273.89/269.54	YES
273.89/269.54	
273.89/269.54	DP problem for innermost termination.
273.89/269.54	P =
273.89/269.54	  init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
273.89/269.54	  f15#(I0, I1, I2, I3) -> f14#(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.54	  f6#(I5, I6, I7, I8) -> f15#(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.54	  f15#(I11, I12, I13, I14) -> f14#(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.54	  f6#(I19, I20, I21, I22) -> f15#(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.54	  f6#(I25, I26, I27, I28) -> f10#(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.54	  f10#(I32, I33, I34, I35) -> f10#(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.54	  f8#(I39, I40, I41, I42) -> f8#(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.54	  f14#(I46, I47, I48, I49) -> f6#(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.54	  f6#(I52, I53, I54, I55) -> f8#(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.54	  f13#(I59, I60, I61, I62) -> f5#(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.54	  f12#(I68, I69, I70, I71) -> f13#(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.54	  f12#(I73, I74, I75, I76) -> f10#(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.54	  f12#(I80, I81, I82, I83) -> f8#(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.54	  f5#(I87, I88, I89, I90) -> f12#(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.54	  f5#(I92, I93, I94, I95) -> f8#(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.54	  f11#(I99, I100, I101, I102) -> f4#(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.54	  f9#(I108, I109, I110, I111) -> f11#(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.54	  f9#(I113, I114, I115, I116) -> f10#(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.54	  f9#(I120, I121, I122, I123) -> f8#(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.54	  f4#(I127, I128, I129, I130) -> f9#(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.54	  f4#(I132, I133, I134, I135) -> f8#(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.54	  f3#(I139, I140, I141, I142) -> f2#(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.54	  f2#(I146, I147, I148, I149) -> f3#(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.54	  f3#(I153, I154, I155, I156) -> f2#(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.54	  f2#(I161, I162, I163, I164) -> f3#(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.54	  f3#(I169, I170, I171, I172) -> f2#(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.54	  f2#(I178, I179, I180, I181) -> f3#(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.54	  f7#(I186, I187, I188, I189) -> f2#(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.54	  f2#(I192, I193, I194, I195) -> f2#(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.54	  f7#(I198, I199, I200, I201) -> f7#(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.54	  f3#(I203, I204, I205, I206) -> f7#(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.54	  f2#(I211, I212, I213, I214) -> f3#(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.54	  f3#(I220, I221, I222, I223) -> f6#(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.54	  f2#(I229, I230, I231, I232) -> f3#(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.54	  f3#(I237, I238, I239, I240) -> f5#(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.54	  f2#(I245, I246, I247, I248) -> f3#(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.54	  f3#(I252, I253, I254, I255) -> f4#(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.54	  f2#(I259, I260, I261, I262) -> f3#(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.54	  f1#(I265, I266, I267, I268) -> f2#(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.54	R = 
273.89/269.54	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.54	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.54	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.54	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.54	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.54	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.54	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.54	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.54	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.54	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.54	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.54	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.54	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.54	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.54	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.54	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.54	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.54	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.54	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.54	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.54	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.54	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.54	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.54	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.54	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.54	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.54	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.54	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.54	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.54	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.54	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.54	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.54	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.54	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.54	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.54	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.54	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.54	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.54	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.54	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.54	
273.89/269.54	The dependency graph for this problem is:
273.89/269.54	  0 -> 39
273.89/269.54	  1 -> 8
273.89/269.54	  2 -> 1, 3
273.89/269.54	  3 -> 8
273.89/269.54	  4 -> 1, 3
273.89/269.54	  5 -> 6
273.89/269.54	  6 -> 6
273.89/269.54	  7 -> 7
273.89/269.54	  8 -> 2, 4, 5, 9
273.89/269.54	  9 -> 7
273.89/269.54	  10 -> 14, 15
273.89/269.54	  11 -> 10
273.89/269.54	  12 -> 6
273.89/269.54	  13 -> 7
273.89/269.54	  14 -> 11, 12, 13
273.89/269.54	  15 -> 7
273.89/269.54	  16 -> 20, 21
273.89/269.54	  17 -> 16
273.89/269.54	  18 -> 6
273.89/269.54	  19 -> 7
273.89/269.54	  20 -> 17, 18, 19
273.89/269.54	  21 -> 7
273.89/269.54	  22 -> 25, 27, 32, 34, 36
273.89/269.54	  23 -> 22, 37
273.89/269.54	  24 -> 23, 38
273.89/269.54	  25 -> 24, 35
273.89/269.54	  26 -> 23, 38
273.89/269.54	  27 -> 24, 26, 33, 35
273.89/269.54	  28 -> 23, 25, 27, 29, 32, 34, 36, 38
273.89/269.54	  29 -> 32
273.89/269.54	  30 -> 28, 30
273.89/269.54	  31 -> 30
273.89/269.54	  32 -> 24, 26, 31, 33, 35
273.89/269.54	  33 -> 2, 4, 5, 9
273.89/269.54	  34 -> 24, 26, 33, 35
