3.92/3.94 MAYBE 3.92/3.94 3.92/3.94 DP problem for innermost termination. 3.92/3.94 P = 3.92/3.94 init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 3.92/3.94 f14#(I0, I1, I2, I3, I4) -> f10#(I5, I6, I7, I3, I4) [I4 + 2 <= I1 /\ I3 + 2 <= I0 /\ I2 + 4 <= I0 /\ -1 <= I7 - 1 /\ 1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I5 <= I0] 3.92/3.94 f13#(I8, I9, I10, I11, I12) -> f14#(I13, I14, I15, I16, I10) [I10 + 2 <= I8 /\ 1 <= I14 - 1 /\ 4 <= I13 - 1 /\ 0 <= I9 - 1 /\ 2 <= I8 - 1 /\ I14 <= I8] 3.92/3.94 f13#(I17, I18, I19, I20, I21) -> f14#(I22, I23, I24, I25, I19) [I19 + 2 <= I17 /\ 1 <= I23 - 1 /\ 2 <= I22 - 1 /\ 0 <= I18 - 1 /\ 2 <= I17 - 1 /\ I23 <= I17] 3.92/3.94 f13#(I26, I27, I28, I29, I30) -> f10#(I31, I32, I33, I34, I28) [I28 + 2 <= I26 /\ -1 <= I33 - 1 /\ 1 <= I32 - 1 /\ 1 <= I31 - 1 /\ 0 <= I27 - 1 /\ 2 <= I26 - 1 /\ I32 <= I26] 3.92/3.94 f13#(I35, I36, I37, I38, I39) -> f13#(I40, I41, I42, I43, I44) [I37 + 2 <= I35 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I36 - 1 /\ 2 <= I35 - 1] 3.92/3.94 f9#(I45, I46, I47, I48, I49) -> f13#(I50, I51, 5, I52, I53) [5 = I47 /\ I46 + 4 <= I45 /\ -1 <= I51 - 1 /\ 6 <= I50 - 1 /\ 6 <= I45 - 1 /\ I50 <= I45] 3.92/3.94 f4#(I54, I55, I56, I57, I58) -> f13#(I59, I60, 5, I61, I62) [5 = I58 /\ I57 + 2 <= I55 /\ I56 + 2 <= I54 /\ -1 <= I60 - 1 /\ 6 <= I59 - 1 /\ 6 <= I55 - 1 /\ 6 <= I54 - 1 /\ I59 <= I55 /\ I59 <= I54] 3.92/3.94 f12#(I63, I64, I65, I66, I67) -> f12#(I68, I69, I70, I71, I72) [I65 + 2 <= I63 /\ -1 <= I69 - 1 /\ 0 <= I68 - 1 /\ 0 <= I64 - 1 /\ 2 <= I63 - 1] 3.92/3.94 f6#(I73, I74, I75, I76, I77) -> f12#(I78, I79, 5, I80, I81) [5 = I75 /\ I74 + 4 <= I73 /\ -1 <= I79 - 1 /\ 6 <= I78 - 1 /\ 6 <= I73 - 1 /\ I78 <= I73] 3.92/3.94 f4#(I82, I83, I84, I85, I86) -> f12#(I87, I88, 5, I89, I90) [5 = I86 /\ I85 + 2 <= I83 /\ I84 + 2 <= I82 /\ -1 <= I88 - 1 /\ 6 <= I87 - 1 /\ 6 <= I83 - 1 /\ 6 <= I82 - 1 /\ I87 <= I83 /\ I87 <= I82] 3.92/3.94 f11#(I91, I92, I93, I94, I95) -> f11#(I96, I97, I98, I99, I100) [I93 + 2 <= I91 /\ -1 <= I97 - 1 /\ 0 <= I96 - 1 /\ 0 <= I92 - 1 /\ 2 <= I91 - 1] 3.92/3.94 f6#(I101, I102, I103, I104, I105) -> f11#(I106, I107, 5, I108, I109) [5 = I103 /\ I102 + 4 <= I101 /\ -1 <= I107 - 1 /\ 6 <= I106 - 1 /\ 6 <= I101 - 1 /\ I106 <= I101] 3.92/3.94 f4#(I110, I111, I112, I113, I114) -> f11#(I115, I116, 5, I117, I118) [5 = I114 /\ I113 + 2 <= I111 /\ I112 + 2 <= I110 /\ -1 <= I116 - 1 /\ 6 <= I115 - 1 /\ 6 <= I111 - 1 /\ 6 <= I110 - 1 /\ I115 <= I111 /\ I115 <= I110] 3.92/3.94 f10#(I119, I120, I121, I122, I123) -> f10#(I124, I125, I126, I127, I123) [I123 + 2 <= I120 /\ I122 + 2 <= I119 /\ -1 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ 2 <= I119 - 1 /\ I125 <= I120] 3.92/3.94 f3#(I128, I129, I130, I131, I132) -> f10#(I133, I134, I135, 5, I131) [I130 + 4 <= I129 /\ I131 + 2 <= I129 /\ I130 + 2 <= I128 /\ -1 <= I135 - 1 /\ 4 <= I134 - 1 /\ 9 <= I133 - 1 /\ 2 <= I129 - 1 /\ 0 <= I128 - 1 /\ I134 - 2 <= I129] 3.92/3.94 f4#(I136, I137, I138, I139, I140) -> f10#(I141, I142, I143, 5, 1) [5 = I140 /\ I139 + 2 <= I137 /\ I138 + 2 <= I136 /\ -1 <= I143 - 1 /\ 6 <= I142 - 1 /\ 6 <= I141 - 1 /\ 6 <= I137 - 1 /\ 6 <= I136 - 1 /\ I142 <= I137 /\ I142 <= I136] 3.92/3.94 f2#(I144, I145, I146, I147, I148) -> f2#(I149, I150, I151, I152, I153) [I149 + 2 <= I144 /\ y2 <= y1 /\ I150 <= I145 /\ 2 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I149 - 1 /\ 0 <= I150 - 1] 3.92/3.94 f2#(I154, I155, I156, I157, I158) -> f2#(I159, I160, I161, I162, I163) [I159 <= I154 /\ I164 <= I165 - 1 /\ I160 + 1 <= I155 /\ 0 <= I154 - 1 /\ 0 <= I155 - 1 /\ 0 <= I159 - 1 /\ -1 <= I160 - 1] 3.92/3.94 f6#(I166, I167, I168, I169, I170) -> f9#(I171, I167, 5, I172, I173) [5 = I168 /\ I167 + 4 <= I166 /\ 6 <= I171 - 1 /\ 6 <= I166 - 1 /\ I171 <= I166] 3.92/3.94 f6#(I174, I175, I176, I177, I178) -> f9#(I179, I175, 5, I180, I181) [5 = I176 /\ I175 + 4 <= I174 /\ 6 <= I179 - 1 /\ 6 <= I174 - 1 /\ I179 <= I174] 3.92/3.94 f8#(I182, I183, I184, I185, I186) -> f6#(I187, 6, 5, I188, I189) [5 = I185 /\ 6 = I184 /\ I183 + 4 <= I182 /\ 9 <= I187 - 1 /\ 9 <= I182 - 1 /\ I187 <= I182] 3.92/3.94 f7#(I190, I191, I192, I193, I194) -> f6#(I195, I192, 5, I196, I197) [5 = I193 /\ I192 + 4 <= I190 /\ I191 + 4 <= I190 /\ 6 <= I195 - 1 /\ 6 <= I190 - 1 /\ I195 <= I190] 3.92/3.94 f3#(I198, I199, I200, I201, I202) -> f6#(I203, 6, 5, I204, I205) [I200 + 4 <= I199 /\ I201 + 2 <= I199 /\ I200 + 2 <= I198 /\ 9 <= I203 - 1 /\ 2 <= I199 - 1 /\ 0 <= I198 - 1 /\ I203 - 