1.51/1.61 YES 1.51/1.61 1.51/1.61 DP problem for innermost termination. 1.51/1.61 P = 1.51/1.61 init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 1.51/1.61 f6#(I0, I1, I2, I3) -> f6#(I4, I5, I6, I7) [-1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] 1.51/1.61 f4#(I8, I9, I10, I11) -> f6#(I12, I13, I14, I15) [I12 <= I9 /\ 1 <= y1 - 1 /\ I13 + 2 <= I9 /\ 0 <= I8 - 1 /\ 4 <= I9 - 1 /\ 4 <= I12 - 1 /\ 2 <= I13 - 1] 1.51/1.61 f3#(I16, I17, I18, I19) -> f6#(I20, I21, I22, I23) [I20 - 3 <= I16 /\ 1 <= I24 - 1 /\ I21 - 1 <= I16 /\ 0 <= I16 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1] 1.51/1.61 f5#(I25, I26, I27, I28) -> f5#(I25 - 1, I26, I29, I30) [1 <= I25 - 1 /\ 0 <= I26 - 1 /\ I25 - 1 <= I25 - 1] 1.51/1.61 f1#(I31, I32, I33, I34) -> f5#(I35, 2, I36, I37) [-1 <= I38 - 1 /\ 1 <= I32 - 1 /\ -1 <= I35 - 1 /\ 0 <= I31 - 1] 1.51/1.61 f2#(I39, I40, I41, I42) -> f5#(I43, 2, I44, I45) [-1 <= I43 - 1 /\ 1 <= I46 - 1 /\ 0 <= I39 - 1 /\ 7 <= I40 - 1 /\ 5 <= I41 - 1] 1.51/1.61 f2#(I47, I48, I49, I50) -> f5#(I51, 2, I52, I53) [I50 <= y2 - 1 /\ 0 <= I50 - 1 /\ I50 <= y3 - 1 /\ I50 <= y4 - 1 /\ 1 <= I54 - 1 /\ -1 <= I51 - 1 /\ 0 <= I47 - 1 /\ 6 <= I48 - 1 /\ 4 <= I49 - 1] 1.51/1.61 f1#(I55, I56, I57, I58) -> f5#(I59, 1, I60, I61) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I59 - 1] 1.51/1.61 f1#(I62, I63, I64, I65) -> f4#(I66, I67, I68, I69) [-1 <= I70 - 1 /\ 1 <= I63 - 1 /\ -1 <= I71 - 1 /\ I66 <= I62 /\ I67 - 5 <= I62 /\ 0 <= I62 - 1 /\ 0 <= I66 - 1 /\ 5 <= I67 - 1] 1.51/1.61 f2#(I72, I73, I74, I75) -> f4#(I76, I77, I78, I79) [I75 <= I80 - 1 /\ 0 <= I75 - 1 /\ I75 <= I81 - 1 /\ I75 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= y5 - 1 /\ I76 <= I72 /\ I76 + 6 <= I73 /\ I76 + 4 <= I74 /\ I77 - 5 <= I72 /\ I77 + 1 <= I73 /\ I77 - 1 <= I74 /\ 0 <= I72 - 1 /\ 6 <= I73 - 1 /\ 4 <= I74 - 1 /\ 0 <= I76 - 1 /\ 5 <= I77 - 1] 1.51/1.61 f1#(I84, I85, I86, I87) -> f4#(I88, I89, I90, I91) [-1 <= I92 - 1 /\ 1 <= I85 - 1 /\ -1 <= I93 - 1 /\ I88 <= I84 /\ 0 <= I84 - 1 /\ 0 <= I88 - 1 /\ 6 <= I89 - 1] 1.51/1.61 f2#(I94, I95, I96, I97) -> f4#(I98, I99, I100, I101) [-1 <= I102 - 1 /\ 1 <= I103 - 1 /\ I98 <= I94 /\ I98 + 7 <= I95 /\ I98 + 5 <= I96 /\ 0 <= I94 - 1 /\ 7 <= I95 - 1 /\ 5 <= I96 - 1 /\ 0 <= I98 - 1 /\ 6 <= I99 - 1] 1.51/1.61 f2#(I104, I105, I106, I107) -> f4#(I108, I109, I110, I111) [-1 <= I112 - 1 /\ 1 <= I113 - 1 /\ I108 <= I104 /\ I108 + 7 <= I105 /\ I108 + 5 <= I106 /\ I109 - 5 <= I104 /\ I109 + 2 <= I105 /\ I109 <= I106 /\ 0 <= I104 - 1 /\ 7 <= I105 - 1 /\ 5 <= I106 - 1 /\ 0 <= I108 - 1 /\ 5 <= I109 - 1] 1.51/1.61 f2#(I114, I115, I116, I117) -> f4#(I118, I119, I120, I121) [I117 <= I122 - 1 /\ 0 <= I117 - 1 /\ I117 <= I123 - 1 /\ I117 <= I124 - 1 /\ 1 <= I125 - 1 /\ -1 <= I126 - 1 /\ I118 <= I114 /\ I118 + 6 <= I115 /\ I118 + 4 <= I116 /\ 0 <= I114 - 1 /\ 6 <= I115 - 1 /\ 4 <= I116 - 1 /\ 0 <= I118 - 1 /\ 6 <= I119 - 1] 1.51/1.61 f1#(I127, I128, I129, I130) -> f3#(I131, I132, I133, I134) [-1 <= I135 - 1 /\ 1 <= I128 - 1 /\ -1 <= I136 - 1 /\ I131 <= I127 /\ 0 <= I127 - 1 /\ 0 <= I131 - 1] 1.51/1.61 f2#(I137, I138, I139, I140) -> f3#(I141, I142, I143, I144) [I140 <= I145 - 1 /\ 0 <= I140 - 1 /\ I140 <= I146 - 1 /\ I140 <= I147 - 1 /\ 1 <= I148 - 1 /\ -1 <= I149 - 1 /\ I141 <= I137 /\ I141 + 6 <= I138 /\ I141 + 4 <= I139 /\ 0 <= I137 - 1 /\ 6 <= I138 - 1 /\ 4 <= I139 - 1 /\ 0 <= I141 - 1] 1.51/1.61 f2#(I150, I151, I152, I153) -> f3#(I154, I155, I156, I157) [-1 <= I158 - 1 /\ 1 <= I159 - 1 /\ I154 <= I150 /\ I154 + 7 <= I151 /\ I154 + 5 <= I152 /\ 0 <= I150 - 1 /\ 7 <= I151 - 1 /\ 5 <= I152 - 1 /\ 0 <= I154 - 1] 1.51/1.61 f1#(I160, I161, I162, I163) -> f2#(I164, I165, I166, I167) [-1 <= I168 - 1 /\ 0 <= I161 - 1 /\ I164 <= I160 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 8 <= I165 - 1 /\ 6 <= I166 - 1] 1.51/1.61 f1#(I169, I170, I171, I172) -> f2#(I173, I174, I175, 0) [-1 <= I176 - 1 /\ 0 <= I170 - 1 /\ I173 <= I169 /\ I174 - 7 <= I169 /\ I175 - 5 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 7 <= I174 - 1 /\ 5 <= I175 - 1] 1.51/1.61 R = 1.51/1.61 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 1.51/1.61 f6(I0, I1, I2, I3) -> f6(I4, I5, I6, I7) [-1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] 1.51/1.61 f4(I8, I9, I10, I11) -> f6(I12, I13, I14, I15) [I12 <= I9 /\ 1 <= y1 - 1 /\ I13 + 2 <= I9 /\ 0 <= I8 - 1 /\ 4 <= I9 - 1 /\ 4 <= I12 - 1 /\ 2 <= I13 - 1] 1.51/1.61 f3(I16, I17, I18, I19) -> f6(I20, I21, I22, I23) [I20 - 3 <= I16 /\ 1 <= I24 - 1 /\ I21 - 1 <= I16 /\ 0 <= I16 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1] 1.51/1.61 f5(I25, I26, I27, I28) -> f5(I25 - 1, I26, I29, I30) [1 <= I25 - 1 /\ 0 <= I26 - 1 /\ I25 - 1 <= I25 - 1] 1.51/1.61 f1(I31, I32, I33, I34) -> f5(I35, 2, I36, I37) [-1 <= I38 - 1 /\ 1 <= I32 - 1 /\ -1 <= I35 - 1 /\ 0 <= I31 - 1] 1.51/1.61 f2(I39, I40, I41, I42) -> f5(I43, 2, I44, I45) [-1 <= I43 - 1 /\ 1 <= I46 - 1 /\ 0 <= I39 - 1 /\ 7 <= I40 - 1 /\ 5 <= I41 - 1] 1.51/1.61 f2(I47, I48, I49, I50) -> f5(I51, 2, I52, I53) [I50 <= y2 - 1 /\ 0 <= I50 - 1 /\ I50 <= y3 - 1 /\ I50 <= y4 - 1 /\ 1 <= I54 - 1 /\ -1 <= I51 - 1 /\ 0 <= I47 - 1 /\ 6 <= I48 - 1 /\ 4 <= I49 - 1] 1.51/1.61 f1(I55, I56, I57, I58) -> f5(I59, 1, I60, I61) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I59 - 1] 1.51/1.61 f1(I62, I63, I64, I65) -> f4(I66, I67, I68, I69) [-1 <= I70 - 1 /\ 1 <= I63 - 1 /\ -1 <= I71 - 1 /\ I66 <= I62 /\ I67 - 5 <= I62 /\ 0 <= I62 - 1 /\ 0 <= I66 - 1 /\ 5 <= I67 - 1] 1.51/1.61 f2(I72, I73, I74, I75) -> f4(I76, I77, I78, I79) [I75 <= I80 - 1 /\ 0 <= I75 - 1 /\ I75 <= I81 - 1 /\ I75 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= y5 - 1 /\ I76 <= I72 /\ I76 + 6 <= I73 /\ I76 + 4 <= I74 /\ I77 - 5 <= I72 /\ I77 + 1 <= I73 /\ I77 - 1 <= I74 /\ 0 <= I72 - 1 /\ 6 <= I73 - 1 /\ 4 <= I74 - 1 /\ 0 <= I76 - 1 /\ 5 <= I77 - 1] 1.51/1.61 f1(I84, I85, I86, I87) -> f4(I88, I89, I90, I91) [-1 <= I92 - 1 /\ 1 <= I85 - 1 /\ -1 <= I93 - 1 /\ I88 <= I84 /\ 0 <= I84 - 1 /\ 0 <= I88 - 1 /\ 6 <= I89 - 1] 1.51/1.61 f2(I94, I95, I96, I97) -> f4(I98, I99, I100, I101) [-1 <= I102 - 1 /\ 1 <= I103 - 1 /\ I98 <= I94 /\ I98 + 7 <= I95 /\ I98 + 5 <= I96 /\ 0 <= I94 - 1 /\ 7 <= I95 - 1 /\ 5 <= I96 - 1 /\ 0 <= I98 - 1 /\ 6 <= I99 - 1] 1.51/1.61 f2(I104, I105, I106, I107) -> f4(I108, I109, I110, I111) [-1 <= I112 - 1 /\ 1 <= I113 - 1 /\ I108 <= I104 /\ I108 + 7 <= I105 /\ I108 + 5 <= I106 /\ I109 - 5 <= I104 /\ I109 + 2 <= I105 /\ I109 <= I106 /\ 0 <= I104 - 1 /\ 7 <= I105 - 1 /\ 5 <= I106 - 1 /\ 0 <= I108 - 1 /\ 5 <= I109 - 1] 1.51/1.61 f2(I114, I115, I116, I117) -> f4(I118, I119, I120, I121) [I117 <= I122 - 1 /\ 0 <= I117 - 1 /\ I117 <= I123 - 1 /\ I117 <= I124 - 1 /\ 1 <= I125 - 1 /\ -1 <= I126 - 1 /\ I118 <= I114 /\ I118 + 6 <= I115 /\ I118 + 4 <= I116 /\ 0 <= I114 - 1 /\ 6 <= I115 - 1 /\ 4 <= I116 - 1 /\ 0 <= I118 - 1 /\ 6 <= I119 - 1] 1.51/1.61 f1(I127, I128, I129, I130) -> f3(I131, I132, I133, I134) [-1 <= I135 - 1 /\ 1 <= I128 - 1 /\ -1 <= I136 - 1 /\ I131 <= I127 /\ 0 <= I127 - 1 /\ 0 <= I131 - 1] 1.51/1.61 f2(I137, I138, I139, I140) -> f3(I141, I142, I143, I144) [I140 <= I145 - 1 /\ 0 <= I140 - 1 /\ I140 <= I146 - 1 /\ I140 <= I147 - 1 /\ 1 <= I148 - 1 /\ -1 <= I149 - 1 /\ I141 <= I137 /\ I141 + 6 <= I138 /\ I141 + 4 <= I139 /\ 0 <= I137 - 1 /\ 6 <= I138 - 1 /\ 4 <= I139 - 1 /\ 0 <= I141 - 1] 1.51/1.61 f2(I150, I151, I152, I153) -> f3(I154, I155, I156, I157) [-1 <= I158 - 1 /\ 1 <= I159 - 1 /\ I154 <= I150 /\ I154 + 7 <= I151 /\ I154 + 5 <= I152 /\ 0 <= I150 - 1 /\ 7 <= I151 - 1 /\ 5 <= I152 - 1 /\ 0 <= I154 - 1] 1.51/1.61 f1(I160, I161, I162, I163) -> f2(I164, I165, I166, I167) [-1 <= I168 - 1 /\ 0 <= I161 - 1 /\ I164 <= I160 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 8 <= I165 - 1 /\ 6 <= I166 - 1] 1.51/1.61 f1(I169, I170, I171, I172) -> f2(I173, I174, I175, 0) [-1 <= I176 - 1 /\ 0 <= I170 - 1 /\ I173 <= I169 /\ I174 - 7 <= I169 /\ I175 - 5 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 7 <= I174 - 1 /\ 5 <= I175 - 1] 1.51/1.61 1.51/1.61 The dependency graph for this problem is: 1.51/1.61 0 -> 5, 8, 9, 