273.89/269.54	  35 -> 14, 15
273.89/269.54	  36 -> 24, 35
273.89/269.54	  37 -> 20, 21
273.89/269.54	  38 -> 22, 37
273.89/269.54	  39 -> 23, 29, 38
273.89/269.54	Where:
273.89/269.54	  0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 
273.89/269.54	  1) f15#(I0, I1, I2, I3) -> f14#(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.54	  2) f6#(I5, I6, I7, I8) -> f15#(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.54	  3) f15#(I11, I12, I13, I14) -> f14#(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.54	  4) f6#(I19, I20, I21, I22) -> f15#(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.54	  5) f6#(I25, I26, I27, I28) -> f10#(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.54	  6) f10#(I32, I33, I34, I35) -> f10#(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.54	  7) f8#(I39, I40, I41, I42) -> f8#(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.54	  8) f14#(I46, I47, I48, I49) -> f6#(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.54	  9) f6#(I52, I53, I54, I55) -> f8#(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.54	  10) f13#(I59, I60, I61, I62) -> f5#(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.54	  11) f12#(I68, I69, I70, I71) -> f13#(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.54	  12) f12#(I73, I74, I75, I76) -> f10#(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.54	  13) f12#(I80, I81, I82, I83) -> f8#(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.54	  14) f5#(I87, I88, I89, I90) -> f12#(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.54	  15) f5#(I92, I93, I94, I95) -> f8#(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.54	  16) f11#(I99, I100, I101, I102) -> f4#(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.54	  17) f9#(I108, I109, I110, I111) -> f11#(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.54	  18) f9#(I113, I114, I115, I116) -> f10#(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.54	  19) f9#(I120, I121, I122, I123) -> f8#(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.54	  20) f4#(I127, I128, I129, I130) -> f9#(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.54	  21) f4#(I132, I133, I134, I135) -> f8#(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.54	  22) f3#(I139, I140, I141, I142) -> f2#(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.54	  23) f2#(I146, I147, I148, I149) -> f3#(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.54	  24) f3#(I153, I154, I155, I156) -> f2#(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.54	  25) f2#(I161, I162, I163, I164) -> f3#(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.54	  26) f3#(I169, I170, I171, I172) -> f2#(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.54	  27) f2#(I178, I179, I180, I181) -> f3#(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.54	  28) f7#(I186, I187, I188, I189) -> f2#(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.54	  29) f2#(I192, I193, I194, I195) -> f2#(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.54	  30) f7#(I198, I199, I200, I201) -> f7#(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.54	  31) f3#(I203, I204, I205, I206) -> f7#(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.54	  32) f2#(I211, I212, I213, I214) -> f3#(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.54	  33) f3#(I220, I221, I222, I223) -> f6#(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.54	  34) f2#(I229, I230, I231, I232) -> f3#(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.54	  35) f3#(I237, I238, I239, I240) -> f5#(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.54	  36) f2#(I245, I246, I247, I248) -> f3#(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.54	  37) f3#(I252, I253, I254, I255) -> f4#(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.54	  38) f2#(I259, I260, I261, I262) -> f3#(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.54	  39) f1#(I265, I266, I267, I268) -> f2#(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.54	
273.89/269.54	We have the following SCCs.
273.89/269.54	  { 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 38 }
273.89/269.54	  { 1, 2, 3, 4, 8 }
273.89/269.54	  { 10, 11, 14 }
273.89/269.54	  { 16, 17, 20 }
273.89/269.54	  { 6 }
273.89/269.54	  { 7 }
273.89/269.54	
273.89/269.54	DP problem for innermost termination.
273.89/269.54	P =
273.89/269.54	  f8#(I39, I40, I41, I42) -> f8#(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.54	R = 
273.89/269.54	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.54	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.54	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.54	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.54	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.54	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.54	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.54	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.54	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.54	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.54	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.54	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.54	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.54	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.54	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.54	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.54	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.54	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.54	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.54	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.54	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.54	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.54	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.54	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.54	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.54	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.54	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.54	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.54	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.54	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.54	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.54	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.54	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.54	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.54	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.54	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.54	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.54	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.54	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.54	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.54	
273.89/269.54	We use the basic value criterion with the projection function NU:
273.89/269.54	  NU[f8#(z1,z2,z3,z4)] = z1
273.89/269.54	
273.89/269.54	This gives the following inequalities:
273.89/269.54	  0 <= I39 - 1  ==>  I39 >! I39 - 1
273.89/269.54	
273.89/269.54	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
273.89/269.54	
273.89/269.54	DP problem for innermost termination.
