3.34/3.34 MAYBE 3.34/3.34 3.34/3.34 DP problem for innermost termination. 3.34/3.34 P = 3.34/3.34 init#(x1, x2, x3, x4) -> f3#(rnd1, rnd2, rnd3, rnd4) 3.34/3.34 f11#(I0, I1, I2, I3) -> f11#(I4, I5, I6, I7) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I2 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 1 <= I2 /\ I6 + 3 <= I1 /\ I5 - 2 <= I1 /\ I4 <= I0] 3.34/3.34 f10#(I8, I9, I10, I11) -> f11#(I12, I13, I14, I15) [-1 <= I14 - 1 /\ 0 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I10 - 1 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ I14 + 1 <= I9 /\ I13 <= I9 /\ I12 <= I9] 3.34/3.34 f10#(I16, I17, I18, I19) -> f11#(I20, I21, I22, I23) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ 0 <= I20 - 1 /\ 0 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I22 + 1 <= I18 /\ I22 + 1 <= I16 /\ I21 <= I18 /\ I21 <= I16 /\ I20 <= I18 /\ I20 <= I16] 3.34/3.34 f10#(I24, I25, I26, I27) -> f10#(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1] 3.34/3.34 f4#(I32, I33, I34, I35) -> f10#(I36, I37, I38, I39) [I35 + 2 <= I33 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I38 <= I33 /\ I36 <= I33] 3.34/3.34 f4#(I40, I41, I42, I43) -> f10#(I44, I45, I46, I47) [I44 <= I41 /\ 0 <= y1 - 1 /\ I45 + 1 <= I40 /\ I45 + 1 <= I41 /\ I46 <= I41 /\ 0 <= I40 - 1 /\ 0 <= I41 - 1 /\ 0 <= I44 - 1 /\ -1 <= I45 - 1 /\ 0 <= I46 - 1 /\ I43 + 2 <= I41] 3.34/3.34 f6#(I48, I49, I50, I51) -> f10#(I52, I53, I54, I55) [I50 + 2 <= I49 /\ -1 <= I54 - 1 /\ 0 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I49 - 1 /\ 0 <= I48 - 1 /\ I54 + 1 <= I49 /\ I54 + 1 <= I48 /\ I53 <= I49 /\ I52 + 1 <= I49 /\ I52 + 1 <= I48] 3.34/3.34 f2#(I56, I57, I58, I59) -> f10#(I60, I61, I62, I63) [0 <= I64 - 1 /\ 0 <= I57 - 1 /\ I60 + 1 <= I56 /\ I61 + 1 <= I56 /\ I62 + 1 <= I56 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1 /\ -1 <= I61 - 1 /\ -1 <= I62 - 1] 3.34/3.34 f9#(I65, I66, I67, I68) -> f9#(I69, I70, I67 - 1, I68 + 1) [0 <= I67 - 1 /\ 0 <= I71 - 1 /\ -1 <= I68 - 1 /\ I69 - 2 <= I65 /\ I69 - 2 <= I66 /\ I70 - 2 <= I65 /\ I70 - 2 <= I66 /\ 1 <= I65 - 1 /\ 1 <= I66 - 1 /\ 3 <= I69 - 1 /\ 3 <= I70 - 1] 3.34/3.34 f9#(I72, I73, I74, I75) -> f9#(I76, I77, I74 - 1, I75 + 1) [3 <= I77 - 1 /\ 3 <= I76 - 1 /\ 1 <= I73 - 1 /\ 1 <= I72 - 1 /\ I77 - 2 <= I73 /\ I77 - 2 <= I72 /\ I76 - 2 <= I73 /\ I76 - 2 <= I72 /\ 0 <= I74 - 1 /\ -1 <= I75 - 1] 3.34/3.34 f9#(I78, I79, I80, I81) -> f9#(I82, I83, I80 - 1, I81 + 1) [0 <= I83 - 1 /\ 0 <= I82 - 1 /\ 1 <= I79 - 1 /\ 0 <= I78 - 1 /\ 0 <= I80 - 1 /\ -1 <= I81 - 1] 3.34/3.34 f9#(I84, I85, I86, I87) -> f9#(I88, I89, I86 - 1, I87 + 1) [0 <= I86 - 1 /\ 0 <= I90 - 1 /\ -1 <= I87 - 1 /\ 0 <= I84 - 1 /\ 1 <= I85 - 1 /\ 0 <= I88 - 1 /\ 0 <= I89 - 1] 3.34/3.34 f9#(I91, I92, I93, I94) -> f9#(I95, I96, I93 - 1, I94 + 1) [0 <= I93 - 1 /\ 0 <= I97 - 1 /\ -1 <= I94 - 1 /\ I95 <= I91 /\ I96 + 2 <= I92 /\ 0 <= I91 - 1 /\ 2 <= I92 - 1 /\ 0 <= I95 - 1 /\ 0 <= I96 - 1] 3.34/3.34 f9#(I98, I99, I100, I101) -> f9#(I102, I103, I100 - 1, I101 + 1) [0 <= I103 - 1 /\ 0 <= I102 - 1 /\ 2 <= I99 - 1 /\ 0 <= I98 - 1 /\ I103 + 2 <= I99 /\ I102 <= I98 /\ 0 <= I100 - 1 /\ -1 <= I101 - 1] 3.34/3.34 f8#(I104, I105, I106, I107) -> f9#(I108, I109, I110, I111) [0 <= I110 - 1 /\ -1 <= I112 - 1 /\ 1 <= I109 - 1 /\ 1 <= I108 - 1 /\ I112 + 1 = I111] 3.34/3.34 f4#(I113, I114, I115, I116) -> f8#(I117, I118, I119, I120) [0 <= I113 - 1 /\ -1 <= I121 - 1 /\ 0 <= I114 - 1 /\ I116 + 2 <= I114] 3.34/3.34 f2#(I122, I123, I124, I125) -> f8#(I126, I127, I128, I129) [-1 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1] 3.34/3.34 f3#(I131, I132, I133, I134) -> f8#(I135, I136, I137, I138) [-1 <= I132 - 1 /\ 0 <= I131 - 1] 3.34/3.34 f7#(I139, I140, I141, I142) -> f6#(I143, I144, I141, I145) [I141 + 2 <= I140 /\ 1 <= I144 - 1 /\ 0 <= I143 - 1 /\ 1 <= I140 - 1 /\ 0 <= I139 - 1 /\ I144 <= I140 /\ I143 + 1 <= I140 /\ I143 <= I139] 3.34/3.34 f2#(I146, I147, I148, I149) -> f6#(I150, I151, I152, I153) [0 <= I151 - 1 /\ 0 <= I150 - 1 /\ 0 <= I146 - 1 /\ 0 <= I147 - 1 /\ I150 <= I146] 3.34/3.34 f5#(I154, I155, I156, I157) -> f4#(I158, I159, I156, I157) [I157 + 2 <= I155 /\ 1 <= I159 - 1 /\ 0 <= I158 - 1 /\ 1 <= I155 - 1 /\ 0 <= I154 - 1 /\ I159 <= I155 /\ I158 + 1 <= I155 /\ I158 <= I154] 3.34/3.34 f3#(I160, I161, I162, I163) -> f4#(I164, I165, I166, I167) [0 <= I165 - 1 /\ 0 <= I164 - 1 /\ 0 <= I160 - 1 /\ I164 <= I160] 3.34/3.34 f3#(I168, I169, I170, I171) -> f2#(I172, I173, I174, I175) [0 <= I172 - 1 /\ 0 <= I168 - 1 /\ I172 <= I168] 3.34/3.34 f1#(I176, I177, I178, I179) -> f2#(I180, I177, I181, I182) [0 <= I180 - 1 /\ 0 <= I176 - 1 /\ I180 <= I176] 3.34/3.34 R = 3.34/3.34 init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) 3.34/3.34 f11(I0, I1, I2, I3) -> f11(I4, I5, I6, I7) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I2 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 1 <= I2 /\ I6 + 3 <= I1 /\ I5 - 2 <= I1 /\ I4 <= I0] 3.34/3.34 f10(I8, I9, I10, I11) -> f11(I12, I13, I14, I15) [-1 <= I14 - 1 /\ 0 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I10 - 1 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ I14 + 1 <= I9 /\ I13 <= I9 /\ I12 <= I9] 3.34/3.34 f10(I16, I17, I18, I19) -> f11(I20, I21, I22, I23) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ 0 <= I20 - 1 /\ 0 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I22 + 1 <= I18 /\ I22 + 1 <= I16 /\ I21 <= I18 /\ I21 <= I16 /\ I20 <= I18 /\ I20 <= I16] 3.34/3.34 f10(I24, I25, I26, I27) -> f10(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1] 3.34/3.34 f4(I32, I33, I34, I35) -> f10(I36, I37, I38, I39) [I35 + 2 <= I33 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I38 <= I33 /\ I36 <= I33] 3.34/3.34 f4(I40, I41, I42, I43) -> f10(I44, I45, I46, I47) [I44 <= I41 /\ 0 <= y1 - 1 /\ I45 + 1 <= I40 /\ I45 + 1 <= I41 /\ I46 <= I41 /\ 0 <= I40 - 1 /\ 0 <= I41 - 1 /\ 0 <= I44 - 1 /\ -1 <= I45 - 1 /\ 0 <= I46 - 1 /\ I43 + 2 <= I41] 3.34/3.34 f6(I48, I49, I50, I51) -> f10(I52, I53, I54, I55) [I50 + 2 <= I49 /\ -1 <= I54 - 1 /\ 0 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I49 - 1 /\ 0 <= I48 - 1 /\ I54 + 1 <= I49 /\ I54 + 1 <= I48 /\ I53 <= I49 /\ I52 + 1 <= I49 /\ I52 + 1 <= I48] 3.34/3.34 f2(I56, I57, I58, I59) -> f10(I60, I61, I62, I63) [0 <= I64 - 1 /\ 0 <= I57 - 1 /\ I60 + 1 <= I56 /\ I61 + 1 <= I56 /\ I62 + 1 <= I56 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1 /\ -1 <= I61 - 1 /\ -1 <= I62 - 1] 3.34/3.34 f9(I65, I66, I67, I68) -> f9(I69, I70, I67 - 1, I68 + 1) [0 <= I67 - 1 /\ 0 <= I71 - 1 /\ -1 <= I68 - 1 /\ I69 - 2 <= I65 /\ I69 - 2 <= I66 /\ I70 - 2 <= I65 /\ I70 - 2 <= I66 /\ 1 <= I65 - 1 /\ 1 <= I66 - 1 /\ 3 <= I69 - 1 /\ 3 <= I70 - 1] 3.34/3.34 f9(I72, I73, I74, I75) -> f9(I76, I77, I74 - 1, I75 + 1) [3 <= I77 - 1 /\ 3 <= I76 - 1 /\ 1 <= I73 - 1 /\ 1 <= I72 - 1 /\ I77 - 2 <= I73 /\ I77 - 2 <= I72 /\ I76 - 2 <= I73 /\ I76 - 2 <= I72 /\ 0 <= I74 - 1 /\ -1 <= I75 - 1] 3.34/3.34 f9(I78, I79, I80, I81) -> f9(I82, I83, I80 - 1, I81 + 1) [0 <= I83 - 1 /\ 0 <= I82 - 1 /\ 1 <= I79 - 1 /\ 0 <= I78 - 1 /\ 0 <= I80 - 1 /\ -1 <= I81 - 1] 3.34/3.34 f9(I84, I85, I86, I87) -> f9(I88, I89, I86 - 1, I87 + 1) [0 <= I86 - 1 /\ 0 <= I90 - 1 /\ -1 <= I87 - 1 /\ 0 <= I84 - 1 /\ 1 <= I85 - 1 /\ 0 <= I88 - 1 /\ 0 <= I89 - 1] 3.34/3.34 f9(I91, I92, I93, I94) -> f9(I95, I96, I93 - 1, I94 + 1) [0 <= I93 - 1 /\ 0 <= I97 - 1 /\ -1 <= I94 - 1 /\ I95 <= I91 /\ I96 + 2 <= I92 /\ 0 <= I91 - 1 /\ 2 <= I92 - 1 /\ 0 <= I95 - 1 /\ 0 <= I96 - 1] 3.34/3.34 f9(I98, I99, I100, I101) -> f9(I102, I103, I100 - 1, I101 + 1) [0 <= I103 - 1 /\ 0 <= I102 - 1 /\ 2 <= I99 - 1 /\ 0 <= I98 - 1 /\ I103 + 2 <= I99 /\ I102 <= I98 /\ 0 <= I100 - 1 /\ -1 <= I101 - 1] 3.34/3.34 f8(I104, I105, I106, I107) -> f9(I108, I109, I110, I111) [0 <= I110 - 1 /\ -1 <= I112 - 1 /\ 1 <= I109 - 1 /\ 1 <= I108 - 1 /\ I112 + 1 = I111] 3.34/3.34 f4(I113, I114, I115, I116) -> f8(I117, I118, I119, I120) [0 <= I113 - 1 /\ -1 <= I121 - 1 /\ 0 <= I114 - 1 /\ I116 + 2 <= I114] 3.34/3.34 f2(I122, I123, I124, I125) -> f8(I126, I127, I128, I129) [-1 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1] 3.34/3.34 f3(I131, I132, I133, I134) -> f8(I135, I136, I137, I138) [-1 <= I132 - 1 /\ 0 <= I131 - 1] 3.34/3.34 f7(I139, I140, I141, I142) -> f6(I143, I144, I141, I145) [I141 + 2 <= I140 /\ 1 <= I144 - 1 /\ 0 <= I143 - 1 /\ 1 <= I140 - 1 /\ 0 <= I139 - 1 /\ I144 <= I140 /\ I143 + 1 <= I140 /\ I143 <= I139] 3.34/3.34 f2(I146, I147, I148, I149) -> f6(I150, I151, I152, I153) [0 <= I151 - 1 /\ 0 <= I150 - 1 /\ 0 <= I146 - 1 /\ 0 <= I147 - 1 /\ I150 <= I146] 3.34/3.34 f5(I154, I155, I156, I157) -> f4(I158, I159, I156, I157) [I157 + 2 <= I155 /\ 1 <= I159 - 1 /\ 0 <= I158 - 1 /\ 1 <= I155 - 1 /\ 0 <= I154 - 1 /\ I159 <= I155 /\ I158 + 1 <= I155 /\ I158 <= I154] 3.34/3.34 f3(I160, I161, I162, I163) -> f4(I164, I165, I166, I167) [0 <= I165 - 1 /\ 0 <= I164 - 1 /\ 0 <= I160 - 1 /\ I164 <= I160] 3.34/3.34 f3(I168, I169, I170, I171) -> f2(I172, I173, I174, I175) [0 <= I172 - 1 /\ 0 <= I168 - 1 /\ I172 <= I168] 3.34/3.34 f1(I176, I177, I178, I179) -> f2(I180, I177, I181, I182) [0 <= I180 - 1 /\ 0 <= I176 - 1 /\ I180 <= I176] 3.34/3.34 3.34/3.34 The dependency graph for this problem is: 3.34/3.34 0 -> 18, 