 - 1 /\ -1 <= I148 - 1 /\ I148 <= 42 /\ 1 <= I146 - 1 /\ I142 - 1 <= I142 - 1 ==> I142 >! I142 - 1 34.75/34.27 1 <= I152 - 1 /\ 0 <= I149 - 1 /\ I150 <= I149 - 1 ==> I150 (>! \union =) I150 34.75/34.27 1 <= I157 - 1 /\ I155 <= I154 - 1 /\ 0 <= I154 - 1 ==> I154 >! I154 - 1 34.75/34.27 0 = I160 /\ 0 <= I159 - 1 /\ 1 <= I162 - 1 ==> I159 >! I159 - 1 34.75/34.27 1 <= I166 - 1 /\ 0 <= I163 - 1 /\ I164 <= I163 - 1 ==> I163 >! I164 34.75/34.27 0 <= I168 - 1 /\ -1 <= I169 - 1 /\ 0 <= I170 - 1 /\ I170 <= I169 - 1 /\ -1 <= I173 - 1 /\ I168 - 1 <= I168 - 1 /\ I173 <= 42 ==> I168 (>! \union =) I168 34.75/34.27 0 <= I176 - 1 /\ -1 <= I175 - 1 /\ I176 <= I175 - 1 /\ I178 <= 42 /\ -1 <= I178 - 1 /\ 1 = I174 ==> I174 (>! \union =) 1 34.75/34.27 0 <= I179 - 1 /\ -1 <= I180 - 1 /\ 0 <= I181 - 1 /\ I181 <= I180 - 1 /\ -1 <= I184 - 1 /\ I179 - 1 <= I179 - 1 /\ I184 <= 42 ==> I179 >! I179 - 1 34.75/34.27 34.75/34.27 We remove all the strictly oriented dependency pairs. 34.75/34.27 34.75/34.27 DP problem for innermost termination. 34.75/34.27 P = 34.75/34.27 f2#(I123, I124, I125, I126) -> f9#(I123, I123 - 1, I124, I127) [0 <= I123 - 1 /\ -1 <= I124 - 1 /\ 0 <= I125 - 1 /\ I125 <= I124 - 1 /\ -1 <= I128 - 1 /\ I128 <= 42 /\ 1 <= I129 - 1 /\ I123 - 1 <= I123 - 1] 34.75/34.27 f2#(I130, I131, I132, I133) -> f9#(1, 0, I131, I134) [0 <= I132 - 1 /\ -1 <= I131 - 1 /\ I132 <= I131 - 1 /\ -1 <= I135 - 1 /\ 1 <= I134 - 1 /\ I135 <= 42 /\ 1 = I130] 34.75/34.27 f8#(I149, I150, I151, I152) -> f2#(I150, I151, I152, I153) [1 <= I152 - 1 /\ 0 <= I149 - 1 /\ I150 <= I149 - 1] 34.75/34.27 f2#(I168, I169, I170, I171) -> f7#(I168, I168 - 1, I169, I172) [0 <= I168 - 1 /\ -1 <= I169 - 1 /\ 0 <= I170 - 1 /\ I170 <= I169 - 1 /\ -1 <= I173 - 1 /\ I168 - 1 <= I168 - 1 /\ I173 <= 42] 34.75/34.27 f2#(I174, I175, I176, I177) -> f7#(1, 0, I175, I176 + 1) [0 <= I176 - 1 /\ -1 <= I175 - 1 /\ I176 <= I175 - 1 /\ I178 <= 42 /\ -1 <= I178 - 1 /\ 1 = I174] 34.75/34.27 R = 34.75/34.27 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 34.75/34.27 f10(I0, I1, I2, I3) -> f5(I4, I5, I6, I7) [-1 <= I4 - 1 /\ -1 <= I3 - 1 /\ -1 <= I1 - 1 /\ 3 <= I0 - 1 /\ I4 <= I3 /\ I4 <= I1 /\ I4 + 2 <= I0] 34.75/34.27 f5(I8, I9, I10, I11) -> f10(I12, I13, I14, I15) [-1 <= I15 - 1 /\ -1 <= I13 - 1 /\ 3 <= I12 - 1 /\ 3 <= I8 - 1 /\ I15 + 2 <= I8 /\ I13 + 2 <= I8 /\ I12 <= I8] 34.75/34.27 f5(I16, I17, I18, I19) -> f10(I20, I21, I22, I23) [-1 <= I23 - 1 /\ -1 <= I21 - 1 /\ 5 <= I20 - 1 /\ 1 <= I16 - 1 /\ I23 + 2 <= I16 /\ I21 + 2 <= I16] 34.75/34.27 f5(I24, I25, I26, I27) -> f10(I28, I29, I30, I31) [-1 <= I31 - 1 /\ -1 <= I29 - 1 /\ 5 <= I28 - 1 /\ 1 <= I24 - 1 /\ I31 + 2 <= I24 /\ I29 + 2 <= I24] 34.75/34.27 f5(I32, I33, I34, I35) -> f10(I36, I37, I38, I39) [-1 <= I39 - 1 /\ -1 <= I37 - 1 /\ 5 <= I36 - 1 /\ 1 <= I32 - 1 /\ I39 + 2 <= I32 /\ I37 + 2 <= I32] 34.75/34.27 f5(I40, I41, I42, I43) -> f10(I44, I45, I46, I47) [-1 <= I47 - 1 /\ -1 <= I45 - 1 /\ 5 <= I44 - 1 /\ 1 <= I40 - 1 /\ I47 + 2 <= I40 /\ I45 + 2 <= I40] 34.75/34.27 f5(I48, I49, I50, I51) -> f10(I52, I53, I54, I55) [-1 <= I55 - 1 /\ -1 <= I53 - 1 /\ 5 <= I52 - 1 /\ 1 <= I48 - 1 /\ I55 + 2 <= I48 /\ I53 + 2 <= I48] 34.75/34.27 f5(I56, I57, I58, I59) -> f10(I60, I61, I62, I63) [-1 <= I63 - 1 /\ -1 <= I61 - 1 /\ 5 <= I60 - 1 /\ 1 <= I56 - 1 /\ I63 + 2 <= I56 /\ I61 + 2 <= I56 /\ I60 - 4 <= I56] 34.75/34.27 f5(I64, I65, I66, I67) -> f10(I68, I69, I70, I71) [-1 <= I71 - 1 /\ -1 <= I69 - 1 /\ 5 <= I68 - 1 /\ 1 <= I64 - 1 /\ I71 + 2 <= I64 /\ I69 + 2 <= I64 /\ I68 - 4 <= I64] 34.75/34.27 f5(I72, I73, I74, I75) -> f10(I76, I77, I78, I79) [-1 <= I79 - 1 /\ -1 <= I77 - 1 /\ 5 <= I76 - 1 /\ 1 <= I72 - 1 /\ I79 + 2 <= I72 /\ I77 + 2 <= I72 /\ I76 - 4 <= I72] 34.75/34.27 f5(I80, I81, I82, I83) -> f5(I84, I85, I86, I87) [-1 <= I84 - 1 /\ 1 <= I80 - 1 /\ I84 + 2 <= I80] 34.75/34.27 f5(I88, I89, I90, I91) -> f5(I92, I93, I94, I95) [2 <= I92 - 1 /\ 2 <= I88 - 1 /\ I92 - 2 <= I88] 34.75/34.27 f5(I96, I97, I98, I99) -> f5(I100, I101, I102, I103) [-1 <= I100 - 1 /\ 1 <= I96 - 1 /\ I100 + 2 <= I96] 34.75/34.27 f5(I104, I105, I106, I107) -> f5(I108, I109, I110, I111) [-1 <= I108 - 1 /\ 1 <= I104 - 1 /\ I108 + 2 <= I104] 34.75/34.27 f2(I112, I113, I114, I115) -> f2(I112 - 1, I113, I116, I117) [0 <= I112 - 1 /\ -1 <= I113 - 1 /\ 0 <= I114 - 1 /\ I114 <= I113 - 1 /\ -1 <= y1 - 1 /\ y1 <= 42 /\ I112 - 1 <= I112 - 1 /\ 1 <= I116 - 1 /\ 1 <= y2 - 1] 34.75/34.27 f9(I118, I119, I120, I121) -> f2(I119, I120, I121, I122) [1 <= I121 - 1 /\ 0 <= I118 - 1 /\ I119 <= I118 - 1] 34.75/34.27 f2(I123, I124, I125, I126) -> f9(I123, I123 - 1, I124, I127) [0 <= I123 - 1 /\ -1 <= I124 - 1 /\ 0 <= I125 - 1 /\ I125 <= I124 - 1 /\ -1 <= I128 - 1 /\ I128 <= 42 /\ 1 <= I129 - 1 /\ I123 - 1 <= I123 - 1] 34.75/34.27 f2(I130, I131, I132, I133) -> f9(1, 0, I131, I134) [0 <= I132 - 1 /\ -1 <= I131 - 1 /\ I132 <= I131 - 1 /\ -1 <= I135 - 1 /\ 1 <= I134 - 1 /\ I135 <= 42 /\ 1 = I130] 34.75/34.27 f7(I136, I137, I138, I139) -> f2(I136 - 1, I138, I140, I141) [I136 - 1 <= I136 - 1 /\ I137 <= I136 - 1 /\ 1 <= I140 - 1 /\ 1 <= I139 - 1 /\ 0 <= I136 - 1] 34.75/34.27 f2(I142, I143, I144, I145) -> f2(I142 - 1, I143, I146, I147) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ 0 <= I144 - 1 /\ I144 <= I143 - 1 /\ -1 <= I148 - 1 /\ I148 <= 42 /\ 1 <= I146 - 1 /\ I142 - 1 <= I142 - 1] 34.75/34.27 f8(I149, I150, I151, I152) -> f2(I150, I151, I152, I153) [1 <= I152 - 1 /\ 0 <= I149 - 1 /\ I150 <= I149 - 1] 34.75/34.27 f7(I154, I155, I156, I157) -> f8(I154, I154 - 1, I156, I158) [1 <= I157 - 1 /\ I155 <= I154 - 1 /\ 0 <= I154 - 1] 34.75/34.27 f7(I159, I160, I161, I162) -> f8(I159, I159 - 1, I161, I162) [0 = I160 /\ 0 <= I159 - 1 /\ 1 <= I162 - 1] 34.75/34.27 f7(I163, I164, I165, I166) -> f2(I164, I165, I166, I167) [1 <= I166 - 1 /\ 0 <= I163 - 1 /\ I164 <= I163 - 1] 34.75/34.27 f2(I168, I169, I170, I171) -> f7(I168, I168 - 1, I169, I172) [0 <= I168 - 1 /\ -1 <= I169 - 1 /\ 0 <= I170 - 1 /\ I170 <= I169 - 1 /\ -1 <= I173 - 1 /\ I168 - 1 <= I168 - 1 /\ I173 <= 42] 34.75/34.27 f2(I174, I175, I176, I177) -> f7(1, 0, I175, I176 + 1) [0 <= I176 - 1 /\ -1 <= I175 - 1 /\ I176 <= I175 - 1 /\ I178 <= 42 /\ -1 <= I178 - 1 /\ 1 = I174] 34.75/34.27 f2(I179, I180, I181, I182) -> f2(I179 - 1, I180, I181 + 1, I183) [0 <= I179 - 1 /\ -1 <= I180 - 1 /\ 0 <= I181 - 1 /\ I181 <= I180 - 1 /\ -1 <= I184 - 1 /\ I179 - 1 <= I179 - 1 /\ I184 <= 42] 34.75/34.27 f6(I185, I186, I187, I188) -> f5(I189, I190, I191, I192) [0 <= I193 - 1 /\ 1 <= I187 - 1 /\ I189 <= I186 /\ 0 <= I185 - 1 /\ 0 <= I186 - 1 /\ 0 <= I189 - 1] 34.75/34.27 f1(I194, I195, I196, I197) -> f6(I198, I199, I200, I201) [-1 <= I202 - 1 /\ 0 <= I195 - 1 /\ I198 <= I194 /\ I199 - 1 <= I194 /\ 0 <= I194 - 1 /\ 0 <= I198 - 1 /\ 1 <= I199 - 1] 34.75/34.27 f1(I203, I204, I205, I206) -> f6(I207, I208, I209, I210) [-1 <= I211 - 1 /\ 0 <= I204 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 2 <= I208 - 1] 34.75/34.27 f1(I212, I213, I214, I215) -> f6(I216, I217, I218, I219) [-1 <= I220 - 1 /\ 0 <= I213 - 