273.89/269.54	P =
273.89/269.54	  f10#(I32, I33, I34, I35) -> f10#(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.54	R = 
273.89/269.54	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.54	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.54	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.54	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.54	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.54	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.54	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.54	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.54	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.54	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.54	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.54	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.54	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.55	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.55	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.55	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.55	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.55	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.55	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.55	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.55	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.55	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.55	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.55	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.55	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.55	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.55	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.55	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.55	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.55	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.55	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.55	
273.89/269.55	We use the basic value criterion with the projection function NU:
273.89/269.55	  NU[f10#(z1,z2,z3,z4)] = z1
273.89/269.55	
273.89/269.55	This gives the following inequalities:
273.89/269.55	  I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1  ==>  I32 >! I32 - 1
273.89/269.55	
273.89/269.55	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
273.89/269.55	
273.89/269.55	DP problem for innermost termination.
273.89/269.55	P =
273.89/269.55	  f11#(I99, I100, I101, I102) -> f4#(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.55	  f9#(I108, I109, I110, I111) -> f11#(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f4#(I127, I128, I129, I130) -> f9#(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	R = 
273.89/269.55	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.55	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.55	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.55	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.55	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.55	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.55	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.55	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.55	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.55	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.55	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.55	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.55	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.55	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.55	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.55	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.55	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.55	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.55	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.55	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.55	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.55	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.55	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.55	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.55	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.55	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.55	
273.89/269.55	We use the basic value criterion with the projection function NU:
273.89/269.55	  NU[f9#(z1,z2,z3,z4)] = z1
273.89/269.55	  NU[f4#(z1,z2,z3,z4)] = z2
273.89/269.55	  NU[f11#(z1,z2,z3,z4)] = z1
273.89/269.55	
273.89/269.55	This gives the following inequalities:
273.89/269.55	  0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107  ==>  I99 >! I99 - 1
273.89/269.55	  0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1  ==>  I108 (>! \union =) I108
273.89/269.55	  0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1  ==>  I128 (>! \union =) I128
273.89/269.55	
273.89/269.55	We remove all the strictly oriented dependency pairs.
273.89/269.55	
273.89/269.55	DP problem for innermost termination.
273.89/269.55	P =
273.89/269.55	  f9#(I108, I109, I110, I111) -> f11#(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f4#(I127, I128, I129, I130) -> f9#(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	R = 
273.89/269.55	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.55	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.55	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.55	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.55	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.55	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.55	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.55	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.55	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.55	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.55	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.55	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.55	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.55	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.55	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.55	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.55	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.55	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.55	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.55	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.55	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.55	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.55	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.55	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.55	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.55	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.55	
273.89/269.55	The dependency graph for this problem is:
273.89/269.55	  17 -> 
273.89/269.55	  20 -> 17
273.89/269.55	Where:
273.89/269.55	  17) f9#(I108, I109, I110, I111) -> f11#(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  20) f4#(I127, I128, I129, I130) -> f9#(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	
273.89/269.55	We have the following SCCs.
273.89/269.55	  
273.89/269.55	
273.89/269.55	DP problem for innermost termination.
273.89/269.55	P =
273.89/269.55	  f13#(I59, I60, I61, I62) -> f5#(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.55	  f12#(I68, I69, I70, I71) -> f13#(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  f5#(I87, I88, I89, I90) -> f12#(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	R = 
273.89/269.55	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.55	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.55	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.55	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.55	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.55	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.55	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.55	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.55	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.55	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.55	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.55	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.55	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.55	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.55	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.55	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.55	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.55	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.55	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.55	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.55	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.55	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.55	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.55	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.55	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.55	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.55	
273.89/269.55	We use the basic value criterion with the projection function NU:
273.89/269.55	  NU[f12#(z1,z2,z3,z4)] = z1
273.89/269.55	  NU[f5#(z1,z2,z3,z4)] = z2
273.89/269.55	  NU[f13#(z1,z2,z3,z4)] = z1
273.89/269.55	
273.89/269.55	This gives the following inequalities:
273.89/269.55	  0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67  ==>  I59 >! I59 - 1
273.89/269.55	  1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1  ==>  I68 (>! \union =) I68
273.89/269.55	  0 <= I87 - 1 /\ 0 <= I88 - 1  ==>  I88 (>! \union =) I88
273.89/269.55	
273.89/269.55	We remove all the strictly oriented dependency pairs.
