30.10/29.70 YES 30.10/29.70 30.10/29.70 DP problem for innermost termination. 30.10/29.70 P = 30.10/29.70 init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 30.10/29.70 f13#(I0, I1, I2, I3, I4) -> f4#(I5, I6, I7, I8, I9) [I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0] 30.10/29.70 f8#(I10, I11, I12, I13, I14) -> f13#(I15, I16, I12, I17, I18) [I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11] 30.10/29.70 f8#(I19, I20, I21, I22, I23) -> f13#(I24, I25, I21, I26, I27) [I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20] 30.10/29.70 f12#(I28, I29, I30, I31, I32) -> f4#(I33, I34, I35, I36, I37) [I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28] 30.10/29.70 f8#(I38, I39, I40, I41, I42) -> f4#(I43, I44, I45, I46, I47) [I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1] 30.10/29.70 f8#(I48, I49, I50, I51, I52) -> f12#(I53, I54, I50, I55, I56) [I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49] 30.10/29.70 f8#(I57, I58, I59, I60, I61) -> f12#(I62, I63, I59, I64, I65) [I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58] 30.10/29.70 f8#(I66, I67, I68, I69, I70) -> f8#(I66, I71, I68, I72, I73) [I71 + 1 <= I67 /\ I66 <= I74 - 1 /\ 0 <= I67 - 1 /\ -1 <= I71 - 1] 30.10/29.70 f8#(I75, I76, I77, I78, I79) -> f8#(I75, I80, I77, I81, I82) [I80 + 1 <= I76 /\ I83 <= I75 /\ 0 <= I76 - 1 /\ -1 <= I80 - 1] 30.10/29.70 f11#(I84, I85, I86, I87, I88) -> f4#(I89, I90, I91, I92, I93) [I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84] 30.10/29.70 f7#(I94, I95, I96, I97, I98) -> f11#(I99, I100, I96, I101, I102) [I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95] 30.10/29.70 f7#(I103, I104, I105, I106, I107) -> f11#(I108, I109, I105, I110, I111) [I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104] 30.10/29.70 f7#(I112, I113, I114, I115, I116) -> f4#(I117, I118, I119, I120, I121) [I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1] 30.10/29.70 f7#(I123, I124, I125, I126, I127) -> f7#(I123, I128, I125, I129, I130) [I128 + 1 <= I124 /\ I131 <= I123 /\ 0 <= I124 - 1 /\ -1 <= I128 - 1] 30.10/29.70 f7#(I132, I133, I134, I135, I136) -> f7#(I132, I137, I134, I138, I139) [I137 + 1 <= I133 /\ I132 <= I140 - 1 /\ 0 <= I133 - 1 /\ -1 <= I137 - 1] 30.10/29.70 f9#(I161, I162, I163, I164, I165) -> f8#(I164, I166, I163, I167, I168) [I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161] 30.10/29.70 f4#(I169, I170, I171, I172, I173) -> f9#(I174, I175, I176, I177, I178) [I178 + 4 <= I169 /\ I177 + 2 <= I169 /\ 2 <= I175 - 1 /\ 4 <= I174 - 1 /\ 4 <= I169 - 1 /\ I175 + 2 <= I169 /\ I174 <= I169] 30.10/29.70 f4#(I179, I180, I181, I182, I183) -> f9#(I184, I185, I186, I187, I188) [I188 + 4 <= I179 /\ I187 + 2 <= I179 /\ 1 <= I185 - 1 /\ 3 <= I184 - 1 /\ 3 <= I179 - 1 /\ I185 + 2 <= I179 /\ I184 <= I179] 30.10/29.70 f4#(I189, I190, I191, I192, I193) -> f8#(I194, I195, I196, I197, I198) [I194 + 2 <= I189 /\ -1 <= I195 - 1 /\ 1 <= I189 - 1 /\ I195 + 2 <= I189] 30.10/29.70 f4#(I199, I200, I201, I202, I203) -> f7#(I204, I205, I206, I207, I208) [I204 + 2 <= I199 /\ -1 <= I205 - 1 /\ 0 <= I199 - 1 /\ I205 + 1 <= I199] 30.10/29.70 f6#(I209, I210, I211, I212, I213) -> f2#(I210, I211, I212, I214, I215) [I210 <= I209 - 1 /\ I212 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I212 - 1 /\ 0 <= I209 - 1] 30.10/29.70 f2#(I216, I217, I218, I219, I220) -> f6#(I216, I216 - 1, I217, I218 + 1, I221) [0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1] 30.10/29.70 f2#(I223, I224, I225, I226, I227) -> f6#(I223, I223 - 1, I224, I225 + 1, I228) [I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1] 30.10/29.70 f2#(I229, I230, I231, I232, I233) -> f2#(I229 - 1, I230, I231, I234, I235) [I230 <= I231 /\ I229 - 1 <= I229 - 1 /\ -1 <= I230 - 1 /\ 0 <= I229 - 1] 30.10/29.70 f5#(I236, I237, I238, I239, I240) -> f4#(I241, I242, I243, I244, I245) [I241 <= I237 /\ 0 <= I246 - 1 /\ 0 <= I236 - 1 /\ 0 <= I237 - 1 /\ 0 <= I241 - 1 /\ I238 + 2 <= I237] 30.10/29.70 f3#(I247, I248, I249, I250, I251) -> f5#(I252, I253, 0, I254, I255) [I252 <= I247 /\ 0 <= I256 - 1 /\ I253 - 1 <= I247 /\ 0 <= I247 - 1 /\ 0 <= I252 - 1 /\ 1 <= I253 - 1] 30.10/29.70 f3#(I257, I258, I259, I260, I261) -> f5#(I262, I263, I264, I265, I266) [I262 <= I257 /\ 0 <= I267 - 1 /\ 0 <= I257 - 1 /\ 0 <= I262 - 1 /\ 1 <= I263 - 1] 30.10/29.70 f3#(I268, I269, I270, I271, I272) -> f5#(I273, I274, I275, I276, I277) [I273 <= I268 /\ 0 <= I278 - 1 /\ 0 <= I268 - 1 /\ 0 <= I273 - 1 /\ 2 <= I274 - 1] 30.10/29.70 f3#(I279, I280, I281, I282, I283) -> f5#(I284, I285, 0, I286, I287) [I284 <= I279 /\ 0 <= I288 - 1 /\ 0 <= I279 - 1 /\ 0 <= I284 - 1 /\ 2 <= I285 - 1] 30.10/29.70 f1#(I289, I290, I291, I292, I293) -> f4#(I294, I295, I296, I297, I298) [0 = I290 /\ 1 <= I294 - 1 /\ 0 <= I289 - 1 /\ I294 - 1 <= I289] 30.10/29.70 f3#(I299, I300, I301, I302, I303) -> f4#(I304, I305, I306, I307, I308) [I304 + 1 <= I299 /\ 0 <= I309 - 1 /\ 0 <= I299 - 1 /\ -1 <= I304 - 1 /\ 0 = I300] 30.10/29.70 f1#(I310, I311, I312, I313, I314) -> f4#(I315, I316, I317, I318, I319) [0 = I311 /\ -1 <= I315 - 1 /\ 0 <= I310 - 1 /\ I315 + 1 <= I310] 30.10/29.70 f3#(I320, I321, I322, I323, I324) -> f2#(I321, I325, 1, I326, I327) [0 <= I325 - 1 /\ 0 <= I320 - 1] 30.10/29.70 f1#(I328, I329, I330, I331, I332) -> f3#(I333, I334, I335, I336, I337) [0 <= I333 - 1 /\ 0 <= I328 - 1 /\ I333 <= I328 /\ 0 <= I329 - 1 /\ -1 <= I334 - 1] 30.10/29.70 f1#(I338, I339, I340, I341, I342) -> f3#(I343, 0, I344, I345, I346) [0 <= I343 - 1 /\ 0 <= I338 - 1 /\ 0 <= I339 - 1 /\ I343 <= I338] 30.10/29.70 f1#(I347, I348, I349, I350, I351) -> f2#(0, 0, 0, I352, I353) [0 = I348 /\ 0 <= I347 - 1] 30.10/29.70 R = 30.10/29.70 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 30.10/29.70 f13(I0, I1, I2, I3, I4) -> f4(I5, I6, I7, I8, I9) [I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0] 30.10/29.70 f8(I10, I11, I12, I13, I14) -> f13(I15, I16, I12, I17, I18) [I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11] 30.10/29.70 f8(I19, I20, I21, I22, I23) -> f13(I24, I25, I21, I26, I27) [I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20] 30.10/29.70 f12(I28, I29, I30, I31, I32) -> f4(I33, I34, I35, I36, I37) [I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28] 30.10/29.70 f8(I38, I39, I40, I41, I42) -> f4(I43, I44, I45, I46, I47) [I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1] 30.10/29.70 f8(I48, I49, I50, I51, I52) -> f12(I53, I54, I50, I55, I56) [I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49] 30.10/29.70 f8(I57, I58, I59, I60, I61) -> f12(I62, I63, I59, I64, I65) [I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58] 30.10/29.70 f8(I66, I67, I68, I69, I70) -> f8(I66, I71, I68, I72, I73) [I71 + 1 <= I67 /\ I66 <= I74 - 1 /\ 0 <= I67 - 1 /\ -1 <= I71 - 1] 30.10/29.70 f8(I75, I76, I77, I78, I79) -> f8(I75, I80, I77, I81, I82) [I80 + 1 <= I76 /\ I83 <= I75 /\ 0 <= I76 - 1 /\ -1 <= I80 - 1] 30.10/29.70 f11(I84, I85, I86, I87, I88) -> f4(I89, I90, I91, I92, I93) [I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84] 30.10/29.70 f7(I94, I95, I96, I97, I98) -> f11(I99, I100, I96, I101, I102) [I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95] 30.10/29.70 f7(I103, I104, I105, I106, I107) -> f11(I108, I109, I105, I110, I111) [I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104] 30.10/29.70 f7(I112, I113, I114, I115, I116) -> f4(I117, I118, I119, I120, I121) [I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1] 30.10/29.70 f7(I123, I124, I125, I126, I127) -> f7(I123, I128, I125, I129, I130) [I128 + 1 <= I124 /\ I131 <= I123 /\ 0 <= I124 - 1 /\ -1 <= I128 - 1] 