1 /\ I216 <= I212 /\ 0 <= I212 - 1 /\ 0 <= I216 - 1 /\ 2 <= I217 - 1] 34.75/34.27 f1(I221, I222, I223, I224) -> f6(I225, I226, I227, I228) [-1 <= I229 - 1 /\ 0 <= I222 - 1 /\ I225 <= I221 /\ 0 <= I221 - 1 /\ 0 <= I225 - 1 /\ 2 <= I226 - 1] 34.75/34.27 f1(I230, I231, I232, I233) -> f6(I234, I235, I236, I237) [-1 <= I238 - 1 /\ 0 <= I231 - 1 /\ I234 <= I230 /\ 0 <= I230 - 1 /\ 0 <= I234 - 1 /\ 2 <= I235 - 1] 34.75/34.27 f1(I239, I240, I241, I242) -> f6(I243, I244, I245, I246) [-1 <= I247 - 1 /\ 0 <= I240 - 1 /\ I243 <= I239 /\ 0 <= I239 - 1 /\ 0 <= I243 - 1 /\ 2 <= I244 - 1] 34.75/34.27 f1(I248, I249, I250, I251) -> f6(I252, I253, I254, I255) [-1 <= I256 - 1 /\ 0 <= I249 - 1 /\ I252 <= I248 /\ 0 <= I248 - 1 /\ 0 <= I252 - 1 /\ 2 <= I253 - 1] 34.75/34.27 f1(I257, I258, I259, I260) -> f6(I261, I262, I263, I264) [-1 <= I265 - 1 /\ 0 <= I258 - 1 /\ I261 <= I257 /\ 0 <= I257 - 1 /\ 0 <= I261 - 1 /\ 2 <= I262 - 1] 34.75/34.27 f3(I266, I267, I268, I269) -> f5(I270, I271, I272, I273) [I270 + 1 <= I266 /\ 0 <= I274 - 1 /\ 0 <= I266 - 1 /\ -1 <= I270 - 1] 34.75/34.27 f4(I275, I276, I277, I278) -> f3(I279, I280, I281, I282) [0 <= I279 - 1 /\ 0 <= I275 - 1 /\ I279 <= I275] 34.75/34.27 f1(I283, I284, I285, I286) -> f3(I287, I288, I289, I290) [-1 <= I291 - 1 /\ 0 <= I284 - 1 /\ I287 <= I283 /\ 0 <= I283 - 1 /\ 0 <= I287 - 1] 34.75/34.27 f1(I292, I293, I294, I295) -> f3(I296, I297, I298, I299) [0 <= I296 - 1 /\ 0 <= I292 - 1 /\ 0 <= I293 - 1 /\ I296 <= I292] 34.75/34.27 f1(I300, I301, I302, I303) -> f2(I304, I301, 1, I305) [0 <= I300 - 1 /\ 0 <= I301 - 1 /\ -1 <= I304 - 1] 34.75/34.27 34.75/34.27 The dependency graph for this problem is: 34.75/34.27 17 -> 34.75/34.27 18 -> 34.75/34.27 21 -> 17, 18, 25, 26 34.75/34.27 25 -> 34.75/34.27 26 -> 34.75/34.27 Where: 34.75/34.27 17) f2#(I123, I124, I125, I126) -> f9#(I123, I123 - 1, I124, I127) [0 <= I123 - 1 /\ -1 <= I124 - 1 /\ 0 <= I125 - 1 /\ I125 <= I124 - 1 /\ -1 <= I128 - 1 /\ I128 <= 42 /\ 1 <= I129 - 1 /\ I123 - 1 <= I123 - 1] 34.75/34.27 18) f2#(I130, I131, I132, I133) -> f9#(1, 0, I131, I134) [0 <= I132 - 1 /\ -1 <= I131 - 1 /\ I132 <= I131 - 1 /\ -1 <= I135 - 1 /\ 1 <= I134 - 1 /\ I135 <= 42 /\ 1 = I130] 34.75/34.27 21) f8#(I149, I150, I151, I152) -> f2#(I150, I151, I152, I153) [1 <= I152 - 1 /\ 0 <= I149 - 1 /\ I150 <= I149 - 1] 34.75/34.27 