273.89/269.55	
273.89/269.55	DP problem for innermost termination.
273.89/269.55	P =
273.89/269.55	  f12#(I68, I69, I70, I71) -> f13#(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  f5#(I87, I88, I89, I90) -> f12#(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	R = 
273.89/269.55	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.55	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.55	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.55	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.55	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.55	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.55	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.55	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.55	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.55	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.55	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.55	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.55	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.55	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.55	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.55	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.55	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.55	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.55	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.55	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.55	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.55	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.55	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.55	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.55	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.55	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.55	
273.89/269.55	The dependency graph for this problem is:
273.89/269.55	  11 -> 
273.89/269.55	  14 -> 11
273.89/269.55	Where:
273.89/269.55	  11) f12#(I68, I69, I70, I71) -> f13#(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  14) f5#(I87, I88, I89, I90) -> f12#(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	
273.89/269.55	We have the following SCCs.
273.89/269.55	  
273.89/269.55	
273.89/269.55	DP problem for innermost termination.
273.89/269.55	P =
273.89/269.55	  f15#(I0, I1, I2, I3) -> f14#(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  f6#(I5, I6, I7, I8) -> f15#(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  f15#(I11, I12, I13, I14) -> f14#(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  f6#(I19, I20, I21, I22) -> f15#(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	  f14#(I46, I47, I48, I49) -> f6#(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.55	R = 
273.89/269.55	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.55	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.55	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.55	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.55	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.55	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.55	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.55	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.55	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.55	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.55	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.55	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.55	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.55	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.55	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.55	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.55	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.55	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.55	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.55	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.55	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.55	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.55	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.55	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.55	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.55	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.55	
273.89/269.55	We use the basic value criterion with the projection function NU:
273.89/269.55	  NU[f6#(z1,z2,z3,z4)] = z2
273.89/269.55	  NU[f14#(z1,z2,z3,z4)] = z1
273.89/269.55	  NU[f15#(z1,z2,z3,z4)] = z2
273.89/269.55	
273.89/269.55	This gives the following inequalities:
273.89/269.55	  0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3  ==>  I1 (>! \union =) I1
273.89/269.55	  0 <= I6 - 1 /\ 0 <= I5 - 1  ==>  I6 (>! \union =) I6
273.89/269.55	  0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18  ==>  I12 (>! \union =) I12
273.89/269.55	  0 <= I19 - 1 /\ 0 <= I20 - 1  ==>  I20 (>! \union =) I20
273.89/269.55	  0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1  ==>  I46 >! I48
273.89/269.55	
273.89/269.55	We remove all the strictly oriented dependency pairs.
273.89/269.55	
273.89/269.55	DP problem for innermost termination.
273.89/269.55	P =
273.89/269.55	  f15#(I0, I1, I2, I3) -> f14#(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  f6#(I5, I6, I7, I8) -> f15#(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  f15#(I11, I12, I13, I14) -> f14#(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  f6#(I19, I20, I21, I22) -> f15#(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	R = 
273.89/269.55	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.55	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.55	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.55	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.55	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.55	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.55	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.55	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.55	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.55	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.55	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.55	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.55	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.55	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.55	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.55	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.55	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.55	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.55	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.55	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.55	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.55	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.55	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.55	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.55	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.55	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.55	
273.89/269.55	The dependency graph for this problem is:
273.89/269.55	  1 -> 
273.89/269.55	  2 -> 1, 3
273.89/269.55	  3 -> 
273.89/269.55	  4 -> 1, 3
273.89/269.55	Where:
273.89/269.55	  1) f15#(I0, I1, I2, I3) -> f14#(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  2) f6#(I5, I6, I7, I8) -> f15#(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  3) f15#(I11, I12, I13, I14) -> f14#(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  4) f6#(I19, I20, I21, I22) -> f15#(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	
273.89/269.55	We have the following SCCs.
273.89/269.55	  
273.89/269.55	
273.89/269.55	DP problem for innermost termination.