30.10/29.70 f7(I132, I133, I134, I135, I136) -> f7(I132, I137, I134, I138, I139) [I137 + 1 <= I133 /\ I132 <= I140 - 1 /\ 0 <= I133 - 1 /\ -1 <= I137 - 1] 30.10/29.70 f9(I141, I142, I143, I144, I145) -> f10(I146, I147, I148, I149, I150) [I145 + 2 <= I142 /\ I144 + 2 <= I141 /\ I145 + 4 <= I141 /\ 3 <= I146 - 1 /\ 1 <= I142 - 1 /\ 3 <= I141 - 1 /\ I146 <= I141] 30.10/29.70 f9(I151, I152, I153, I154, I155) -> f10(I156, I157, I158, I159, I160) [I155 + 2 <= I152 /\ I154 + 2 <= I151 /\ I155 + 4 <= I151 /\ 4 <= I156 - 1 /\ 2 <= I152 - 1 /\ 4 <= I151 - 1 /\ I156 <= I151] 30.10/29.70 f9(I161, I162, I163, I164, I165) -> f8(I164, I166, I163, I167, I168) [I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161] 30.10/29.70 f4(I169, I170, I171, I172, I173) -> f9(I174, I175, I176, I177, I178) [I178 + 4 <= I169 /\ I177 + 2 <= I169 /\ 2 <= I175 - 1 /\ 4 <= I174 - 1 /\ 4 <= I169 - 1 /\ I175 + 2 <= I169 /\ I174 <= I169] 30.10/29.70 f4(I179, I180, I181, I182, I183) -> f9(I184, I185, I186, I187, I188) [I188 + 4 <= I179 /\ I187 + 2 <= I179 /\ 1 <= I185 - 1 /\ 3 <= I184 - 1 /\ 3 <= I179 - 1 /\ I185 + 2 <= I179 /\ I184 <= I179] 30.10/29.70 f4(I189, I190, I191, I192, I193) -> f8(I194, I195, I196, I197, I198) [I194 + 2 <= I189 /\ -1 <= I195 - 1 /\ 1 <= I189 - 1 /\ I195 + 2 <= I189] 30.10/29.70 f4(I199, I200, I201, I202, I203) -> f7(I204, I205, I206, I207, I208) [I204 + 2 <= I199 /\ -1 <= I205 - 1 /\ 0 <= I199 - 1 /\ I205 + 1 <= I199] 30.10/29.70 f6(I209, I210, I211, I212, I213) -> f2(I210, I211, I212, I214, I215) [I210 <= I209 - 1 /\ I212 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I212 - 1 /\ 0 <= I209 - 1] 30.10/29.70 f2(I216, I217, I218, I219, I220) -> f6(I216, I216 - 1, I217, I218 + 1, I221) [0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1] 30.10/29.70 f2(I223, I224, I225, I226, I227) -> f6(I223, I223 - 1, I224, I225 + 1, I228) [I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1] 30.10/29.70 f2(I229, I230, I231, I232, I233) -> f2(I229 - 1, I230, I231, I234, I235) [I230 <= I231 /\ I229 - 1 <= I229 - 1 /\ -1 <= I230 - 1 /\ 0 <= I229 - 1] 30.10/29.70 f5(I236, I237, I238, I239, I240) -> f4(I241, I242, I243, I244, I245) [I241 <= I237 /\ 0 <= I246 - 1 /\ 0 <= I236 - 1 /\ 0 <= I237 - 1 /\ 0 <= I241 - 1 /\ I238 + 2 <= I237] 30.10/29.70 f3(I247, I248, I249, I250, I251) -> f5(I252, I253, 0, I254, I255) [I252 <= I247 /\ 0 <= I256 - 1 /\ I253 - 1 <= I247 /\ 0 <= I247 - 1 /\ 0 <= I252 - 1 /\ 1 <= I253 - 1] 30.10/29.70 f3(I257, I258, I259, I260, I261) -> f5(I262, I263, I264, I265, I266) [I262 <= I257 /\ 0 <= I267 - 1 /\ 0 <= I257 - 1 /\ 0 <= I262 - 1 /\ 1 <= I263 - 1] 30.10/29.70 f3(I268, I269, I270, I271, I272) -> f5(I273, I274, I275, I276, I277) [I273 <= I268 /\ 0 <= I278 - 1 /\ 0 <= I268 - 1 /\ 0 <= I273 - 1 /\ 2 <= I274 - 1] 30.10/29.70 f3(I279, I280, I281, I282, I283) -> f5(I284, I285, 0, I286, I287) [I284 <= I279 /\ 0 <= I288 - 1 /\ 0 <= I279 - 1 /\ 0 <= I284 - 1 /\ 2 <= I285 - 1] 30.10/29.70 f1(I289, I290, I291, I292, I293) -> f4(I294, I295, I296, I297, I298) [0 = I290 /\ 1 <= I294 - 1 /\ 0 <= I289 - 1 /\ I294 - 1 <= I289] 30.10/29.70 f3(I299, I300, I301, I302, I303) -> f4(I304, I305, I306, I307, I308) [I304 + 1 <= I299 /\ 0 <= I309 - 1 /\ 0 <= I299 - 1 /\ -1 <= I304 - 1 /\ 0 = I300] 30.10/29.70 f1(I310, I311, I312, I313, I314) -> f4(I315, I316, I317, I318, I319) [0 = I311 /\ -1 <= I315 - 1 /\ 0 <= I310 - 1 /\ I315 + 1 <= I310] 30.10/29.70 f3(I320, I321, I322, I323, I324) -> f2(I321, I325, 1, I326, I327) [0 <= I325 - 1 /\ 0 <= I320 - 1] 30.10/29.70 f1(I328, I329, I330, I331, I332) -> f3(I333, I334, I335, I336, I337) [0 <= I333 - 1 /\ 0 <= I328 - 1 /\ I333 <= I328 /\ 0 <= I329 - 1 /\ -1 <= I334 - 1] 30.10/29.70 f1(I338, I339, I340, I341, I342) -> f3(I343, 0, I344, I345, I346) [0 <= I343 - 1 /\ 0 <= I338 - 1 /\ 0 <= I339 - 1 /\ I343 <= I338] 30.10/29.70 f1(I347, I348, I349, I350, I351) -> f2(0, 0, 0, I352, I353) [0 = I348 /\ 0 <= I347 - 1] 30.10/29.70 30.10/29.70 The dependency graph for this problem is: 30.10/29.70 0 -> 30, 32, 34, 35, 36 30.10/29.70 1 -> 17, 18, 19, 20 30.10/29.70 2 -> 1 30.10/29.70 3 -> 1 30.10/29.70 4 -> 17, 18, 19, 20 30.10/29.70 5 -> 17, 18, 19, 20 30.10/29.70 6 -> 4 30.10/29.70 7 -> 4 30.10/29.70 8 -> 2, 3, 5, 6, 7, 8, 9 30.10/29.70 9 -> 2, 3, 5, 6, 7, 8, 9 30.10/29.70 10 -> 17, 18, 19, 20 30.10/29.70 11 -> 10 30.10/29.70 12 -> 10 30.10/29.70 13 -> 17, 18, 19, 20 30.10/29.70 14 -> 11, 12, 13, 14, 15 30.10/29.70 15 -> 11, 12, 13, 14, 15 30.10/29.70 16 -> 2, 3, 5, 6, 7, 8, 9 30.10/29.70 17 -> 16 30.10/29.70 18 -> 16 30.10/29.70 19 -> 2, 3, 5, 6, 7, 8, 9 30.10/29.70 20 -> 11, 12, 13, 14, 15 30.10/29.70 21 -> 22, 23, 24 30.10/29.70 22 -> 21 30.10/29.70 23 -> 21 30.10/29.70 24 -> 24 30.10/29.70 25 -> 17, 18, 19, 20 30.10/29.70 26 -> 25 30.10/29.70 27 -> 25 30.10/29.70 28 -> 25 30.10/29.70 29 -> 25 30.10/29.70 30 -> 17, 18, 19, 20 30.10/29.70 31 -> 17, 18, 19, 20 30.10/29.70 32 -> 17, 18, 19, 20 30.10/29.70 33 -> 22, 23, 24 30.10/29.70 34 -> 26, 27, 28, 29, 31, 33 30.10/29.70 35 -> 26, 27, 28, 29, 31, 33 30.10/29.70 36 -> 30.10/29.70 Where: 30.10/29.70 0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 30.10/29.70 1) f13#(I0, I1, I2, I3, I4) -> f4#(I5, I6, I7, I8, I9) [I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0] 30.10/29.70 2) f8#(I10, I11, I12, I13, I14) -> f13#(I15, I16, I12, I17, I18) [I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11] 30.10/29.70 3) f8#(I19, I20, I21, I22, I23) -> f13#(I24, I25, I21, I26, I27) [I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20] 30.10/29.70 4) f12#(I28, I29, I30, I31, I32) -> f4#(I33, I34, I35, I36, I37) [I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28] 30.10/29.70 5) f8#(I38, I39, I40, I41, I42) -> f4#(I43, I44, I45, I46, I47) [I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1] 30.10/29.70 6) f8#(I48, I49, I50, I51, I52) -> f12#(I53, I54, I50, I55, I56) [I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49] 30.10/29.70 7) f8#(I57, I58, I59, I60, I61) -> f12#(I62, I63, I59, I64, I65) [I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58] 30.10/29.70 8) f8#(I66, I67, I68, I69, I70) -> f8#(I66, I71, I68, I72, I73) [I71 + 1 <= I67 /\ I66 <= I74 - 1 /\ 0 <= I67 - 1 /\ -1 <= I71 - 1] 30.10/29.70 9) f8#(I75, I76, I77, I78, I79) -> f8#(I75, I80, I77, I81, I82) [I80 + 1 <= I76 /\ I83 <= I75 /\ 0 <= I76 - 1 /\ -1 <= I80 - 1] 30.10/29.70 10) f11#(I84, I85, I86, I87, I88) -> f4#(I89, I90, I91, I92, I93) [I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84] 30.10/29.70 11) f7#(I94, I95, I96, I97, I98) -> f11#(I99, I100, I96, I101, I102) [I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95] 30.10/29.70 12) f7#(I103, I104, I105, I106, I107) -> f11#(I108, I109, I105, I110, I111) [I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104] 30.10/29.70 13) f7#(I112, I113, I114, I115, I116) -> f4#(I117, I118, I119, I120, I121) [I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1] 30.10/29.70 14) f7#(I123, I124, I125, I126, I127) -> f7#(I123, I128, I125, I129, I130) [I128 + 1 <= I124 /\ I131 <= I123 /\ 0 <= I124 - 1 /\ -1 <= I128 - 1] 30.10/29.70 15) f7#(I132, I133, I134, I135, I136) -> f7#(I132, I137, I134, I138, I139) [I137 + 1 <= I133 /\ I132 <= I140 - 1 /\ 0 <= I133 - 1 /\ -1 <= I137 - 1] 30.10/29.70 16) f9#(I161, I162, I163, I164, I165) -> f8#(I164, I166, I163, I167, I168) [I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161] 30.10/29.70 17) f4#(I169, I170, I171, I172, I173) -> f9#(I174, I175, I176, I177, I178) [I178 + 4 <= I169 /\ I177 + 2 <= I169 /\ 2 <= I175 - 1 /\ 4 <= I174 - 1 /\ 4 <= I169 - 1 /\ I175 + 2 <= I169 /\ I174 <= I169] 30.10/29.70 18) f4#(I179, I180, I181, I182, I183) -> f9#(I184, I185, I186, I187, I188) [I188 + 4 <= I179 /\ I187 + 2 <= I179 /\ 1 <= I185 - 1 /\ 3 <= I184 - 1 /\ 3 <= I179 - 1 /\ I185 + 2 <= I179 /\ I184 <= I179] 30.10/29.70 19) f4#(I189, I190, I191, I192, I193) -> f8#(I194, I195, I196, I197, I198) [I194 + 2 <= I189 /\ -1 <= I195 - 1 /\ 1 <= I189 - 1 /\ I195 + 2 <= I189] 30.10/29.70 20) f4#(I199, I200, I201, I202, I203) -> f7#(I204, I205, I206, I207, I208) [I204 + 2 <= I199 /\ -1 <= I205 - 1 /\ 0 <= I199 - 1 /\ I205 + 1 <= I199] 30.10/29.70 21) f6#(I209, I210, I211, I212, I213) -> f2#(I210, I211, I212, I214, I215) [I210 <= I209 - 1 /\ I212 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I212 - 1 /\ 0 <= I209 - 1] 30.10/29.70 22) f2#(I216, I217, I218, I219, I220) -> f6#(I216, I216 - 1, I217, I218 + 1, I221) [0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1] 30.10/29.70 23) f2#(I223, I224, I225, I226, I227) -> f6#(I223, I223 - 1, I224, I225 + 1, I228) [I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1] 30.10/29.70 24) f2#(I229, I230, I231, I232, I233) -> f2#(I229 - 1, I230, I231, I234, I235) [I230 <= I231 /\ I229 - 1 <= I229 - 1 /\ -1 <= I230 - 1 /\ 0 <= I229 - 1] 30.10/29.70 25) f5#(I236, I237, I238, I239, I240) -> f4#(I241, I242, I243, I244, I245) [I241 <= I237 /\ 0 <= I246 - 1 /\ 0 <= I236 - 1 /\ 0 <= I237 - 1 /\ 0 <= I241 - 1 /\ I238 + 2 <= I237] 30.10/29.70 26) f3#(I247, I248, I249, I250, I251) -> f5#(I252, I253, 0, I254, I255) [I252 <= I247 /\ 0 <= I256 - 1 /\ I253 - 1 <= I247 /\ 0 <= I247 - 1 /\ 0 <= I252 - 1 /\ 1 <= I253 - 1] 30.10/29.70 27) f3#(I257, I258, I259, I260, I261) -> f5#(I262, I263, I264, I265, I266) [I262 <= I257 /\ 0 <= I267 - 1 /\ 0 <= I257 - 1 /\ 0 <= I262 - 1 /\ 1 <= I263 - 1] 30.10/29.70 28) f3#(I268, I269, I270, I271, I272) -> f5#(I273, I274, I275, I276, I277) [I273 <= I268 /\ 0 <= I278 - 1 /\ 0 <= I268 - 1 /\ 0 <= I273 - 1 /\ 2 <= I274 - 1] 30.10/29.70 29) f3#(I279, I280, I281, I282, I283) -> f5#(I284, I285, 0, I286, I287) [I284 <= I279 /\ 0 <= I288 - 1 /\ 0 <= I279 - 1 /\ 0 <= I284 - 1 /\ 2 <= I285 - 1] 30.10/29.70 30) f1#(I289, I290, I291, I292, I293) -> f4#(I294, I295, I296, I297, I298) [0 = I290 /\ 1 <= I294 - 1 /\ 0 <= I289 - 1 /\ I294 - 1 <= I289] 30.10/29.70 31) f3#(I299, I300, I301, I302, I303) -> f4#(I304, I305, I306, I307, I308) [I304 + 1 <= I299 /\ 0 <= I309 - 1 /\ 0 <= I299 - 1 /\ -1 <= I304 - 1 /\ 0 = I300] 30.10/29.70 32) f1#(I310, I311, I312, I313, I314) -> f4#(I315, I316, I317, I318, I319) [0 = I311 /\ -1 <= I315 - 1 /\ 0 <= I310 - 1 /\ I315 + 1 <= I310] 30.10/29.70 33) f3#(I320, I321, I322, I323, I324) -> f2#(I321, I325, 1, I326, I327) [0 <= I325 - 1 /\ 0 <= I320 - 1] 30.10/29.70 34) f1#(I328, I329, I330, I331, I332) -> f3#(I333, I334, I335, I336, I337) [0 <= I333 - 1 /\ 0 <= I328 - 1 /\ I333 <= I328 /\ 0 <= I329 - 1 /\ -1 <= I334 - 1] 30.10/29.70 35) f1#(I338, I339, I340, I341, I342) -> f3#(I343, 0, I344, I345, I346) [0 <= I343 - 1 /\ 0 <= I338 - 1 /\ 0 <= I339 - 1 /\ I343 <= I338] 30.10/29.70 36) f1#(I347, I348, I349, I350, I351) -> f2#(0, 0, 0, I352, I353) [0 = I348 /\ 0 <= I347 - 1] 30.10/29.70 30.10/29.70 We have the following SCCs. 30.10/29.70 { 21, 22, 23 } 30.10/29.70 { 24 } 30.10/29.70 { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 } 30.10/29.70 30.10/29.70 DP problem for innermost termination. 30.10/29.70 P = 30.10/29.70 f13#(I0, I1, I2, I3, I4) -> f4#(I5, I6, I7, I8, I9) [I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0] 30.10/29.70 f8#(I10, I11, I12, I13, I14) -> f13#(I15, I16, I12, I17, I18) [I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11] 30.10/29.70 f8#(I19, I20, I21, I22, I23) -> f13#(I24, I25, I21, I26, I27) [I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20] 30.10/29.70 f12#(I28, I29, I30, I31, I32) -> f4#(I33, I34, I35, I36, I37) [I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28] 30.10/29.70 f8#(I38, I39, I40, I41, I42) -> f4#(I43, I44, I45, I46, I47) [I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1] 30.10/29.70 f8#(I48, I49, I50, I51, I52) -> f12#(I53, I54, I50, I55, I56) [I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49] 30.10/29.70 f8#(I57, I58, I59, I60, I61) -> f12#(I62, I63, I59, I64, I65) [I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58] 30.10/29.70 f8#(I66, I67, I68, I69, I70) -> f8#(I66, I71, I68, I72, I73) [I71 + 1 <= I67 /\ I66 <= I74 - 1 /\ 0 <= I67 - 1 /\ -1 <= I71 - 1] 30.10/29.70 f8#(I75, I76, I77, I78, I79) -> f8#(I75, I80, I77, I81, I82) [I80 + 1 <= I76 /\ I83 <= I75 /\ 0 <= I76 - 1 /\ -1 <= I80 - 1] 30.10/29.70 f11#(I84, I85, I86, I87, I88) -> f4#(I89, I90, I91, I92, I93) [I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84] 30.10/29.70 f7#(I94, I95, I96, I97, I98) -> f11#(I99, I100, I96, I101, I102) [I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95] 30.10/29.70 f7#(I103, I104, I105, I106, I107) -> f11#(I108, I109, I105, I110, I111) [I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104] 30.10/29.70 f7#(I112, I113, I114, I115, I116) -> f4#(I117, I118, I119, I120, I121) [I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1] 30.10/29.70 f7#(I123, I124, I125, I126, I127) -> f7#(I123, I128, I125, I129, I130) [I128 + 1 <= I124 /\ I131 <= I123 /\ 0 <= I124 - 1 /\ -1 <= I128 - 1] 30.10/29.70 f7#(I132, I133, I134, I135, I136) -> f7#(I132, I137, I134, I138, I139) [I137 + 1 <= I133 /\ I132 <= I140 - 1 /\ 0 <= I133 - 1 /\ -1 <= I137 - 1] 30.10/29.70 f9#(I161, I162, I163, I164, I165) -> f8#(I164, I166, I163, I167, I168) [I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161] 30.10/29.70 f4#(I169, I170, I171, I172, I173) -> f9#(I174, I175, I176, I177, I178) [I178 + 4 <= I169 /\ I177 + 2 <= I169 /\ 2 <= I175 - 1 /\ 4 <= I174 - 1 /\ 4 <= I169 - 1 /\ I175 + 2 <= I169 /\ I174 <= I169] 30.10/29.70 f4#(I179, I180, I181, I182, I183) -> f9#(I184, I185, I186, I187, I188) [I188 + 4 <= I179 /\ I187 + 2 <= I179 /\ 1 <= I185 - 1 /\ 3 <= I184 - 1 /\ 3 <= I179 - 1 /\ I185 + 2 <= I179 /\ I184 <= I179] 30.10/29.70 f4#(I189, I190, I191, I192, I193) -> f8#(I194, I195, I196, I197, I198) [I194 + 2 <= I189 /\ -1 <= I195 - 1 /\ 1 <= I189 - 1 /\ I195 + 2 <= I189] 30.10/29.70 f4#(I199, I200, I201, I202, I203) -> f7#(I204, I205, I206, I207, I208) [I204 + 2 <= I199 /\ -1 <= I205 - 1 /\ 0 <= I199 - 1 /\ I205 + 1 <= I199] 30.10/29.70 R = 30.10/29.70 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 30.10/29.70 f13(I0, I1, I2, I3, I4) -> f4(I5, I6, I7, I8, I9) [I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0] 30.10/29.70 f8(I10, I11, I12, I13, I14) -> f13(I15, I16, I12, I17, I18) [I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11] 30.10/29.70 f8(I19, I20, I21, I22, I23) -> f13(I24, I25, I21, I26, I27) [I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20] 30.10/29.70 f12(I28, I29, I30, I31, I32) -> f4(I33, I34, I35, I36, I37) [I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28] 30.10/29.70 f8(I38, I39, I40, I41, I42) -> f4(I43, I44, I45, I46, I47) [I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1] 30.10/29.70 f8(I48, I49, I50, I51, I52) -> f12(I53, I54, I50, I55, I56) [I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49] 30.10/29.70 f8(I57, I58, I59, I60, I61) -> f12(I62, I63, I59, I64, I65) [I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58] 30.10/29.70 f8(I66, I67, I68, I69, I70) -> f8(I66, I71, I68, I72, I73) [I71 + 1 <= I67 /\ I66 <= I74 - 1 /\ 0 <= I67 - 1 /\ -1 <= I71 - 1] 30.10/29.70 f8(I75, I76, I77, I78, I79) -> f8(I75, I80, I77, I81, I82) [I80 + 1 <= I76 /\ I83 <= I75 /\ 0 <= I76 - 1 /\ -1 <= I80 - 