25) f2#(I168, I169, I170, I171) -> f7#(I168, I168 - 1, I169, I172) [0 <= I168 - 1 /\ -1 <= I169 - 1 /\ 0 <= I170 - 1 /\ I170 <= I169 - 1 /\ -1 <= I173 - 1 /\ I168 - 1 <= I168 - 1 /\ I173 <= 42] 34.75/34.27 26) f2#(I174, I175, I176, I177) -> f7#(1, 0, I175, I176 + 1) [0 <= I176 - 1 /\ -1 <= I175 - 1 /\ I176 <= I175 - 1 /\ I178 <= 42 /\ -1 <= I178 - 1 /\ 1 = I174] 34.75/34.27 34.75/34.27 We have the following SCCs. 34.75/34.27 34.75/34.27 34.75/34.27 DP problem for innermost termination. 34.75/34.27 P = 34.75/34.27 f10#(I0, I1, I2, I3) -> f5#(I4, I5, I6, I7) [-1 <= I4 - 1 /\ -1 <= I3 - 1 /\ -1 <= I1 - 1 /\ 3 <= I0 - 1 /\ I4 <= I3 /\ I4 <= I1 /\ I4 + 2 <= I0] 34.75/34.27 f5#(I8, I9, I10, I11) -> f10#(I12, I13, I14, I15) [-1 <= I15 - 1 /\ -1 <= I13 - 1 /\ 3 <= I12 - 1 /\ 3 <= I8 - 1 /\ I15 + 2 <= I8 /\ I13 + 2 <= I8 /\ I12 <= I8] 34.75/34.27 f5#(I16, I17, I18, I19) -> f10#(I20, I21, I22, I23) [-1 <= I23 - 1 /\ -1 <= I21 - 1 /\ 5 <= I20 - 1 /\ 1 <= I16 - 1 /\ I23 + 2 <= I16 /\ I21 + 2 <= I16] 34.75/34.27 f5#(I24, I25, I26, I27) -> f10#(I28, I29, I30, I31) [-1 <= I31 - 1 /\ -1 <= I29 - 1 /\ 5 <= I28 - 1 /\ 1 <= I24 - 1 /\ I31 + 2 <= I24 /\ I29 + 2 <= I24] 34.75/34.27 f5#(I32, I33, I34, I35) -> f10#(I36, I37, I38, I39) [-1 <= I39 - 1 /\ -1 <= I37 - 1 /\ 5 <= I36 - 1 /\ 1 <= I32 - 1 /\ I39 + 2 <= I32 /\ I37 + 2 <= I32] 34.75/34.27 f5#(I40, I41, I42, I43) -> f10#(I44, I45, I46, I47) [-1 <= I47 - 1 /\ -1 <= I45 - 1 /\ 5 <= I44 - 1 /\ 1 <= I40 - 1 /\ I47 + 2 <= I40 /\ I45 + 2 <= I40] 34.75/34.27 f5#(I48, I49, I50, I51) -> f10#(I52, I53, I54, I55) [-1 <= I55 - 1 /\ -1 <= I53 - 1 /\ 5 <= I52 - 1 /\ 1 <= I48 - 1 /\ I55 + 2 <= I48 /\ I53 + 2 <= I48] 34.75/34.27 f5#(I56, I57, I58, I59) -> f10#(I60, I61, I62, I63) [-1 <= I63 - 1 /\ -1 <= I61 - 1 /\ 5 <= I60 - 1 /\ 1 <= I56 - 1 /\ I63 + 2 <= I56 /\ I61 + 2 <= I56 /\ I60 - 4 <= I56] 34.75/34.27 f5#(I64, I65, I66, I67) -> f10#(I68, I69, I70, I71) [-1 <= I71 - 1 /\ -1 <= I69 - 1 /\ 5 <= I68 - 1 /\ 1 <= I64 - 1 /\ I71 + 2 <= I64 /\ I69 + 2 <= I64 /\ I68 - 4 <= I64] 34.75/34.27 f5#(I72, I73, I74, I75) -> f10#(I76, I77, I78, I79) [-1 <= I79 - 1 /\ -1 <= I77 - 1 /\ 5 <= I76 - 1 /\ 1 <= I72 - 1 /\ I79 + 2 <= I72 /\ I77 + 2 <= I72 /\ I76 - 4 <= I72] 34.75/34.27 f5#(I80, I81, I82, I83) -> f5#(I84, I85, I86, I87) [-1 <= I84 - 1 /\ 1 <= I80 - 1 /\ I84 + 2 <= I80] 34.75/34.27 