4.92/4.94 MAYBE 4.92/4.94 4.92/4.94 DP problem for innermost termination. 4.92/4.94 P = 4.92/4.94 init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.92/4.94 f5#(I34, I35, I36, I37, I38, I39) -> f5#(I40, I41, I36 - 1, I42, I43, I44) [-1 <= I37 - 1 /\ 0 <= I45 - 1 /\ 0 <= I36 - 1 /\ I40 - 2 <= I34 /\ I40 - 2 <= I35 /\ I41 - 2 <= I34 /\ I41 - 2 <= I35 /\ 1 <= I34 - 1 /\ 1 <= I35 - 1 /\ 3 <= I40 - 1 /\ 3 <= I41 - 1] 4.92/4.94 f5#(I46, I47, I48, I49, I50, I51) -> f5#(I52, I53, I48 - 1, I54, I55, I56) [3 <= I53 - 1 /\ 3 <= I52 - 1 /\ 1 <= I47 - 1 /\ 1 <= I46 - 1 /\ I53 - 2 <= I47 /\ I53 - 2 <= I46 /\ I52 - 2 <= I47 /\ I52 - 2 <= I46 /\ -1 <= I49 - 1 /\ 0 <= I48 - 1] 4.92/4.94 f5#(I57, I58, I59, I60, I61, I62) -> f5#(I63, I64, I59 - 1, I65, I66, I67) [0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 1 <= I58 - 1 /\ 0 <= I57 - 1 /\ -1 <= I60 - 1 /\ 0 <= I59 - 1] 4.92/4.94 f5#(I68, I69, I70, I71, I72, I73) -> f5#(I74, I75, I70 - 1, I76, I77, I78) [-1 <= I71 - 1 /\ 0 <= I79 - 1 /\ 0 <= I70 - 1 /\ 0 <= I68 - 1 /\ 1 <= I69 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1] 4.92/4.94 f5#(I80, I81, I82, I83, I84, I85) -> f5#(I86, I87, I82 - 1, I83 + 1, I88, I89) [0 <= I82 - 1 /\ 0 <= I90 - 1 /\ -1 <= I83 - 1 /\ I86 <= I80 /\ I87 + 2 <= I81 /\ 0 <= I80 - 1 /\ 2 <= I81 - 1 /\ 0 <= I86 - 1 /\ 0 <= I87 - 1] 4.92/4.94 f5#(I91, I92, I93, I94, I95, I96) -> f5#(I97, I98, I93 - 1, I94 + 1, I99, I100) [0 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I92 - 1 /\ 0 <= I91 - 1 /\ I98 + 2 <= I92 /\ I97 <= I91 /\ 0 <= I93 - 1 /\ -1 <= I94 - 1] 4.92/4.94 f2#(I101, I102, I103, I104, I105, I106) -> f5#(I107, I108, I109, I110, I111, I112) [0 <= I109 - 1 /\ 0 <= I113 - 1 /\ 0 <= I103 - 1 /\ -1 <= I104 - 1 /\ I107 - 1 <= I101 /\ I107 - 2 <= I102 /\ I108 - 1 <= I101 /\ I108 - 2 <= I102 /\ 0 <= I101 - 1 /\ -1 <= I102 - 1 /\ 1 <= I107 - 1 /\ 1 <= I108 - 1] 4.92/4.94 f4#(I114, I115, I116, I117, I118, I119) -> f4#(I120, I121, I122, I123, I124, I125) [2 <= I121 - 1 /\ 2 <= I120 - 1 /\ 2 <= I115 - 1 /\ 2 <= I114 - 1 /\ I121 - 2 <= I115 /\ I121 - 2 <= I114 /\ I120 - 2 <= I115 /\ I120 - 2 <= I114] 4.92/4.94 f4#(I126, I127, I128, I129, I130, I131) -> f4#(I132, I133, I134, I135, I136, I137) [-1 <= I133 - 1 /\ -1 <= I132 - 1 /\ 1 <= I127 - 1 /\ 1 <= I126 - 1 /\ I133 + 2 <= I127 /\ I133 + 2 <= I126 /\ I132 + 2 <= I127 /\ I132 + 2 <= I126] 4.92/4.94 f2#(I138, I139, I140, I141, I142, I143) -> f4#(I144, I145, I146, I147, I148, I149) [I144 <= I139 /\ 0 <= I150 - 1 /\ I145 <= I139 /\ 0 <= I138 - 1 /\ -1 <= I139 - 1 /\ -1 <= I144 - 1 /\ -1 <= I145 - 1 /\ 0 = I140] 4.92/4.94 f3#(I151, I152, I153, I154, I155, I156) -> f2#(I157, I158, I153 - 1, I155, I159, I160) [I156 + 2 <= I154 /\ 3 <= I158 - 1 /\ 0 <= I157 - 1 /\ 1 <= I154 - 1 /\ 0 <= I151 - 1 /\ I157 + 1 <= I154 /\ I157 <= I151] 4.92/4.94 f2#(I161, I162, I163, I164, I165, I166) -> f2#(I167, I168, I163 - 