273.89/269.55	P =
273.89/269.55	  f3#(I139, I140, I141, I142) -> f2#(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f2#(I146, I147, I148, I149) -> f3#(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.55	  f3#(I153, I154, I155, I156) -> f2#(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f2#(I161, I162, I163, I164) -> f3#(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.55	  f3#(I169, I170, I171, I172) -> f2#(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f2#(I178, I179, I180, I181) -> f3#(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.55	  f7#(I186, I187, I188, I189) -> f2#(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f2#(I192, I193, I194, I195) -> f2#(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.55	  f7#(I198, I199, I200, I201) -> f7#(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3#(I203, I204, I205, I206) -> f7#(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	  f2#(I211, I212, I213, I214) -> f3#(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.55	  f2#(I229, I230, I231, I232) -> f3#(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.55	  f2#(I245, I246, I247, I248) -> f3#(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.55	  f2#(I259, I260, I261, I262) -> f3#(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.55	R = 
273.89/269.55	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.55	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.55	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.55	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.55	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.55	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.55	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.55	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.55	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.55	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.55	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.55	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.55	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.55	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.55	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.55	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.55	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.55	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.55	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.55	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.55	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.55	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.55	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.55	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.55	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.55	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.55	
273.89/269.55	We use the reverse value criterion with the projection function NU:
273.89/269.55	  NU[f7#(z1,z2,z3,z4)] = z4 - 1 + -1 * (z2 + 1)
273.89/269.55	  NU[f2#(z1,z2,z3,z4)] = z3 - 1 + -1 * z2
273.89/269.55	  NU[f3#(z1,z2,z3,z4)] = z3 - 1 + -1 * (z2 + 1)
273.89/269.55	
273.89/269.55	This gives the following inequalities:
273.89/269.55	  I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145  ==>  I141 - 1 + -1 * (I140 + 1) >= I141 - 1 + -1 * (I140 + 1)
273.89/269.55	  I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1  ==>  I148 - 1 + -1 * I147 > I148 - 1 + -1 * (I147 + 1)  with  I148 - 1 + -1 * I147 >= 0
273.89/269.55	  I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160  ==>  I155 - 1 + -1 * (I154 + 1) >= I155 - 1 + -1 * (I154 + 1)
273.89/269.55	  I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1  ==>  I163 - 1 + -1 * I162 > I163 - 1 + -1 * (I162 + 1)  with  I163 - 1 + -1 * I162 >= 0
273.89/269.55	  0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177  ==>  I171 - 1 + -1 * (I170 + 1) >= I171 - 1 + -1 * (I170 + 1)
273.89/269.55	  I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1  ==>  I180 - 1 + -1 * I179 > I180 - 1 + -1 * (I179 + 1)  with  I180 - 1 + -1 * I179 >= 0
273.89/269.55	  0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1  ==>  I189 - 1 + -1 * (I187 + 1) >= I189 - 1 + -1 * (I187 + 1)
273.89/269.55	  0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192  ==>  I194 - 1 + -1 * I193 > I194 - 1 + -1 * 1  with  I194 - 1 + -1 * I193 >= 0
273.89/269.55	  0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198  ==>  I201 - 1 + -1 * (I199 + 1) >= I201 - 1 + -1 * (I199 + 1)
273.89/269.55	  0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4  ==>  I205 - 1 + -1 * (I204 + 1) >= I205 - 1 + -1 * (I204 + 1)
273.89/269.55	  I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1  ==>  I213 - 1 + -1 * I212 > I213 - 1 + -1 * (I212 + 1)  with  I213 - 1 + -1 * I212 >= 0
273.89/269.55	  I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1  ==>  I231 - 1 + -1 * I230 > I231 - 1 + -1 * (I230 + 1)  with  I231 - 1 + -1 * I230 >= 0
273.89/269.55	  I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1  ==>  I247 - 1 + -1 * I246 > I247 - 1 + -1 * (I246 + 1)  with  I247 - 1 + -1 * I246 >= 0
273.89/269.55	  I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1  ==>  I261 - 1 + -1 * I260 > I261 - 1 + -1 * (I260 + 1)  with  I261 - 1 + -1 * I260 >= 0
273.89/269.55	
273.89/269.55	We remove all the strictly oriented dependency pairs.
273.89/269.55	
273.89/269.55	DP problem for innermost termination.