f5#(I88, I89, I90, I91) -> f5#(I92, I93, I94, I95) [2 <= I92 - 1 /\ 2 <= I88 - 1 /\ I92 - 2 <= I88] 34.75/34.27 f5#(I96, I97, I98, I99) -> f5#(I100, I101, I102, I103) [-1 <= I100 - 1 /\ 1 <= I96 - 1 /\ I100 + 2 <= I96] 34.75/34.27 f5#(I104, I105, I106, I107) -> f5#(I108, I109, I110, I111) [-1 <= I108 - 1 /\ 1 <= I104 - 1 /\ I108 + 2 <= I104] 34.75/34.27 R = 34.75/34.27 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 34.75/34.27 f10(I0, I1, I2, I3) -> f5(I4, I5, I6, I7) [-1 <= I4 - 1 /\ -1 <= I3 - 1 /\ -1 <= I1 - 1 /\ 3 <= I0 - 1 /\ I4 <= I3 /\ I4 <= I1 /\ I4 + 2 <= I0] 34.75/34.27 f5(I8, I9, I10, I11) -> f10(I12, I13, I14, I15) [-1 <= I15 - 1 /\ -1 <= I13 - 1 /\ 3 <= I12 - 1 /\ 3 <= I8 - 1 /\ I15 + 2 <= I8 /\ I13 + 2 <= I8 /\ I12 <= I8] 34.75/34.27 f5(I16, I17, I18, I19) -> f10(I20, I21, I22, I23) [-1 <= I23 - 1 /\ -1 <= I21 - 1 /\ 5 <= I20 - 1 /\ 1 <= I16 - 1 /\ I23 + 2 <= I16 /\ I21 + 2 <= I16] 34.75/34.27 f5(I24, I25, I26, I27) -> f10(I28, I29, I30, I31) [-1 <= I31 - 1 /\ -1 <= I29 - 1 /\ 5 <= I28 - 1 /\ 1 <= I24 - 1 /\ I31 + 2 <= I24 /\ I29 + 2 <= I24] 34.75/34.27 f5(I32, I33, I34, I35) -> f10(I36, I37, I38, I39) [-1 <= I39 - 1 /\ -1 <= I37 - 1 /\ 5 <= I36 - 1 /\ 1 <= I32 - 1 /\ I39 + 2 <= I32 /\ I37 + 2 <= I32] 34.75/34.27 f5(I40, I41, I42, I43) -> f10(I44, I45, I46, I47) [-1 <= I47 - 1 /\ -1 <= I45 - 1 /\ 5 <= I44 - 1 /\ 1 <= I40 - 1 /\ I47 + 2 <= I40 /\ I45 + 2 <= I40] 34.75/34.27 f5(I48, I49, I50, I51) -> f10(I52, I53, I54, I55) [-1 <= I55 - 1 /\ -1 <= I53 - 1 /\ 5 <= I52 - 1 /\ 1 <= I48 - 1 /\ I55 + 2 <= I48 /\ I53 + 2 <= I48] 34.75/34.27 f5(I56, I57, I58, I59) -> f10(I60, I61, I62, I63) [-1 <= I63 - 1 /\ -1 <= I61 - 1 /\ 5 <= I60 - 1 /\ 1 <= I56 - 1 /\ I63 + 2 <= I56 /\ I61 + 2 <= I56 /\ I60 - 4 <= I56] 34.75/34.27 f5(I64, I65, I66, I67) -> f10(I68, I69, I70, I71) [-1 <= I71 - 1 /\ -1 <= I69 - 1 /\ 5 <= I68 - 1 /\ 1 <= I64 - 1 /\ I71 + 2 <= I64 /\ I69 + 2 <= I64 /\ I68 - 4 <= I64] 34.75/34.27 f5(I72, I73, I74, I75) -> f10(I76, I77, I78, I79) [-1 <= I79 - 1 /\ -1 <= I77 - 1 /\ 5 <= I76 - 1 /\ 1 <= I72 - 1 /\ I79 + 2 <= I72 /\ I77 + 2 <= I72 /\ I76 - 4 <= I72] 34.75/34.27 f5(I80, I81, I82, I83) -> f5(I84, I85, I86, I87) [-1 <= I84 - 1 /\ 1 <= I80 - 1 /\ I84 + 2 <= I80] 34.75/34.27 f5(I88, I89, I90, I91) -> f5(I92, I93, I94, I95) [2 <= I92 - 1 /\ 2 <= I88 - 1 /\ I92 - 2 <= I88] 