1, I169, I170, I171) [0 <= I163 - 1 /\ 0 <= I172 - 1 /\ I167 <= I161 /\ I167 - 1 <= I162 /\ 0 <= I161 - 1 /\ -1 <= I162 - 1 /\ 0 <= I167 - 1 /\ 2 <= I168 - 1] 4.92/4.94 f2#(I173, I174, I175, I176, I177, I178) -> f2#(I179, I180, I175 - 1, I181, I182, I183) [0 <= I175 - 1 /\ 0 <= I184 - 1 /\ I179 <= I173 /\ I179 - 1 <= I174 /\ I180 - 2 <= I174 /\ 0 <= I173 - 1 /\ -1 <= I174 - 1 /\ 0 <= I179 - 1 /\ 1 <= I180 - 1] 4.92/4.94 f1#(I185, I186, I187, I188, I189, I190) -> f2#(I191, I192, I193, 1, I194, I195) [-1 <= I192 - 1 /\ 0 <= I191 - 1 /\ 0 <= I185 - 1 /\ I192 + 1 <= I185 /\ I191 <= I185 /\ -1 <= I193 - 1 /\ -1 <= I186 - 1] 4.92/4.94 R = 4.92/4.94 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.92/4.94 f5(I0, I1, I2, I3, I4, I5) -> f6(I6, I3 + 1, I7, I8, I9, I10) [-1 <= I3 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I6 <= I0 /\ I6 + 1 <= I1 /\ 0 <= I0 - 1 /\ 1 <= I1 - 1 /\ 0 <= I6 - 1] 4.92/4.94 f5(I11, I12, I13, I14, I15, I16) -> f6(I17, I14 + 1, I18, I19, I20, I21) [0 <= I17 - 1 /\ 1 <= I12 - 1 /\ 0 <= I11 - 1 /\ I17 + 1 <= I12 /\ I17 <= I11 /\ -1 <= I14 - 1 /\ 0 <= I13 - 1] 4.92/4.94 f2(I22, I23, I24, I25, I26, I27) -> f6(I28, I25 + 1, I29, I30, I31, I32) [0 <= I33 - 1 /\ 0 <= y2 - 1 /\ 0 <= I24 - 1 /\ -1 <= I25 - 1 /\ I28 <= I22 /\ I28 - 1 <= I23 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1 /\ 0 <= I28 - 1] 4.92/4.94 f5(I34, I35, I36, I37, I38, I39) -> f5(I40, I41, I36 - 1, I42, I43, I44) [-1 <= I37 - 1 /\ 0 <= I45 - 1 /\ 0 <= I36 - 1 /\ I40 - 2 <= I34 /\ I40 - 2 <= I35 /\ I41 - 2 <= I34 /\ I41 - 2 <= I35 /\ 1 <= I34 - 1 /\ 1 <= I35 - 1 /\ 3 <= I40 - 1 /\ 3 <= I41 - 1] 4.92/4.94 f5(I46, I47, I48, I49, I50, I51) -> f5(I52, I53, I48 - 1, I54, I55, I56) [3 <= I53 - 1 /\ 3 <= I52 - 1 /\ 1 <= I47 - 1 /\ 1 <= I46 - 1 /\ I53 - 2 <= I47 /\ I53 - 2 <= I46 /\ I52 - 2 <= I47 /\ I52 - 2 <= I46 /\ -1 <= I49 - 1 /\ 0 <= I48 - 1] 4.92/4.94 f5(I57, I58, I59, I60, I61, I62) -> f5(I63, I64, I59 - 1, I65, I66, I67) [0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 1 <= I58 - 1 /\ 0 <= I57 - 1 /\ -1 <= I60 - 1 /\ 0 <= I59 - 1] 4.92/4.94 f5(I68, I69, I70, I71, I72, I73) -> f5(I74, I75, I70 - 1, I76, I77, I78) [-1 <= I71 - 1 /\ 0 <= I79 - 1 /\ 0 <= I70 - 1 /\ 0 <= I68 - 1 /\ 1 <= I69 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1] 4.92/4.94 f5(I80, I81, I82, I83, I84, I85) -> f5(I86, I87, I82 - 1, I83 + 1, I88, I89) [0 <= I82 - 1 /\ 0 <= I90 - 1 /\ -1 <= I83 - 1 /\ I86 <= I80 /\ I87 + 2 <= I81 /\ 0 <= I80 - 1 /\ 2 <= I81 - 1 /\ 0 <= I86 - 1 /\ 0 <= I87 - 1] 4.92/4.94 f5(I91, I92, I93, I94, I95, I96) -> f5(I97, I98, I93 - 1, I94 + 1, I99, I100) [0 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I92 - 1 /\ 0 <= I91 - 1 /\ I98 + 2 <= I92 /\ I97 <= I91 /\ 0 <= I93 - 1 /\ -1 <= I94 - 1] 4.92/4.94 f2(I101, I102, I103, I104, I105, I106) -> f5(I107, I108, I109, I110, I111, I112) [0 <= I109 - 1 /\ 0 <= I113 - 1 /\ 0 <= I103 - 1 /\ -1 <= I104 - 1 /\ I107 - 1 <= I101 /\ I107 - 2 <= I102 /\ I108 - 1 <= I101 /\ I108 - 2 <= I102 /\ 0 <= I101 - 1 /\ -1 <= I102 - 1 /\ 1 <= I107 - 1 /\ 1 <= I108 - 1] 4.92/4.94 f4(I114, I115, I116, I117, I118, I119) -> f4(I120, I121, I122, I123, I124, I125) [2 <= I121 - 1 /\ 2 <= I120 - 1 /\ 2 <= I115 - 1 /\ 2 <= I114 - 1 /\ I121 - 2 <= I115 /\ I121 - 2 <= I114 /\ I120 - 2 <= I115 /\ I120 - 2 <= I114] 4.92/4.94 f4(I126, I127, I128, I129, I130, I131) -> f4(I132, I133, I134, I135, I136, I137) [-1 <= I133 - 1 /\ -1 <= I132 - 1 /\ 1 <= I127 - 1 /\ 1 <= I126 - 1 /\ I133 + 2 <= I127 /\ I133 + 2 <= I126 /\ I132 + 2 <= I127 /\ I132 + 2 <= I126] 4.92/4.94 f2(I138, I139, I140, I141, I142, I143) -> f4(I144, I145, I146, I147, I148, I149) [I144 <= I139 /\ 0 <= I150 - 1 /\ I145 <= I139 /\ 0 <= I138 - 1 /\ -1 <= I139 - 1 /\ -1 <= I144 - 1 /\ -1 <= I145 - 1 /\ 0 = I140] 4.92/4.94 f3(I151, I152, I153, I154, I155, I156) -> f2(I157, I158, I153 - 1, I155, I159, I160) [I156 + 2 <= I154 /\ 3 <= I158 - 1 /\ 0 <= I157 - 1 /\ 1 <= I154 - 1 /\ 0 <= I151 - 1 /\ I157 + 1 <= I154 /\ I157 <= I151] 4.92/4.94 f2(I161, I162, I163, I164, I165, I166) -> f2(I167, I168, I163 - 1, I169, I170, I171) [0 <= I163 - 1 /\ 0 <= I172 - 1 /\ I167 <= I161 /\ I167 - 1 <= I162 /\ 0 <= I161 - 1 /\ -1 <= I162 - 1 /\ 0 <= I167 - 1 /\ 2 <= I168 - 1] 4.92/4.94 f2(I173, I174, I175, I176, I177, I178) -> f2(I179, I180, I175 - 1, I181, I182, I183) [0 <= I175 - 1 /\ 0 <= I184 - 1 /\ I179 <= I173 /\ I179 - 1 <= I174 /\ I180 - 2 <= I174 /\ 0 <= I173 - 1 /\ -1 <= I174 - 1 /\ 0 <= I179 - 1 /\ 1 <= I180 - 1] 4.92/4.94 f1(I185, I186, I187, I188, I189, I190) -> f2(I191, I192, I193, 1, I194, I195) [-1 <= I192 - 1 /\ 0 <= I191 - 1 /\ 0 <= I185 - 1 /\ I192 + 1 <= I185 /\ I191 <= I185 /\ -1 <= I193 - 1 /\ -1 <= I186 - 1] 4.92/4.94 4.92/4.94 The dependency graph for this problem is: 4.92/4.94 0 -> 14 4.92/4.94 1 -> 1, 2, 3, 4, 5, 6 4.92/4.94 2 -> 1, 2, 3, 4, 5, 6 4.92/4.94 3 -> 1, 2, 3, 4, 5, 6 4.92/4.94 4 -> 1, 2, 3, 4, 5, 6 4.92/4.94 5 -> 1, 2, 3, 4, 5, 6 4.92/4.94 6 -> 1, 2, 3, 4, 5, 6 4.92/4.94 7 -> 1, 2, 3, 4, 5, 6 4.92/4.94 8 -> 8, 9 4.92/4.94 9 -> 8, 9 4.92/4.94 10 -> 8, 9 4.92/4.94 11 -> 7, 10, 12, 13 4.92/4.94 12 -> 7, 10, 12, 13 4.92/4.94 13 -> 7, 10, 12, 13 4.92/4.94 14 -> 7, 10, 12, 13 4.92/4.94 Where: 4.92/4.94 0) init#(x1, x2, x3, x4, x5, x6) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.92/4.94 1) f5#(I34, I35, I36, I37, I38, I39) -> f5#(I40, I41, I36 - 1, I42, I43, I44) [-1 <= I37 - 1 /\ 0 <= I45 - 1 /\ 0 <= I36 - 1 /\ I40 - 2 <= I34 /\ I40 - 2 <= I35 /\ I41 - 2 <= I34 /\ I41 - 2 <= I35 /\ 1 <= I34 - 1 /\ 1 <= I35 - 1 /\ 3 <= I40 - 1 /\ 3 <= I41 - 1] 4.92/4.94 2) f5#(I46, I47, I48, I49, I50, I51) -> f5#(I52, I53, I48 - 1, I54, I55, I56) [3 <= I53 - 1 /\ 3 <= I52 - 1 /\ 1 <= I47 - 1 /\ 1 <= I46 - 1 /\ I53 - 2 <= I47 /\ I53 - 2 <= I46 /\ I52 - 2 <= I47 /\ I52 - 2 <= I46 /\ -1 <= I49 - 1 /\ 0 <= I48 - 1] 4.92/4.94 3) f5#(I57, I58, I59, I60, I61, I62) -> f5#(I63, I64, I59 - 1, I65, I66, I67) [0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 1 <= I58 - 1 /\ 0 <= I57 - 1 /\ -1 <= I60 - 1 /\ 0 <= I59 - 1] 4.92/4.94 4) f5#(I68, I69, I70, I71, I72, I73) -> f5#(I74, I75, I70 - 1, I76, I77, I78) [-1 <= I71 - 1 /\ 0 <= I79 - 1 /\ 0 <= I70 - 1 /\ 0 <= I68 - 1 /\ 1 <= I69 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1] 4.92/4.94 5) f5#(I80, I81, I82, I83, I84, I85) -> f5#(I86, I87, I82 - 1, I83 + 1, I88, I89) [0 <= I82 - 1 /\ 0 <= I90 - 1 /\ -1 <= I83 - 1 /\ I86 <= I80 /\ I87 + 2 <= I81 /\ 0 <= I80 - 1 /\ 2 <= I81 - 1 /\ 0 <= I86 - 1 /\ 0 <= I87 - 1] 4.92/4.94 6) f5#(I91, I92, I93, I94, I95, I96) -> f5#(I97, I98, I93 - 1, I94 + 1, I99, I100) [0 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I92 - 1 /\ 0 <= I91 - 1 /\ I98 + 2 <= I92 /\ I97 <= I91 /\ 0 <= I93 - 1 /\ -1 <= I94 - 1] 4.92/4.94 7) f2#(I101, I102, I103, I104, I105, I106) -> f5#(I107, I108, I109, I110, I111, I112) [0 <= I109 - 1 /\ 0 <= I113 - 1 /\ 0 <= I103 - 1 /\ -1 <= I104 - 1 /\ I107 - 1 <= I101 /\ I107 - 2 <= I102 /\ I108 - 1 <= I101 /\ I108 - 2 <= I102 /\ 0 <= I101 - 1 /\ -1 <= I102 - 1 /\ 1 <= I107 - 1 /\ 1 <= I108 - 1] 4.92/4.94 8) f4#(I114, I115, I116, I117, I118, I119) -> f4#(I120, I121, I122, I123, I124, I125) [2 <= I121 - 1 /\ 2 <= I120 - 1 /\ 2 <= I115 - 1 /\ 2 <= I114 - 1 /\ I121 - 2 <= I115 /\ I121 - 2 <= I114 /\ I120 - 2 <= I115 /\ I120 - 2 <= I114] 4.92/4.94 9) f4#(I126, I127, I128, I129, I130, I131) -> f4#(I132, I133, I134, I135, I136, I137) [-1 <= I133 - 1 /\ -1 <= I132 - 1 /\ 1 <= I127 - 1 /\ 1 <= I126 - 1 /\ I133 + 2 <= I127 /\ I133 + 2 <= I126 /\ I132 + 2 <= I127 /\ I132 + 2 <= I126] 4.92/4.94 10) f2#(I138, I139, I140, I141, I142, I143) -> f4#(I144, I145, I146, I147, I148, I149) [I144 <= I139 /\ 0 <= I150 - 1 /\ I145 <= I139 /\ 0 <= I138 - 1 /\ -1 <= I139 - 1 /\ -1 <= I144 - 1 /\ -1 <= I145 - 1 /\ 0 = I140] 4.92/4.94 11) f3#(I151, I152, I153, I154, I155, I156) -> f2#(I157, I158, I153 - 1, I155, I159, I160) [I156 + 2 <= I154 /\ 3 <= I158 - 1 /\ 0 <= I157 - 1 /\ 1 <= I154 - 1 /\ 0 <= I151 - 1 /\ I157 + 1 <= I154 /\ I157 <= I151] 4.92/4.94 12) f2#(I161, I162, I163, I164, I165, I166) -> f2#(I167, I168, I163 - 1, I169, I170, I171) [0 <= I163 - 1 /\ 0 <= I172 - 1 /\ I167 <= I161 /\ I167 - 1 <= I162 /\ 0 <= I161 - 1 /\ -1 <= I162 - 1 /\ 0 <= I167 - 1 /\ 2 <= I168 - 1] 4.92/4.94 13) f2#(I173, I174, I175, I176, I177, I178) -> f2#(I179, I180, I175 - 1, I181, I182, I183) [0 <= I175 - 1 /\ 0 <= I184 - 1 /\ I179 <= I173 /\ I179 - 1 <= I174 /\ I180 - 2 <= I174 /\ 0 <= I173 - 1 /\ -1 <= I174 - 1 /\ 0 <= I179 - 1 /\ 1 <= I180 - 1] 4.92/4.94 14) f1#(I185, I186, I187, I188, I189, I190) -> f2#(I191, I192, I193, 1, I194, I195) [-1 <= I192 - 1 /\ 0 <= I191 - 1 /\ 0 <= I185 - 1 /\ I192 + 1 <= I185 /\ I191 <= I185 /\ -1 <= I193 - 1 /\ -1 <= I186 - 1] 4.92/4.94 4.92/4.94 We have the following SCCs. 4.92/4.94 { 12, 13 } 4.92/4.94 { 8, 9 } 4.92/4.94 { 1, 2, 3, 4, 5, 6 } 4.92/4.94 4.92/4.94 DP problem for innermost termination. 