273.89/269.55	P =
273.89/269.55	  f3#(I139, I140, I141, I142) -> f2#(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f3#(I153, I154, I155, I156) -> f2#(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f3#(I169, I170, I171, I172) -> f2#(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f7#(I186, I187, I188, I189) -> f2#(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f7#(I198, I199, I200, I201) -> f7#(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3#(I203, I204, I205, I206) -> f7#(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	R = 
273.89/269.55	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.55	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.55	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.55	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.55	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.55	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.55	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.55	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.55	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.55	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.55	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.55	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.55	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.55	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.55	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.55	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.55	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.55	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.55	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.55	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.55	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.55	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.55	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.55	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.55	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.55	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.55	
273.89/269.55	The dependency graph for this problem is:
273.89/269.55	  22 -> 
273.89/269.55	  24 -> 
273.89/269.55	  26 -> 
273.89/269.55	  28 -> 
273.89/269.55	  30 -> 28, 30
273.89/269.55	  31 -> 30
273.89/269.55	Where:
273.89/269.55	  22) f3#(I139, I140, I141, I142) -> f2#(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  24) f3#(I153, I154, I155, I156) -> f2#(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  26) f3#(I169, I170, I171, I172) -> f2#(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  28) f7#(I186, I187, I188, I189) -> f2#(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  30) f7#(I198, I199, I200, I201) -> f7#(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  31) f3#(I203, I204, I205, I206) -> f7#(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	
273.89/269.55	We have the following SCCs.
273.89/269.55	  { 30 }
273.89/269.55	
273.89/269.55	DP problem for innermost termination.
273.89/269.55	P =
273.89/269.55	  f7#(I198, I199, I200, I201) -> f7#(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	R = 
273.89/269.55	  init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 
273.89/269.55	  f15(I0, I1, I2, I3) -> f14(I1, I0, I1 - 1, I4) [0 <= I1 - 1 /\ 0 <= I0 - 1 /\ y2 - y1 * y3 <= y1 - 1 /\ 0 <= y2 - y1 * y3]
273.89/269.55	  f6(I5, I6, I7, I8) -> f15(I5, I6, I9, I10) [0 <= I6 - 1 /\ 0 <= I5 - 1]