1] 30.10/29.70 f11(I84, I85, I86, I87, I88) -> f4(I89, I90, I91, I92, I93) [I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84] 30.10/29.70 f7(I94, I95, I96, I97, I98) -> f11(I99, I100, I96, I101, I102) [I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95] 30.10/29.70 f7(I103, I104, I105, I106, I107) -> f11(I108, I109, I105, I110, I111) [I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104] 30.10/29.70 f7(I112, I113, I114, I115, I116) -> f4(I117, I118, I119, I120, I121) [I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1] 30.10/29.70 f7(I123, I124, I125, I126, I127) -> f7(I123, I128, I125, I129, I130) [I128 + 1 <= I124 /\ I131 <= I123 /\ 0 <= I124 - 1 /\ -1 <= I128 - 1] 30.10/29.70 f7(I132, I133, I134, I135, I136) -> f7(I132, I137, I134, I138, I139) [I137 + 1 <= I133 /\ I132 <= I140 - 1 /\ 0 <= I133 - 1 /\ -1 <= I137 - 1] 30.10/29.70 f9(I141, I142, I143, I144, I145) -> f10(I146, I147, I148, I149, I150) [I145 + 2 <= I142 /\ I144 + 2 <= I141 /\ I145 + 4 <= I141 /\ 3 <= I146 - 1 /\ 1 <= I142 - 1 /\ 3 <= I141 - 1 /\ I146 <= I141] 30.10/29.70 f9(I151, I152, I153, I154, I155) -> f10(I156, I157, I158, I159, I160) [I155 + 2 <= I152 /\ I154 + 2 <= I151 /\ I155 + 4 <= I151 /\ 4 <= I156 - 1 /\ 2 <= I152 - 1 /\ 4 <= I151 - 1 /\ I156 <= I151] 30.10/29.70 f9(I161, I162, I163, I164, I165) -> f8(I164, I166, I163, I167, I168) [I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161] 30.10/29.70 f4(I169, I170, I171, I172, I173) -> f9(I174, I175, I176, I177, I178) [I178 + 4 <= I169 /\ I177 + 2 <= I169 /\ 2 <= I175 - 1 /\ 4 <= I174 - 1 /\ 4 <= I169 - 1 /\ I175 + 2 <= I169 /\ I174 <= I169] 30.10/29.70 f4(I179, I180, I181, I182, I183) -> f9(I184, I185, I186, I187, I188) [I188 + 4 <= I179 /\ I187 + 2 <= I179 /\ 1 <= I185 - 1 /\ 3 <= I184 - 1 /\ 3 <= I179 - 1 /\ I185 + 2 <= I179 /\ I184 <= I179] 30.10/29.70 f4(I189, I190, I191, I192, I193) -> f8(I194, I195, I196, I197, I198) [I194 + 2 <= I189 /\ -1 <= I195 - 1 /\ 1 <= I189 - 1 /\ I195 + 2 <= I189] 30.10/29.70 f4(I199, I200, I201, I202, I203) -> f7(I204, I205, I206, I207, I208) [I204 + 2 <= I199 /\ -1 <= I205 - 1 /\ 0 <= I199 - 1 /\ I205 + 1 <= I199] 30.10/29.70 f6(I209, I210, I211, I212, I213) -> f2(I210, I211, I212, I214, I215) [I210 <= I209 - 1 /\ I212 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I212 - 1 /\ 0 <= I209 - 1] 30.10/29.70 f2(I216, I217, I218, I219, I220) -> f6(I216, I216 - 1, I217, I218 + 1, I221) [0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1] 30.10/29.70 f2(I223, I224, I225, I226, I227) -> f6(I223, I223 - 1, I224, I225 + 1, I228) [I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1] 30.10/29.70 f2(I229, I230, I231, I232, I233) -> f2(I229 - 1, I230, I231, I234, I235) [I230 <= I231 /\ I229 - 1 <= I229 - 1 /\ -1 <= I230 - 1 /\ 0 <= I229 - 1] 30.10/29.70 f5(I236, I237, I238, I239, I240) -> f4(I241, I242, I243, I244, I245) [I241 <= I237 /\ 0 <= I246 - 1 /\ 0 <= I236 - 1 /\ 0 <= I237 - 1 /\ 0 <= I241 - 1 /\ I238 + 2 <= I237] 30.10/29.70 f3(I247, I248, I249, I250, I251) -> f5(I252, I253, 0, I254, I255) [I252 <= I247 /\ 0 <= I256 - 1 /\ I253 - 1 <= I247 /\ 0 <= I247 - 1 /\ 0 <= I252 - 1 /\ 1 <= I253 - 1] 30.10/29.70 f3(I257, I258, I259, I260, I261) -> f5(I262, I263, I264, I265, I266) [I262 <= I257 /\ 0 <= I267 - 1 /\ 0 <= I257 - 1 /\ 0 <= I262 - 1 /\ 1 <= I263 - 1] 30.10/29.70 f3(I268, I269, I270, I271, I272) -> f5(I273, I274, I275, I276, I277) [I273 <= I268 /\ 0 <= I278 - 1 /\ 0 <= I268 - 1 /\ 0 <= I273 - 1 /\ 2 <= I274 - 1] 30.10/29.70 f3(I279, I280, I281, I282, I283) -> f5(I284, I285, 0, I286, I287) [I284 <= I279 /\ 0 <= I288 - 1 /\ 0 <= I279 - 1 /\ 0 <= I284 - 1 /\ 2 <= I285 - 1] 30.10/29.70 f1(I289, I290, I291, I292, I293) -> f4(I294, I295, I296, I297, I298) [0 = I290 /\ 1 <= I294 - 1 /\ 0 <= I289 - 1 /\ I294 - 1 <= I289] 30.10/29.70 f3(I299, I300, I301, I302, I303) -> f4(I304, I305, I306, I307, I308) [I304 + 1 <= I299 /\ 0 <= I309 - 1 /\ 0 <= I299 - 1 /\ -1 <= I304 - 1 /\ 0 = I300] 30.10/29.70 f1(I310, I311, I312, I313, I314) -> f4(I315, I316, I317, I318, I319) [0 = I311 /\ -1 <= I315 - 1 /\ 0 <= I310 - 1 /\ I315 + 1 <= I310] 30.10/29.70 f3(I320, I321, I322, I323, I324) -> f2(I321, I325, 1, I326, I327) [0 <= I325 - 1 /\ 0 <= I320 - 1] 30.10/29.70 f1(I328, I329, I330, I331, I332) -> f3(I333, I334, I335, I336, I337) [0 <= I333 - 1 /\ 0 <= I328 - 1 /\ I333 <= I328 /\ 0 <= I329 - 1 /\ -1 <= I334 - 1] 30.10/29.70 f1(I338, I339, I340, I341, I342) -> f3(I343, 0, I344, I345, I346) [0 <= I343 - 1 /\ 0 <= I338 - 1 /\ 0 <= I339 - 1 /\ I343 <= I338] 30.10/29.70 f1(I347, I348, I349, I350, I351) -> f2(0, 0, 0, I352, I353) [0 = I348 /\ 0 <= I347 - 1] 30.10/29.70 30.10/29.70 We use the basic value criterion with the projection function NU: 30.10/29.70 NU[f9#(z1,z2,z3,z4,z5)] = z2 30.10/29.70 NU[f7#(z1,z2,z3,z4,z5)] = z2 30.10/29.70 NU[f11#(z1,z2,z3,z4,z5)] = z2 30.10/29.70 NU[f12#(z1,z2,z3,z4,z5)] = z2 30.10/29.70 NU[f8#(z1,z2,z3,z4,z5)] = z2 30.10/29.70 NU[f4#(z1,z2,z3,z4,z5)] = z1 30.10/29.70 NU[f13#(z1,z2,z3,z4,z5)] = z1 30.10/29.70 30.10/29.70 This gives the following inequalities: 30.10/29.70 I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0 ==> I0 (>! \union =) I5 30.10/29.70 I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11 ==> I11 (>! \union =) I15 30.10/29.70 I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20 ==> I20 (>! \union =) I24 30.10/29.70 I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28 ==> I29 (>! \union =) I33 30.10/29.70 I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1 ==> I39 (>! \union =) I43 30.10/29.70 I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49 ==> I49 (>! \union =) I54 30.10/29.70 I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58 ==> I58 (>! \union =) I63 30.10/29.70 I71 + 1 <= I67 /\ I66 <= I74 - 1 /\ 0 <= I67 - 1 /\ -1 <= I71 - 1 ==> I67 >! I71 30.10/29.70 I80 + 1 <= I76 /\ I83 <= I75 /\ 0 <= I76 - 1 /\ -1 <= I80 - 1 ==> I76 >! I80 30.10/29.70 I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84 ==> I85 (>! \union =) I89 30.10/29.70 I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95 ==> I95 (>! \union =) I100 30.10/29.70 I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104 ==> I104 (>! \union =) I109 30.10/29.70 I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1 ==> I113 (>! \union =) I117 30.10/29.70 I128 + 1 <= I124 /\ I131 <= I123 /\ 0 <= I124 - 1 /\ -1 <= I128 - 1 ==> I124 >! I128 30.10/29.70 I137 + 1 <= I133 /\ I132 <= I140 - 1 /\ 0 <= I133 - 1 /\ -1 <= I137 - 1 ==> I133 >! I137 30.10/29.70 I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161 ==> I162 (>! \union =) I166 30.10/29.70 I178 + 4 <= I169 /\ I177 + 2 <= I169 /\ 2 <= I175 - 1 /\ 4 <= I174 - 1 /\ 4 <= I169 - 1 /\ I175 + 2 <= I169 /\ I174 <= I169 ==> I169 >! I175 30.10/29.70 I188 + 4 <= I179 /\ I187 + 2 <= I179 /\ 1 <= I185 - 1 /\ 3 <= I184 - 1 /\ 3 <= I179 - 1 /\ I185 + 2 <= I179 /\ I184 <= I179 ==> I179 >! I185 30.10/29.70 I194 + 2 <= I189 /\ -1 <= I195 - 1 /\ 1 <= I189 - 1 /\ I195 + 2 <= I189 ==> I189 >! I195 30.10/29.70 I204 + 2 <= I199 /\ -1 <= I205 - 1 /\ 0 <= I199 - 1 /\ I205 + 1 <= I199 ==> I199 >! I205 30.10/29.70 30.10/29.70 We remove all the strictly oriented dependency pairs. 30.10/29.70 30.10/29.70 DP problem for innermost termination. 