7 <= I199 /\ I203 - 9 <= I198] 3.92/3.94 f4#(I206, I207, I208, I209, I210) -> f6#(I211, I212, 5, I213, I214) [5 = I210 /\ I209 + 2 <= I207 /\ I208 + 2 <= I206 /\ 6 <= I211 - 1 /\ 6 <= I207 - 1 /\ 6 <= I206 - 1] 3.92/3.94 f3#(I215, I216, I217, I218, I219) -> f6#(I220, 6, 5, I221, I222) [I217 + 4 <= I216 /\ I218 + 2 <= I216 /\ I217 + 2 <= I215 /\ 9 <= I220 - 1 /\ 2 <= I216 - 1 /\ 0 <= I215 - 1] 3.92/3.94 f4#(I223, I224, I225, I226, I227) -> f6#(I228, I229, 5, I230, I231) [5 = I227 /\ I226 + 2 <= I224 /\ I225 + 2 <= I223 /\ 6 <= I228 - 1 /\ 6 <= I224 - 1 /\ 6 <= I223 - 1] 3.92/3.94 f5#(I232, I233, I234, I235, I236) -> f4#(I237, I238, I239, I240, 5) [5 = I234 /\ I233 + 2 <= I232 /\ 6 <= I238 - 1 /\ 6 <= I237 - 1 /\ 6 <= I232 - 1] 3.92/3.94 f1#(I241, I242, I243, I244, I245) -> f4#(I246, I247, I248, I249, 5) [6 <= I246 - 1 /\ 6 <= I247 - 1] 3.92/3.94 f1#(I250, I251, I252, I253, I254) -> f3#(I255, I256, 3, 1, I257) [4 <= I255 - 1 /\ 6 <= I256 - 1] 3.92/3.94 f1#(I258, I259, I260, I261, I262) -> f2#(I263, I264, I265, I266, I267) [9 <= I263 - 1 /\ 6 <= I264 - 1] 3.92/3.94 R = 3.92/3.94 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 3.92/3.94 f14(I0, I1, I2, I3, I4) -> f10(I5, I6, I7, I3, I4) [I4 + 2 <= I1 /\ I3 + 2 <= I0 /\ I2 + 4 <= I0 /\ -1 <= I7 - 1 /\ 1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I5 <= I0] 3.92/3.94 f13(I8, I9, I10, I11, I12) -> f14(I13, I14, I15, I16, I10) [I10 + 2 <= I8 /\ 1 <= I14 - 1 /\ 4 <= I13 - 1 /\ 0 <= I9 - 1 /\ 2 <= I8 - 1 /\ I14 <= I8] 3.92/3.94 f13(I17, I18, I19, I20, I21) -> f14(I22, I23, I24, I25, I19) [I19 + 2 <= I17 /\ 1 <= I23 - 1 /\ 2 <= I22 - 1 /\ 0 <= I18 - 1 /\ 2 <= I17 - 1 /\ I23 <= I17] 3.92/3.94 f13(I26, I27, I28, I29, I30) -> f10(I31, I32, I33, I34, I28) [I28 + 2 <= I26 /\ -1 <= I33 - 1 /\ 1 <= I32 - 1 /\ 1 <= I31 - 1 /\ 0 <= I27 - 1 /\ 2 <= I26 - 1 /\ I32 <= I26] 3.92/3.94 f13(I35, I36, I37, I38, I39) -> f13(I40, I41, I42, I43, I44) [I37 + 2 <= I35 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I36 - 1 /\ 2 <= I35 - 1] 3.92/3.94 f9(I45, I46, I47, I48, I49) -> f13(I50, I51, 5, I52, I53) [5 = I47 /\ I46 + 4 <= I45 /\ -1 <= I51 - 1 /\ 6 <= I50 - 1 /\ 6 <= I45 - 1 /\ I50 <= I45] 3.92/3.94 f4(I54, I55, I56, I57, I58) -> f13(I59, I60, 5, I61, I62) [5 = I58 /\ I57 + 2 <= I55 /\ I56 + 2 <= I54 /\ -1 <= I60 - 1 /\ 6 <= I59 - 1 /\ 6 <= I55 - 1 /\ 6 <= I54 - 1 /\ I59 <= I55 /\ I59 <= I54] 3.92/3.94 f12(I63, I64, I65, I66, I67) -> f12(I68, I69, I70, I71, I72) [I65 + 2 <= I63 /\ -1 <= I69 - 1 /\ 0 <= I68 - 1 /\ 0 <= I64 - 1 /\ 2 <= I63 - 1] 3.92/3.94 f6(I73, I74, I75, I76, I77) -> f12(I78, I79, 5, I80, I81) [5 = I75 /\ I74 + 4 <= I73 /\ -1 <= I79 - 1 /\ 6 <= I78 - 1 /\ 6 <= I73 - 1 /\ I78 <= I73] 3.92/3.94 f4(I82, I83, I84, I85, I86) -> f12(I87, I88, 5, I89, I90) [5 = I86 /\ I85 + 2 <= I83 /\ I84 + 2 <= I82 /\ -1 <= I88 - 1 /\ 6 <= I87 - 1 /\ 6 <= I83 - 1 /\ 6 <= I82 - 1 /\ I87 <= I83 /\ I87 <= I82] 3.92/3.94 f11(I91, I92, I93, I94, I95) -> f11(I96, I97, I98, I99, I100) [I93 + 2 <= I91 /\ -1 <= I97 - 1 /\ 0 <= I96 - 1 /\ 0 <= I92 - 1 /\ 2 <= I91 - 1] 3.92/3.94 f6(I101, I102, I103, I104, I105) -> f11(I106, I107, 5, I108, I109) [5 = I103 /\ I102 + 4 <= I101 /\ -1 <= I107 - 1 /\ 6 <= I106 - 1 /\ 6 <= I101 - 1 /\ I106 <= I101] 3.92/3.94 f4(I110, I111, I112, I113, I114) -> f11(I115, I116, 5, I117, I118) [5 = I114 /\ I113 + 2 <= I111 /\ I112 + 2 <= I110 /\ -1 <= I116 - 1 /\ 6 <= I115 - 1 /\ 6 <= I111 - 1 /\ 6 <= I110 - 1 /\ I115 <= I111 /\ I115 <= I110] 3.92/3.94 f10(I119, I120, I121, I122, I123) -> f10(I124, I125, I126, I127, I123) [I123 + 2 <= I120 /\ I122 + 2 <= I119 /\ -1 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ 2 <= I119 - 1 /\ I125 <= I120] 3.92/3.94 f3(I128, I129, I130, I131, I132) -> f10(I133, I134, I135, 5, I131) [I130 + 4 <= I129 /\ I131 + 2 <= I129 /\ I130 + 2 <= I128 /\ -1 <= I135 - 1 /\ 4 <= I134 - 1 /\ 9 <= I133 - 1 /\ 2 <= I129 - 1 /\ 0 <= I128 - 1 /\ I134 - 2 <= I129] 3.92/3.94 f4(I136, I137, I138, I139, I140) -> f10(I141, I142, I143, 5, 1) [5 = I140 /\ I139 + 2 <= I137 /\ I138 + 2 <= I136 /\ -1 <= I143 - 1 /\ 6 <= I142 - 1 /\ 6 <= I141 - 1 /\ 6 <= I137 - 1 /\ 6 <= I136 - 1 /\ I142 <= I137 /\ I142 <= I136] 3.92/3.94 f2(I144, I145, I146, I147, I148) -> f2(I149, I150, I151, I152, I153) [I149 + 2 <= I144 /\ y2 <= y1 /\ I150 <= I145 /\ 2 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I149 - 1 /\ 0 <= I150 - 1] 3.92/3.94 f2(I154, I155, I156, I157, I158) -> f2(I159, I160, I161, I162, I163) [I159 <= I154 /\ I164 <= I165 - 1 /\ I160 + 1 <= I155 /\ 0 <= I154 - 1 /\ 0 <= I155 - 1 /\ 0 <= I159 - 1 /\ -1 <= I160 - 1] 3.92/3.94 f6(I166, I167, I168, I169, I170) -> f9(I171, I167, 5, I172, I173) [5 = I168 /\ I167 + 4 <= I166 /\ 6 <= I171 - 1 /\ 6 <= I166 - 1 /\ I171 <= I166] 3.92/3.94 f6(I174, I175, I176, I177, I178) -> f9(I179, I175, 5, I180, I181) [5 = I176 /\ I175 + 4 <= I174 /\ 6 <= I179 - 1 /\ 6 <= I174 - 1 /\ I179 <= I174] 3.92/3.94 f8(I182, I183, I184, I185, I186) -> f6(I187, 6, 5, I188, I189) [5 = I185 /\ 6 = I184 /\ I183 + 4 <= I182 /\ 9 <= I187 - 1 /\ 9 <= I182 - 1 /\ I187 <= I182] 3.92/3.94 f7(I190, I191, I192, I193, I194) -> f6(I195, I192, 5, I196, I197) [5 = I193 /\ I192 + 4 <= I190 /\ I191 + 4 <= I190 /\ 6 <= I195 - 1 /\ 6 <= I190 - 1 /\ I195 <= I190] 3.92/3.94 f3(I198, I199, I200, I201, I202) -> f6(I203, 6, 5, I204, I205) [I200 + 4 <= I199 /\ I201 + 2 <= I199 /\ I200 + 2 <= I198 /\ 9 <= I203 - 1 /\ 2 <= I199 - 1 /\ 0 <= I198 - 1 /\ I203 - 7 <= I199 /\ I203 - 9 <= I198] 3.92/3.94 f4(I206, I207, I208, I209, I210) -> f6(I211, I212, 5, I213, I214) [5 = I210 /\ I209 + 2 <= I207 /\ I208 + 2 <= I206 /\ 6 <= I211 - 1 /\ 6 <= I207 - 1 /\ 6 <= I206 - 1] 3.92/3.94 f3(I215, I216, I217, I218, I219) -> f6(I220, 6, 5, I221, I222) [I217 + 4 <= I216 /\ I218 + 2 <= I216 /\ I217 + 2 <= I215 /\ 9 <= I220 - 1 /\ 2 <= I216 - 1 /\ 0 <= I215 - 1] 3.92/3.94 f4(I223, I224, I225, I226, I227) -> f6(I228, I229, 5, I230, I231) [5 = I227 /\ I226 + 2 <= I224 /\ I225 + 2 <= I223 /\ 6 <= I228 - 1 /\ 6 <= I224 - 1 /\ 6 <= I223 - 1] 3.92/3.94 f5(I232, I233, I234, I235, I236) -> f4(I237, I238, I239, I240, 5) [5 = I234 /\ I233 + 2 <= I232 /\ 6 <= I238 - 1 /\ 6 <= I237 - 1 /\ 6 <= I232 - 1] 3.92/3.94 f1(I241, I242, I243, I244, I245) -> f4(I246, I247, I248, I249, 5) [6 <= I246 - 1 /\ 6 <= I247 - 1] 3.92/3.94 f1(I250, I251, I252, I253, I254) -> f3(I255, I256, 3, 1, I257) [4 <= I255 - 1 /\ 6 <= I256 - 1] 3.92/3.94 f1(I258, I259, I260, I261, I262) -> f2(I263, I264, I265, I266, I267) [9 <= I263 - 1 /\ 6 <= I264 - 1] 3.92/3.94 3.92/3.94 The dependency graph for this problem is: 3.92/3.94 0 -> 28, 29, 30 3.92/3.94 1 -> 14 3.92/3.94 2 -> 1 3.92/3.94 3 -> 1 3.92/3.94 4 -> 14 3.92/3.94 5 -> 2, 3, 4, 5 3.92/3.94 6 -> 2, 3, 4, 5 3.92/3.94 7 -> 2, 3, 4, 5 3.92/3.94 8 -> 8 3.92/3.94 9 -> 8 3.92/3.94 10 -> 8 3.92/3.94 11 -> 11 3.92/3.94 12 -> 11 3.92/3.94 13 -> 11 3.92/3.94 14 -> 14 3.92/3.94 15 -> 14 3.92/3.94 16 -> 14 3.92/3.94 17 -> 17, 18 3.92/3.94 18 -> 17, 18 3.92/3.94 19 -> 6 3.92/3.94 20 -> 6 3.92/3.94 21 -> 9, 12, 19, 20 3.92/3.94 22 -> 9, 12, 19, 20 3.92/3.94 23 -> 9, 12, 19, 20 3.92/3.94 24 -> 9, 12, 19, 20 3.92/3.94 25 -> 9, 12, 19, 20 3.92/3.94 26 -> 9, 12, 19, 20 3.92/3.94 27 -> 7, 10, 13, 16, 24, 26 3.92/3.94 28 -> 7, 10, 13, 16, 24, 26 3.92/3.94 29 -> 15, 23, 25 3.92/3.94 30 -> 17, 18 3.92/3.94 Where: 3.92/3.94 0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 3.92/3.94 1) f14#(I0, I1, I2, I3, I4) -> f10#(I5, I6, I7, I3, I4) [I4 + 2 <= I1 /\ I3 + 2 <= I0 /\ I2 + 4 <= I0 /\ -1 <= I7 - 1 /\ 1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I5 <= I0] 3.92/3.94 2) f13#(I8, I9, I10, I11, I12) -> f14#(I13, I14, I15, I16, I10) [I10 + 2 <= I8 /\ 1 <= I14 - 1 /\ 4 <= I13 - 1 /\ 0 <= I9 - 1 /\ 2 <= I8 - 1 /\ I14 <= I8] 3.92/3.94 3) f13#(I17, I18, I19, I20, I21) -> f14#(I22, I23, I24, I25, I19) [I19 + 2 <= I17 /\ 1 <= I23 - 1 /\ 2 <= I22 - 1 /\ 0 <= I18 - 1 /\ 2 <= I17 - 1 /\ I23 <= I17] 3.92/3.94 4) f13#(I26, I27, I28, I29, I30) -> f10#(I31, I32, I33, I34, I28) [I28 + 2 <= I26 /\ -1 <= I33 - 1 /\ 1 <= I32 - 1 /\ 1 <= I31 - 1 /\ 0 <= I27 - 1 /\ 2 <= I26 - 1 /\ I32 <= I26] 3.92/3.94 5) f13#(I35, I36, I37, I38, I39) -> f13#(I40, I41, I42, I43, I44) [I37 + 2 <= I35 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I36 - 1 /\ 2 <= I35 - 1] 3.92/3.94 6) f9#(I45, I46, I47, I48, I49) -> f13#(I50, I51, 5, I52, I53) [5 = I47 /\ I46 + 4 <= I45 /\ -1 <= I51 - 1 /\ 6 <= I50 - 1 /\ 6 <= I45 - 1 /\ I50 <= I45] 3.92/3.94 7) f4#(I54, I55, I56, I57, I58) -> f13#(I59, I60, 5, I61, I62) [5 = I58 /\ I57 + 2 <= I55 /\ I56 + 2 <= I54 /\ -1 <= I60 - 1 /\ 6 <= I59 - 1 /\ 6 <= I55 - 1 /\ 6 <= I54 - 1 /\ I59 <= I55 /\ I59 <= I54] 3.92/3.94 8) f12#(I63, I64, I65, I66, I67) -> f12#(I68, I69, I70, I71, I72) [I65 + 2 <= I63 /\ -1 <= I69 - 1 /\ 0 <= I68 - 1 /\ 0 <= I64 - 1 /\ 2 <= I63 - 1] 3.92/3.94 9) f6#(I73, I74, I75, I76, I77) -> f12#(I78, I79, 5, I80, I81) [5 = I75 /\ I74 + 4 <= I73 /\ -1 <= I79 - 1 /\ 6 <= I78 - 1 /\ 6 <= I73 - 1 /\ I78 <= I73] 3.92/3.94 