34.75/34.27 f5(I96, I97, I98, I99) -> f5(I100, I101, I102, I103) [-1 <= I100 - 1 /\ 1 <= I96 - 1 /\ I100 + 2 <= I96] 34.75/34.27 f5(I104, I105, I106, I107) -> f5(I108, I109, I110, I111) [-1 <= I108 - 1 /\ 1 <= I104 - 1 /\ I108 + 2 <= I104] 34.75/34.27 f2(I112, I113, I114, I115) -> f2(I112 - 1, I113, I116, I117) [0 <= I112 - 1 /\ -1 <= I113 - 1 /\ 0 <= I114 - 1 /\ I114 <= I113 - 1 /\ -1 <= y1 - 1 /\ y1 <= 42 /\ I112 - 1 <= I112 - 1 /\ 1 <= I116 - 1 /\ 1 <= y2 - 1] 34.75/34.27 f9(I118, I119, I120, I121) -> f2(I119, I120, I121, I122) [1 <= I121 - 1 /\ 0 <= I118 - 1 /\ I119 <= I118 - 1] 34.75/34.27 f2(I123, I124, I125, I126) -> f9(I123, I123 - 1, I124, I127) [0 <= I123 - 1 /\ -1 <= I124 - 1 /\ 0 <= I125 - 1 /\ I125 <= I124 - 1 /\ -1 <= I128 - 1 /\ I128 <= 42 /\ 1 <= I129 - 1 /\ I123 - 1 <= I123 - 1] 34.75/34.27 f2(I130, I131, I132, I133) -> f9(1, 0, I131, I134) [0 <= I132 - 1 /\ -1 <= I131 - 1 /\ I132 <= I131 - 1 /\ -1 <= I135 - 1 /\ 1 <= I134 - 1 /\ I135 <= 42 /\ 1 = I130] 34.75/34.27 f7(I136, I137, I138, I139) -> f2(I136 - 1, I138, I140, I141) [I136 - 1 <= I136 - 1 /\ I137 <= I136 - 1 /\ 1 <= I140 - 1 /\ 1 <= I139 - 1 /\ 0 <= I136 - 1] 34.75/34.27 f2(I142, I143, I144, I145) -> f2(I142 - 1, I143, I146, I147) [0 <= I142 - 1 /\ -1 <= I143 - 1 /\ 0 <= I144 - 1 /\ I144 <= I143 - 1 /\ -1 <= I148 - 1 /\ I148 <= 42 /\ 1 <= I146 - 1 /\ I142 - 1 <= I142 - 1] 34.75/34.27 f8(I149, I150, I151, I152) -> f2(I150, I151, I152, I153) [1 <= I152 - 1 /\ 0 <= I149 - 1 /\ I150 <= I149 - 1] 34.75/34.27 f7(I154, I155, I156, I157) -> f8(I154, I154 - 1, I156, I158) [1 <= I157 - 1 /\ I155 <= I154 - 1 /\ 0 <= I154 - 1] 34.75/34.27 f7(I159, I160, I161, I162) -> f8(I159, I159 - 1, I161, I162) [0 = I160 /\ 0 <= I159 - 1 /\ 1 <= I162 - 1] 34.75/34.27 f7(I163, I164, I165, I166) -> f2(I164, I165, I166, I167) [1 <= I166 - 1 /\ 0 <= I163 - 1 /\ I164 <= I163 - 1] 34.75/34.27 f2(I168, I169, I170, I171) -> f7(I168, I168 - 1, I169, I172) [0 <= I168 - 1 /\ -1 <= I169 - 1 /\ 0 <= I170 - 1 /\ I170 <= I169 - 1 /\ -1 <= I173 - 1 /\ I168 - 1 <= I168 - 1 /\ I173 <= 42] 34.75/34.27 f2(I174, I175, I176, I177) -> f7(1, 0, I175, I176 + 1) [0 <= I176 - 1 /\ -1 <= I175 - 1 /\ I176 <= I175 - 1 /\ I178 <= 42 /\ -1 <= I178 - 1 /\ 1 = I174] 34.75/34.27 f2(I179, I180, I181, I182) -> f2(I179 - 1, I180, I181 + 1, I183) [0 <= I179 - 1 /\ -1 <= I180 - 1 /\ 0 <= I181 - 1 /\ I181 <= I180 - 1 /\ -1 <= I184 - 1 /\ I179 - 1 <= I179 - 1 /\ I184 <= 42] 34.75/34.27 f6(I185, I186, I187, I188) -> f5(I189, I190, I191, I192) [0 <= I193 - 1 /\ 1 <= I187 - 1 /\ I189 <= I186 /\ 0 <= I185 - 1 /\ 0 <= I186 - 1 /\ 0 <= I189 - 1] 34.75/34.27 f1(I194, I195, I196, I197) -> f6(I198, I199, I200, I201) [-1 <= I202 - 1 /\ 0 <= I195 - 1 /\ I198 <= I194 /\ I199 - 1 <= I194 /\ 0 <= I194 - 1 /\ 0 <= I198 - 1 /\ 1 <= I199 - 1] 34.75/34.27 f1(I203, I204, I205, I206) -> f6(I207, I208, I209, I210) [-1 <= I211 - 1 /\ 0 <= I204 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 2 <= I208 - 1] 34.75/34.27 f1(I212, I213, I214, I215) -> f6(I216, I217, I218, I219) [-1 <= I220 - 1 /\ 0 <= I213 - 1 /\ I216 <= I212 /\ 0 <= I212 - 1 /\ 0 <= I216 - 1 /\ 2 <= I217 - 1] 34.75/34.27 f1(I221, I222, I223, I224) -> f6(I225, I226, I227, I228) [-1 <= I229 - 1 /\ 0 <= I222 - 1 /\ I225 <= I221 /\ 0 <= I221 - 1 /\ 0 <= I225 - 1 /\ 2 <= I226 - 1] 34.75/34.27 f1(I230, I231, I232, I233) -> f6(I234, I235, I236, I237) [-1 <= I238 - 1 /\ 0 <= I231 - 1 /\ I234 <= I230 /\ 0 <= I230 - 1 /\ 0 <= I234 - 1 /\ 2 <= I235 - 1] 34.75/34.27 f1(I239, I240, I241, I242) -> f6(I243, I244, I245, I246) [-1 <= I247 - 1 /\ 0 <= I240 - 1 /\ I243 <= I239 /\ 0 <= I239 - 1 /\ 0 <= I243 - 1 /\ 2 <= I244 - 1] 34.75/34.27 f1(I248, I249, I250, I251) -> f6(I252, I253, I254, I255) [-1 <= I256 - 1 /\ 0 <= I249 - 1 /\ I252 <= I248 /\ 0 <= I248 - 1 /\ 0 <= I252 - 1 /\ 2 <= I253 - 1] 34.75/34.27 f1(I257, I258, I259, I260) -> f6(I261, I262, I263, I264) [-1 <= I265 - 1 /\ 0 <= I258 - 1 /\ I261 <= I257 /\ 0 <= I257 - 1 /\ 0 <= I261 - 1 /\ 2 <= I262 - 1] 34.75/34.27 f3(I266, I267, I268, I269) -> f5(I270, I271, I272, I273) [I270 + 1 <= I266 /\ 0 <= I274 - 1 /\ 0 <= I266 - 1 /\ -1 <= I270 - 1] 34.75/34.27 f4(I275, I276, I277, I278) -> f3(I279, I280, I281, I282) [0 <= I279 - 1 /\ 0 <= I275 - 1 /\ I279 <= I275] 34.75/34.27 f1(I283, I284, I285, I286) -> f3(I287, I288, I289, I290) [-1 <= I291 - 1 /\ 0 <= I284 - 1 /\ I287 <= I283 /\ 0 <= I283 - 1 /\ 0 <= I287 - 1] 34.75/34.27 f1(I292, I293, I294, I295) -> f3(I296, I297, I298, I299) [0 <= I296 - 1 /\ 0 <= I292 - 1 /\ 0 <= I293 - 1 /\ I296 <= I292] 34.75/34.27 f1(I300, I301, I302, I303) -> f2(I304, I301, 1, I305) [0 <= I300 - 1 /\ 0 <= I301 - 1 /\ -1 <= I304 - 1] 34.75/34.27 34.75/37.24 EOF