30.10/29.70 P = 30.10/29.70 f13#(I0, I1, I2, I3, I4) -> f4#(I5, I6, I7, I8, I9) [I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0] 30.10/29.70 f8#(I10, I11, I12, I13, I14) -> f13#(I15, I16, I12, I17, I18) [I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11] 30.10/29.70 f8#(I19, I20, I21, I22, I23) -> f13#(I24, I25, I21, I26, I27) [I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20] 30.10/29.70 f12#(I28, I29, I30, I31, I32) -> f4#(I33, I34, I35, I36, I37) [I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28] 30.10/29.70 f8#(I38, I39, I40, I41, I42) -> f4#(I43, I44, I45, I46, I47) [I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1] 30.10/29.70 f8#(I48, I49, I50, I51, I52) -> f12#(I53, I54, I50, I55, I56) [I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49] 30.10/29.70 f8#(I57, I58, I59, I60, I61) -> f12#(I62, I63, I59, I64, I65) [I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58] 30.10/29.70 f11#(I84, I85, I86, I87, I88) -> f4#(I89, I90, I91, I92, I93) [I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84] 30.10/29.70 f7#(I94, I95, I96, I97, I98) -> f11#(I99, I100, I96, I101, I102) [I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95] 30.10/29.70 f7#(I103, I104, I105, I106, I107) -> f11#(I108, I109, I105, I110, I111) [I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104] 30.10/29.70 f7#(I112, I113, I114, I115, I116) -> f4#(I117, I118, I119, I120, I121) [I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1] 30.10/29.70 f9#(I161, I162, I163, I164, I165) -> f8#(I164, I166, I163, I167, I168) [I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161] 30.10/29.70 R = 30.10/29.70 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 30.10/29.70 f13(I0, I1, I2, I3, I4) -> f4(I5, I6, I7, I8, I9) [I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0] 30.10/29.70 f8(I10, I11, I12, I13, I14) -> f13(I15, I16, I12, I17, I18) [I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11] 30.10/29.70 f8(I19, I20, I21, I22, I23) -> f13(I24, I25, I21, I26, I27) [I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20] 30.10/29.70 f12(I28, I29, I30, I31, I32) -> f4(I33, I34, I35, I36, I37) [I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28] 30.10/29.70 f8(I38, I39, I40, I41, I42) -> f4(I43, I44, I45, I46, I47) [I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1] 30.10/29.70 f8(I48, I49, I50, I51, I52) -> f12(I53, I54, I50, I55, I56) [I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49] 30.10/29.70 f8(I57, I58, I59, I60, I61) -> f12(I62, I63, I59, I64, I65) [I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58] 30.10/29.70 f8(I66, I67, I68, I69, I70) -> f8(I66, I71, I68, I72, I73) [I71 + 1 <= I67 /\ I66 <= I74 - 1 /\ 0 <= I67 - 1 /\ -1 <= I71 - 1] 30.10/29.70 f8(I75, I76, I77, I78, I79) -> f8(I75, I80, I77, I81, I82) [I80 + 1 <= I76 /\ I83 <= I75 /\ 0 <= I76 - 1 /\ -1 <= I80 - 1] 30.10/29.70 f11(I84, I85, I86, I87, I88) -> f4(I89, I90, I91, I92, I93) [I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84] 30.10/29.70 f7(I94, I95, I96, I97, I98) -> f11(I99, I100, I96, I101, I102) [I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95] 30.10/29.70 f7(I103, I104, I105, I106, I107) -> f11(I108, I109, I105, I110, I111) [I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104] 30.10/29.70 f7(I112, I113, I114, I115, I116) -> f4(I117, I118, I119, I120, I121) [I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1] 30.10/29.70 f7(I123, I124, I125, I126, I127) -> f7(I123, I128, I125, I129, I130) [I128 + 1 <= I124 /\ I131 <= I123 /\ 0 <= I124 - 1 /\ -1 <= I128 - 1] 30.10/29.70 f7(I132, I133, I134, I135, I136) -> f7(I132, I137, I134, I138, I139) [I137 + 1 <= I133 /\ I132 <= I140 - 1 /\ 0 <= I133 - 1 /\ -1 <= I137 - 1] 30.10/29.70 f9(I141, I142, I143, I144, I145) -> f10(I146, I147, I148, I149, I150) [I145 + 2 <= I142 /\ I144 + 2 <= I141 /\ I145 + 4 <= I141 /\ 3 <= I146 - 1 /\ 1 <= I142 - 1 /\ 3 <= I141 - 1 /\ I146 <= I141] 30.10/29.70 f9(I151, I152, I153, I154, I155) -> f10(I156, I157, I158, I159, I160) [I155 + 2 <= I152 /\ I154 + 2 <= I151 /\ I155 + 4 <= I151 /\ 4 <= I156 - 1 /\ 2 <= I152 - 1 /\ 4 <= I151 - 1 /\ I156 <= I151] 30.10/29.70 f9(I161, I162, I163, I164, I165) -> f8(I164, I166, I163, I167, I168) [I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161] 30.10/29.70 f4(I169, I170, I171, I172, I173) -> f9(I174, I175, I176, I177, I178) [I178 + 4 <= I169 /\ I177 + 2 <= I169 /\ 2 <= I175 - 1 /\ 4 <= I174 - 1 /\ 4 <= I169 - 1 /\ I175 + 2 <= I169 /\ I174 <= I169] 30.10/29.70 f4(I179, I180, I181, I182, I183) -> f9(I184, I185, I186, I187, I188) [I188 + 4 <= I179 /\ I187 + 2 <= I179 /\ 1 <= I185 - 1 /\ 3 <= I184 - 1 /\ 3 <= I179 - 1 /\ I185 + 2 <= I179 /\ I184 <= I179] 30.10/29.70 f4(I189, I190, I191, I192, I193) -> f8(I194, I195, I196, I197, I198) [I194 + 2 <= I189 /\ -1 <= I195 - 1 /\ 1 <= I189 - 1 /\ I195 + 2 <= I189] 30.10/29.70 f4(I199, I200, I201, I202, I203) -> f7(I204, I205, I206, I207, I208) [I204 + 2 <= I199 /\ -1 <= I205 - 1 /\ 0 <= I199 - 1 /\ I205 + 1 <= I199] 30.10/29.70 f6(I209, I210, I211, I212, I213) -> f2(I210, I211, I212, I214, I215) [I210 <= I209 - 1 /\ I212 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I212 - 1 /\ 0 <= I209 - 1] 30.10/29.70 f2(I216, I217, I218, I219, I220) -> f6(I216, I216 - 1, I217, I218 + 1, I221) [0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1] 30.10/29.70 f2(I223, I224, I225, I226, I227) -> f6(I223, I223 - 1, I224, I225 + 1, I228) [I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1] 30.10/29.70 f2(I229, I230, I231, I232, I233) -> f2(I229 - 1, I230, I231, I234, I235) [I230 <= I231 /\ I229 - 1 <= I229 - 1 /\ -1 <= I230 - 1 /\ 0 <= I229 - 1] 30.10/29.70 f5(I236, I237, I238, I239, I240) -> f4(I241, I242, I243, I244, I245) [I241 <= I237 /\ 0 <= I246 - 1 /\ 0 <= I236 - 1 /\ 0 <= I237 - 1 /\ 0 <= I241 - 1 /\ I238 + 2 <= I237] 30.10/29.70 f3(I247, I248, I249, I250, I251) -> f5(I252, I253, 0, I254, I255) [I252 <= I247 /\ 0 <= I256 - 1 /\ I253 - 1 <= I247 /\ 0 <= I247 - 1 /\ 0 <= I252 - 1 /\ 1 <= I253 - 1] 30.10/29.70 f3(I257, I258, I259, I260, I261) -> f5(I262, I263, I264, I265, I266) [I262 <= I257 /\ 0 <= I267 - 1 /\ 0 <= I257 - 1 /\ 0 <= I262 - 1 /\ 1 <= I263 - 1] 30.10/29.70 f3(I268, I269, I270, I271, I272) -> f5(I273, I274, I275, I276, I277) [I273 <= I268 /\ 0 <= I278 - 1 /\ 0 <= I268 - 1 /\ 0 <= I273 - 1 /\ 2 <= I274 - 1] 30.10/29.70 f3(I279, I280, I281, I282, I283) -> f5(I284, I285, 0, I286, I287) [I284 <= I279 /\ 0 <= I288 - 1 /\ 0 <= I279 - 1 /\ 0 <= I284 - 1 /\ 2 <= I285 - 1] 30.10/29.70 f1(I289, I290, I291, I292, I293) -> f4(I294, I295, I296, I297, I298) [0 = I290 /\ 1 <= I294 - 1 /\ 0 <= I289 - 1 /\ I294 - 1 <= I289] 30.10/29.70 f3(I299, I300, I301, I302, I303) -> f4(I304, I305, I306, I307, I308) [I304 + 1 <= I299 /\ 0 <= I309 - 1 /\ 0 <= I299 - 1 /\ -1 <= I304 - 1 /\ 0 = I300] 30.10/29.70 f1(I310, I311, I312, I313, I314) -> f4(I315, I316, I317, I318, I319) [0 = I311 /\ -1 <= I315 - 1 /\ 0 <= I310 - 1 /\ I315 + 1 <= I310] 30.10/29.70 f3(I320, I321, I322, I323, I324) -> f2(I321, I325, 1, I326, I327) [0 <= I325 - 1 /\ 0 <= I320 - 1] 30.10/29.70 f1(I328, I329, I330, I331, I332) -> f3(I333, I334, I335, I336, I337) [0 <= I333 - 1 /\ 0 <= I328 - 1 /\ I333 <= I328 /\ 0 <= I329 - 1 /\ -1 <= I334 - 1] 30.10/29.70 f1(I338, I339, I340, I341, I342) -> f3(I343, 0, I344, I345, I346) [0 <= I343 - 1 /\ 0 <= I338 - 1 /\ 0 <= I339 - 1 /\ I343 <= I338] 30.10/29.70 f1(I347, I348, I349, I350, I351) -> f2(0, 0, 0, I352, I353) [0 = I348 /\ 0 <= I347 - 1] 30.10/29.70 30.10/29.70 The dependency graph for this problem is: 30.10/29.70 1 -> 30.10/29.70 2 -> 1 30.10/29.70 3 -> 1 30.10/29.70 4 -> 30.10/29.70 5 -> 30.10/29.70 6 -> 4 30.10/29.70 7 -> 4 30.10/29.70 10 -> 30.10/29.70 11 -> 10 30.10/29.70 12 -> 10 30.10/29.70 13 -> 30.10/29.70 16 -> 2, 3, 5, 6, 7 30.10/29.70 Where: 30.10/29.70 1) f13#(I0, I1, I2, I3, I4) -> f4#(I5, I6, I7, I8, I9) [I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0] 