22, 23 3.34/3.34 1 -> 1 3.34/3.34 2 -> 1 3.34/3.34 3 -> 1 3.34/3.34 4 -> 2, 3, 4 3.34/3.34 5 -> 2, 3, 4 3.34/3.34 6 -> 2, 3, 4 3.34/3.34 7 -> 2, 3, 4 3.34/3.34 8 -> 2, 3, 4 3.34/3.34 9 -> 9, 10, 11, 12, 13, 14 3.34/3.34 10 -> 9, 10, 11, 12, 13, 14 3.34/3.34 11 -> 9, 10, 11, 12, 13, 14 3.34/3.34 12 -> 9, 10, 11, 12, 13, 14 3.34/3.34 13 -> 9, 10, 11, 12, 13, 14 3.34/3.34 14 -> 9, 10, 11, 12, 13, 14 3.34/3.34 15 -> 9, 10, 11, 12, 13, 14 3.34/3.34 16 -> 15 3.34/3.34 17 -> 15 3.34/3.34 18 -> 15 3.34/3.34 19 -> 7 3.34/3.34 20 -> 7 3.34/3.34 21 -> 5, 6, 16 3.34/3.34 22 -> 5, 6, 16 3.34/3.34 23 -> 8, 17, 20 3.34/3.34 24 -> 8, 17, 20 3.34/3.34 Where: 3.34/3.34 0) init#(x1, x2, x3, x4) -> f3#(rnd1, rnd2, rnd3, rnd4) 3.34/3.34 1) f11#(I0, I1, I2, I3) -> f11#(I4, I5, I6, I7) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I2 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 1 <= I2 /\ I6 + 3 <= I1 /\ I5 - 2 <= I1 /\ I4 <= I0] 3.34/3.34 2) f10#(I8, I9, I10, I11) -> f11#(I12, I13, I14, I15) [-1 <= I14 - 1 /\ 0 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I10 - 1 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ I14 + 1 <= I9 /\ I13 <= I9 /\ I12 <= I9] 3.34/3.34 3) f10#(I16, I17, I18, I19) -> f11#(I20, I21, I22, I23) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ 0 <= I20 - 1 /\ 0 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I22 + 1 <= I18 /\ I22 + 1 <= I16 /\ I21 <= I18 /\ I21 <= I16 /\ I20 <= I18 /\ I20 <= I16] 3.34/3.34 4) f10#(I24, I25, I26, I27) -> f10#(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1] 3.34/3.34 5) f4#(I32, I33, I34, I35) -> f10#(I36, I37, I38, I39) [I35 + 2 <= I33 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I38 <= I33 /\ I36 <= I33] 3.34/3.34 6) f4#(I40, I41, I42, I43) -> f10#(I44, I45, I46, I47) [I44 <= I41 /\ 0 <= y1 - 1 /\ I45 + 1 <= I40 /\ I45 + 1 <= I41 /\ I46 <= I41 /\ 0 <= I40 - 1 /\ 0 <= I41 - 1 /\ 0 <= I44 - 1 /\ -1 <= I45 - 1 /\ 0 <= I46 - 1 /\ I43 + 2 <= I41] 3.34/3.34 7) f6#(I48, I49, I50, I51) -> f10#(I52, I53, I54, I55) [I50 + 2 <= I49 /\ -1 <= I54 - 1 /\ 0 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I49 - 1 /\ 0 <= I48 - 1 /\ I54 + 1 <= I49 /\ I54 + 1 <= I48 /\ I53 <= I49 /\ I52 + 1 <= I49 /\ I52 + 1 <= I48] 3.34/3.34 8) f2#(I56, I57, I58, I59) -> f10#(I60, I61, I62, I63) [0 <= I64 - 1 /\ 0 <= I57 - 1 /\ I60 + 1 <= I56 /\ I61 + 1 <= I56 /\ I62 + 1 <= I56 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1 /\ -1 <= I61 - 1 /\ -1 <= I62 - 1] 3.34/3.34 9) f9#(I65, I66, I67, I68) -> f9#(I69, I70, I67 - 1, I68 + 1) [0 <= I67 - 1 /\ 0 <= I71 - 1 /\ -1 <= I68 - 1 /\ I69 - 2 <= I65 /\ I69 - 2 <= I66 /\ I70 - 2 <= I65 /\ I70 - 2 <= I66 /\ 1 <= I65 - 1 /\ 1 <= I66 - 1 /\ 3 <= I69 - 1 /\ 3 <= I70 - 1] 3.34/3.34 10) f9#(I72, I73, I74, I75) -> f9#(I76, I77, I74 - 1, I75 + 1) [3 <= I77 - 1 /\ 3 <= I76 - 1 /\ 1 <= I73 - 1 /\ 1 <= I72 - 1 /\ I77 - 2 <= I73 /\ I77 - 2 <= I72 /\ I76 - 2 <= I73 /\ I76 - 2 <= I72 /\ 0 <= I74 - 1 /\ -1 <= I75 - 1] 3.34/3.34 11) f9#(I78, I79, I80, I81) -> f9#(I82, I83, I80 - 1, I81 + 1) [0 <= I83 - 1 /\ 0 <= I82 - 1 /\ 1 <= I79 - 1 /\ 0 <= I78 - 1 /\ 0 <= I80 - 1 /\ -1 <= I81 - 1] 3.34/3.34 12) f9#(I84, I85, I86, I87) -> f9#(I88, I89, I86 - 1, I87 + 1) [0 <= I86 - 1 /\ 0 <= I90 - 1 /\ -1 <= I87 - 1 /\ 0 <= I84 - 1 /\ 1 <= I85 - 1 /\ 0 <= I88 - 1 /\ 0 <= I89 - 1] 3.34/3.34 13) f9#(I91, I92, I93, I94) -> f9#(I95, I96, I93 - 1, I94 + 1) [0 <= I93 - 1 /\ 0 <= I97 - 1 /\ -1 <= I94 - 1 /\ I95 <= I91 /\ I96 + 2 <= I92 /\ 0 <= I91 - 1 /\ 2 <= I92 - 1 /\ 0 <= I95 - 1 /\ 0 <= I96 - 1] 3.34/3.34 14) f9#(I98, I99, I100, I101) -> f9#(I102, I103, I100 - 1, I101 + 1) [0 <= I103 - 1 /\ 0 <= I102 - 1 /\ 2 <= I99 - 1 /\ 0 <= I98 - 1 /\ I103 + 2 <= I99 /\ I102 <= I98 /\ 0 <= I100 - 1 /\ -1 <= I101 - 1] 3.34/3.34 15) f8#(I104, I105, I106, I107) -> f9#(I108, I109, I110, I111) [0 <= I110 - 1 /\ -1 <= I112 - 1 /\ 1 <= I109 - 1 /\ 1 <= I108 - 1 /\ I112 + 1 = I111] 3.34/3.34 16) f4#(I113, I114, I115, I116) -> f8#(I117, I118, I119, I120) [0 <= I113 - 1 /\ -1 <= I121 - 1 /\ 0 <= I114 - 1 /\ I116 + 2 <= I114] 3.34/3.34 17) f2#(I122, I123, I124, I125) -> f8#(I126, I127, I128, I129) [-1 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1] 3.34/3.34 18) f3#(I131, I132, I133, I134) -> f8#(I135, I136, I137, I138) [-1 <= I132 - 1 /\ 0 <= I131 - 1] 3.34/3.34 19) f7#(I139, I140, I141, I142) -> f6#(I143, I144, I141, I145) [I141 + 2 <= I140 /\ 1 <= I144 - 1 /\ 0 <= I143 - 1 /\ 1 <= I140 - 1 /\ 0 <= I139 - 1 /\ I144 <= I140 /\ I143 + 1 <= I140 /\ I143 <= I139] 3.34/3.34 20) f2#(I146, I147, I148, I149) -> f6#(I150, I151, I152, I153) [0 <= I151 - 1 /\ 0 <= I150 - 1 /\ 0 <= I146 - 1 /\ 0 <= I147 - 1 /\ I150 <= I146] 3.34/3.34 21) f5#(I154, I155, I156, I157) -> f4#(I158, I159, I156, I157) [I157 + 2 <= I155 /\ 1 <= I159 - 1 /\ 0 <= I158 - 1 /\ 1 <= I155 - 1 /\ 0 <= I154 - 1 /\ I159 <= I155 /\ I158 + 1 <= I155 /\ I158 <= I154] 3.34/3.34 22) f3#(I160, I161, I162, I163) -> f4#(I164, I165, I166, I167) [0 <= I165 - 1 /\ 0 <= I164 - 1 /\ 0 <= I160 - 1 /\ I164 <= I160] 3.34/3.34 23) f3#(I168, I169, I170, I171) -> f2#(I172, I173, I174, I175) [0 <= I172 - 1 /\ 0 <= I168 - 1 /\ I172 <= I168] 3.34/3.34 24) f1#(I176, I177, I178, I179) -> f2#(I180, I177, I181, I182) [0 <= I180 - 1 /\ 0 <= I176 - 1 /\ I180 <= I176] 3.34/3.34 3.34/3.34 We have the following SCCs. 3.34/3.34 { 9, 10, 11, 12, 13, 14 } 3.34/3.34 { 4 } 3.34/3.34 { 1 } 3.34/3.34 3.34/3.34 DP problem for innermost termination. 3.34/3.34 P = 3.34/3.34 f11#(I0, I1, I2, I3) -> f11#(I4, I5, I6, I7) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I2 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 1 <= I2 /\ I6 + 3 <= I1 /\ I5 - 2 <= I1 /\ I4 <= I0] 3.34/3.34 R = 3.34/3.34 init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) 3.34/3.34 f11(I0, I1, I2, I3) -> f11(I4, I5, I6, I7) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I2 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 1 <= I2 /\ I6 + 3 <= I1 /\ I5 - 2 <= I1 /\ I4 <= I0] 3.34/3.34 f10(I8, I9, I10, I11) -> f11(I12, I13, I14, I15) [-1 <= I14 - 1 /\ 0 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I10 - 1 