4.92/4.94 P = 4.92/4.94 f5#(I34, I35, I36, I37, I38, I39) -> f5#(I40, I41, I36 - 1, I42, I43, I44) [-1 <= I37 - 1 /\ 0 <= I45 - 1 /\ 0 <= I36 - 1 /\ I40 - 2 <= I34 /\ I40 - 2 <= I35 /\ I41 - 2 <= I34 /\ I41 - 2 <= I35 /\ 1 <= I34 - 1 /\ 1 <= I35 - 1 /\ 3 <= I40 - 1 /\ 3 <= I41 - 1] 4.92/4.94 f5#(I46, I47, I48, I49, I50, I51) -> f5#(I52, I53, I48 - 1, I54, I55, I56) [3 <= I53 - 1 /\ 3 <= I52 - 1 /\ 1 <= I47 - 1 /\ 1 <= I46 - 1 /\ I53 - 2 <= I47 /\ I53 - 2 <= I46 /\ I52 - 2 <= I47 /\ I52 - 2 <= I46 /\ -1 <= I49 - 1 /\ 0 <= I48 - 1] 4.92/4.94 f5#(I57, I58, I59, I60, I61, I62) -> f5#(I63, I64, I59 - 1, I65, I66, I67) [0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 1 <= I58 - 1 /\ 0 <= I57 - 1 /\ -1 <= I60 - 1 /\ 0 <= I59 - 1] 4.92/4.94 f5#(I68, I69, I70, I71, I72, I73) -> f5#(I74, I75, I70 - 1, I76, I77, I78) [-1 <= I71 - 1 /\ 0 <= I79 - 1 /\ 0 <= I70 - 1 /\ 0 <= I68 - 1 /\ 1 <= I69 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1] 4.92/4.94 f5#(I80, I81, I82, I83, I84, I85) -> f5#(I86, I87, I82 - 1, I83 + 1, I88, I89) [0 <= I82 - 1 /\ 0 <= I90 - 1 /\ -1 <= I83 - 1 /\ I86 <= I80 /\ I87 + 2 <= I81 /\ 0 <= I80 - 1 /\ 2 <= I81 - 1 /\ 0 <= I86 - 1 /\ 0 <= I87 - 1] 4.92/4.94 f5#(I91, I92, I93, I94, I95, I96) -> f5#(I97, I98, I93 - 1, I94 + 1, I99, I100) [0 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I92 - 1 /\ 0 <= I91 - 1 /\ I98 + 2 <= I92 /\ I97 <= I91 /\ 0 <= I93 - 1 /\ -1 <= I94 - 1] 4.92/4.94 R = 4.92/4.94 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.92/4.94 f5(I0, I1, I2, I3, I4, I5) -> f6(I6, I3 + 1, I7, I8, I9, I10) [-1 <= I3 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I6 <= I0 /\ I6 + 1 <= I1 /\ 0 <= I0 - 1 /\ 1 <= I1 - 1 /\ 0 <= I6 - 1] 4.92/4.94 f5(I11, I12, I13, I14, I15, I16) -> f6(I17, I14 + 1, I18, I19, I20, I21) [0 <= I17 - 1 /\ 1 <= I12 - 1 /\ 0 <= I11 - 1 /\ I17 + 1 <= I12 /\ I17 <= I11 /\ -1 <= I14 - 1 /\ 0 <= I13 - 1] 4.92/4.94 f2(I22, I23, I24, I25, I26, I27) -> f6(I28, I25 + 1, I29, I30, I31, I32) [0 <= I33 - 1 /\ 0 <= y2 - 1 /\ 0 <= I24 - 1 /\ -1 <= I25 - 1 /\ I28 <= I22 /\ I28 - 1 <= I23 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1 /\ 0 <= I28 - 1] 4.92/4.94 f5(I34, I35, I36, I37, I38, I39) -> f5(I40, I41, I36 - 1, I42, I43, I44) [-1 <= I37 - 1 /\ 0 <= I45 - 1 /\ 0 <= I36 - 1 /\ I40 - 2 <= I34 /\ I40 - 2 <= I35 /\ I41 - 2 <= I34 /\ I41 - 2 <= I35 /\ 1 <= I34 - 1 /\ 1 <= I35 - 1 /\ 3 <= I40 - 1 /\ 3 <= I41 - 1] 4.92/4.94 f5(I46, I47, I48, I49, I50, I51) -> f5(I52, I53, I48 - 1, I54, I55, I56) [3 <= I53 - 1 /\ 3 <= I52 - 1 /\ 1 <= I47 - 1 /\ 1 <= I46 - 1 /\ I53 - 2 <= I47 /\ I53 - 2 <= I46 /\ I52 - 2 <= I47 /\ I52 - 2 <= I46 /\ -1 <= I49 - 1 /\ 0 <= I48 - 1] 4.92/4.94 