273.89/269.55	  f15(I11, I12, I13, I14) -> f14(I12, I11, I12 - 1, I15) [0 <= I11 - 1 /\ 0 <= I12 - 1 /\ I16 - I17 * I18 <= I17 - 1 /\ 0 <= I16 - I17 * I18]
273.89/269.55	  f6(I19, I20, I21, I22) -> f15(I19, I20, I23, I24) [0 <= I19 - 1 /\ 0 <= I20 - 1]
273.89/269.55	  f6(I25, I26, I27, I28) -> f10(I26, I29, I30, I31) [0 <= I25 - 1 /\ 0 <= I26 - 1]
273.89/269.55	  f10(I32, I33, I34, I35) -> f10(I32 - 1, I36, I37, I38) [I32 - 1 <= I32 - 1 /\ 0 <= I32 - 1]
273.89/269.55	  f8(I39, I40, I41, I42) -> f8(I39 - 1, I43, I44, I45) [0 <= I39 - 1]
273.89/269.55	  f14(I46, I47, I48, I49) -> f6(I47, I48, I50, I51) [0 <= I46 - 1 /\ 0 <= I47 - 1 /\ I48 <= I46 - 1]
273.89/269.55	  f6(I52, I53, I54, I55) -> f8(I53, I56, I57, I58) [0 <= I52 - 1 /\ 0 <= I53 - 1]
273.89/269.55	  f13(I59, I60, I61, I62) -> f5(I60, I59 - 1, I63, I64) [0 <= I60 - 1 /\ 0 <= I59 - 1 /\ 1 <= I61 - 1 /\ 1 <= 2 * I59 - 1 /\ I59 - 1 <= I59 - 1 /\ I65 - I66 * I67 <= I66 - 1 /\ 0 <= I65 - I66 * I67]
273.89/269.55	  f12(I68, I69, I70, I71) -> f13(I68, I69, I70, I72) [1 <= 2 * I68 - 1 /\ I68 - 1 <= I68 - 1 /\ 1 <= I70 - 1 /\ 0 <= I68 - 1 /\ 0 <= I69 - 1]
273.89/269.55	  f12(I73, I74, I75, I76) -> f10(2 * I73, I77, I78, I79) [1 <= I75 - 1 /\ 1 <= 2 * I73 - 1 /\ 0 <= I73 - 1 /\ 0 <= I74 - 1]
273.89/269.55	  f12(I80, I81, I82, I83) -> f8(I82, I84, I85, I86) [0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 1 <= I82 - 1]
273.89/269.55	  f5(I87, I88, I89, I90) -> f12(I88, I87, 2 * I88, I91) [0 <= I87 - 1 /\ 0 <= I88 - 1]
273.89/269.55	  f5(I92, I93, I94, I95) -> f8(I93, I96, I97, I98) [0 <= I92 - 1 /\ 0 <= I93 - 1]
273.89/269.55	  f11(I99, I100, I101, I102) -> f4(I100, I99 - 1, I103, I104) [0 <= I100 - 1 /\ 0 <= I99 - 1 /\ 1 <= I101 - 1 /\ 0 <= 2 * I99 - 1 /\ I99 - 1 <= I99 - 1 /\ I105 - I106 * I107 <= I106 - 1 /\ 0 <= I105 - I106 * I107]
273.89/269.55	  f9(I108, I109, I110, I111) -> f11(I108, I109, I110, I112) [0 <= 2 * I108 - 1 /\ I108 - 1 <= I108 - 1 /\ 1 <= I110 - 1 /\ 0 <= I108 - 1 /\ 0 <= I109 - 1]
273.89/269.55	  f9(I113, I114, I115, I116) -> f10(2 * I113 + 1, I117, I118, I119) [1 <= I115 - 1 /\ 0 <= 2 * I113 - 1 /\ 0 <= I113 - 1 /\ 0 <= I114 - 1]
273.89/269.55	  f9(I120, I121, I122, I123) -> f8(I122, I124, I125, I126) [0 <= I120 - 1 /\ 1 <= I122 - 1 /\ 0 <= I121 - 1]
273.89/269.55	  f4(I127, I128, I129, I130) -> f9(I128, I127, 2 * I128 + 1, I131) [0 <= I128 - 1 /\ 0 <= 2 * I128 - 1 /\ 0 <= I127 - 1]
273.89/269.55	  f4(I132, I133, I134, I135) -> f8(I133, I136, I137, I138) [0 <= I132 - 1 /\ 0 <= I133 - 1]
273.89/269.55	  f3(I139, I140, I141, I142) -> f2(I143, I140 + 1, I141, I144) [I140 <= I141 - 1 /\ 0 <= I141 - 1 /\ I140 - 2 * I145 = 0 /\ I143 <= I139 /\ 0 <= I139 - 1 /\ 0 <= I143 - 1 /\ I140 - 2 * I145 <= 1 /\ 0 <= I140 - 2 * I145]
273.89/269.55	  f2(I146, I147, I148, I149) -> f3(I146, I147, I148, I150) [I147 <= I148 - 1 /\ 0 <= I148 - 1 /\ I147 - 2 * I151 = 0 /\ I152 <= I146 /\ 0 <= I146 - 1 /\ 0 <= I152 - 1]
273.89/269.55	  f3(I153, I154, I155, I156) -> f2(I157, I154 + 1, I155, I158) [I154 <= I155 - 1 /\ 0 <= I155 - 1 /\ I154 - 2 * I159 = 1 /\ I154 - 3 * I160 = 0 /\ I157 <= I153 /\ 0 <= I153 - 1 /\ 0 <= I157 - 1 /\ 0 <= I154 - 2 * I159 /\ I154 - 2 * I159 <= 1 /\ I154 - 3 * I160 <= 2 /\ 0 <= I154 - 3 * I160]
273.89/269.55	  f2(I161, I162, I163, I164) -> f3(I161, I162, I163, I165) [I162 <= I163 - 1 /\ 0 <= I163 - 1 /\ I162 - 2 * I166 = 1 /\ I162 - 3 * I167 = 0 /\ I168 <= I161 /\ 0 <= I161 - 1 /\ 0 <= I168 - 1]