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ I14 + 1 <= I9 /\ I13 <= I9 /\ I12 <= I9] 3.34/3.34 f10(I16, I17, I18, I19) -> f11(I20, I21, I22, I23) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ 0 <= I20 - 1 /\ 0 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I22 + 1 <= I18 /\ I22 + 1 <= I16 /\ I21 <= I18 /\ I21 <= I16 /\ I20 <= I18 /\ I20 <= I16] 3.34/3.34 f10(I24, I25, I26, I27) -> f10(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1] 3.34/3.34 f4(I32, I33, I34, I35) -> f10(I36, I37, I38, I39) [I35 + 2 <= I33 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I38 <= I33 /\ I36 <= I33] 3.34/3.34 f4(I40, I41, I42, I43) -> f10(I44, I45, I46, I47) [I44 <= I41 /\ 0 <= y1 - 1 /\ I45 + 1 <= I40 /\ I45 + 1 <= I41 /\ I46 <= I41 /\ 0 <= I40 - 1 /\ 0 <= I41 - 1 /\ 0 <= I44 - 1 /\ -1 <= I45 - 1 /\ 0 <= I46 - 1 /\ I43 + 2 <= I41] 3.34/3.34 f6(I48, I49, I50, I51) -> f10(I52, I53, I54, I55) [I50 + 2 <= I49 /\ -1 <= I54 - 1 /\ 0 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I49 - 1 /\ 0 <= I48 - 1 /\ I54 + 1 <= I49 /\ I54 + 1 <= I48 /\ I53 <= I49 /\ I52 + 1 <= I49 /\ I52 + 1 <= I48] 3.34/3.34 f2(I56, I57, I58, I59) -> f10(I60, I61, I62, I63) [0 <= I64 - 1 /\ 0 <= I57 - 1 /\ I60 + 1 <= I56 /\ I61 + 1 <= I56 /\ I62 + 1 <= I56 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1 /\ -1 <= I61 - 1 /\ -1 <= I62 - 1] 3.34/3.34 f9(I65, I66, I67, I68) -> f9(I69, I70, I67 - 1, I68 + 1) [0 <= I67 - 1 /\ 0 <= I71 - 1 /\ -1 <= I68 - 1 /\ I69 - 2 <= I65 /\ I69 - 2 <= I66 /\ I70 - 2 <= I65 /\ I70 - 2 <= I66 /\ 1 <= I65 - 1 /\ 1 <= I66 - 1 /\ 3 <= I69 - 1 /\ 3 <= I70 - 1] 3.34/3.34 f9(I72, I73, I74, I75) -> f9(I76, I77, I74 - 1, I75 + 1) [3 <= I77 - 1 /\ 3 <= I76 - 1 /\ 1 <= I73 - 1 /\ 1 <= I72 - 1 /\ I77 - 2 <= I73 /\ I77 - 2 <= I72 /\ I76 - 2 <= I73 /\ I76 - 2 <= I72 /\ 0 <= I74 - 1 /\ -1 <= I75 - 1] 3.34/3.34 f9(I78, I79, I80, I81) -> f9(I82, I83, I80 - 1, I81 + 1) [0 <= I83 - 1 /\ 0 <= I82 - 1 /\ 1 <= I79 - 1 /\ 0 <= I78 - 1 /\ 0 <= I80 - 1 /\ -1 <= I81 - 1] 3.34/3.34 f9(I84, I85, I86, I87) -> f9(I88, I89, I86 - 1, I87 + 1) [0 <= I86 - 1 /\ 0 <= I90 - 1 /\ -1 <= I87 - 1 /\ 0 <= I84 - 1 /\ 1 <= I85 - 1 /\ 0 <= I88 - 1 /\ 0 <= I89 - 1] 3.34/3.34 f9(I91, I92, I93, I94) -> f9(I95, I96, I93 - 1, I94 + 1) [0 <= I93 - 1 /\ 0 <= I97 - 1 /\ -1 <= I94 - 1 /\ I95 <= I91 /\ I96 + 2 <= I92 /\ 0 <= I91 - 1 /\ 2 <= I92 - 1 /\ 0 <= I95 - 1 /\ 0 <= I96 - 1] 3.34/3.34 f9(I98, I99, I100, I101) -> f9(I102, I103, I100 - 1, I101 + 1) [0 <= I103 - 1 /\ 0 <= I102 - 1 /\ 2 <= I99 - 1 /\ 0 <= I98 - 1 /\ I103 + 2 <= I99 /\ I102 <= I98 /\ 0 <= I100 - 1 /\ -1 <= I101 - 1] 3.34/3.34 f8(I104, I105, I106, I107) -> f9(I108, I109, I110, I111) [0 <= I110 - 1 /\ -1 <= I112 - 1 /\ 1 <= I109 - 1 /\ 1 <= I108 - 1 /\ I112 + 1 = I111] 3.34/3.34 f4(I113, I114, I115, I116) -> f8(I117, I118, I119, I120) [0 <= I113 - 1 /\ -1 <= I121 - 1 /\ 0 <= I114 - 1 /\ I116 + 2 <= I114] 3.34/3.34 f2(I122, I123, I124, I125) -> f8(I126, I127, I128, I129) [-1 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1] 3.34/3.34 f3(I131, I132, I133, I134) -> f8(I135, I136, I137, I138) [-1 <= I132 - 1 /\ 0 <= I131 - 1] 3.34/3.34 f7(I139, I140, I141, I142) -> f6(I143, I144, I141, I145) [I141 + 2 <= I140 /\ 1 <= I144 - 1 /\ 0 <= I143 - 1 /\ 1 <= I140 - 1 /\ 0 <= I139 - 1 /\ I144 <= I140 /\ I143 + 1 <= I140 /\ I143 <= I139] 3.34/3.34 f2(I146, I147, I148, I149) -> f6(I150, I151, I152, I153) [0 <= I151 - 1 /\ 0 <= I150 - 1 /\ 0 <= I146 - 1 /\ 0 <= I147 - 1 /\ I150 <= I146] 3.34/3.34 f5(I154, I155, I156, I157) -> f4(I158, I159, I156, I157) [I157 + 2 <= I155 /\ 1 <= I159 - 1 /\ 0 <= I158 - 1 /\ 1 <= I155 - 1 /\ 0 <= I154 - 1 /\ I159 <= I155 /\ I158 + 1 <= I155 /\ I158 <= I154] 3.34/3.34 f3(I160, I161, I162, I163) -> f4(I164, I165, I166, I167) [0 <= I165 - 1 /\ 0 <= I164 - 1 /\ 0 <= I160 - 1 /\ I164 <= I160] 3.34/3.34 f3(I168, I169, I170, I171) -> f2(I172, I173, I174, I175) [0 <= I172 - 1 /\ 0 <= I168 - 1 /\ I172 <= I168] 3.34/3.34 f1(I176, I177, I178, I179) -> f2(I180, I177, I181, I182) [0 <= I180 - 1 /\ 0 <= I176 - 1 /\ I180 <= I176] 3.34/3.34 3.34/3.34 We use the basic value criterion with the projection function NU: 3.34/3.34 NU[f11#(z1,z2,z3,z4)] = z3 3.34/3.34 3.34/3.34 This gives the following inequalities: 3.34/3.34 -1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I2 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 1 <= I2 /\ I6 + 3 <= I1 /\ I5 - 2 <= I1 /\ I4 <= I0 ==> I2 >! I6 3.34/3.34 3.34/3.34 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 3.34/3.34 3.34/3.34 DP problem for innermost termination. 3.34/3.34 P = 3.34/3.34 f10#(I24, I25, I26, I27) -> f10#(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1] 3.34/3.34 R = 3.34/3.34 init(x1, x2, x3, x4) -> f3(rnd1, rnd2, rnd3, rnd4) 3.34/3.34 f11(I0, I1, I2, I3) -> f11(I4, I5, I6, I7) [-1 <= I6 - 1 /\ 2 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I2 - 1 /\ 2 <= I1 - 1 /\ 0 <= I0 - 1 /\ I6 + 1 <= I2 /\ I6 + 3 <= I1 /\ I5 - 2 <= I1 /\ I4 <= I0] 3.34/3.34 f10(I8, I9, I10, I11) -> f11(I12, I13, I14, I15) [-1 <= I14 - 1 /\ 0 <= I13 - 1 /\ 0 <= I12 - 1 /\ 0 <= I10 - 1 /\ 0 <= I9 - 1 /\ 0 <= I8 - 1 /\ I14 + 1 <= I9 /\ I13 <= I9 /\ I12 <= I9] 3.34/3.34 f10(I16, I17, I18, I19) -> f11(I20, I21, I22, I23) [-1 <= I22 - 1 /\ 0 <= I21 - 1 /\ 0 <= I20 - 1 /\ 0 <= I18 - 1 /\ 0 <= I17 - 1 /\ 0 <= I16 - 1 /\ I22 + 1 <= I18 /\ I22 + 1 <= I16 /\ I21 <= I18 /\ I21 <= I16 /\ I20 <= I18 /\ I20 <= I16] 3.34/3.34 f10(I24, I25, I26, I27) -> f10(I28, I29, I30, I31) [-1 <= I30 - 1 /\ -1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 0 <= I26 - 1 /\ 0 <= I25 - 1 /\ 0 <= I24 - 1] 3.34/3.34 f4(I32, I33, I34, I35) -> f10(I36, I37, I38, I39) [I35 + 2 <= I33 /\ 0 <= I38 - 1 /\ 0 <= I37 - 1 /\ 0 <= I36 - 1 /\ 0 <= I33 - 1 /\ 0 <= I32 - 1 /\ I38 <= I33 /\ I36 <= I33] 3.34/3.34 f4(I40, I41, I42, I43) -> f10(I44, I45, I46, I47) [I44 <= I41 /\ 0 <= y1 - 1 /\ I45 + 1 <= I40 /\ I45 + 1 <= I41 /\ I46 <= I41 /\ 0 <= I40 - 1 /\ 0 <= I41 - 1 /\ 0 <= I44 - 1 /\ -1 <= I45 - 1 /\ 0 <= I46 - 1 /\ I43 + 2 <= I41] 3.34/3.34 f6(I48, I49, I50, I51) -> f10(I52, I53, I54, I55) [I50 + 2 <= I49 /\ -1 <= I54 - 1 /\ 0 