10) f4#(I82, I83, I84, I85, I86) -> f12#(I87, I88, 5, I89, I90) [5 = I86 /\ I85 + 2 <= I83 /\ I84 + 2 <= I82 /\ -1 <= I88 - 1 /\ 6 <= I87 - 1 /\ 6 <= I83 - 1 /\ 6 <= I82 - 1 /\ I87 <= I83 /\ I87 <= I82] 3.92/3.94 11) f11#(I91, I92, I93, I94, I95) -> f11#(I96, I97, I98, I99, I100) [I93 + 2 <= I91 /\ -1 <= I97 - 1 /\ 0 <= I96 - 1 /\ 0 <= I92 - 1 /\ 2 <= I91 - 1] 3.92/3.94 12) f6#(I101, I102, I103, I104, I105) -> f11#(I106, I107, 5, I108, I109) [5 = I103 /\ I102 + 4 <= I101 /\ -1 <= I107 - 1 /\ 6 <= I106 - 1 /\ 6 <= I101 - 1 /\ I106 <= I101] 3.92/3.94 13) f4#(I110, I111, I112, I113, I114) -> f11#(I115, I116, 5, I117, I118) [5 = I114 /\ I113 + 2 <= I111 /\ I112 + 2 <= I110 /\ -1 <= I116 - 1 /\ 6 <= I115 - 1 /\ 6 <= I111 - 1 /\ 6 <= I110 - 1 /\ I115 <= I111 /\ I115 <= I110] 3.92/3.94 14) f10#(I119, I120, I121, I122, I123) -> f10#(I124, I125, I126, I127, I123) [I123 + 2 <= I120 /\ I122 + 2 <= I119 /\ -1 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ 2 <= I119 - 1 /\ I125 <= I120] 3.92/3.94 15) f3#(I128, I129, I130, I131, I132) -> f10#(I133, I134, I135, 5, I131) [I130 + 4 <= I129 /\ I131 + 2 <= I129 /\ I130 + 2 <= I128 /\ -1 <= I135 - 1 /\ 4 <= I134 - 1 /\ 9 <= I133 - 1 /\ 2 <= I129 - 1 /\ 0 <= I128 - 1 /\ I134 - 2 <= I129] 3.92/3.94 16) f4#(I136, I137, I138, I139, I140) -> f10#(I141, I142, I143, 5, 1) [5 = I140 /\ I139 + 2 <= I137 /\ I138 + 2 <= I136 /\ -1 <= I143 - 1 /\ 6 <= I142 - 1 /\ 6 <= I141 - 1 /\ 6 <= I137 - 1 /\ 6 <= I136 - 1 /\ I142 <= I137 /\ I142 <= I136] 3.92/3.94 17) f2#(I144, I145, I146, I147, I148) -> f2#(I149, I150, I151, I152, I153) [I149 + 2 <= I144 /\ y2 <= y1 /\ I150 <= I145 /\ 2 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I149 - 1 /\ 0 <= I150 - 1] 3.92/3.94 18) f2#(I154, I155, I156, I157, I158) -> f2#(I159, I160, I161, I162, I163) [I159 <= I154 /\ I164 <= I165 - 1 /\ I160 + 1 <= I155 /\ 0 <= I154 - 1 /\ 0 <= I155 - 1 /\ 0 <= I159 - 1 /\ -1 <= I160 - 1] 3.92/3.94 19) f6#(I166, I167, I168, I169, I170) -> f9#(I171, I167, 5, I172, I173) [5 = I168 /\ I167 + 4 <= I166 /\ 6 <= I171 - 1 /\ 6 <= I166 - 1 /\ I171 <= I166] 3.92/3.94 20) f6#(I174, I175, I176, I177, I178) -> f9#(I179, I175, 5, I180, I181) [5 = I176 /\ I175 + 4 <= I174 /\ 6 <= I179 - 1 /\ 6 <= I174 - 1 /\ I179 <= I174] 3.92/3.94 21) f8#(I182, I183, I184, I185, I186) -> f6#(I187, 6, 5, I188, I189) [5 = I185 /\ 6 = I184 /\ I183 + 4 <= I182 /\ 9 <= I187 - 1 /\ 9 <= I182 - 1 /\ I187 <= I182] 3.92/3.94 22) f7#(I190, I191, I192, I193, I194) -> f6#(I195, I192, 5, I196, I197) [5 = I193 /\ I192 + 4 <= I190 /\ I191 + 4 <= I190 /\ 6 <= I195 - 1 /\ 6 <= I190 - 1 /\ I195 <= I190] 3.92/3.94 23) f3#(I198, I199, I200, I201, I202) -> f6#(I203, 6, 5, I204, I205) [I200 + 4 <= I199 /\ I201 + 2 <= I199 /\ I200 + 2 <= I198 /\ 9 <= I203 - 1 /\ 2 <= I199 - 1 /\ 0 <= I198 - 1 /\ I203 - 7 <= I199 /\ I203 - 9 <= I198] 3.92/3.94 24) f4#(I206, I207, I208, I209, I210) -> f6#(I211, I212, 5, I213, I214) [5 = I210 /\ I209 + 2 <= I207 /\ I208 + 2 <= I206 /\ 6 <= I211 - 1 /\ 6 <= I207 - 1 /\ 6 <= I206 - 1] 3.92/3.94 25) f3#(I215, I216, I217, I218, I219) -> f6#(I220, 6, 5, I221, I222) [I217 + 4 <= I216 /\ I218 + 2 <= I216 /\ I217 + 2 <= I215 /\ 9 <= I220 - 1 /\ 2 <= I216 - 1 /\ 0 <= I215 - 1] 3.92/3.94 26) f4#(I223, I224, I225, I226, I227) -> f6#(I228, I229, 5, I230, I231) [5 = I227 /\ I226 + 2 <= I224 /\ I225 + 2 <= I223 /\ 6 <= I228 - 1 /\ 6 <= I224 - 1 /\ 6 <= I223 - 1] 3.92/3.94 27) f5#(I232, I233, I234, I235, I236) -> f4#(I237, I238, I239, I240, 5) [5 = I234 /\ I233 + 2 <= I232 /\ 6 <= I238 - 1 /\ 6 <= I237 - 1 /\ 6 <= I232 - 1] 3.92/3.94 28) f1#(I241, I242, I243, I244, I245) -> f4#(I246, I247, I248, I249, 5) [6 <= I246 - 1 /\ 6 <= I247 - 1] 3.92/3.94 29) f1#(I250, I251, I252, I253, I254) -> f3#(I255, I256, 3, 1, I257) [4 <= I255 - 1 /\ 6 <= I256 - 1] 3.92/3.94 30) f1#(I258, I259, I260, I261, I262) -> f2#(I263, I264, I265, I266, I267) [9 <= I263 - 1 /\ 6 <= I264 - 1] 3.92/3.94 3.92/3.94 We have the following SCCs. 3.92/3.94 { 5 } 3.92/3.94 { 11 } 3.92/3.94 { 8 } 3.92/3.94 { 14 } 3.92/3.94 { 17, 18 } 3.92/3.94 3.92/3.94 DP problem for innermost termination. 