11, 15, 18, 19 1.51/1.61 1 -> 1 1.51/1.61 2 -> 1 1.51/1.61 3 -> 1 1.51/1.61 4 -> 4 1.51/1.61 5 -> 4 1.51/1.61 6 -> 4 1.51/1.61 7 -> 4 1.51/1.61 8 -> 4 1.51/1.61 9 -> 2 1.51/1.61 10 -> 2 1.51/1.61 11 -> 2 1.51/1.61 12 -> 2 1.51/1.61 13 -> 2 1.51/1.61 14 -> 2 1.51/1.61 15 -> 3 1.51/1.61 16 -> 3 1.51/1.61 17 -> 3 1.51/1.61 18 -> 6, 7, 10, 12, 13, 14, 16, 17 1.51/1.61 19 -> 6, 12, 13, 17 1.51/1.61 Where: 1.51/1.61 0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 1.51/1.61 1) f6#(I0, I1, I2, I3) -> f6#(I4, I5, I6, I7) [-1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] 1.51/1.61 2) f4#(I8, I9, I10, I11) -> f6#(I12, I13, I14, I15) [I12 <= I9 /\ 1 <= y1 - 1 /\ I13 + 2 <= I9 /\ 0 <= I8 - 1 /\ 4 <= I9 - 1 /\ 4 <= I12 - 1 /\ 2 <= I13 - 1] 1.51/1.61 3) f3#(I16, I17, I18, I19) -> f6#(I20, I21, I22, I23) [I20 - 3 <= I16 /\ 1 <= I24 - 1 /\ I21 - 1 <= I16 /\ 0 <= I16 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1] 1.51/1.61 4) f5#(I25, I26, I27, I28) -> f5#(I25 - 1, I26, I29, I30) [1 <= I25 - 1 /\ 0 <= I26 - 1 /\ I25 - 1 <= I25 - 1] 1.51/1.61 5) f1#(I31, I32, I33, I34) -> f5#(I35, 2, I36, I37) [-1 <= I38 - 1 /\ 1 <= I32 - 1 /\ -1 <= I35 - 1 /\ 0 <= I31 - 1] 1.51/1.61 6) f2#(I39, I40, I41, I42) -> f5#(I43, 2, I44, I45) [-1 <= I43 - 1 /\ 1 <= I46 - 1 /\ 0 <= I39 - 1 /\ 7 <= I40 - 1 /\ 5 <= I41 - 1] 1.51/1.61 7) f2#(I47, I48, I49, I50) -> f5#(I51, 2, I52, I53) [I50 <= y2 - 1 /\ 0 <= I50 - 1 /\ I50 <= y3 - 1 /\ I50 <= y4 - 1 /\ 1 <= I54 - 1 /\ -1 <= I51 - 1 /\ 0 <= I47 - 1 /\ 6 <= I48 - 1 /\ 4 <= I49 - 1] 1.51/1.61 8) f1#(I55, I56, I57, I58) -> f5#(I59, 1, I60, I61) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I59 - 1] 1.51/1.61 9) f1#(I62, I63, I64, I65) -> f4#(I66, I67, I68, I69) [-1 <= I70 - 1 /\ 1 <= I63 - 1 /\ -1 <= I71 - 1 /\ I66 <= I62 /\ I67 - 5 <= I62 /\ 0 <= I62 - 1 /\ 0 <= I66 - 1 /\ 5 <= I67 - 1] 1.51/1.61 10) f2#(I72, I73, I74, I75) -> f4#(I76, I77, I78, I79) [I75 <= I80 - 1 /\ 0 <= I75 - 1 /\ I75 <= I81 - 1 /\ I75 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= y5 - 1 /\ I76 <= I72 /\ I76 + 6 <= I73 /\ I76 + 4 <= I74 /\ I77 - 5 <= I72 /\ I77 + 1 <= I73 /\ I77 - 1 <= I74 /\ 0 <= I72 - 1 /\ 6 <= I73 - 1 /\ 4 <= I74 - 1 /\ 0 <= I76 - 1 /\ 5 <= I77 - 1] 1.51/1.61 11) f1#(I84, I85, I86, I87) -> f4#(I88, I89, I90, I91) [-1 <= I92 - 1 /\ 1 <= I85 - 1 /\ -1 <= I93 - 1 /\ I88 <= I84 /\ 0 <= I84 - 1 /\ 0 <= I88 - 1 /\ 6 <= I89 - 1] 1.51/1.61 12) f2#(I94, I95, I96, I97) -> f4#(I98, I99, I100, I101) [-1 <= I102 - 1 /\ 1 <= I103 - 1 /\ I98 <= I94 /\ I98 + 7 <= I95 /\ I98 + 5 <= I96 /\ 0 <= I94 - 1 /\ 7 <= I95 - 1 /\ 5 <= I96 - 1 /\ 0 <= I98 - 1 /\ 6 <= I99 - 1] 1.51/1.61 13) f2#(I104, I105, I106, I107) -> f4#(I108, I109, I110, I111) [-1 <= I112 - 1 /\ 1 <= I113 - 1 /\ I108 <= I104 /\ I108 + 7 <= I105 /\ I108 + 5 <= I106 /\ I109 - 5 <= I104 /\ I109 + 2 <= I105 /\ I109 <= I106 /\ 0 <= I104 - 1 /\ 7 <= I105 - 1 /\ 5 <= I106 - 1 /\ 0 <= I108 - 1 /\ 5 <= I109 - 1] 1.51/1.61 14) f2#(I114, I115, I116, I117) -> f4#(I118, I119, I120, I121) [I117 <= I122 - 1 /\ 0 <= I117 - 1 /\ I117 <= I123 - 1 /\ I117 <= I124 - 1 /\ 1 <= I125 - 1 /\ -1 <= I126 - 1 /\ I118 <= I114 /\ I118 + 6 <= I115 /\ I118 + 4 <= I116 /\ 0 <= I114 - 1 /\ 6 <= I115 - 1 /\ 4 <= I116 - 1 /\ 0 <= I118 - 1 /\ 6 <= I119 - 1] 1.51/1.61 15) f1#(I127, I128, I129, I130) -> f3#(I131, I132, I133, I134) [-1 <= I135 - 1 /\ 1 <= I128 - 1 /\ -1 <= I136 - 1 /\ I131 <= I127 /\ 0 <= I127 - 1 /\ 0 <= I131 - 1] 1.51/1.61 16) f2#(I137, I138, I139, I140) -> f3#(I141, I142, I143, I144) [I140 <= I145 - 1 /\ 0 <= I140 - 1 /\ I140 <= I146 - 1 /\ I140 <= I147 - 1 /\ 1 <= I148 - 1 /\ -1 <= I149 - 1 /\ I141 <= I137 /\ I141 + 6 <= I138 /\ I141 + 4 <= I139 /\ 0 <= I137 - 1 /\ 6 <= I138 - 1 /\ 4 <= I139 - 1 /\ 0 <= I141 - 1] 1.51/1.61 17) f2#(I150, I151, I152, I153) -> f3#(I154, I155, I156, I157) [-1 <= I158 - 1 /\ 1 <= I159 - 1 /\ I154 <= I150 /\ I154 + 7 <= I151 /\ I154 + 5 <= I152 /\ 0 <= I150 - 1 /\ 7 <= I151 - 1 /\ 5 <= I152 - 1 /\ 0 <= I154 - 1] 1.51/1.61 18) f1#(I160, I161, I162, I163) -> f2#(I164, I165, I166, I167) [-1 <= I168 - 1 /\ 0 <= I161 - 1 /\ I164 <= I160 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 8 <= I165 - 1 /\ 6 <= I166 - 1] 1.51/1.61 19) f1#(I169, I170, I171, I172) -> f2#(I173, I174, I175, 0) [-1 <= I176 - 1 /\ 0 <= I170 - 1 /\ I173 <= I169 /\ I174 - 7 <= I169 /\ I175 - 5 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 7 <= I174 - 1 /\ 5 <= I175 - 1] 1.51/1.61 1.51/1.61 We have the following SCCs. 1.51/1.61 { 1 } 1.51/1.61 { 4 } 1.51/1.61 1.51/1.61 DP problem for innermost termination. 1.51/1.61 P = 1.51/1.61 f5#(I25, I26, I27, I28) -> f5#(I25 - 1, I26, I29, I30) [1 <= I25 - 1 /\ 0 <= I26 - 1 /\ I25 - 1 <= I25 - 1] 1.51/1.61 R = 1.51/1.61 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 1.51/1.61 f6(I0, I1, I2, I3) -> f6(I4, I5, I6, I7) [-1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] 1.51/1.61 f4(I8, I9, I10, I11) -> f6(I12, I13, I14, I15) [I12 <= I9 /\ 1 <= y1 - 1 /\ I13 + 2 <= I9 /\ 0 <= I8 - 1 /\ 4 <= I9 - 1 /\ 4 <= I12 - 1 /\ 2 <= I13 - 1] 1.51/1.61 f3(I16, I17, I18, I19) -> f6(I20, I21, I22, I23) [I20 - 3 <= I16 /\ 1 <= I24 - 1 /\ I21 - 1 <= I16 /\ 0 <= I16 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1] 1.51/1.61 f5(I25, I26, I27, I28) -> f5(I25 - 1, I26, I29, I30) [1 <= I25 - 1 /\ 0 <= I26 - 1 /\ I25 - 1 <= I25 - 1] 1.51/1.61 f1(I31, I32, I33, I34) -> f5(I35, 