f5(I57, I58, I59, I60, I61, I62) -> f5(I63, I64, I59 - 1, I65, I66, I67) [0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 1 <= I58 - 1 /\ 0 <= I57 - 1 /\ -1 <= I60 - 1 /\ 0 <= I59 - 1] 4.92/4.94 f5(I68, I69, I70, I71, I72, I73) -> f5(I74, I75, I70 - 1, I76, I77, I78) [-1 <= I71 - 1 /\ 0 <= I79 - 1 /\ 0 <= I70 - 1 /\ 0 <= I68 - 1 /\ 1 <= I69 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1] 4.92/4.94 f5(I80, I81, I82, I83, I84, I85) -> f5(I86, I87, I82 - 1, I83 + 1, I88, I89) [0 <= I82 - 1 /\ 0 <= I90 - 1 /\ -1 <= I83 - 1 /\ I86 <= I80 /\ I87 + 2 <= I81 /\ 0 <= I80 - 1 /\ 2 <= I81 - 1 /\ 0 <= I86 - 1 /\ 0 <= I87 - 1] 4.92/4.94 f5(I91, I92, I93, I94, I95, I96) -> f5(I97, I98, I93 - 1, I94 + 1, I99, I100) [0 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I92 - 1 /\ 0 <= I91 - 1 /\ I98 + 2 <= I92 /\ I97 <= I91 /\ 0 <= I93 - 1 /\ -1 <= I94 - 1] 4.92/4.94 f2(I101, I102, I103, I104, I105, I106) -> f5(I107, I108, I109, I110, I111, I112) [0 <= I109 - 1 /\ 0 <= I113 - 1 /\ 0 <= I103 - 1 /\ -1 <= I104 - 1 /\ I107 - 1 <= I101 /\ I107 - 2 <= I102 /\ I108 - 1 <= I101 /\ I108 - 2 <= I102 /\ 0 <= I101 - 1 /\ -1 <= I102 - 1 /\ 1 <= I107 - 1 /\ 1 <= I108 - 1] 4.92/4.94 f4(I114, I115, I116, I117, I118, I119) -> f4(I120, I121, I122, I123, I124, I125) [2 <= I121 - 1 /\ 2 <= I120 - 1 /\ 2 <= I115 - 1 /\ 2 <= I114 - 1 /\ I121 - 2 <= I115 /\ I121 - 2 <= I114 /\ I120 - 2 <= I115 /\ I120 - 2 <= I114] 4.92/4.94 f4(I126, I127, I128, I129, I130, I131) -> f4(I132, I133, I134, I135, I136, I137) [-1 <= I133 - 1 /\ -1 <= I132 - 1 /\ 1 <= I127 - 1 /\ 1 <= I126 - 1 /\ I133 + 2 <= I127 /\ I133 + 2 <= I126 /\ I132 + 2 <= I127 /\ I132 + 2 <= I126] 4.92/4.94 f2(I138, I139, I140, I141, I142, I143) -> f4(I144, I145, I146, I147, I148, I149) [I144 <= I139 /\ 0 <= I150 - 1 /\ I145 <= I139 /\ 0 <= I138 - 1 /\ -1 <= I139 - 1 /\ -1 <= I144 - 1 /\ -1 <= I145 - 1 /\ 0 = I140] 4.92/4.94 f3(I151, I152, I153, I154, I155, I156) -> f2(I157, I158, I153 - 1, I155, I159, I160) [I156 + 2 <= I154 /\ 3 <= I158 - 1 /\ 0 <= I157 - 1 /\ 1 <= I154 - 1 /\ 0 <= I151 - 1 /\ I157 + 1 <= I154 /\ I157 <= I151] 4.92/4.94 f2(I161, I162, I163, I164, I165, I166) -> f2(I167, I168, I163 - 1, I169, I170, I171) [0 <= I163 - 1 /\ 0 <= I172 - 1 /\ I167 <= I161 /\ I167 - 1 <= I162 /\ 0 <= I161 - 1 /\ -1 <= I162 - 1 /\ 0 <= I167 - 1 /\ 2 <= I168 - 1] 4.92/4.94 f2(I173, I174, I175, I176, I177, I178) -> f2(I179, I180, I175 - 1, I181, I182, I183) [0 <= I175 - 1 /\ 0 <= I184 - 1 /\ I179 <= I173 /\ I179 - 1 <= I174 /\ I180 - 2 <= I174 /\ 0 <= I173 - 1 /\ -1 <= I174 - 1 /\ 0 <= I179 - 1 /\ 1 <= I180 - 1] 4.92/4.94 f1(I185, I186, I187, I188, I189, I190) -> f2(I191, I192, I193, 1, I194, I195) [-1 <= I192 - 1 /\ 0 <= I191 - 1 /\ 0 <= I185 - 1 /\ I192 + 1 <= I185 /\ I191 <= I185 /\ -1 <= I193 - 1 /\ -1 <= I186 - 1] 4.92/4.94 4.92/4.94 We use the basic value criterion with the projection function NU: 4.92/4.94 