3.92/3.94 P = 3.92/3.94 f2#(I144, I145, I146, I147, I148) -> f2#(I149, I150, I151, I152, I153) [I149 + 2 <= I144 /\ y2 <= y1 /\ I150 <= I145 /\ 2 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I149 - 1 /\ 0 <= I150 - 1] 3.92/3.94 f2#(I154, I155, I156, I157, I158) -> f2#(I159, I160, I161, I162, I163) [I159 <= I154 /\ I164 <= I165 - 1 /\ I160 + 1 <= I155 /\ 0 <= I154 - 1 /\ 0 <= I155 - 1 /\ 0 <= I159 - 1 /\ -1 <= I160 - 1] 3.92/3.94 R = 3.92/3.94 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 3.92/3.94 f14(I0, I1, I2, I3, I4) -> f10(I5, I6, I7, I3, I4) [I4 + 2 <= I1 /\ I3 + 2 <= I0 /\ I2 + 4 <= I0 /\ -1 <= I7 - 1 /\ 1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I5 <= I0] 3.92/3.94 f13(I8, I9, I10, I11, I12) -> f14(I13, I14, I15, I16, I10) [I10 + 2 <= I8 /\ 1 <= I14 - 1 /\ 4 <= I13 - 1 /\ 0 <= I9 - 1 /\ 2 <= I8 - 1 /\ I14 <= I8] 3.92/3.94 f13(I17, I18, I19, I20, I21) -> f14(I22, I23, I24, I25, I19) [I19 + 2 <= I17 /\ 1 <= I23 - 1 /\ 2 <= I22 - 1 /\ 0 <= I18 - 1 /\ 2 <= I17 - 1 /\ I23 <= I17] 3.92/3.94 f13(I26, I27, I28, I29, I30) -> f10(I31, I32, I33, I34, I28) [I28 + 2 <= I26 /\ -1 <= I33 - 1 /\ 1 <= I32 - 1 /\ 1 <= I31 - 1 /\ 0 <= I27 - 1 /\ 2 <= I26 - 1 /\ I32 <= I26] 3.92/3.94 f13(I35, I36, I37, I38, I39) -> f13(I40, I41, I42, I43, I44) [I37 + 2 <= I35 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I36 - 1 /\ 2 <= I35 - 1] 3.92/3.94 f9(I45, I46, I47, I48, I49) -> f13(I50, I51, 5, I52, I53) [5 = I47 /\ I46 + 4 <= I45 /\ -1 <= I51 - 1 /\ 6 <= I50 - 1 /\ 6 <= I45 - 1 /\ I50 <= I45] 3.92/3.94 f4(I54, I55, I56, I57, I58) -> f13(I59, I60, 5, I61, I62) [5 = I58 /\ I57 + 2 <= I55 /\ I56 + 2 <= I54 /\ -1 <= I60 - 1 /\ 6 <= I59 - 1 /\ 6 <= I55 - 1 /\ 6 <= I54 - 1 /\ I59 <= I55 /\ I59 <= I54] 3.92/3.94 f12(I63, I64, I65, I66, I67) -> f12(I68, I69, I70, I71, I72) [I65 + 2 <= I63 /\ -1 <= I69 - 1 /\ 0 <= I68 - 1 /\ 0 <= I64 - 1 /\ 2 <= I63 - 1] 3.92/3.94 f6(I73, I74, I75, I76, I77) -> f12(I78, I79, 5, I80, I81) [5 = I75 /\ I74 + 4 <= I73 /\ -1 <= I79 - 1 /\ 6 <= I78 - 1 /\ 6 <= I73 - 1 /\ I78 <= I73] 3.92/3.94 f4(I82, I83, I84, I85, I86) -> f12(I87, I88, 5, I89, I90) [5 = I86 /\ I85 + 2 <= I83 /\ I84 + 2 <= I82 /\ -1 <= I88 - 1 /\ 6 <= I87 - 1 /\ 6 <= I83 - 1 /\ 6 <= I82 - 1 /\ I87 <= I83 /\ I87 <= I82] 3.92/3.94 f11(I91, I92, I93, I94, I95) -> f11(I96, I97, I98, I99, I100) [I93 + 2 <= I91 /\ -1 <= I97 - 1 /\ 0 <= I96 - 1 /\ 0 <= I92 - 1 /\ 2 <= I91 - 1] 3.92/3.94 f6(I101, I102, I103, I104, I105) -> f11(I106, I107, 5, I108, I109) [5 = I103 /\ I102 + 4 <= I101 /\ -1 <= I107 - 1 /\ 6 <= I106 - 1 /\ 6 <= I101 - 1 /\ I106 <= I101] 3.92/3.94 f4(I110, I111, I112, I113, I114) -> f11(I115, I116, 5, I117, I118) [5 = I114 /\ I113 + 2 <= I111 /\ I112 + 2 <= I110 /\ -1 <= I116 - 1 /\ 6 <= I115 - 1 /\ 6 <= I111 - 1 /\ 6 <= I110 - 1 /\ I115 <= I111 /\ I115 <= I110] 3.92/3.94 f10(I119, I120, I121, I122, I123) -> f10(I124, I125, I126, I127, I123) [I123 + 2 <= I120 /\ I122 + 2 <= I119 /\ -1 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ 2 <= I119 - 1 /\ I125 <= I120] 3.92/3.94 f3(I128, I129, I130, I131, I132) -> f10(I133, I134, I135, 5, I131) [I130 + 4 <= I129 /\ I131 + 2 <= I129 /\ I130 + 2 <= I128 /\ -1 <= I135 - 1 /\ 4 <= I134 - 1 /\ 9 <= I133 - 1 /\ 2 <= I129 - 1 /\ 0 <= I128 - 1 /\ I134 - 2 <= I129] 3.92/3.94 f4(I136, I137, I138, I139, I140) -> f10(I141, I142, I143, 5, 1) [5 = I140 /\ I139 + 2 <= I137 /\ I138 + 2 <= I136 /\ -1 <= I143 - 1 /\ 6 <= I142 - 1 /\ 6 <= I141 - 1 /\ 6 <= I137 - 1 /\ 6 <= I136 - 1 /\ I142 <= I137 /\ I142 <= I136] 3.92/3.94 f2(I144, I145, I146, I147, I148) -> f2(I149, I150, I151, I152, I153) [I149 + 2 <= I144 /\ y2 <= y1 /\ I150 <= I145 /\ 2 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I149 - 1 /\ 0 <= I150 - 1] 3.92/3.94 f2(I154, I155, I156, I157, I158) -> f2(I159, I160, I161, I162, I163) [I159 <= I154 /\ I164 <= I165 - 1 /\ I160 + 1 <= I155 /\ 0 <= I154 - 1 /\ 0 <= I155 - 1 /\ 0 <= I159 - 1 /\ -1 <= I160 - 1] 3.92/3.94 f6(I166, I167, I168, I169, I170) -> f9(I171, I167, 5, I172, I173) [5 = I168 /\ I167 + 4 <= I166 /\ 6 <= I171 - 1 /\ 6 <= I166 - 1 /\ I171 <= I166] 3.92/3.94 f6(I174, I175, I176, I177, I178) -> f9(I179, I175, 5, I180, I181) [5 = I176 /\ I175 + 4 <= I174 /\ 6 <= I179 - 1 /\ 6 <= I174 - 1 /\ I179 <= I174] 3.92/3.94 f8(I182, I183, I184, I185, I186) -> f6(I187, 6, 5, I188, I189) [5 = I185 /\ 6 = I184 /\ I183 + 4 <= I182 /\ 9 <= I187 - 1 /\ 9 <= I182 - 1 /\ I187 <= I182] 3.92/3.94 f7(I190, I191, I192, I193, I194) -> f6(I195, I192, 5, I196, I197) [5 = I193 /\ I192 + 4 <= I190 /\ I191 + 4 <= I190 /\ 6 <= I195 - 1 /\ 6 <= I190 - 1 /\ I195 <= I190] 3.92/3.94 f3(I198, I199, I200, I201, I202) -> f6(I203, 6, 5, I204, I205) [I200 + 4 <= I199 /\ I201 + 2 <= I199 /\ I200 + 2 <= I198 /\ 9 <= I203 - 1 /\ 2 <= I199 - 1 /\ 0 <= I198 - 1 /\ I203 - 7 <= I199 /\ I203 - 9 <= I198] 3.92/3.94 f4(I206, I207, I208, I209, I210) -> f6(I211, I212, 