2, I36, I37) [-1 <= I38 - 1 /\ 1 <= I32 - 1 /\ -1 <= I35 - 1 /\ 0 <= I31 - 1] 1.51/1.61 f2(I39, I40, I41, I42) -> f5(I43, 2, I44, I45) [-1 <= I43 - 1 /\ 1 <= I46 - 1 /\ 0 <= I39 - 1 /\ 7 <= I40 - 1 /\ 5 <= I41 - 1] 1.51/1.61 f2(I47, I48, I49, I50) -> f5(I51, 2, I52, I53) [I50 <= y2 - 1 /\ 0 <= I50 - 1 /\ I50 <= y3 - 1 /\ I50 <= y4 - 1 /\ 1 <= I54 - 1 /\ -1 <= I51 - 1 /\ 0 <= I47 - 1 /\ 6 <= I48 - 1 /\ 4 <= I49 - 1] 1.51/1.61 f1(I55, I56, I57, I58) -> f5(I59, 1, I60, I61) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I59 - 1] 1.51/1.61 f1(I62, I63, I64, I65) -> f4(I66, I67, I68, I69) [-1 <= I70 - 1 /\ 1 <= I63 - 1 /\ -1 <= I71 - 1 /\ I66 <= I62 /\ I67 - 5 <= I62 /\ 0 <= I62 - 1 /\ 0 <= I66 - 1 /\ 5 <= I67 - 1] 1.51/1.61 f2(I72, I73, I74, I75) -> f4(I76, I77, I78, I79) [I75 <= I80 - 1 /\ 0 <= I75 - 1 /\ I75 <= I81 - 1 /\ I75 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= y5 - 1 /\ I76 <= I72 /\ I76 + 6 <= I73 /\ I76 + 4 <= I74 /\ I77 - 5 <= I72 /\ I77 + 1 <= I73 /\ I77 - 1 <= I74 /\ 0 <= I72 - 1 /\ 6 <= I73 - 1 /\ 4 <= I74 - 1 /\ 0 <= I76 - 1 /\ 5 <= I77 - 1] 1.51/1.61 f1(I84, I85, I86, I87) -> f4(I88, I89, I90, I91) [-1 <= I92 - 1 /\ 1 <= I85 - 1 /\ -1 <= I93 - 1 /\ I88 <= I84 /\ 0 <= I84 - 1 /\ 0 <= I88 - 1 /\ 6 <= I89 - 1] 1.51/1.61 f2(I94, I95, I96, I97) -> f4(I98, I99, I100, I101) [-1 <= I102 - 1 /\ 1 <= I103 - 1 /\ I98 <= I94 /\ I98 + 7 <= I95 /\ I98 + 5 <= I96 /\ 0 <= I94 - 1 /\ 7 <= I95 - 1 /\ 5 <= I96 - 1 /\ 0 <= I98 - 1 /\ 6 <= I99 - 1] 1.51/1.61 f2(I104, I105, I106, I107) -> f4(I108, I109, I110, I111) [-1 <= I112 - 1 /\ 1 <= I113 - 1 /\ I108 <= I104 /\ I108 + 7 <= I105 /\ I108 + 5 <= I106 /\ I109 - 5 <= I104 /\ I109 + 2 <= I105 /\ I109 <= I106 /\ 0 <= I104 - 1 /\ 7 <= I105 - 1 /\ 5 <= I106 - 1 /\ 0 <= I108 - 1 /\ 5 <= I109 - 1] 1.51/1.61 f2(I114, I115, I116, I117) -> f4(I118, I119, I120, I121) [I117 <= I122 - 1 /\ 0 <= I117 - 1 /\ I117 <= I123 - 1 /\ I117 <= I124 - 1 /\ 1 <= I125 - 1 /\ -1 <= I126 - 1 /\ I118 <= I114 /\ I118 + 6 <= I115 /\ I118 + 4 <= I116 /\ 0 <= I114 - 1 /\ 6 <= I115 - 1 /\ 4 <= I116 - 1 /\ 0 <= I118 - 1 /\ 6 <= I119 - 1] 1.51/1.61 f1(I127, I128, I129, I130) -> f3(I131, I132, I133, I134) [-1 <= I135 - 1 /\ 1 <= I128 - 1 /\ -1 <= I136 - 1 /\ I131 <= I127 /\ 0 <= I127 - 1 /\ 0 <= I131 - 1] 1.51/1.61 f2(I137, I138, I139, I140) -> f3(I141, I142, I143, I144) [I140 <= I145 - 1 /\ 0 <= I140 - 1 /\ I140 <= I146 - 1 /\ I140 <= I147 - 1 /\ 1 <= I148 - 1 /\ -1 <= I149 - 1 /\ I141 <= I137 /\ I141 + 6 <= I138 /\ I141 + 4 <= I139 /\ 0 <= I137 - 1 /\ 6 <= I138 - 1 /\ 4 <= I139 - 1 /\ 0 <= I141 - 1] 1.51/1.61 f2(I150, I151, I152, I153) -> f3(I154, I155, I156, I157) [-1 <= I158 - 1 /\ 1 <= I159 - 1 /\ I154 <= I150 /\ I154 + 7 <= I151 /\ I154 + 5 <= I152 /\ 0 <= I150 - 1 /\ 7 <= I151 - 1 /\ 5 <= I152 - 1 /\ 0 <= I154 - 1] 1.51/1.61 f1(I160, I161, I162, I163) -> f2(I164, I165, I166, I167) [-1 <= I168 - 1 /\ 0 <= I161 - 1 /\ I164 <= I160 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 8 <= I165 - 1 /\ 6 <= I166 - 1] 1.51/1.61 f1(I169, I170, I171, I172) -> f2(I173, I174, I175, 0) [-1 <= I176 - 1 /\ 0 <= I170 - 1 /\ I173 <= I169 /\ I174 - 7 <= I169 /\ I175 - 5 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 7 <= I174 - 1 /\ 5 <= I175 - 1] 1.51/1.61 1.51/1.61 We use the basic value criterion with the projection function NU: 1.51/1.61 NU[f5#(z1,z2,z3,z4)] = z1 1.51/1.61 1.51/1.61 This gives the following inequalities: 1.51/1.61 1 <= I25 - 1 /\ 0 <= I26 - 1 /\ I25 - 1 <= I25 - 1 ==> I25 >! I25 - 1 1.51/1.61 1.51/1.61 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 1.51/1.61 1.51/1.61 DP problem for innermost termination. 1.51/1.61 P = 1.51/1.61 f6#(I0, I1, I2, I3) -> f6#(I4, I5, I6, I7) [-1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] 1.51/1.61 R = 1.51/1.61 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 1.51/1.61 f6(I0, I1, I2, I3) -> f6(I4, I5, I6, I7) [-1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0] 1.51/1.61 f4(I8, I9, I10, I11) -> f6(I12, I13, I14, I15) [I12 <= I9 /\ 1 <= y1 - 1 /\ I13 + 2 <= I9 /\ 0 <= I8 - 1 /\ 4 <= I9 - 1 /\ 4 <= I12 - 1 /\ 2 <= I13 - 1] 1.51/1.61 f3(I16, I17, I18, I19) -> f6(I20, I21, I22, I23) [I20 - 3 <= I16 /\ 1 <= I24 - 1 /\ I21 - 1 <= I16 /\ 0 <= I16 - 1 /\ 3 <= I20 - 1 /\ 1 <= I21 - 1] 1.51/1.61 f5(I25, I26, I27, I28) -> f5(I25 - 1, I26, I29, I30) [1 <= I25 - 1 /\ 0 <= I26 - 1 /\ I25 - 1 <= I25 - 1] 1.51/1.61 f1(I31, I32, I33, I34) -> f5(I35, 2, I36, I37) [-1 <= I38 - 1 /\ 1 <= I32 - 1 /\ -1 <= I35 - 1 /\ 0 <= I31 - 1] 1.51/1.61 f2(I39, I40, I41, I42) -> f5(I43, 2, I44, I45) [-1 <= I43 - 1 /\ 1 <= I46 - 1 /\ 0 <= I39 - 1 /\ 7 <= I40 - 1 /\ 5 <= I41 - 1] 1.51/1.61 f2(I47, I48, I49, I50) -> f5(I51, 2, I52, I53) [I50 <= y2 - 1 /\ 0 <= I50 - 1 /\ I50 <= y3 - 1 /\ I50 <= y4 - 1 /\ 1 <= I54 - 1 /\ -1 <= I51 - 1 /\ 0 <= I47 - 1 /\ 6 <= I48 - 1 /\ 4 <= I49 - 1] 1.51/1.61 f1(I55, I56, I57, I58) -> f5(I59, 1, I60, I61) [0 <= I55 - 1 /\ 0 <= I56 - 1 /\ -1 <= I59 - 1] 1.51/1.61 f1(I62, I63, I64, I65) -> f4(I66, I67, I68, I69) [-1 <= I70 - 1 /\ 1 <= I63 - 1 /\ -1 <= I71 - 1 /\ I66 <= I62 /\ I67 - 5 <= I62 /\ 0 <= I62 - 1 /\ 0 <= I66 - 1 /\ 5 <= I67 - 1] 1.51/1.61 f2(I72, I73, I74, I75) -> f4(I76, I77, I78, I79) [I75 <= I80 - 1 /\ 0 <= I75 - 1 /\ I75 <= I81 - 1 /\ I75 <= I82 - 1 /\ 1 <= I83 - 1 /\ -1 <= y5 - 1 /\ I76 <= I72 /\ I76 + 6 <= I73 /\ I76 + 4 <= I74 /\ I77 - 5 <= I72 /\ I77 + 1 <= I73 /\ I77 - 1 <= I74 /\ 0 <= I72 - 1 /\ 6 <= I73 - 1 /\ 4 <= I74 - 1 /\ 0 <= I76 - 1 /\ 5 <= I77 - 1] 1.51/1.61 f1(I84, I85, I86, I87) -> f4(I88, I89, I90, I91) [-1 <= I92 - 1 /\ 1 <= I85 - 1 /\ -1 <= I93 - 1 /\ I88 <= I84 /\ 0 <= I84 - 1 /\ 0 <= I88 - 1 /\ 6 <= I89 - 1] 1.51/1.61 f2(I94, I95, I96, I97) -> f4(I98, I99, I100, I101) [-1 <= I102 - 1 /\ 1 <= I103 - 1 /\ I98 <= I94 /\ I98 + 7 <= I95 /\ I98 + 5 <= I96 /\ 0 <= I94 - 1 /\ 7 <= I95 - 1 /\ 5 <= I96 - 1 /\ 0 <= I98 - 1 /\ 6 <= I99 - 1] 1.51/1.61 f2(I104, I105, I106, I107) -> f4(I108, I109, I110, I111) [-1 <= I112 - 1 /\ 1 <= I113 - 1 /\ I108 <= I104 /\ I108 + 7 <= I105 /\ I108 + 5 <= I106 /\ I109 - 5 <= I104 /\ I109 + 2 <= I105 /\ I109 <= I106 /\ 0 <= I104 - 1 /\ 7 <= I105 - 1 /\ 5 <= I106 - 1 /\ 0 <= I108 - 1 /\ 5 <= I109 - 1] 1.51/1.61 f2(I114, I115, I116, I117) -> f4(I118, I119, I120, I121) [I117 <= I122 - 1 /\ 0 <= I117 - 1 /\ I117 <= I123 - 1 /\ I117 <= I124 - 1 /\ 1 <= I125 - 1 /\ -1 <= I126 - 1 /\ I118 <= I114 /\ I118 + 6 <= I115 /\ I118 + 4 <= I116 /\ 0 <= I114 - 1 /\ 6 <= I115 - 1 /\ 4 <= I116 - 1 /\ 0 <= I118 - 1 /\ 6 <= I119 - 1] 1.51/1.61 f1(I127, I128, I129, I130) -> f3(I131, I132, I133, I134) [-1 <= I135 - 1 /\ 1 <= I128 - 1 /\ -1 <= I136 - 1 /\ I131 <= I127 /\ 0 <= I127 - 1 /\ 0 <= I131 - 1] 1.51/1.61 f2(I137, I138, I139, I140) -> f3(I141, I142, I143, I144) [I140 <= I145 - 1 /\ 0 <= I140 - 1 /\ I140 <= I146 - 1 /\ I140 <= I147 - 1 /\ 1 <= I148 - 1 /\ -1 <= I149 - 1 /\ I141 <= I137 /\ I141 + 6 <= I138 /\ I141 + 4 <= I139 /\ 0 <= I137 - 1 /\ 6 <= I138 - 1 /\ 4 <= I139 - 1 /\ 0 <= I141 - 1] 1.51/1.61 f2(I150, I151, I152, I153) -> f3(I154, I155, I156, I157) [-1 <= I158 - 1 /\ 1 <= I159 - 1 /\ I154 <= I150 /\ I154 + 7 <= I151 /\ I154 + 5 <= I152 /\ 0 <= I150 - 1 /\ 7 <= I151 - 1 /\ 5 <= I152 - 1 /\ 0 <= I154 - 1] 1.51/1.61 f1(I160, I161, I162, I163) -> f2(I164, I165, I166, I167) [-1 <= I168 - 1 /\ 0 <= I161 - 1 /\ I164 <= I160 /\ 0 <= I160 - 1 /\ 0 <= I164 - 1 /\ 8 <= I165 - 1 /\ 6 <= I166 - 1] 1.51/1.61 f1(I169, I170, I171, I172) -> f2(I173, I174, I175, 0) [-1 <= I176 - 1 /\ 0 <= I170 - 1 /\ I173 <= I169 /\ I174 - 7 <= I169 /\ I175 - 5 <= I169 /\ 0 <= I169 - 1 /\ 0 <= I173 - 1 /\ 7 <= I174 - 1 /\ 5 <= I175 - 1] 1.51/1.61 1.51/1.61 We use the basic value criterion with the projection function NU: 1.51/1.61 NU[f6#(z1,z2,z3,z4)] = z2 1.51/1.61 1.51/1.61 This gives the following inequalities: 1.51/1.61 -1 <= I5 - 1 /\ 0 <= I4 - 1 /\ 0 <= I1 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I1 /\ I5 + 3 <= I0 /\ I4 <= I1 /\ I4 + 2 <= I0 ==> I1 >! I5 1.51/1.61 1.51/1.61 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 1.51/4.60 EOF