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I49 - 1 /\ 0 <= I48 - 1 /\ I54 + 1 <= I49 /\ I54 + 1 <= I48 /\ I53 <= I49 /\ I52 + 1 <= I49 /\ I52 + 1 <= I48] 3.34/3.34 f2(I56, I57, I58, I59) -> f10(I60, I61, I62, I63) [0 <= I64 - 1 /\ 0 <= I57 - 1 /\ I60 + 1 <= I56 /\ I61 + 1 <= I56 /\ I62 + 1 <= I56 /\ 0 <= I56 - 1 /\ -1 <= I60 - 1 /\ -1 <= I61 - 1 /\ -1 <= I62 - 1] 3.34/3.34 f9(I65, I66, I67, I68) -> f9(I69, I70, I67 - 1, I68 + 1) [0 <= I67 - 1 /\ 0 <= I71 - 1 /\ -1 <= I68 - 1 /\ I69 - 2 <= I65 /\ I69 - 2 <= I66 /\ I70 - 2 <= I65 /\ I70 - 2 <= I66 /\ 1 <= I65 - 1 /\ 1 <= I66 - 1 /\ 3 <= I69 - 1 /\ 3 <= I70 - 1] 3.34/3.34 f9(I72, I73, I74, I75) -> f9(I76, I77, I74 - 1, I75 + 1) [3 <= I77 - 1 /\ 3 <= I76 - 1 /\ 1 <= I73 - 1 /\ 1 <= I72 - 1 /\ I77 - 2 <= I73 /\ I77 - 2 <= I72 /\ I76 - 2 <= I73 /\ I76 - 2 <= I72 /\ 0 <= I74 - 1 /\ -1 <= I75 - 1] 3.34/3.34 f9(I78, I79, I80, I81) -> f9(I82, I83, I80 - 1, I81 + 1) [0 <= I83 - 1 /\ 0 <= I82 - 1 /\ 1 <= I79 - 1 /\ 0 <= I78 - 1 /\ 0 <= I80 - 1 /\ -1 <= I81 - 1] 3.34/3.34 f9(I84, I85, I86, I87) -> f9(I88, I89, I86 - 1, I87 + 1) [0 <= I86 - 1 /\ 0 <= I90 - 1 /\ -1 <= I87 - 1 /\ 0 <= I84 - 1 /\ 1 <= I85 - 1 /\ 0 <= I88 - 1 /\ 0 <= I89 - 1] 3.34/3.34 f9(I91, I92, I93, I94) -> f9(I95, I96, I93 - 1, I94 + 1) [0 <= I93 - 1 /\ 0 <= I97 - 1 /\ -1 <= I94 - 1 /\ I95 <= I91 /\ I96 + 2 <= I92 /\ 0 <= I91 - 1 /\ 2 <= I92 - 1 /\ 0 <= I95 - 1 /\ 0 <= I96 - 1] 3.34/3.34 f9(I98, I99, I100, I101) -> f9(I102, I103, I100 - 1, I101 + 1) [0 <= I103 - 1 /\ 0 <= I102 - 1 /\ 2 <= I99 - 1 /\ 0 <= I98 - 1 /\ I103 + 2 <= I99 /\ I102 <= I98 /\ 0 <= I100 - 1 /\ -1 <= I101 - 1] 3.34/3.34 f8(I104, I105, I106, I107) -> f9(I108, I109, I110, I111) [0 <= I110 - 1 /\ -1 <= I112 - 1 /\ 1 <= I109 - 1 /\ 1 <= I108 - 1 /\ I112 + 1 = I111] 3.34/3.34 f4(I113, I114, I115, I116) -> f8(I117, I118, I119, I120) [0 <= I113 - 1 /\ -1 <= I121 - 1 /\ 0 <= I114 - 1 /\ I116 + 2 <= I114] 3.34/3.34 f2(I122, I123, I124, I125) -> f8(I126, I127, I128, I129) [-1 <= I130 - 1 /\ 0 <= I123 - 1 /\ 0 <= I122 - 1] 3.34/3.34 f3(I131, I132, I133, I134) -> f8(I135, I136, I137, I138) [-1 <= I132 - 1 /\ 0 <= I131 - 1] 3.34/3.34 f7(I139, I140, I141, I142) -> f6(I143, I144, I141, I145) [I141 + 2 <= I140 /\ 1 <= I144 - 1 /\ 0 <= I143 - 1 /\ 1 <= I140 - 1 /\ 0 <= I139 - 1 /\ I144 <= I140 /\ I143 + 1 <= I140 /\ I143 <= I139] 3.34/3.34 f2(I146, I147, I148, I149) -> f6(I150, I151, I152, I153) [0 <= I151 - 1 /\ 0 <= I150 - 1 /\ 0 <= I146 - 1 /\ 0 <= I147 - 1 /\ I150 <= I146] 3.34/3.34 f5(I154, I155, I156, I157) -> f4(I158, I159, I156, I157) [I157 + 2 <= I155 /\ 1 <= I159 - 1 /\ 0 <= I158 - 1 /\ 1 <= I155 - 1 /\ 0 <= I154 - 1 /\ I159 <= I155 /\ I158 + 1 <= I155 /\ I158 <= I154] 3.34/3.34 f3(I160, I161, I162, I163) -> f4(I164, I165, I166, I167) [0 <= I165 - 1 /\ 0 <= I164 - 1 /\ 0 <= I160 - 1 /\ I164 <= I160] 3.34/3.34 f3(I168, I169, I170, I171) -> f2(I172, I173, I174, I175) [0 <= I172 - 1 /\ 0 <= I168 - 1 /\ I172 <= I168] 3.34/3.34 f1(I176, I177, I178, I179) -> f2(I180, I177, I181, I182) [0 <= I180 - 1 /\ 0 <= I176 - 1 /\ I180 <= I176] 3.34/3.34 3.34/6.32 EOF