5, I213, I214) [5 = I210 /\ I209 + 2 <= I207 /\ I208 + 2 <= I206 /\ 6 <= I211 - 1 /\ 6 <= I207 - 1 /\ 6 <= I206 - 1] 3.92/3.94 f3(I215, I216, I217, I218, I219) -> f6(I220, 6, 5, I221, I222) [I217 + 4 <= I216 /\ I218 + 2 <= I216 /\ I217 + 2 <= I215 /\ 9 <= I220 - 1 /\ 2 <= I216 - 1 /\ 0 <= I215 - 1] 3.92/3.94 f4(I223, I224, I225, I226, I227) -> f6(I228, I229, 5, I230, I231) [5 = I227 /\ I226 + 2 <= I224 /\ I225 + 2 <= I223 /\ 6 <= I228 - 1 /\ 6 <= I224 - 1 /\ 6 <= I223 - 1] 3.92/3.94 f5(I232, I233, I234, I235, I236) -> f4(I237, I238, I239, I240, 5) [5 = I234 /\ I233 + 2 <= I232 /\ 6 <= I238 - 1 /\ 6 <= I237 - 1 /\ 6 <= I232 - 1] 3.92/3.94 f1(I241, I242, I243, I244, I245) -> f4(I246, I247, I248, I249, 5) [6 <= I246 - 1 /\ 6 <= I247 - 1] 3.92/3.94 f1(I250, I251, I252, I253, I254) -> f3(I255, I256, 3, 1, I257) [4 <= I255 - 1 /\ 6 <= I256 - 1] 3.92/3.94 f1(I258, I259, I260, I261, I262) -> f2(I263, I264, I265, I266, I267) [9 <= I263 - 1 /\ 6 <= I264 - 1] 3.92/3.94 3.92/3.94 We use the basic value criterion with the projection function NU: 3.92/3.94 NU[f2#(z1,z2,z3,z4,z5)] = z2 3.92/3.94 3.92/3.94 This gives the following inequalities: 3.92/3.94 I149 + 2 <= I144 /\ y2 <= y1 /\ I150 <= I145 /\ 2 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I149 - 1 /\ 0 <= I150 - 1 ==> I145 (>! \union =) I150 3.92/3.94 I159 <= I154 /\ I164 <= I165 - 1 /\ I160 + 1 <= I155 /\ 0 <= I154 - 1 /\ 0 <= I155 - 1 /\ 0 <= I159 - 1 /\ -1 <= I160 - 1 ==> I155 >! I160 3.92/3.94 3.92/3.94 We remove all the strictly oriented dependency pairs. 3.92/3.94 3.92/3.94 DP problem for innermost termination. 3.92/3.94 P = 3.92/3.94 f2#(I144, I145, I146, I147, I148) -> f2#(I149, I150, I151, I152, I153) [I149 + 2 <= I144 /\ y2 <= y1 /\ I150 <= I145 /\ 2 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I149 - 1 /\ 0 <= I150 - 1] 3.92/3.94 R = 3.92/3.94 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 3.92/3.94 f14(I0, I1, I2, I3, I4) -> f10(I5, I6, I7, I3, I4) [I4 + 2 <= I1 /\ I3 + 2 <= I0 /\ I2 + 4 <= I0 /\ -1 <= I7 - 1 /\ 1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I5 <= I0] 3.92/3.94 f13(I8, I9, I10, I11, I12) -> f14(I13, I14, I15, I16, I10) [I10 + 2 <= I8 /\ 1 <= I14 - 1 /\ 4 <= I13 - 1 /\ 0 <= I9 - 1 /\ 2 <= I8 - 1 /\ I14 <= I8] 3.92/3.94 f13(I17, I18, I19, I20, I21) -> f14(I22, I23, I24, I25, I19) [I19 + 2 <= I17 /\ 1 <= I23 - 1 /\ 2 <= I22 - 1 /\ 0 <= I18 - 1 /\ 2 <= I17 - 1 /\ I23 <= I17] 3.92/3.94 f13(I26, I27, I28, I29, I30) -> f10(I31, I32, I33, I34, I28) [I28 + 2 <= I26 /\ -1 <= I33 - 1 /\ 1 <= I32 - 1 /\ 1 <= I31 - 1 /\ 0 <= I27 - 1 /\ 2 <= I26 - 1 /\ I32 <= I26] 3.92/3.94 f13(I35, I36, I37, I38, I39) -> f13(I40, I41, I42, I43, I44) [I37 + 2 <= I35 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I36 - 1 /\ 2 <= I35 - 1] 3.92/3.94 f9(I45, I46, I47, I48, I49) -> f13(I50, I51, 5, I52, I53) [5 = I47 /\ I46 + 4 <= I45 /\ -1 <= I51 - 1 /\ 6 <= I50 - 1 /\ 6 <= I45 - 1 /\ I50 <= I45] 3.92/3.94 f4(I54, I55, I56, I57, I58) -> f13(I59, I60, 5, I61, I62) [5 = I58 /\ I57 + 2 <= I55 /\ I56 + 2 <= I54 /\ -1 <= I60 - 1 /\ 6 <= I59 - 1 /\ 6 <= I55 - 1 /\ 6 <= I54 - 1 /\ I59 <= I55 /\ I59 <= I54] 3.92/3.94 f12(I63, I64, I65, I66, I67) -> f12(I68, I69, I70, I71, I72) [I65 + 2 <= I63 /\ -1 <= I69 - 1 /\ 0 <= I68 - 1 /\ 0 <= I64 - 1 /\ 2 <= I63 - 1] 3.92/3.94 f6(I73, I74, I75, I76, I77) -> f12(I78, I79, 5, I80, I81) [5 = I75 /\ I74 + 4 <= I73 /\ -1 <= I79 - 1 /\ 6 <= I78 - 1 /\ 6 <= I73 - 1 /\ I78 <= I73] 3.92/3.94 f4(I82, I83, I84, I85, I86) -> f12(I87, I88, 5, I89, I90) [5 = I86 /\ I85 + 2 <= I83 /\ I84 + 2 <= I82 /\ -1 <= I88 - 1 /\ 6 <= I87 - 1 /\ 6 <= I83 - 1 /\ 6 <= I82 - 1 /\ I87 <= I83 /\ I87 <= I82] 3.92/3.94 f11(I91, I92, I93, I94, I95) -> f11(I96, I97, I98, I99, I100) [I93 + 2 <= I91 /\ -1 <= I97 - 1 /\ 0 <= I96 - 1 /\ 0 <= I92 - 1 /\ 2 <= I91 - 1] 3.92/3.94 f6(I101, I102, I103, I104, I105) -> f11(I106, I107, 5, I108, I109) [5 = I103 /\ I102 + 4 <= I101 /\ -1 <= I107 - 1 /\ 6 <= I106 - 1 /\ 6 <= I101 - 1 /\ I106 <= I101] 3.92/3.94 f4(I110, I111, I112, I113, I114) -> f11(I115, I116, 5, I117, I118) [5 = I114 /\ I113 + 2 <= I111 /\ I112 + 2 <= I110 /\ -1 <= I116 - 1 /\ 6 <= I115 - 1 /\ 6 <= I111 - 1 /\ 6 <= I110 - 1 /\ I115 <= I111 /\ I115 <= I110] 3.92/3.94 f10(I119, I120, I121, I122, I123) -> f10(I124, I125, I126, I127, I123) [I123 + 2 <= I120 /\ I122 + 2 <= I119 /\ -1 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ 2 <= I119 - 1 /\ I125 <= I120] 3.92/3.94 