30.10/29.70 2) f8#(I10, I11, I12, I13, I14) -> f13#(I15, I16, I12, I17, I18) [I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11] 30.10/29.70 3) f8#(I19, I20, I21, I22, I23) -> f13#(I24, I25, I21, I26, I27) [I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20] 30.10/29.70 4) f12#(I28, I29, I30, I31, I32) -> f4#(I33, I34, I35, I36, I37) [I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28] 30.10/29.70 5) f8#(I38, I39, I40, I41, I42) -> f4#(I43, I44, I45, I46, I47) [I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1] 30.10/29.70 6) f8#(I48, I49, I50, I51, I52) -> f12#(I53, I54, I50, I55, I56) [I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49] 30.10/29.70 7) f8#(I57, I58, I59, I60, I61) -> f12#(I62, I63, I59, I64, I65) [I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58] 30.10/29.70 10) f11#(I84, I85, I86, I87, I88) -> f4#(I89, I90, I91, I92, I93) [I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84] 30.10/29.70 11) f7#(I94, I95, I96, I97, I98) -> f11#(I99, I100, I96, I101, I102) [I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95] 30.10/29.70 12) f7#(I103, I104, I105, I106, I107) -> f11#(I108, I109, I105, I110, I111) [I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104] 30.10/29.70 13) f7#(I112, I113, I114, I115, I116) -> f4#(I117, I118, I119, I120, I121) [I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1] 30.10/29.70 16) f9#(I161, I162, I163, I164, I165) -> f8#(I164, I166, I163, I167, I168) [I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161] 30.10/29.70 30.10/29.70 We have the following SCCs. 30.10/29.70 30.10/29.70 30.10/29.70 DP problem for innermost termination. 30.10/29.70 P = 30.10/29.70 f2#(I229, I230, I231, I232, I233) -> f2#(I229 - 1, I230, I231, I234, I235) [I230 <= I231 /\ I229 - 1 <= I229 - 1 /\ -1 <= I230 - 1 /\ 0 <= I229 - 1] 30.10/29.70 R = 30.10/29.70 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 30.10/29.70 f13(I0, I1, I2, I3, I4) -> f4(I5, I6, I7, I8, I9) [I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0] 30.10/29.70 f8(I10, I11, I12, I13, I14) -> f13(I15, I16, I12, I17, I18) [I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11] 30.10/29.70 f8(I19, I20, I21, I22, I23) -> f13(I24, I25, I21, I26, I27) [I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20] 30.10/29.70 f12(I28, I29, I30, I31, I32) -> f4(I33, I34, I35, I36, I37) [I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28] 30.10/29.70 f8(I38, I39, I40, I41, I42) -> f4(I43, I44, I45, I46, I47) [I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1] 30.10/29.70 f8(I48, I49, I50, I51, I52) -> f12(I53, I54, I50, I55, I56) [I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49] 30.10/29.70 f8(I57, I58, I59, I60, I61) -> f12(I62, I63, I59, I64, I65) [I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58] 30.10/29.70 f8(I66, I67, I68, I69, I70) -> f8(I66, I71, I68, I72, I73) [I71 + 1 <= I67 /\ I66 <= I74 - 1 /\ 0 <= I67 - 1 /\ -1 <= I71 - 1] 30.10/29.70 f8(I75, I76, I77, I78, I79) -> f8(I75, I80, I77, I81, I82) [I80 + 1 <= I76 /\ I83 <= I75 /\ 0 <= I76 - 1 /\ -1 <= I80 - 1] 30.10/29.70 f11(I84, I85, I86, I87, I88) -> f4(I89, I90, I91, I92, I93) [I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84] 30.10/29.70 f7(I94, I95, I96, I97, I98) -> f11(I99, I100, I96, I101, I102) [I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95] 30.10/29.70 f7(I103, I104, I105, I106, I107) -> f11(I108, I109, I105, I110, I111) [I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104] 30.10/29.70 f7(I112, I113, I114, I115, I116) -> f4(I117, I118, I119, I120, I121) [I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1] 30.10/29.70 f7(I123, I124, I125, I126, I127) -> f7(I123, I128, I125, I129, I130) [I128 + 1 <= I124 /\ I131 <= I123 /\ 0 <= I124 - 1 /\ -1 <= I128 - 1] 30.10/29.70 f7(I132, I133, I134, I135, I136) -> f7(I132, I137, I134, I138, I139) [I137 + 1 <= I133 /\ I132 <= I140 - 1 /\ 0 <= I133 - 1 /\ -1 <= I137 - 1] 30.10/29.70 f9(I141, I142, I143, I144, I145) -> f10(I146, I147, I148, I149, I150) [I145 + 2 <= I142 /\ I144 + 2 <= I141 /\ I145 + 4 <= I141 /\ 3 <= I146 - 1 /\ 1 <= I142 - 1 /\ 3 <= I141 - 1 /\ I146 <= I141] 30.10/29.70 f9(I151, I152, I153, I154, I155) -> f10(I156, I157, I158, I159, I160) [I155 + 2 <= I152 /\ I154 + 2 <= I151 /\ I155 + 4 <= I151 /\ 4 <= I156 - 1 /\ 2 <= I152 - 1 /\ 4 <= I151 - 1 /\ I156 <= I151] 30.10/29.70 f9(I161, I162, I163, I164, I165) -> f8(I164, I166, I163, I167, I168) [I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161] 30.10/29.70 f4(I169, I170, I171, I172, I173) -> f9(I174, I175, I176, I177, I178) [I178 + 4 <= I169 /\ I177 + 2 <= I169 /\ 2 <= I175 - 1 /\ 4 <= I174 - 1 /\ 4 <= I169 - 1 /\ I175 + 2 <= I169 /\ I174 <= I169] 30.10/29.70 f4(I179, I180, I181, I182, I183) -> f9(I184, I185, I186, I187, I188) [I188 + 4 <= I179 /\ I187 + 2 <= I179 /\ 1 <= I185 - 1 /\ 3 <= I184 - 1 /\ 3 <= I179 - 1 /\ I185 + 2 <= I179 /\ I184 <= I179] 30.10/29.70 f4(I189, I190, I191, I192, I193) -> f8(I194, I195, I196, I197, I198) [I194 + 2 <= I189 /\ -1 <= I195 - 1 /\ 1 <= I189 - 1 /\ I195 + 2 <= I189] 30.10/29.70 f4(I199, I200, I201, I202, I203) -> f7(I204, I205, I206, I207, I208) [I204 + 2 <= I199 /\ -1 <= I205 - 1 /\ 0 <= I199 - 1 /\ I205 + 1 <= I199] 30.10/29.70 f6(I209, I210, I211, I212, I213) -> f2(I210, I211, I212, I214, I215) [I210 <= I209 - 1 /\ I212 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I212 - 1 /\ 0 <= I209 - 1] 30.10/29.70 f2(I216, I217, I218, I219, I220) -> f6(I216, I216 - 1, I217, I218 + 1, I221) [0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1] 30.10/29.70 f2(I223, I224, I225, I226, I227) -> f6(I223, I223 - 1, I224, I225 + 1, I228) [I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1] 30.10/29.70 f2(I229, I230, I231, I232, I233) -> f2(I229 - 1, I230, I231, I234, I235) [I230 <= I231 /\ I229 - 1 <= I229 - 1 /\ -1 <= I230 - 1 /\ 0 <= I229 - 1] 30.10/29.70 f5(I236, I237, I238, I239, I240) -> f4(I241, I242, I243, I244, I245) [I241 <= I237 /\ 0 <= I246 - 1 /\ 0 <= I236 - 1 /\ 0 <= I237 - 1 /\ 0 <= I241 - 1 /\ I238 + 2 <= I237] 30.10/29.70 f3(I247, I248, I249, I250, I251) -> f5(I252, I253, 0, I254, I255) [I252 <= I247 /\ 0 <= I256 - 1 /\ I253 - 1 <= I247 /\ 0 <= I247 - 1 /\ 0 <= I252 - 1 /\ 1 <= I253 - 1] 30.10/29.70 f3(I257, I258, I259, I260, I261) -> f5(I262, I263, I264, I265, I266) [I262 <= I257 /\ 0 <= I267 - 1 /\ 0 <= I257 - 1 /\ 0 <= I262 - 1 /\ 1 <= I263 - 1] 30.10/29.70 f3(I268, I269, I270, I271, I272) -> f5(I273, I274, I275, I276, I277) [I273 <= I268 /\ 0 <= I278 - 1 /\ 0 <= I268 - 1 /\ 0 <= I273 - 1 /\ 2 <= I274 - 1] 30.10/29.70 f3(I279, I280, I281, I282, I283) -> f5(I284, I285, 0, I286, I287) [I284 <= I279 /\ 0 <= I288 - 1 /\ 0 <= I279 - 1 /\ 0 <= I284 - 1 /\ 2 <= I285 - 1] 30.10/29.70 f1(I289, I290, I291, I292, I293) -> f4(I294, I295, I296, I297, I298) [0 = I290 /\ 1 <= I294 - 1 /\ 0 <= I289 - 1 /\ I294 - 1 <= I289] 30.10/29.70 f3(I299, I300, I301, I302, I303) -> f4(I304, I305, I306, I307, I308) [I304 + 1 <= I299 /\ 0 <= I309 - 1 /\ 0 <= I299 - 1 /\ -1 <= I304 - 1 /\ 0 = I300] 30.10/29.70 f1(I310, I311, I312, I313, I314) -> f4(I315, I316, I317, I318, I319) [0 = I311 /\ -1 <= I315 - 1 /\ 0 <= I310 - 1 /\ I315 + 1 <= I310] 30.10/29.70 f3(I320, I321, I322, I323, I324) -> f2(I321, I325, 1, I326, I327) [0 <= I325 - 1 /\ 0 <= I320 - 1] 30.10/29.70 f1(I328, I329, I330, I331, I332) -> f3(I333, I334, I335, I336, I337) [0 <= I333 - 1 /\ 0 <= I328 - 1 /\ I333 <= I328 /\ 0 <= I329 - 1 /\ -1 <= I334 - 1] 30.10/29.70 f1(I338, I339, I340, I341, I342) -> f3(I343, 0, I344, I345, I346) [0 <= I343 - 1 /\ 0 <= I338 - 1 /\ 0 <= I339 - 1 /\ I343 <= I338] 30.10/29.70 f1(I347, I348, I349, I350, I351) -> f2(0, 0, 0, I352, I353) [0 = I348 /\ 0 <= I347 - 1] 30.10/29.70 30.10/29.70 We use the basic value criterion with the projection function NU: 30.10/29.70 NU[f2#(z1,z2,z3,z4,z5)] = z1 30.10/29.70 30.10/29.70 This gives the following inequalities: 30.10/29.70 I230 <= I231 /\ I229 - 1 <= I229 - 1 /\ -1 <= I230 - 1 /\ 0 <= I229 - 1 ==> I229 >! I229 - 1 30.10/29.70 30.10/29.70 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 30.10/29.70 30.10/29.70 DP problem for innermost termination. 