2.92/2.98 MAYBE 2.92/2.98 2.92/2.98 DP problem for innermost termination. 2.92/2.98 P = 2.92/2.98 init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 2.92/2.98 f5#(I0, I1, I2, I3, I4) -> f5#(I5, I6, I7, I8, I9) [y1 - 1 <= y1 - 1 /\ 0 <= y1 - 1 /\ I5 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I5 - 1] 2.92/2.98 f5#(I10, I11, I12, I13, I14) -> f5#(I15, I16, I17, I18, I19) [I15 + 1 <= I10 /\ I20 <= 0 /\ 0 <= I10 - 1 /\ -1 <= I15 - 1] 2.92/2.98 f8#(I21, I22, I23, I24, I25) -> f2#(I22, I23, I24, I26, I27) [I22 <= I21 - 1 /\ I24 <= I23 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= I21 - 1] 2.92/2.98 f2#(I28, I29, I30, I31, I32) -> f8#(I28, I28 - 1, I29, I30 + 1, I33) [0 <= I28 - 1 /\ -1 <= I29 - 1 /\ I30 <= I29 - 1 /\ -1 <= I34 - 1 /\ -1 <= I30 - 1] 2.92/2.98 f2#(I35, I36, I37, I38, I39) -> f8#(I35, I35 - 1, I36, I37 + 1, I40) [I37 <= I36 - 1 /\ -1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 0 <= I35 - 1] 2.92/2.98 f2#(I41, I42, I43, I44, I45) -> f2#(I41 - 1, I42, I43, I46, I47) [I42 <= I43 /\ I41 - 1 <= I41 - 1 /\ -1 <= I42 - 1 /\ 0 <= I41 - 1] 2.92/2.98 f7#(I48, I49, I50, I51, I52) -> f5#(I53, I54, I55, I56, I57) [0 <= I58 - 1 /\ 0 <= I50 - 1 /\ I53 <= I49 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ 0 <= I53 - 1 /\ I52 + 2 <= I49 /\ I51 + 2 <= I49] 2.92/2.98 f6#(I59, I60, I61, I62, I63) -> f7#(I64, I65, I66, I61, I67) [y2 <= I68 - 1 /\ -1 <= y2 - 1 /\ -1 <= y3 - 1 /\ I64 <= I59 /\ I64 <= I60 /\ I65 <= I60 /\ 0 <= I59 - 1 /\ 0 <= I60 - 1 /\ 0 <= I64 - 1 /\ 0 <= I65 - 1 /\ I67 + 2 <= I60 /\ I61 + 2 <= I60 /\ y2 + 1 = I66] 2.92/2.98 f6#(I69, I70, I71, I72, I73) -> f7#(I74, I75, I76, I71, I77) [I78 <= I79 - 1 /\ -1 <= I78 - 1 /\ I74 <= I69 /\ I74 <= I70 /\ I75 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1 /\ I77 + 2 <= I70 /\ I71 + 2 <= I70 /\ I78 + 1 = I76] 2.92/2.98 f6#(I80, I81, I82, I83, I84) -> f7#(I85, I86, I87, I82, I88) [I85 <= I80 /\ I89 <= I87 /\ I85 <= I81 /\ I86 <= I81 /\ 0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 0 <= I85 - 1 /\ 0 <= I86 - 1 /\ I88 + 2 <= I81 /\ I82 + 2 <= I81] 2.92/2.98 f3#(I90, I91, I92, I93, I94) -> f6#(I95, I96, 0, I97, I98) [I95 <= I90 /\ 0 <= I99 - 1 /\ I96 - 1 <= I90 /\ 0 <= I90 - 1 /\ 0 <= I95 - 1 /\ 1 <= I96 - 1] 2.92/2.98 f3#(I100, I101, I102, I103, I104) -> f6#(I105, I106, I107, I108, I109) [I105 <= I100 /\ 0 <= I110 - 1 /\ 0 <= I100 - 1 /\ 0 <= I105 - 1 /\ 1 <= I106 - 1] 2.92/2.98 f3#(I111, I112, I113, I114, I115) -> f6#(I116, I117, I118, I119, I120) [I116 <= I111 /\ 0 <= I121 - 1 /\ 0 <= I111 - 1 /\ 0 <= I116 - 1 /\ 2 <= I117 - 1] 2.92/2.98 f3#(I122, I123, I124, I125, I126) -> f6#(I127, I128, 0, I129, I130) [I127 <= I122 /\ 0 <= I131 - 1 /\ 0 <= I122 - 1 /\ 0 <= I127 - 1 /\ 2 <= I128 - 1] 2.92/2.98 f1#(I132, I133, I134, I135, I136) -> f5#(I137, I138, I139, I140, I141) [0 = I133 /\ 1 <= I137 - 1 /\ 0 <= I132 - 1 /\ I137 - 1 <= I132] 2.92/2.98 f3#(I142, I143, I144, I145, I146) -> f4#(I147, I148, I149, I150, I151) [-1 <= I152 - 1 /\ 1 <= I153 - 1 /\ I147 <= I142 /\ 0 <= I142 - 1 /\ 0 <= I147 - 1 /\ 0 = I143] 2.92/2.98 f3#(I154, I155, I156, I157, I158) -> f4#(I159, I160, I161, I162, I163) [I159 <= I154 /\ 1 <= I164 - 1 /\ 0 <= I154 - 1 /\ 0 <= I159 - 1 /\ 0 = I155] 2.92/2.98 f3#(I165, I166, I167, I168, I169) -> f5#(I170, I171, I172, I173, I174) [0 = I166 /\ -1 <= I170 - 1 /\ 0 <= I165 - 1 /\ I170 + 1 <= I165] 2.92/2.98 f1#(I175, I176, I177, I178, I179) -> f5#(I180, I181, I182, I183, I184) [0 = I176 /\ -1 <= I180 - 1 /\ 0 <= I175 - 1 /\ I180 + 1 <= I175] 2.92/2.98 f4#(I185, I186, I187, I188, I189) -> f5#(I190, I191, I192, I193, I194) [I190 + 1 <= I185 /\ 1 <= I195 - 1 /\ 0 <= I185 - 1 /\ -1 <= I190 - 1] 2.92/2.98 f3#(I196, I197, I198, I199, I200) -> f2#(I197, I201, 1, I202, I203) [0 <= I201 - 1 /\ 0 <= I196 - 1] 2.92/2.98 f1#(I204, I205, I206, I207, I208) -> f3#(I209, I210, I211, I212, I213) [0 <= I209 - 1 /\ 0 <= I204 - 1 /\ I209 <= I204 /\ 0 <= I205 - 1 /\ -1 <= I210 - 1] 2.92/2.98 f1#(I214, I215, I216, I217, I218) -> f3#(I219, 0, I220, I221, I222) [0 <= I219 - 1 /\ 0 <= I214 - 1 /\ 0 <= I215 - 1 /\ I219 <= I214] 2.92/2.98 f1#(I223, I224, I225, I226, I227) -> f2#(0, 0, 0, I228, I229) [0 = I224 /\ 0 <= I223 - 1] 2.92/2.98 R = 2.92/2.98 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 2.92/2.98 f5(I0, I1, I2, I3, I4) -> f5(I5, I6, I7, I8, I9) [y1 - 1 <= y1 - 1 /\ 0 <= y1 - 1 /\ I5 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I5 - 1] 2.92/2.98 f5(I10, I11, I12, I13, I14) -> f5(I15, I16, I17, I18, I19) [I15 + 1 <= I10 /\ I20 <= 0 /\ 0 <= I10 - 1 /\ -1 <= I15 - 1] 2.92/2.98 f8(I21, I22, I23, I24, I25) -> f2(I22, I23, I24, I26, I27) [I22 <= I21 - 1 /\ I24 <= I23 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= I21 - 1] 2.92/2.98 f2(I28, I29, I30, I31, I32) -> f8(I28, I28 - 1, I29, I30 + 1, I33) [0 <= I28 - 1 /\ -1 <= I29 - 1 /\ I30 <= I29 - 1 /\ -1 <= I34 - 1 /\ -1 <= I30 - 1] 2.92/2.98 f2(I35, I36, I37, I38, I39) -> f8(I35, I35 - 1, I36, I37 + 1, I40) [I37 <= I36 - 1 /\ -1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 0 <= I35 - 1] 2.92/2.98 f2(I41, I42, I43, I44, I45) -> f2(I41 - 1, I42, I43, I46, I47) [I42 <= I43 /\ I41 - 1 <= I41 - 1 /\ -1 <= I42 - 1 /\ 0 <= I41 - 1] 2.92/2.98 f7(I48, I49, I50, I51, I52) -> f5(I53, I54, I55, I56, I57) [0 <= I58 - 1 /\ 0 <= I50 - 1 /\ I53 <= I49 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ 0 <= I53 - 1 /\ I52 + 2 <= I49 /\ I51 + 2 <= I49] 2.92/2.98 f6(I59, I60, I61, I62, I63) -> f7(I64, I65, I66, I61, I67) [y2 <= I68 - 1 /\ -1 <= y2 - 1 /\ -1 <= y3 - 1 /\ I64 <= I59 /\ I64 <= I60 /\ I65 <= I60 /\ 0 <= I59 - 1 /\ 0 <= I60 - 1 /\ 