f3(I128, I129, I130, I131, I132) -> f10(I133, I134, I135, 5, I131) [I130 + 4 <= I129 /\ I131 + 2 <= I129 /\ I130 + 2 <= I128 /\ -1 <= I135 - 1 /\ 4 <= I134 - 1 /\ 9 <= I133 - 1 /\ 2 <= I129 - 1 /\ 0 <= I128 - 1 /\ I134 - 2 <= I129] 3.92/3.94 f4(I136, I137, I138, I139, I140) -> f10(I141, I142, I143, 5, 1) [5 = I140 /\ I139 + 2 <= I137 /\ I138 + 2 <= I136 /\ -1 <= I143 - 1 /\ 6 <= I142 - 1 /\ 6 <= I141 - 1 /\ 6 <= I137 - 1 /\ 6 <= I136 - 1 /\ I142 <= I137 /\ I142 <= I136] 3.92/3.94 f2(I144, I145, I146, I147, I148) -> f2(I149, I150, I151, I152, I153) [I149 + 2 <= I144 /\ y2 <= y1 /\ I150 <= I145 /\ 2 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I149 - 1 /\ 0 <= I150 - 1] 3.92/3.94 f2(I154, I155, I156, I157, I158) -> f2(I159, I160, I161, I162, I163) [I159 <= I154 /\ I164 <= I165 - 1 /\ I160 + 1 <= I155 /\ 0 <= I154 - 1 /\ 0 <= I155 - 1 /\ 0 <= I159 - 1 /\ -1 <= I160 - 1] 3.92/3.94 f6(I166, I167, I168, I169, I170) -> f9(I171, I167, 5, I172, I173) [5 = I168 /\ I167 + 4 <= I166 /\ 6 <= I171 - 1 /\ 6 <= I166 - 1 /\ I171 <= I166] 3.92/3.94 f6(I174, I175, I176, I177, I178) -> f9(I179, I175, 5, I180, I181) [5 = I176 /\ I175 + 4 <= I174 /\ 6 <= I179 - 1 /\ 6 <= I174 - 1 /\ I179 <= I174] 3.92/3.94 f8(I182, I183, I184, I185, I186) -> f6(I187, 6, 5, I188, I189) [5 = I185 /\ 6 = I184 /\ I183 + 4 <= I182 /\ 9 <= I187 - 1 /\ 9 <= I182 - 1 /\ I187 <= I182] 3.92/3.94 f7(I190, I191, I192, I193, I194) -> f6(I195, I192, 5, I196, I197) [5 = I193 /\ I192 + 4 <= I190 /\ I191 + 4 <= I190 /\ 6 <= I195 - 1 /\ 6 <= I190 - 1 /\ I195 <= I190] 3.92/3.94 f3(I198, I199, I200, I201, I202) -> f6(I203, 6, 5, I204, I205) [I200 + 4 <= I199 /\ I201 + 2 <= I199 /\ I200 + 2 <= I198 /\ 9 <= I203 - 1 /\ 2 <= I199 - 1 /\ 0 <= I198 - 1 /\ I203 - 7 <= I199 /\ I203 - 9 <= I198] 3.92/3.94 f4(I206, I207, I208, I209, I210) -> f6(I211, I212, 5, I213, I214) [5 = I210 /\ I209 + 2 <= I207 /\ I208 + 2 <= I206 /\ 6 <= I211 - 1 /\ 6 <= I207 - 1 /\ 6 <= I206 - 1] 3.92/3.94 f3(I215, I216, I217, I218, I219) -> f6(I220, 6, 5, I221, I222) [I217 + 4 <= I216 /\ I218 + 2 <= I216 /\ I217 + 2 <= I215 /\ 9 <= I220 - 1 /\ 2 <= I216 - 1 /\ 0 <= I215 - 1] 3.92/3.94 f4(I223, I224, I225, I226, I227) -> f6(I228, I229, 5, I230, I231) [5 = I227 /\ I226 + 2 <= I224 /\ I225 + 2 <= I223 /\ 6 <= I228 - 1 /\ 6 <= I224 - 1 /\ 6 <= I223 - 1] 3.92/3.94 f5(I232, I233, I234, I235, I236) -> f4(I237, I238, I239, I240, 5) [5 = I234 /\ I233 + 2 <= I232 /\ 6 <= I238 - 1 /\ 6 <= I237 - 1 /\ 6 <= I232 - 1] 3.92/3.94 f1(I241, I242, I243, I244, I245) -> f4(I246, I247, I248, I249, 5) [6 <= I246 - 1 /\ 6 <= I247 - 1] 3.92/3.94 f1(I250, I251, I252, I253, I254) -> f3(I255, I256, 3, 1, I257) [4 <= I255 - 1 /\ 6 <= I256 - 1] 3.92/3.94 f1(I258, I259, I260, I261, I262) -> f2(I263, I264, I265, I266, I267) [9 <= I263 - 1 /\ 6 <= I264 - 1] 3.92/3.94 3.92/3.94 We use the basic value criterion with the projection function NU: 3.92/3.94 NU[f2#(z1,z2,z3,z4,z5)] = z1 3.92/3.94 3.92/3.94 This gives the following inequalities: 3.92/3.94 I149 + 2 <= I144 /\ y2 <= y1 /\ I150 <= I145 /\ 2 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I149 - 1 /\ 0 <= I150 - 1 ==> I144 >! I149 3.92/3.94 3.92/3.94 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 3.92/3.94 3.92/3.94 DP problem for innermost termination. 3.92/3.94 P = 3.92/3.94 f10#(I119, I120, I121, I122, I123) -> f10#(I124, I125, I126, I127, I123) [I123 + 2 <= I120 /\ I122 + 2 <= I119 /\ -1 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ 2 <= I119 - 1 /\ I125 <= I120] 3.92/3.94 R = 3.92/3.94 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 3.92/3.94 f14(I0, I1, I2, I3, I4) -> f10(I5, I6, I7, I3, I4) [I4 + 2 <= I1 /\ I3 + 2 <= I0 /\ I2 + 4 <= I0 /\ -1 <= I7 - 1 /\ 1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 1 <= I1 - 1 /\ 2 <= I0 - 1 /\ I6 <= I1 /\ I5 <= I0] 3.92/3.94 f13(I8, I9, I10, I11, I12) -> f14(I13, I14, I15, I16, I10) [I10 + 2 <= I8 /\ 1 <= I14 - 1 /\ 4 <= I13 - 1 /\ 0 <= I9 - 1 /\ 2 <= I8 - 1 /\ I14 <= I8] 3.92/3.94 f13(I17, I18, I19, I20, I21) -> f14(I22, I23, I24, I25, I19) [I19 + 2 <= I17 /\ 1 <= I23 - 1 /\ 2 <= I22 - 1 /\ 0 <= I18 - 1 /\ 2 <= I17 - 1 /\ I23 <= I17] 3.92/3.94 f13(I26, I27, I28, I29, I30) -> f10(I31, I32, I33, I34, I28) [I28 + 2 <= I26 /\ -1 <= I33 - 1 /\ 1 <= I32 - 1 /\ 1 <= I31 - 1 /\ 0 <= I27 - 1 /\ 2 <= I26 - 1 /\ I32 <= I26] 3.92/3.94 f13(I35, I36, I37, I38, I39) -> f13(I40, I41, I42, I43, I44) [I37 + 2 <= I35 /\ -1 <= I41 - 1 /\ 0 <= I40 - 1 /\ 0 <= I36 - 1 /\ 2 <= I35 - 1] 3.92/3.94 