273.89/269.55	  f3(I169, I170, I171, I172) -> f2(I173, I170 + 1, I171, I174) [0 <= I170 - 3 * I175 - 1 /\ I170 <= I171 - 1 /\ 0 <= I171 - 1 /\ I170 - 2 * I176 = 1 /\ I170 - 5 * I177 = 0 /\ I173 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 0 <= I170 - 2 * I176 /\ I170 - 2 * I176 <= 1 /\ I170 - 3 * I175 <= 2 /\ I170 - 5 * I177 <= 4 /\ 0 <= I170 - 5 * I177]
273.89/269.55	  f2(I178, I179, I180, I181) -> f3(I178, I179, I180, I182) [I179 <= I180 - 1 /\ 0 <= I180 - 1 /\ I179 - 2 * I183 = 1 /\ 0 <= I179 - 3 * I184 - 1 /\ I179 - 5 * I185 = 0 /\ y4 <= I178 /\ 0 <= I178 - 1 /\ 0 <= y4 - 1]
273.89/269.55	  f7(I186, I187, I188, I189) -> f2(I190, I187 + 1, I189, I191) [0 <= I190 - 1 /\ 0 <= I186 - 1 /\ I190 <= I186 /\ 99 <= I188 - 1 /\ -1 <= I189 - 1]
273.89/269.55	  f2(I192, I193, I194, I195) -> f2(I196, 1, I194, I197) [0 = I193 /\ 0 <= I196 - 1 /\ 0 <= I192 - 1 /\ 0 <= I194 - 1 /\ I196 <= I192]
273.89/269.55	  f7(I198, I199, I200, I201) -> f7(I202, I199, I200 + 1, I201) [0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198]
273.89/269.55	  f3(I203, I204, I205, I206) -> f7(I207, I204, 0, I205) [0 <= I204 - 5 * I208 - 1 /\ 0 <= I204 - 3 * I209 - 1 /\ I204 - 2 * I210 = 1 /\ I204 <= I205 - 1 /\ I207 <= I203 /\ 0 <= I203 - 1 /\ 0 <= I207 - 1 /\ 0 <= I204 - 2 * I210 /\ I204 - 2 * I210 <= 1 /\ I204 - 3 * I209 <= 2 /\ I204 - 5 * I208 <= 4]
273.89/269.55	  f2(I211, I212, I213, I214) -> f3(I211, I212, I213, I215) [I212 - 2 * I216 = 1 /\ I212 <= I213 - 1 /\ 0 <= I212 - 5 * I217 - 1 /\ 0 <= I212 - 3 * I218 - 1 /\ I219 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I219 - 1]
273.89/269.55	  f3(I220, I221, I222, I223) -> f6(I222, I221, I224, I225) [0 <= I221 - 3 * I226 - 1 /\ I221 <= I222 - 1 /\ 0 <= I222 - 1 /\ I221 - 2 * I227 = 1 /\ I221 - 5 * I228 = 0 /\ 0 <= I220 - 1 /\ 0 <= I221 - 2 * I227 /\ I221 - 2 * I227 <= 1 /\ I221 - 3 * I226 <= 2 /\ I221 - 5 * I228 <= 4 /\ 0 <= I221 - 5 * I228]
273.89/269.55	  f2(I229, I230, I231, I232) -> f3(I229, I230, I231, I233) [I230 <= I231 - 1 /\ 0 <= I231 - 1 /\ I230 - 2 * I234 = 1 /\ 0 <= I230 - 3 * I235 - 1 /\ I230 - 5 * I236 = 0 /\ 0 <= I229 - 1]
273.89/269.55	  f3(I237, I238, I239, I240) -> f5(I239, I238, I241, I242) [I238 <= I239 - 1 /\ 0 <= I239 - 1 /\ I238 - 2 * I243 = 1 /\ I238 - 3 * I244 = 0 /\ 0 <= I237 - 1 /\ 0 <= I238 - 2 * I243 /\ I238 - 2 * I243 <= 1 /\ I238 - 3 * I244 <= 2 /\ 0 <= I238 - 3 * I244]
273.89/269.55	  f2(I245, I246, I247, I248) -> f3(I245, I246, I247, I249) [I246 <= I247 - 1 /\ 0 <= I247 - 1 /\ I246 - 2 * I250 = 1 /\ I246 - 3 * I251 = 0 /\ 0 <= I245 - 1]
273.89/269.55	  f3(I252, I253, I254, I255) -> f4(I254, I253, I256, I257) [I253 <= I254 - 1 /\ 0 <= I254 - 1 /\ I253 - 2 * I258 = 0 /\ 0 <= I252 - 1 /\ I253 - 2 * I258 <= 1 /\ 0 <= I253 - 2 * I258]
273.89/269.55	  f2(I259, I260, I261, I262) -> f3(I259, I260, I261, I263) [I260 <= I261 - 1 /\ 0 <= I261 - 1 /\ I260 - 2 * I264 = 0 /\ 0 <= I259 - 1]
273.89/269.55	  f1(I265, I266, I267, I268) -> f2(I269, 0, I266, I270) [0 <= I269 - 1 /\ 0 <= I265 - 1 /\ -1 <= I266 - 1 /\ I269 <= I265]
273.89/269.55	
273.89/269.55	We use the reverse value criterion with the projection function NU:
273.89/269.55	  NU[f7#(z1,z2,z3,z4)] = 99 + -1 * z3
273.89/269.55	
273.89/269.55	This gives the following inequalities:
273.89/269.55	  0 <= I202 - 1 /\ 0 <= I198 - 1 /\ I200 <= 99 /\ I202 <= I198  ==>  99 + -1 * I200 > 99 + -1 * (I200 + 1)  with  99 + -1 * I200 >= 0
273.89/269.55	
273.89/269.55	All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed.
273.89/272.52	EOF