NU[f5#(z1,z2,z3,z4,z5,z6)] = z3 4.92/4.94 4.92/4.94 This gives the following inequalities: 4.92/4.94 -1 <= I37 - 1 /\ 0 <= I45 - 1 /\ 0 <= I36 - 1 /\ I40 - 2 <= I34 /\ I40 - 2 <= I35 /\ I41 - 2 <= I34 /\ I41 - 2 <= I35 /\ 1 <= I34 - 1 /\ 1 <= I35 - 1 /\ 3 <= I40 - 1 /\ 3 <= I41 - 1 ==> I36 >! I36 - 1 4.92/4.94 3 <= I53 - 1 /\ 3 <= I52 - 1 /\ 1 <= I47 - 1 /\ 1 <= I46 - 1 /\ I53 - 2 <= I47 /\ I53 - 2 <= I46 /\ I52 - 2 <= I47 /\ I52 - 2 <= I46 /\ -1 <= I49 - 1 /\ 0 <= I48 - 1 ==> I48 >! I48 - 1 4.92/4.94 0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 1 <= I58 - 1 /\ 0 <= I57 - 1 /\ -1 <= I60 - 1 /\ 0 <= I59 - 1 ==> I59 >! I59 - 1 4.92/4.94 -1 <= I71 - 1 /\ 0 <= I79 - 1 /\ 0 <= I70 - 1 /\ 0 <= I68 - 1 /\ 1 <= I69 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1 ==> I70 >! I70 - 1 4.92/4.94 0 <= I82 - 1 /\ 0 <= I90 - 1 /\ -1 <= I83 - 1 /\ I86 <= I80 /\ I87 + 2 <= I81 /\ 0 <= I80 - 1 /\ 2 <= I81 - 1 /\ 0 <= I86 - 1 /\ 0 <= I87 - 1 ==> I82 >! I82 - 1 4.92/4.94 0 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I92 - 1 /\ 0 <= I91 - 1 /\ I98 + 2 <= I92 /\ I97 <= I91 /\ 0 <= I93 - 1 /\ -1 <= I94 - 1 ==> I93 >! I93 - 1 4.92/4.94 4.92/4.94 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 4.92/4.94 4.92/4.94 DP problem for innermost termination. 4.92/4.94 P = 4.92/4.94 f4#(I114, I115, I116, I117, I118, I119) -> f4#(I120, I121, I122, I123, I124, I125) [2 <= I121 - 1 /\ 2 <= I120 - 1 /\ 2 <= I115 - 1 /\ 2 <= I114 - 1 /\ I121 - 2 <= I115 /\ I121 - 2 <= I114 /\ I120 - 2 <= I115 /\ I120 - 2 <= I114] 4.92/4.94 f4#(I126, I127, I128, I129, I130, I131) -> f4#(I132, I133, I134, I135, I136, I137) [-1 <= I133 - 1 /\ -1 <= I132 - 1 /\ 1 <= I127 - 1 /\ 1 <= I126 - 1 /\ I133 + 2 <= I127 /\ I133 + 2 <= I126 /\ I132 + 2 <= I127 /\ I132 + 2 <= I126] 4.92/4.94 R = 4.92/4.94 init(x1, x2, x3, x4, x5, x6) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5, rnd6) 4.92/4.94 f5(I0, I1, I2, I3, I4, I5) -> f6(I6, I3 + 1, I7, I8, I9, I10) [-1 <= I3 - 1 /\ 0 <= y1 - 1 /\ 0 <= I2 - 1 /\ I6 <= I0 /\ I6 + 1 <= I1 /\ 0 <= I0 - 1 /\ 1 <= I1 - 1 /\ 0 <= I6 - 1] 4.92/4.94 f5(I11, I12, I13, I14, I15, I16) -> f6(I17, I14 + 1, I18, I19, I20, I21) [0 <= I17 - 1 /\ 1 <= I12 - 1 /\ 0 <= I11 - 1 /\ I17 + 1 <= I12 /\ I17 <= I11 /\ -1 <= I14 - 1 /\ 0 <= I13 - 1] 4.92/4.94 f2(I22, I23, I24, I25, I26, I27) -> f6(I28, I25 + 1, I29, I30, I31, I32) [0 <= I33 - 1 /\ 0 <= y2 - 1 /\ 0 <= I24 - 1 /\ -1 <= I25 - 1 /\ I28 <= I22 /\ I28 - 1 <= I23 /\ 0 <= I22 - 1 /\ -1 <= I23 - 1 /\ 0 <= I28 - 1] 4.92/4.94 f5(I34, I35, I36, I37, I38, I39) -> f5(I40, I41, I36 - 1, I42, I43, I44) [-1 <= I37 - 1 /\ 0 <= I45 - 1 /\ 0 <= I36 - 1 /\ I40 - 2 <= I34 /\ I40 - 2 <= I35 /\ I41 - 2 <= I34 /\ I41 - 2 <= I35 /\ 1 <= I34 - 1 /\ 1 <= I35 - 1 /\ 3 <= I40 - 1 /\ 3 <= I41 - 1] 4.92/4.94 f5(I46, I47, I48, I49, I50, I51) -> f5(I52, I53, I48 - 1, I54, I55, I56) [3 <= I53 - 1 /\ 3 <= I52 - 1 /\ 1 <= I47 - 1 /\ 1 <= I46 - 1 /\ I53 - 2 <= I47 /\ I53 - 2 <= I46 /\ I52 - 2 <= I47 /\ I52 - 2 <= I46 /\ -1 <= I49 - 1 /\ 0 <= I48 - 1] 4.92/4.94 f5(I57, I58, I59, I60, I61, I62) -> f5(I63, I64, I59 - 1, I65, I66, I67) [0 <= I64 - 1 /\ 0 <= I63 - 1 /\ 1 <= I58 - 1 /\ 0 <= I57 - 1 /\ -1 <= I60 - 1 /\ 0 <= I59 - 1] 4.92/4.94 f5(I68, I69, I70, I71, I72, I73) -> f5(I74, I75, I70 - 1, I76, I77, I78) [-1 <= I71 - 1 /\ 0 <= I79 - 1 /\ 0 <= I70 - 1 /\ 0 <= I68 - 1 /\ 1 <= I69 - 1 /\ 0 <= I74 - 1 /\ 0 <= I75 - 1] 4.92/4.94 f5(I80, I81, I82, I83, I84, I85) -> f5(I86, I87, I82 - 1, I83 + 1, I88, I89) [0 <= I82 - 1 /\ 0 <= I90 - 1 /\ -1 <= I83 - 1 /\ I86 <= I80 /\ I87 + 2 <= I81 /\ 0 <= I80 - 1 /\ 2 <= I81 - 1 /\ 0 <= I86 - 1 /\ 0 <= I87 - 1] 4.92/4.94 f5(I91, I92, I93, I94, I95, I96) -> f5(I97, I98, I93 - 1, I94 + 1, I99, I100) [0 <= I98 - 1 /\ 0 <= I97 - 1 /\ 2 <= I92 - 1 /\ 0 <= I91 - 1 /\ I98 + 2 <= I92 /\ I97 <= I91 /\ 0 <= I93 - 1 /\ -1 <= I94 - 1] 4.92/4.94 f2(I101, I102, I103, I104, I105, I106) -> f5(I107, I108, I109, I110, I111, I112) [0 <= I109 - 1 /\ 0 <= I113 - 1 /\ 0 <= I103 - 1 /\ -1 <= I104 - 1 /\ I107 - 1 <= I101 /\ I107 - 2 <= I102 /\ I108 - 1 <= I101 /\ I108 - 2 <= I102 /\ 0 <= I101 - 1 /\ -1 <= I102 - 1 /\ 1 <= I107 - 1 /\ 1 <= I108 - 1] 4.92/4.94 f4(I114, I115, I116, I117, I118, I119) -> f4(I120, I121, I122, I123, I124, I125) [2 <= I121 - 1 /\ 2 <= I120 - 1 /\ 2 <= I115 - 1 /\ 2 <= I114 - 1 /\ I121 - 2 <= I115 /\ I121 - 2 <= I114 /\ I120 - 2 <= I115 /\ I120 - 2 <= I114] 4.92/4.94 f4(I126, I127, I128, I129, I130, I131) -> f4(I132, I133, I134, I135, I136, I137) [-1 <= I133 - 1 /\ -1 <= I132 - 1 /\ 1 <= I127 - 1 /\ 1 <= I126 - 1 /\ I133 + 2 <= I127 /\ I133 + 2 <= I126 /\ I132 + 2 <= I127 /\ I132 + 2 <= I126] 4.92/4.94 f2(I138, I139, I140, I141, I142, I143) -> f4(I144, I145, I146, I147, I148, I149) [I144 <= I139 /\ 0 <= I150 - 1 /\ I145 <= I139 /\ 0 <= I138 - 1 /\ -1 <= I139 - 1 /\ -1 <= I144 - 1 /\ -1 <= I145 - 1 /\ 0 = I140] 4.92/4.94 f3(I151, I152, I153, I154, I155, I156) -> f2(I157, I158, I153 - 1, I155, I159, I160) [I156 + 2 <= I154 /\ 3 <= I158 - 1 /\ 0 <= I157 - 1 /\ 1 <= I154 - 1 /\ 0 <= I151 - 1 /\ I157 + 1 <= I154 /\ I157 <= I151] 4.92/4.94 f2(I161, I162, I163, I164, I165, I166) -> f2(I167, I168, I163 - 1, I169, I170, I171) [0 <= I163 - 1 /\ 0 <= I172 - 1 /\ I167 <= I161 /\ I167 - 1 <= I162 /\ 0 <= I161 - 1 /\ -1 <= I162 - 1 /\ 0 <= I167 - 1 /\ 2 <= I168 - 1] 4.92/4.94 f2(I173, I174, I175, I176, I177, I178) -> f2(I179, I180, I175 - 1, I181, I182, I183) [0 <= I175 - 1 /\ 0 <= I184 - 1 /\ I179 <= I173 /\ I179 - 1 <= I174 /\ I180 - 2 <= I174 /\ 0 <= I173 - 1 /\ -1 <= I174 - 1 /\ 0 <= I179 - 1 /\ 1 <= I180 - 1] 4.92/4.94 f1(I185, I186, I187, I188, I189, I190) -> f2(I191, I192, I193, 1, I194, I195) [-1 <= I192 - 1 /\ 0 <= I191 - 1 /\ 0 <= I185 - 1 /\ I192 + 1 <= I185 /\ I191 <= I185 /\ -1 <= I193 - 1 /\ -1 <= I186 - 1] 4.92/4.94 4.92/7.92 EOF