f9(I45, I46, I47, I48, I49) -> f13(I50, I51, 5, I52, I53) [5 = I47 /\ I46 + 4 <= I45 /\ -1 <= I51 - 1 /\ 6 <= I50 - 1 /\ 6 <= I45 - 1 /\ I50 <= I45] 3.92/3.94 f4(I54, I55, I56, I57, I58) -> f13(I59, I60, 5, I61, I62) [5 = I58 /\ I57 + 2 <= I55 /\ I56 + 2 <= I54 /\ -1 <= I60 - 1 /\ 6 <= I59 - 1 /\ 6 <= I55 - 1 /\ 6 <= I54 - 1 /\ I59 <= I55 /\ I59 <= I54] 3.92/3.94 f12(I63, I64, I65, I66, I67) -> f12(I68, I69, I70, I71, I72) [I65 + 2 <= I63 /\ -1 <= I69 - 1 /\ 0 <= I68 - 1 /\ 0 <= I64 - 1 /\ 2 <= I63 - 1] 3.92/3.94 f6(I73, I74, I75, I76, I77) -> f12(I78, I79, 5, I80, I81) [5 = I75 /\ I74 + 4 <= I73 /\ -1 <= I79 - 1 /\ 6 <= I78 - 1 /\ 6 <= I73 - 1 /\ I78 <= I73] 3.92/3.94 f4(I82, I83, I84, I85, I86) -> f12(I87, I88, 5, I89, I90) [5 = I86 /\ I85 + 2 <= I83 /\ I84 + 2 <= I82 /\ -1 <= I88 - 1 /\ 6 <= I87 - 1 /\ 6 <= I83 - 1 /\ 6 <= I82 - 1 /\ I87 <= I83 /\ I87 <= I82] 3.92/3.94 f11(I91, I92, I93, I94, I95) -> f11(I96, I97, I98, I99, I100) [I93 + 2 <= I91 /\ -1 <= I97 - 1 /\ 0 <= I96 - 1 /\ 0 <= I92 - 1 /\ 2 <= I91 - 1] 3.92/3.94 f6(I101, I102, I103, I104, I105) -> f11(I106, I107, 5, I108, I109) [5 = I103 /\ I102 + 4 <= I101 /\ -1 <= I107 - 1 /\ 6 <= I106 - 1 /\ 6 <= I101 - 1 /\ I106 <= I101] 3.92/3.94 f4(I110, I111, I112, I113, I114) -> f11(I115, I116, 5, I117, I118) [5 = I114 /\ I113 + 2 <= I111 /\ I112 + 2 <= I110 /\ -1 <= I116 - 1 /\ 6 <= I115 - 1 /\ 6 <= I111 - 1 /\ 6 <= I110 - 1 /\ I115 <= I111 /\ I115 <= I110] 3.92/3.94 f10(I119, I120, I121, I122, I123) -> f10(I124, I125, I126, I127, I123) [I123 + 2 <= I120 /\ I122 + 2 <= I119 /\ -1 <= I126 - 1 /\ 0 <= I125 - 1 /\ 0 <= I124 - 1 /\ 0 <= I121 - 1 /\ 0 <= I120 - 1 /\ 2 <= I119 - 1 /\ I125 <= I120] 3.92/3.94 f3(I128, I129, I130, I131, I132) -> f10(I133, I134, I135, 5, I131) [I130 + 4 <= I129 /\ I131 + 2 <= I129 /\ I130 + 2 <= I128 /\ -1 <= I135 - 1 /\ 4 <= I134 - 1 /\ 9 <= I133 - 1 /\ 2 <= I129 - 1 /\ 0 <= I128 - 1 /\ I134 - 2 <= I129] 3.92/3.94 f4(I136, I137, I138, I139, I140) -> f10(I141, I142, I143, 5, 1) [5 = I140 /\ I139 + 2 <= I137 /\ I138 + 2 <= I136 /\ -1 <= I143 - 1 /\ 6 <= I142 - 1 /\ 6 <= I141 - 1 /\ 6 <= I137 - 1 /\ 6 <= I136 - 1 /\ I142 <= I137 /\ I142 <= I136] 3.92/3.94 f2(I144, I145, I146, I147, I148) -> f2(I149, I150, I151, I152, I153) [I149 + 2 <= I144 /\ y2 <= y1 /\ I150 <= I145 /\ 2 <= I144 - 1 /\ 0 <= I145 - 1 /\ 0 <= I149 - 1 /\ 0 <= I150 - 1] 3.92/3.94 f2(I154, I155, I156, I157, I158) -> f2(I159, I160, I161, I162, I163) [I159 <= I154 /\ I164 <= I165 - 1 /\ I160 + 1 <= I155 /\ 0 <= I154 - 1 /\ 0 <= I155 - 1 /\ 0 <= I159 - 1 /\ -1 <= I160 - 1] 3.92/3.94 f6(I166, I167, I168, I169, I170) -> f9(I171, I167, 5, I172, I173) [5 = I168 /\ I167 + 4 <= I166 /\ 6 <= I171 - 1 /\ 6 <= I166 - 1 /\ I171 <= I166] 3.92/3.94 f6(I174, I175, I176, I177, I178) -> f9(I179, I175, 5, I180, I181) [5 = I176 /\ I175 + 4 <= I174 /\ 6 <= I179 - 1 /\ 6 <= I174 - 1 /\ I179 <= I174] 3.92/3.94 f8(I182, I183, I184, I185, I186) -> f6(I187, 6, 5, I188, I189) [5 = I185 /\ 6 = I184 /\ I183 + 4 <= I182 /\ 9 <= I187 - 1 /\ 9 <= I182 - 1 /\ I187 <= I182] 3.92/3.94 f7(I190, I191, I192, I193, I194) -> f6(I195, I192, 5, I196, I197) [5 = I193 /\ I192 + 4 <= I190 /\ I191 + 4 <= I190 /\ 6 <= I195 - 1 /\ 6 <= I190 - 1 /\ I195 <= I190] 3.92/3.94 f3(I198, I199, I200, I201, I202) -> f6(I203, 6, 5, I204, I205) [I200 + 4 <= I199 /\ I201 + 2 <= I199 /\ I200 + 2 <= I198 /\ 9 <= I203 - 1 /\ 2 <= I199 - 1 /\ 0 <= I198 - 1 /\ I203 - 7 <= I199 /\ I203 - 9 <= I198] 3.92/3.94 f4(I206, I207, I208, I209, I210) -> f6(I211, I212, 5, I213, I214) [5 = I210 /\ I209 + 2 <= I207 /\ I208 + 2 <= I206 /\ 6 <= I211 - 1 /\ 6 <= I207 - 1 /\ 6 <= I206 - 1] 3.92/3.94 f3(I215, I216, I217, I218, I219) -> f6(I220, 6, 5, I221, I222) [I217 + 4 <= I216 /\ I218 + 2 <= I216 /\ I217 + 2 <= I215 /\ 9 <= I220 - 1 /\ 2 <= I216 - 1 /\ 0 <= I215 - 1] 3.92/3.94 f4(I223, I224, I225, I226, I227) -> f6(I228, I229, 5, I230, I231) [5 = I227 /\ I226 + 2 <= I224 /\ I225 + 2 <= I223 /\ 6 <= I228 - 1 /\ 6 <= I224 - 1 /\ 6 <= I223 - 1] 3.92/3.94 f5(I232, I233, I234, I235, I236) -> f4(I237, I238, I239, I240, 5) [5 = I234 /\ I233 + 2 <= I232 /\ 6 <= I238 - 1 /\ 6 <= I237 - 1 /\ 6 <= I232 - 1] 3.92/3.94 f1(I241, I242, I243, I244, I245) -> f4(I246, I247, I248, I249, 5) [6 <= I246 - 1 /\ 6 <= I247 - 1] 3.92/3.94 f1(I250, I251, I252, I253, I254) -> f3(I255, I256, 3, 1, I257) [4 <= I255 - 1 /\ 6 <= I256 - 1] 3.92/3.94 f1(I258, I259, I260, I261, I262) -> f2(I263, I264, I265, I266, I267) [9 <= I263 - 1 /\ 6 <= I264 - 1] 3.92/3.94 3.92/6.92 EOF