0 <= I64 - 1 /\ 0 <= I65 - 1 /\ I67 + 2 <= I60 /\ I61 + 2 <= I60 /\ y2 + 1 = I66] 2.92/2.98 f6(I69, I70, I71, I72, I73) -> f7(I74, I75, I76, I71, I77) [I78 <= I79 - 1 /\ -1 <= I78 - 1 /\ I74 <= I69 /\ I74 <= I70 /\ I75 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1 /\ I77 + 2 <= I70 /\ I71 + 2 <= I70 /\ I78 + 1 = I76] 2.92/2.98 f6(I80, I81, I82, I83, I84) -> f7(I85, I86, I87, I82, I88) [I85 <= I80 /\ I89 <= I87 /\ I85 <= I81 /\ I86 <= I81 /\ 0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 0 <= I85 - 1 /\ 0 <= I86 - 1 /\ I88 + 2 <= I81 /\ I82 + 2 <= I81] 2.92/2.98 f3(I90, I91, I92, I93, I94) -> f6(I95, I96, 0, I97, I98) [I95 <= I90 /\ 0 <= I99 - 1 /\ I96 - 1 <= I90 /\ 0 <= I90 - 1 /\ 0 <= I95 - 1 /\ 1 <= I96 - 1] 2.92/2.98 f3(I100, I101, I102, I103, I104) -> f6(I105, I106, I107, I108, I109) [I105 <= I100 /\ 0 <= I110 - 1 /\ 0 <= I100 - 1 /\ 0 <= I105 - 1 /\ 1 <= I106 - 1] 2.92/2.98 f3(I111, I112, I113, I114, I115) -> f6(I116, I117, I118, I119, I120) [I116 <= I111 /\ 0 <= I121 - 1 /\ 0 <= I111 - 1 /\ 0 <= I116 - 1 /\ 2 <= I117 - 1] 2.92/2.98 f3(I122, I123, I124, I125, I126) -> f6(I127, I128, 0, I129, I130) [I127 <= I122 /\ 0 <= I131 - 1 /\ 0 <= I122 - 1 /\ 0 <= I127 - 1 /\ 2 <= I128 - 1] 2.92/2.98 f1(I132, I133, I134, I135, I136) -> f5(I137, I138, I139, I140, I141) [0 = I133 /\ 1 <= I137 - 1 /\ 0 <= I132 - 1 /\ I137 - 1 <= I132] 2.92/2.98 f3(I142, I143, I144, I145, I146) -> f4(I147, I148, I149, I150, I151) [-1 <= I152 - 1 /\ 1 <= I153 - 1 /\ I147 <= I142 /\ 0 <= I142 - 1 /\ 0 <= I147 - 1 /\ 0 = I143] 2.92/2.98 f3(I154, I155, I156, I157, I158) -> f4(I159, I160, I161, I162, I163) [I159 <= I154 /\ 1 <= I164 - 1 /\ 0 <= I154 - 1 /\ 0 <= I159 - 1 /\ 0 = I155] 2.92/2.98 f3(I165, I166, I167, I168, I169) -> f5(I170, I171, I172, I173, I174) [0 = I166 /\ -1 <= I170 - 1 /\ 0 <= I165 - 1 /\ I170 + 1 <= I165] 2.92/2.98 f1(I175, I176, I177, I178, I179) -> f5(I180, I181, I182, I183, I184) [0 = I176 /\ -1 <= I180 - 1 /\ 0 <= I175 - 1 /\ I180 + 1 <= I175] 2.92/2.98 f4(I185, I186, I187, I188, I189) -> f5(I190, I191, I192, I193, I194) [I190 + 1 <= I185 /\ 1 <= I195 - 1 /\ 0 <= I185 - 1 /\ -1 <= I190 - 1] 2.92/2.98 f3(I196, I197, I198, I199, I200) -> f2(I197, I201, 1, I202, I203) [0 <= I201 - 1 /\ 0 <= I196 - 1] 2.92/2.98 f1(I204, I205, I206, I207, I208) -> f3(I209, I210, I211, I212, I213) [0 <= I209 - 1 /\ 0 <= I204 - 1 /\ I209 <= I204 /\ 0 <= I205 - 1 /\ -1 <= I210 - 1] 2.92/2.98 f1(I214, I215, I216, I217, I218) -> f3(I219, 0, I220, I221, I222) [0 <= I219 - 1 /\ 0 <= I214 - 1 /\ 0 <= I215 - 1 /\ I219 <= I214] 2.92/2.98 f1(I223, I224, I225, I226, I227) -> f2(0, 0, 0, I228, I229) [0 = I224 /\ 0 <= I223 - 1] 2.92/2.98 2.92/2.98 The dependency graph for this problem is: 2.92/2.98 0 -> 15, 19, 22, 23, 24 2.92/2.98 1 -> 1, 2 2.92/2.98 2 -> 1, 2 2.92/2.98 3 -> 4, 5, 6 2.92/2.98 4 -> 3 2.92/2.98 5 -> 3 2.92/2.98 6 -> 6 2.92/2.98 7 -> 1, 2 2.92/2.98 8 -> 7 2.92/2.98 9 -> 7 2.92/2.98 10 -> 7 2.92/2.98 11 -> 8, 9, 10 2.92/2.98 12 -> 8, 9, 10 2.92/2.98 13 -> 8, 9, 10 2.92/2.98 14 -> 8, 9, 10 2.92/2.98 15 -> 1, 2 2.92/2.98 16 -> 20 2.92/2.98 17 -> 20 2.92/2.98 18 -> 1, 2 2.92/2.98 19 -> 1, 2 2.92/2.98 20 -> 1, 2 2.92/2.98 21 -> 4, 5, 6 2.92/2.98 22 -> 11, 12, 13, 14, 16, 17, 18, 21 2.92/2.98 23 -> 11, 12, 13, 14, 16, 17, 18, 21 2.92/2.98 24 -> 2.92/2.98 Where: 2.92/2.98 0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 2.92/2.98 1) f5#(I0, I1, I2, I3, I4) -> f5#(I5, I6, I7, I8, I9) [y1 - 1 <= y1 - 1 /\ 0 <= y1 - 1 /\ I5 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I5 - 1] 2.92/2.98 2) f5#(I10, I11, I12, I13, I14) -> f5#(I15, I16, I17, I18, I19) [I15 + 1 <= I10 /\ I20 <= 0 /\ 0 <= I10 - 1 /\ -1 <= I15 - 1] 2.92/2.98 3) f8#(I21, I22, I23, I24, I25) -> f2#(I22, I23, I24, I26, I27) [I22 <= I21 - 1 /\ I24 <= I23 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= I21 - 1] 2.92/2.98 4) f2#(I28, I29, I30, I31, I32) -> f8#(I28, I28 - 1, I29, I30 + 1, I33) [0 <= I28 - 1 /\ -1 <= I29 - 1 /\ I30 <= I29 - 1 /\ -1 <= I34 - 1 /\ -1 <= I30 - 1] 2.92/2.98 5) f2#(I35, I36, I37, I38, I39) -> f8#(I35, I35 - 1, I36, I37 + 1, I40) [I37 <= I36 - 1 /\ -1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 0 <= I35 - 1] 2.92/2.98 6) f2#(I41, I42, I43, I44, I45) -> f2#(I41 - 1, I42, I43, I46, I47) [I42 <= I43 /\ I41 - 1 <= I41 - 1 /\ -1 <= I42 - 1 /\ 0 <= I41 - 1] 2.92/2.98 7) f7#(I48, I49, I50, I51, I52) -> f5#(I53, I54, I55, I56, I57) [0 <= I58 - 1 /\ 0 <= I50 - 1 /\ I53 <= I49 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ 0 <= I53 - 1 /\ I52 + 2 <= I49 /\ I51 + 2 <= I49] 2.92/2.98 8) f6#(I59, I60, I61, I62, I63) -> f7#(I64, I65, I66, I61, I67) [y2 <= I68 - 1 /\ -1 <= y2 - 1 /\ -1 <= y3 - 1 /\ I64 <= I59 /\ I64 <= I60 /\ I65 <= I60 /\ 0 <= I59 - 1 /\ 0 <= I60 - 1 /\ 0 <= I64 - 1 /\ 0 <= I65 - 1 /\ I67 + 2 <= I60 /\ I61 + 2 <= I60 /\ y2 + 1 = I66] 2.92/2.98 9) f6#(I69, I70, I71, I72, I73) -> f7#(I74, I75, I76, I71, I77) [I78 <= I79 - 1 /\ -1 <= I78 - 1 /\ I74 <= I69 /\ I74 <= I70 /\ I75 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1 /\ I77 + 2 <= I70 /\ I71 + 2 <= I70 /\ I78 + 1 = I76] 2.92/2.98 10) f6#(I80, I81, I82, I83, I84) -> f7#(I85, I86, I87, I82, I88) [I85 <= I80 /\ I89 <= I87 /\ I85 <= I81 /\ I86 <= I81 /\ 0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 0 <= I85 - 1 /\ 0 <= I86 - 1 /\ I88 + 2 <= I81 /\ I82 + 2 <= I81] 2.92/2.98 11) f3#(I90, I91, I92, I93, I94) -> f6#(I95, I96, 0, I97, I98) [I95 <= I90 /\ 0 <= I99 - 1 /\ I96 - 1 <= I90 /\ 0 <= I90 - 1 /\ 0 <= I95 - 1 /\ 1 <= I96 - 1] 2.92/2.98 12) f3#(I100, I101, I102, I103, I104) -> f6#(I105, I106, I107, I108, I109) [I105 <= I100 /\ 0 <= I110 - 1 /\ 0 <= I100 - 1 /\ 0 <= I105 - 1 /\ 1 <= I106 - 1] 2.92/2.98 13) f3#(I111, I112, I113, I114, I115) -> f6#(I116, I117, I118, I119, I120) [I116 <= I111 /\ 0 <= I121 - 1 /\ 0 <= I111 - 1 /\ 0 <= I116 - 1 /\ 2 <= I117 - 1] 2.92/2.98 14) f3#(I122, I123, I124, I125, I126) -> f6#(I127, I128, 0, I129, I130) [I127 <= I122 /\ 0 <= I131 - 1 /\ 0 <= I122 - 1 /\ 0 <= I127 - 1 /\ 2 <= I128 - 1] 2.92/2.98 15) f1#(I132, I133, I134, I135, I136) -> f5#(I137, I138, I139, I140, I141) [0 = I133 /\ 1 <= I137 - 1 /\ 0 <= I132 - 1 /\ I137 - 1 <= I132] 2.92/2.98 16) f3#(I142, I143, I144, I145, I146) -> f4#(I147, I148, I149, I150, I151) [-1 <= I152 - 1 /\ 1 <= I153 - 1 /\ I147 <= I142 /\ 0 <= I142 - 1 /\ 0 <= I147 - 1 /\ 0 = I143] 2.92/2.98 17) f3#(I154, I155, I156, I157, I158) -> f4#(I159, I160, I161, I162, I163) [I159 <= I154 /\ 1 <= I164 - 1 /\ 0 <= I154 - 1 /\ 0 <= I159 - 1 /\ 0 = I155] 2.92/2.98 18) f3#(I165, I166, I167, I168, I169) -> f5#(I170, I171, I172, I173, I174) [0 = I166 /\ -1 <= I170 - 1 /\ 0 <= I165 - 1 /\ I170 + 1 <= I165] 2.92/2.98 19) f1#(I175, I176, I177, I178, I179) -> f5#(I180, I181, I182, I183, I184) [0 = I176 /\ -1 <= I180 - 1 /\ 0 <= I175 - 1 /\ I180 + 1 <= I175] 2.92/2.98 20) f4#(I185, I186, I187, I188, I189) -> f5#(I190, I191, I192, I193, I194) [I190 + 1 <= I185 /\ 1 <= I195 - 1 /\ 0 <= I185 - 1 /\ -1 <= I190 - 1] 2.92/2.98 21) f3#(I196, I197, I198, I199, I200) -> f2#(I197, I201, 1, I202, I203) [0 <= I201 - 1 /\ 0 <= I196 - 1] 2.92/2.98 22) f1#(I204, I205, I206, I207, I208) -> f3#(I209, I210, I211, I212, I213) [0 <= I209 - 1 /\ 0 <= I204 - 1 /\ I209 <= I204 /\ 0 <= I205 - 1 /\ -1 <= I210 - 1] 2.92/2.98 23) f1#(I214, I215, I216, I217, I218) -> f3#(I219, 0, I220, I221, I222) [0 <= I219 - 1 /\ 0 <= I214 - 1 /\ 0 <= I215 - 1 /\ I219 <= I214] 2.92/2.98 24) f1#(I223, I224, I225, I226, I227) -> f2#(0, 0, 0, I228, I229) [0 = I224 /\ 0 <= I223 - 1] 2.92/2.98 2.92/2.98 We have the following SCCs. 2.92/2.98 { 3, 4, 5 } 2.92/2.98 { 6 } 2.92/2.98 { 1, 2 } 2.92/2.98 2.92/2.98 DP problem for innermost termination. 2.92/2.98 P = 2.92/2.98 f5#(I0, I1, I2, I3, I4) -> f5#(I5, I6, I7, I8, I9) [y1 - 1 <= y1 - 1 /\ 0 <= y1 - 1 /\ I5 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I5 - 1] 2.92/2.98 f5#(I10, I11, I12, I13, I14) -> f5#(I15, I16, I17, I18, I19) [I15 + 1 <= I10 /\ I20 <= 0 /\ 0 <= I10 - 1 /\ -1 <= I15 - 1] 2.92/2.98 R = 2.92/2.98 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 2.92/2.98 f5(I0, I1, I2, I3, I4) -> f5(I5, I6, I7, I8, I9) [y1 - 1 <= y1 - 1 /\ 0 <= y1 - 1 /\ I5 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I5 - 1] 2.92/2.98 f5(I10, I11, I12, I13, I14) -> f5(I15, I16, I17, I18, I19) [I15 + 1 <= I10 /\ I20 <= 0 /\ 0 <= I10 - 1 /\ -1 <= I15 - 1] 2.92/2.98 f8(I21, I22, I23, I24, I25) -> f2(I22, I23, I24, I26, I27) [I22 <= I21 - 1 /\ I24 <= I23 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= I21 - 1] 2.92/2.98 f2(I28, I29, I30, I31, I32) -> f8(I28, I28 - 1, I29, I30 + 1, I33) [0 <= I28 - 1 /\ -1 <= I29 - 1 /\ I30 <= I29 - 1 /\ -1 <= I34 - 1 /\ -1 <= I30 - 1] 2.92/2.98 f2(I35, I36, I37, I38, I39) -> f8(I35, I35 - 1, I36, I37 + 1, I40) [I37 <= I36 - 1 /\ -1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 0 <= I35 - 1] 2.92/2.98 f2(I41, I42, I43, I44, I45) -> f2(I41 - 1, I42, I43, I46, I47) [I42 <= I43 /\ I41 - 1 <= I41 - 1 /\ -1 <= I42 - 1 /\ 0 <= I41 - 1] 2.92/2.98 f7(I48, I49, I50, I51, I52) -> f5(I53, I54, I55, I56, I57) [0 <= I58 - 1 /\ 0 <= I50 - 1 /\ I53 <= I49 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ 0 <= I53 - 1 /\ I52 + 2 <= I49 /\ I51 + 2 <= I49] 2.92/2.98 f6(I59, I60, I61, I62, I63) -> f7(I64, I65, I66, I61, I67) [y2 <= I68 - 1 /\ -1 <= y2 - 1 /\ -1 <= y3 - 1 /\ I64 <= I59 /\ I64 <= I60 /\ I65 <= I60 /\ 0 <= I59 - 1 /\ 0 <= I60 - 1 /\ 0 <= I64 - 1 /\ 0 <= I65 - 1 /\ I67 + 2 <= I60 /\ I61 + 2 <= I60 /\ y2 + 1 = I66] 2.92/2.98 f6(I69, I70, I71, I72, I73) -> f7(I74, I75, I76, I71, I77) [I78 <= I79 - 1 /\ -1 <= I78 - 1 /\ I74 <= I69 /\ I74 <= I70 /\ I75 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1 /\ I77 + 2 <= I70 /\ I71 + 2 <= I70 /\ I78 + 1 = I76] 2.92/2.98 f6(I80, I81, I82, I83, I84) -> f7(I85, I86, I87, I82, I88) [I85 <= I80 /\ I89 <= I87 /\ I85 <= I81 /\ I86 <= I81 /\ 0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 0 <= I85 - 1 /\ 0 <= I86 - 1 /\ I88 + 2 <= I81 /\ I82 + 2 <= I81] 2.92/2.98 f3(I90, I91, I92, I93, I94) -> f6(I95, I96, 0, I97, I98) [I95 <= I90 /\ 0 <= I99 - 1 /\ I96 - 1 <= I90 /\ 0 <= I90 - 1 /\ 0 <= I95 - 1 /\ 1 <= I96 - 1] 2.92/2.98 f3(I100, I101, I102, I103, I104) -> f6(I105, I106, I107, I108, I109) [I105 <= I100 /\ 0 <= I110 - 1 /\ 0 <= I100 - 1 /\ 0 <= I105 - 1 /\ 1 <= I106 - 1] 2.92/2.98 f3(I111, I112, I113, I114, I115) -> f6(I116, I117, I118, I119, I120) [I116 <= I111 /\ 0 <= I121 - 1 /\ 0 <= I111 - 1 /\ 0 <= I116 - 1 /\ 2 <= I117 - 1] 2.92/2.98 f3(I122, I123, I124, I125, I126) -> f6(I127, I128, 0, I129, I130) [I127 <= I122 /\ 0 <= I131 - 1 /\ 0 <= I122 - 1 /\ 0 <= I127 - 1 /\ 2 <= I128 - 1] 2.92/2.98 f1(I132, I133, I134, I135, I136) -> f5(I137, I138, I139, I140, I141) [0 = I133 /\ 1 <= I137 - 1 /\ 0 <= I132 - 1 /\ I137 - 1 <= I132] 2.92/2.98 f3(I142, I143, I144, I145, I146) -> f4(I147, I148, I149, I150, I151) [-1 <= I152 - 1 /\ 1 <= I153 - 1 /\ I147 <= I142 /\ 0 <= I142 - 1 /\ 0 <= I147 - 1 /\ 0 = I143] 2.92/2.98 f3(I154, I155, I156, I157, I158) -> f4(I159, I160, I161, I162, I163) [I159 <= I154 /\ 1 <= I164 - 1 /\ 0 <= I154 - 1 /\ 0 <= I159 - 1 /\ 0 = I155] 2.92/2.98 f3(I165, I166, I167, I168, I169) -> f5(I170, I171, I172, I173, I174) [0 = I166 /\ -1 <= I170 - 1 /\ 0 <= I165 - 1 /\ I170 + 1 <= I165] 2.92/2.98 f1(I175, I176, I177, I178, I179) -> f5(I180, I181, I182, I183, I184) [0 = I176 /\ -1 <= I180 - 1 /\ 0 <= I175 - 1 /\ I180 + 1 <= I175] 2.92/2.98 f4(I185, I186, I187, I188, I189) -> f5(I190, I191, I192, I193, I194) [I190 + 1 <= I185 /\ 1 <= I195 - 1 /\ 0 <= I185 - 1 /\ -1 <= I190 - 1] 2.92/2.98 f3(I196, I197, I198, I199, I200) -> f2(I197, I201, 1, I202, I203) [0 <= I201 - 1 /\ 0 <= I196 - 1] 2.92/2.98 f1(I204, I205, I206, I207, I208) -> f3(I209, I210, I211, I212, I213) [0 <= I209 - 1 /\ 0 <= I204 - 1 /\ I209 <= I204 /\ 0 <= I205 - 1 /\ -1 <= I210 - 1] 2.92/2.98 f1(I214, I215, I216, I217, I218) -> f3(I219, 0, I220, I221, I222) [0 <= I219 - 1 /\ 0 <= I214 - 1 /\ 0 <= I215 - 1 /\ I219 <= I214] 2.92/2.98 f1(I223, I224, I225, I226, I227) -> f2(0, 0, 0, I228, I229) [0 = I224 /\ 0 <= I223 - 1] 2.92/2.98 2.92/2.98 We use the basic value criterion with the projection function NU: 2.92/2.98 NU[f5#(z1,z2,z3,z4,z5)] = z1 2.92/2.98 2.92/2.98 This gives the following inequalities: 2.92/2.98 y1 - 1 <= y1 - 1 /\ 0 <= y1 - 1 /\ I5 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I5 - 1 ==> I0 (>! \union =) I5 2.92/2.98 I15 + 1 <= I10 /\ I20 <= 0 /\ 0 <= I10 - 1 /\ -1 <= I15 - 1 ==> I10 >! I15 2.92/2.98 2.92/2.98 We remove all the strictly oriented dependency pairs. 2.92/2.98 2.92/2.98 DP problem for innermost termination. 2.92/2.98 P = 2.92/2.98 f5#(I0, I1, I2, I3, I4) -> f5#(I5, I6, I7, I8, I9) [y1 - 1 <= y1 - 1 /\ 0 <= y1 - 1 /\ I5 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I5 - 1] 2.92/2.98 R = 2.92/2.98 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 2.92/2.98 f5(I0, I1, I2, I3, I4) -> f5(I5, I6, I7, I8, I9) [y1 - 1 <= y1 - 1 /\ 0 <= y1 - 1 /\ I5 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I5 - 1] 2.92/2.98 f5(I10, I11, I12, I13, I14) -> f5(I15, I16, I17, I18, I19) [I15 + 1 <= I10 /\ I20 <= 0 /\ 0 <= I10 - 1 /\ -1 <= I15 - 1] 2.92/2.98 f8(I21, I22, I23, I24, I25) -> f2(I22, I23, I24, I26, I27) [I22 <= I21 - 1 /\ I24 <= I23 /\ 0 <= I23 - 1 /\ 0 <= I24 - 1 /\ 0 <= I21 - 1] 2.92/2.98 f2(I28, I29, I30, I31, I32) -> f8(I28, I28 - 1, I29, I30 + 1, I33) [0 <= I28 - 1 /\ -1 <= I29 - 1 /\ I30 <= I29 - 1 /\ -1 <= I34 - 1 /\ -1 <= I30 - 1] 2.92/2.98 f2(I35, I36, I37, I38, I39) -> f8(I35, I35 - 1, I36, I37 + 1, I40) [I37 <= I36 - 1 /\ -1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 0 <= I35 - 1] 2.92/2.98 f2(I41, I42, I43, I44, I45) -> f2(I41 - 1, I42, I43, I46, I47) [I42 <= I43 /\ I41 - 1 <= I41 - 1 /\ -1 <= I42 - 1 /\ 0 <= I41 - 1] 2.92/2.98 f7(I48, I49, I50, I51, I52) -> f5(I53, I54, I55, I56, I57) [0 <= I58 - 1 /\ 0 <= I50 - 1 /\ I53 <= I49 /\ 0 <= I48 - 1 /\ 0 <= I49 - 1 /\ 0 <= I53 - 1 /\ I52 + 2 <= I49 /\ I51 + 2 <= I49] 2.92/2.98 f6(I59, I60, I61, I62, I63) -> f7(I64, I65, I66, I61, I67) [y2 <= I68 - 1 /\ -1 <= y2 - 1 /\ -1 <= y3 - 1 /\ I64 <= I59 /\ I64 <= I60 /\ I65 <= I60 /\ 0 <= I59 - 1 /\ 0 <= I60 - 1 /\ 0 <= I64 - 1 /\ 0 <= I65 - 1 /\ I67 + 2 <= I60 /\ I61 + 2 <= I60 /\ y2 + 1 = I66] 2.92/2.98 f6(I69, I70, I71, I72, I73) -> f7(I74, I75, I76, I71, I77) [I78 <= I79 - 1 /\ -1 <= I78 - 1 /\ I74 <= I69 /\ I74 <= I70 /\ I75 <= I70 /\ 0 <= I69 - 1 /\ 0 <= I70 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1 /\ I77 + 2 <= I70 /\ I71 + 2 <= I70 /\ I78 + 1 = I76] 2.92/2.98 f6(I80, I81, I82, I83, I84) -> f7(I85, I86, I87, I82, I88) [I85 <= I80 /\ I89 <= I87 /\ I85 <= I81 /\ I86 <= I81 /\ 0 <= I80 - 1 /\ 0 <= I81 - 1 /\ 0 <= I85 - 1 /\ 0 <= I86 - 1 /\ I88 + 2 <= I81 /\ I82 + 2 <= I81] 2.92/2.98 f3(I90, I91, I92, I93, I94) -> f6(I95, I96, 0, I97, I98) [I95 <= I90 /\ 0 <= I99 - 1 /\ I96 - 1 <= I90 /\ 0 <= I90 - 1 /\ 0 <= I95 - 1 /\ 1 <= I96 - 1] 2.92/2.98 f3(I100, I101, I102, I103, I104) -> f6(I105, I106, I107, I108, I109) [I105 <= I100 /\ 0 <= I110 - 1 /\ 0 <= I100 - 1 /\ 0 <= I105 - 1 /\ 1 <= I106 - 1] 2.92/2.98 f3(I111, I112, I113, I114, I115) -> f6(I116, I117, I118, I119, I120) [I116 <= I111 /\ 0 <= I121 - 1 /\ 0 <= I111 - 1 /\ 0 <= I116 - 1 /\ 2 <= I117 - 1] 2.92/2.98 f3(I122, I123, I124, I125, I126) -> f6(I127, I128, 0, I129, I130) [I127 <= I122 /\ 0 <= I131 - 1 /\ 0 <= I122 - 1 /\ 0 <= I127 - 1 /\ 2 <= I128 - 1] 2.92/2.98 f1(I132, I133, I134, I135, I136) -> f5(I137, I138, I139, I140, I141) [0 = I133 /\ 1 <= I137 - 1 /\ 0 <= I132 - 1 /\ I137 - 1 <= I132] 2.92/2.98 f3(I142, I143, I144, I145, I146) -> f4(I147, I148, I149, I150, I151) [-1 <= I152 - 1 /\ 1 <= I153 - 1 /\ I147 <= I142 /\ 0 <= I142 - 1 /\ 0 <= I147 - 1 /\ 0 = I143] 2.92/2.98 f3(I154, I155, I156, I157, I158) -> f4(I159, I160, I161, I162, I163) [I159 <= I154 /\ 1 <= I164 - 1 /\ 0 <= I154 - 1 /\ 0 <= I159 - 1 /\ 0 = I155] 2.92/2.98 f3(I165, I166, I167, I168, I169) -> f5(I170, I171, I172, I173, I174) [0 = I166 /\ -1 <= I170 - 1 /\ 0 <= I165 - 1 /\ I170 + 1 <= I165] 2.92/2.98 f1(I175, I176, I177, I178, I179) -> f5(I180, I181, I182, I183, I184) [0 = I176 /\ -1 <= I180 - 1 /\ 0 <= I175 - 1 /\ I180 + 1 <= I175] 2.92/2.98 f4(I185, I186, I187, I188, I189) -> f5(I190, I191, I192, I193, I194) [I190 + 1 <= I185 /\ 1 <= I195 - 1 /\ 0 <= I185 - 1 /\ -1 <= I190 - 1] 2.92/2.98 f3(I196, I197, I198, I199, I200) -> f2(I197, I201, 1, I202, I203) [0 <= I201 - 1 /\ 0 <= I196 - 1] 2.92/2.98 f1(I204, I205, I206, I207, I208) -> f3(I209, I210, I211, I212, I213) [0 <= I209 - 1 /\ 0 <= I204 - 1 /\ I209 <= I204 /\ 0 <= I205 - 1 /\ -1 <= I210 - 1] 2.92/2.98 f1(I214, I215, I216, I217, I218) -> f3(I219, 0, I220, I221, I222) [0 <= I219 - 1 /\ 0 <= I214 - 1 /\ 0 <= I215 - 1 /\ I219 <= I214] 2.92/2.98 f1(I223, I224, I225, I226, I227) -> f2(0, 0, 0, I228, I229) [0 = I224 /\ 0 <= I223 - 1] 2.92/2.98 2.92/5.96 EOF