30.10/29.70 P = 30.10/29.70 f6#(I209, I210, I211, I212, I213) -> f2#(I210, I211, I212, I214, I215) [I210 <= I209 - 1 /\ I212 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I212 - 1 /\ 0 <= I209 - 1] 30.10/29.70 f2#(I216, I217, I218, I219, I220) -> f6#(I216, I216 - 1, I217, I218 + 1, I221) [0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1] 30.10/29.70 f2#(I223, I224, I225, I226, I227) -> f6#(I223, I223 - 1, I224, I225 + 1, I228) [I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1] 30.10/29.70 R = 30.10/29.70 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 30.10/29.70 f13(I0, I1, I2, I3, I4) -> f4(I5, I6, I7, I8, I9) [I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0] 30.10/29.70 f8(I10, I11, I12, I13, I14) -> f13(I15, I16, I12, I17, I18) [I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11] 30.10/29.70 f8(I19, I20, I21, I22, I23) -> f13(I24, I25, I21, I26, I27) [I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20] 30.10/29.70 f12(I28, I29, I30, I31, I32) -> f4(I33, I34, I35, I36, I37) [I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28] 30.10/29.70 f8(I38, I39, I40, I41, I42) -> f4(I43, I44, I45, I46, I47) [I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1] 30.10/29.70 f8(I48, I49, I50, I51, I52) -> f12(I53, I54, I50, I55, I56) [I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49] 30.10/29.70 f8(I57, I58, I59, I60, I61) -> f12(I62, I63, I59, I64, I65) [I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58] 30.10/29.70 f8(I66, I67, I68, I69, I70) -> f8(I66, I71, I68, I72, I73) [I71 + 1 <= I67 /\ I66 <= I74 - 1 /\ 0 <= I67 - 1 /\ -1 <= I71 - 1] 30.10/29.70 f8(I75, I76, I77, I78, I79) -> f8(I75, I80, I77, I81, I82) [I80 + 1 <= I76 /\ I83 <= I75 /\ 0 <= I76 - 1 /\ -1 <= I80 - 1] 30.10/29.70 f11(I84, I85, I86, I87, I88) -> f4(I89, I90, I91, I92, I93) [I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84] 30.10/29.70 f7(I94, I95, I96, I97, I98) -> f11(I99, I100, I96, I101, I102) [I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95] 30.10/29.70 f7(I103, I104, I105, I106, I107) -> f11(I108, I109, I105, I110, I111) [I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104] 30.10/29.70 f7(I112, I113, I114, I115, I116) -> f4(I117, I118, I119, I120, I121) [I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1] 30.10/29.70 f7(I123, I124, I125, I126, I127) -> f7(I123, I128, I125, I129, I130) [I128 + 1 <= I124 /\ I131 <= I123 /\ 0 <= I124 - 1 /\ -1 <= I128 - 1] 30.10/29.70 f7(I132, I133, I134, I135, I136) -> f7(I132, I137, I134, I138, I139) [I137 + 1 <= I133 /\ I132 <= I140 - 1 /\ 0 <= I133 - 1 /\ -1 <= I137 - 1] 30.10/29.70 f9(I141, I142, I143, I144, I145) -> f10(I146, I147, I148, I149, I150) [I145 + 2 <= I142 /\ I144 + 2 <= I141 /\ I145 + 4 <= I141 /\ 3 <= I146 - 1 /\ 1 <= I142 - 1 /\ 3 <= I141 - 1 /\ I146 <= I141] 30.10/29.70 f9(I151, I152, I153, I154, I155) -> f10(I156, I157, I158, I159, I160) [I155 + 2 <= I152 /\ I154 + 2 <= I151 /\ I155 + 4 <= I151 /\ 4 <= I156 - 1 /\ 2 <= I152 - 1 /\ 4 <= I151 - 1 /\ I156 <= I151] 30.10/29.70 f9(I161, I162, I163, I164, I165) -> f8(I164, I166, I163, I167, I168) [I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161] 30.10/29.70 f4(I169, I170, I171, I172, I173) -> f9(I174, I175, I176, I177, I178) [I178 + 4 <= I169 /\ I177 + 2 <= I169 /\ 2 <= I175 - 1 /\ 4 <= I174 - 1 /\ 4 <= I169 - 1 /\ I175 + 2 <= I169 /\ I174 <= I169] 30.10/29.70 f4(I179, I180, I181, I182, I183) -> f9(I184, I185, I186, I187, I188) [I188 + 4 <= I179 /\ I187 + 2 <= I179 /\ 1 <= I185 - 1 /\ 3 <= I184 - 1 /\ 3 <= I179 - 1 /\ I185 + 2 <= I179 /\ I184 <= I179] 30.10/29.70 f4(I189, I190, I191, I192, I193) -> f8(I194, I195, I196, I197, I198) [I194 + 2 <= I189 /\ -1 <= I195 - 1 /\ 1 <= I189 - 1 /\ I195 + 2 <= I189] 30.10/29.70 f4(I199, I200, I201, I202, I203) -> f7(I204, I205, I206, I207, I208) [I204 + 2 <= I199 /\ -1 <= I205 - 1 /\ 0 <= I199 - 1 /\ I205 + 1 <= I199] 30.10/29.70 f6(I209, I210, I211, I212, I213) -> f2(I210, I211, I212, I214, I215) [I210 <= I209 - 1 /\ I212 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I212 - 1 /\ 0 <= I209 - 1] 30.10/29.70 f2(I216, I217, I218, I219, I220) -> f6(I216, I216 - 1, I217, I218 + 1, I221) [0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1] 30.10/29.70 f2(I223, I224, I225, I226, I227) -> f6(I223, I223 - 1, I224, I225 + 1, I228) [I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1] 30.10/29.70 f2(I229, I230, I231, I232, I233) -> f2(I229 - 1, I230, I231, I234, I235) [I230 <= I231 /\ I229 - 1 <= I229 - 1 /\ -1 <= I230 - 1 /\ 0 <= I229 - 1] 30.10/29.70 f5(I236, I237, I238, I239, I240) -> f4(I241, I242, I243, I244, I245) [I241 <= I237 /\ 0 <= I246 - 1 /\ 0 <= I236 - 1 /\ 0 <= I237 - 1 /\ 0 <= I241 - 1 /\ I238 + 2 <= I237] 30.10/29.70 f3(I247, I248, I249, I250, I251) -> f5(I252, I253, 0, I254, I255) [I252 <= I247 /\ 0 <= I256 - 1 /\ I253 - 1 <= I247 /\ 0 <= I247 - 1 /\ 0 <= I252 - 1 /\ 1 <= I253 - 1] 30.10/29.70 f3(I257, I258, I259, I260, I261) -> f5(I262, I263, I264, I265, I266) [I262 <= I257 /\ 0 <= I267 - 1 /\ 0 <= I257 - 1 /\ 0 <= I262 - 1 /\ 1 <= I263 - 1] 30.10/29.70 f3(I268, I269, I270, I271, I272) -> f5(I273, I274, I275, I276, I277) [I273 <= I268 /\ 0 <= I278 - 1 /\ 0 <= I268 - 1 /\ 0 <= I273 - 1 /\ 2 <= I274 - 1] 30.10/29.70 f3(I279, I280, I281, I282, I283) -> f5(I284, I285, 0, I286, I287) [I284 <= I279 /\ 0 <= I288 - 1 /\ 0 <= I279 - 1 /\ 0 <= I284 - 1 /\ 2 <= I285 - 1] 30.10/29.71 f1(I289, I290, I291, I292, I293) -> f4(I294, I295, I296, I297, I298) [0 = I290 /\ 1 <= I294 - 1 /\ 0 <= I289 - 1 /\ I294 - 1 <= I289] 30.10/29.71 f3(I299, I300, I301, I302, I303) -> f4(I304, I305, I306, I307, I308) [I304 + 1 <= I299 /\ 0 <= I309 - 1 /\ 0 <= I299 - 1 /\ -1 <= I304 - 1 /\ 0 = I300] 30.10/29.71 f1(I310, I311, I312, I313, I314) -> f4(I315, I316, I317, I318, I319) [0 = I311 /\ -1 <= I315 - 1 /\ 0 <= I310 - 1 /\ I315 + 1 <= I310] 30.10/29.71 f3(I320, I321, I322, I323, I324) -> f2(I321, I325, 1, I326, I327) [0 <= I325 - 1 /\ 0 <= I320 - 1] 30.10/29.71 f1(I328, I329, I330, I331, I332) -> f3(I333, I334, I335, I336, I337) [0 <= I333 - 1 /\ 0 <= I328 - 1 /\ I333 <= I328 /\ 0 <= I329 - 1 /\ -1 <= I334 - 1] 30.10/29.71 f1(I338, I339, I340, I341, I342) -> f3(I343, 0, I344, I345, I346) [0 <= I343 - 1 /\ 0 <= I338 - 1 /\ 0 <= I339 - 1 /\ I343 <= I338] 30.10/29.71 f1(I347, I348, I349, I350, I351) -> f2(0, 0, 0, I352, I353) [0 = I348 /\ 0 <= I347 - 1] 30.10/29.71 30.10/29.71 We use the basic value criterion with the projection function NU: 30.10/29.71 NU[f2#(z1,z2,z3,z4,z5)] = z1 30.10/29.71 NU[f6#(z1,z2,z3,z4,z5)] = z1 30.10/29.71 30.10/29.71 This gives the following inequalities: 30.10/29.71 I210 <= I209 - 1 /\ I212 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I212 - 1 /\ 0 <= I209 - 1 ==> I209 >! I210 30.10/29.71 0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1 ==> I216 (>! \union =) I216 30.10/29.71 I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1 ==> I223 (>! \union =) I223 30.10/29.71 30.10/29.71 We remove all the strictly oriented dependency pairs. 30.10/29.71 30.10/29.71 DP problem for innermost termination. 30.10/29.71 P = 30.10/29.71 f2#(I216, I217, I218, I219, I220) -> f6#(I216, I216 - 1, I217, I218 + 1, I221) [0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1] 30.10/29.71 f2#(I223, I224, I225, I226, I227) -> f6#(I223, I223 - 1, I224, I225 + 1, I228) [I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1] 30.10/29.71 R = 30.10/29.71 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 30.10/29.71 f13(I0, I1, I2, I3, I4) -> f4(I5, I6, I7, I8, I9) [I4 + 2 <= I1 /\ I4 + 2 <= I0 /\ I3 + 4 <= I0 /\ 1 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 <= I1 /\ I5 <= I0] 30.10/29.71 f8(I10, I11, I12, I13, I14) -> f13(I15, I16, I12, I17, I18) [I17 + 4 <= I11 /\ I18 + 2 <= I11 /\ 1 <= I16 - 1 /\ 4 <= I15 - 1 /\ 4 <= I11 - 1 /\ I16 <= I11 /\ I10 <= I18 - 1 /\ I15 <= I11] 30.10/29.71 f8(I19, I20, I21, I22, I23) -> f13(I24, I25, I21, I26, I27) [I26 + 4 <= I20 /\ I27 + 2 <= I20 /\ 1 <= I25 - 1 /\ 3 <= I24 - 1 /\ 3 <= I20 - 1 /\ I25 <= I20 /\ I19 <= I27 - 1 /\ I24 <= I20] 30.10/29.71 f12(I28, I29, I30, I31, I32) -> f4(I33, I34, I35, I36, I37) [I32 + 2 <= I29 /\ I32 + 2 <= I28 /\ I31 + 4 <= I28 /\ 1 <= I33 - 1 /\ 1 <= I29 - 1 /\ 2 <= I28 - 1 /\ I33 <= I29 /\ I33 <= I28] 30.10/29.71 f8(I38, I39, I40, I41, I42) -> f4(I43, I44, I45, I46, I47) [I43 <= I39 /\ I38 <= y1 - 1 /\ 1 <= I39 - 1 /\ 1 <= I43 - 1] 30.10/29.71 f8(I48, I49, I50, I51, I52) -> f12(I53, I54, I50, I55, I56) [I55 + 4 <= I49 /\ I56 + 2 <= I49 /\ 1 <= I54 - 1 /\ 4 <= I53 - 1 /\ 4 <= I49 - 1 /\ I54 <= I49 /\ I48 <= I56 - 1 /\ I53 <= I49] 30.10/29.71 f8(I57, I58, I59, I60, I61) -> f12(I62, I63, I59, I64, I65) [I64 + 4 <= I58 /\ I65 + 2 <= I58 /\ 1 <= I63 - 1 /\ 3 <= I62 - 1 /\ 3 <= I58 - 1 /\ I63 <= I58 /\ I57 <= I65 - 1 /\ I62 <= I58] 30.10/29.71 f8(I66, I67, I68, I69, I70) -> f8(I66, I71, I68, I72, I73) [I71 + 1 <= I67 /\ I66 <= I74 - 1 /\ 0 <= I67 - 1 /\ -1 <= I71 - 1] 30.10/29.71 f8(I75, I76, I77, I78, I79) -> f8(I75, I80, I77, I81, I82) [I80 + 1 <= I76 /\ I83 <= I75 /\ 0 <= I76 - 1 /\ -1 <= I80 - 1] 30.10/29.71 f11(I84, I85, I86, I87, I88) -> f4(I89, I90, I91, I92, I93) [I88 + 2 <= I85 /\ I88 + 2 <= I84 /\ I87 + 4 <= I84 /\ 1 <= I89 - 1 /\ 1 <= I85 - 1 /\ 2 <= I84 - 1 /\ I89 <= I85 /\ I89 <= I84] 30.10/29.71 f7(I94, I95, I96, I97, I98) -> f11(I99, I100, I96, I101, I102) [I101 + 4 <= I95 /\ I102 + 2 <= I95 /\ 1 <= I100 - 1 /\ 4 <= I99 - 1 /\ 4 <= I95 - 1 /\ I100 <= I95 /\ I102 <= I94 /\ I99 <= I95] 30.10/29.71 f7(I103, I104, I105, I106, I107) -> f11(I108, I109, I105, I110, I111) [I110 + 4 <= I104 /\ I111 + 2 <= I104 /\ 1 <= I109 - 1 /\ 3 <= I108 - 1 /\ 3 <= I104 - 1 /\ I109 <= I104 /\ I111 <= I103 /\ I108 <= I104] 30.10/29.71 f7(I112, I113, I114, I115, I116) -> f4(I117, I118, I119, I120, I121) [I117 <= I113 /\ I122 <= I112 /\ 1 <= I113 - 1 /\ 1 <= I117 - 1] 30.10/29.71 f7(I123, I124, I125, I126, I127) -> f7(I123, I128, I125, I129, I130) [I128 + 1 <= I124 /\ I131 <= I123 /\ 0 <= I124 - 1 /\ -1 <= I128 - 1] 30.10/29.71 f7(I132, I133, I134, I135, I136) -> f7(I132, I137, I134, I138, I139) [I137 + 1 <= I133 /\ I132 <= I140 - 1 /\ 0 <= I133 - 1 /\ -1 <= I137 - 1] 30.10/29.71 f9(I141, I142, I143, I144, I145) -> f10(I146, I147, I148, I149, I150) [I145 + 2 <= I142 /\ I144 + 2 <= I141 /\ I145 + 4 <= I141 /\ 3 <= I146 - 1 /\ 1 <= I142 - 1 /\ 3 <= I141 - 1 /\ I146 <= I141] 30.10/29.71 f9(I151, I152, I153, I154, I155) -> f10(I156, I157, I158, I159, I160) [I155 + 2 <= I152 /\ I154 + 2 <= I151 /\ I155 + 4 <= I151 /\ 4 <= I156 - 1 /\ 2 <= I152 - 1 /\ 4 <= I151 - 1 /\ I156 <= I151] 30.10/29.71 f9(I161, I162, I163, I164, I165) -> f8(I164, I166, I163, I167, I168) [I165 + 2 <= I162 /\ I164 + 2 <= I161 /\ I165 + 4 <= I161 /\ 0 <= I166 - 1 /\ 0 <= I162 - 1 /\ 2 <= I161 - 1 /\ I166 <= I162 /\ I166 + 2 <= I161] 30.10/29.71 f4(I169, I170, I171, I172, I173) -> f9(I174, I175, I176, I177, I178) [I178 + 4 <= I169 /\ I177 + 2 <= I169 /\ 2 <= I175 - 1 /\ 4 <= I174 - 1 /\ 4 <= I169 - 1 /\ I175 + 2 <= I169 /\ I174 <= I169] 30.10/29.71 f4(I179, I180, I181, I182, I183) -> f9(I184, I185, I186, I187, I188) [I188 + 4 <= I179 /\ I187 + 2 <= I179 /\ 1 <= I185 - 1 /\ 3 <= I184 - 1 /\ 3 <= I179 - 1 /\ I185 + 2 <= I179 /\ I184 <= I179] 30.10/29.71 f4(I189, I190, I191, I192, I193) -> f8(I194, I195, I196, I197, I198) [I194 + 2 <= I189 /\ -1 <= I195 - 1 /\ 1 <= I189 - 1 /\ I195 + 2 <= I189] 30.10/29.71 f4(I199, I200, I201, I202, I203) -> f7(I204, I205, I206, I207, I208) [I204 + 2 <= I199 /\ -1 <= I205 - 1 /\ 0 <= I199 - 1 /\ I205 + 1 <= I199] 30.10/29.71 f6(I209, I210, I211, I212, I213) -> f2(I210, I211, I212, I214, I215) [I210 <= I209 - 1 /\ I212 <= I211 /\ 0 <= I211 - 1 /\ 0 <= I212 - 1 /\ 0 <= I209 - 1] 30.10/29.71 f2(I216, I217, I218, I219, I220) -> f6(I216, I216 - 1, I217, I218 + 1, I221) [0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1] 30.10/29.71 f2(I223, I224, I225, I226, I227) -> f6(I223, I223 - 1, I224, I225 + 1, I228) [I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1] 30.10/29.71 f2(I229, I230, I231, I232, I233) -> f2(I229 - 1, I230, I231, I234, I235) [I230 <= I231 /\ I229 - 1 <= I229 - 1 /\ -1 <= I230 - 1 /\ 0 <= I229 - 1] 30.10/29.71 f5(I236, I237, I238, I239, I240) -> f4(I241, I242, I243, I244, I245) [I241 <= I237 /\ 0 <= I246 - 1 /\ 0 <= I236 - 1 /\ 0 <= I237 - 1 /\ 0 <= I241 - 1 /\ I238 + 2 <= I237] 30.10/29.71 f3(I247, I248, I249, I250, I251) -> f5(I252, I253, 0, I254, I255) [I252 <= I247 /\ 0 <= I256 - 1 /\ I253 - 1 <= I247 /\ 0 <= I247 - 1 /\ 0 <= I252 - 1 /\ 1 <= I253 - 1] 30.10/29.71 f3(I257, I258, I259, I260, I261) -> f5(I262, I263, I264, I265, I266) [I262 <= I257 /\ 0 <= I267 - 1 /\ 0 <= I257 - 1 /\ 0 <= I262 - 1 /\ 1 <= I263 - 1] 30.10/29.71 f3(I268, I269, I270, I271, I272) -> f5(I273, I274, I275, I276, I277) [I273 <= I268 /\ 0 <= I278 - 1 /\ 0 <= I268 - 1 /\ 0 <= I273 - 1 /\ 2 <= I274 - 1] 30.10/29.71 f3(I279, I280, I281, I282, I283) -> f5(I284, I285, 0, I286, I287) [I284 <= I279 /\ 0 <= I288 - 1 /\ 0 <= I279 - 1 /\ 0 <= I284 - 1 /\ 2 <= I285 - 1] 30.10/29.71 f1(I289, I290, I291, I292, I293) -> f4(I294, I295, I296, I297, I298) [0 = I290 /\ 1 <= I294 - 1 /\ 0 <= I289 - 1 /\ I294 - 1 <= I289] 30.10/29.71 f3(I299, I300, I301, I302, I303) -> f4(I304, I305, I306, I307, I308) [I304 + 1 <= I299 /\ 0 <= I309 - 1 /\ 0 <= I299 - 1 /\ -1 <= I304 - 1 /\ 0 = I300] 30.10/29.71 f1(I310, I311, I312, I313, I314) -> f4(I315, I316, I317, I318, I319) [0 = I311 /\ -1 <= I315 - 1 /\ 0 <= I310 - 1 /\ I315 + 1 <= I310] 30.10/29.71 f3(I320, I321, I322, I323, I324) -> f2(I321, I325, 1, I326, I327) [0 <= I325 - 1 /\ 0 <= I320 - 1] 30.10/29.71 f1(I328, I329, I330, I331, I332) -> f3(I333, I334, I335, I336, I337) [0 <= I333 - 1 /\ 0 <= I328 - 1 /\ I333 <= I328 /\ 0 <= I329 - 1 /\ -1 <= I334 - 1] 30.10/29.71 f1(I338, I339, I340, I341, I342) -> f3(I343, 0, I344, I345, I346) [0 <= I343 - 1 /\ 0 <= I338 - 1 /\ 0 <= I339 - 1 /\ I343 <= I338] 30.10/29.71 f1(I347, I348, I349, I350, I351) -> f2(0, 0, 0, I352, I353) [0 = I348 /\ 0 <= I347 - 1] 30.10/29.71 30.10/29.71 The dependency graph for this problem is: 30.10/29.71 22 -> 30.10/29.71 23 -> 30.10/29.71 Where: 30.10/29.71 22) f2#(I216, I217, I218, I219, I220) -> f6#(I216, I216 - 1, I217, I218 + 1, I221) [0 <= I216 - 1 /\ -1 <= I217 - 1 /\ I218 <= I217 - 1 /\ -1 <= I222 - 1 /\ -1 <= I218 - 1] 30.10/29.71 23) f2#(I223, I224, I225, I226, I227) -> f6#(I223, I223 - 1, I224, I225 + 1, I228) [I225 <= I224 - 1 /\ -1 <= I225 - 1 /\ -1 <= I224 - 1 /\ 0 <= I223 - 1] 30.10/29.71 30.10/29.71 We have the following SCCs. 30.10/29.71 30.10/32.68 EOF