2.80/2.87 MAYBE 2.80/2.87 2.80/2.87 DP problem for innermost termination. 2.80/2.87 P = 2.80/2.87 init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 2.80/2.87 f6#(I0, I1, I2, I3) -> f6#(I4, I5, I6, I7) [2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I4 - 2 <= I0] 2.80/2.87 f6#(I8, I9, I10, I11) -> f6#(I12, I13, I14, I15) [-1 <= I12 - 1 /\ 1 <= I8 - 1 /\ I12 + 2 <= I8] 2.80/2.87 f5#(I16, I17, I18, I19) -> f6#(I20, I21, I22, I23) [2 <= I20 - 1 /\ 2 <= I17 - 1 /\ 2 <= I16 - 1 /\ I20 <= I17 /\ I20 <= I16] 2.80/2.87 f5#(I24, I25, I26, I27) -> f5#(I28, I29, I30, I31) [-1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1] 2.80/2.87 f5#(I32, I33, I34, I35) -> f5#(I36, I37, I38, I39) [-1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 1 <= I33 - 1 /\ 1 <= I32 - 1 /\ I37 + 2 <= I33 /\ I37 + 2 <= I32 /\ I36 + 2 <= I33 /\ I36 + 2 <= I32] 2.80/2.87 f2#(I40, I41, I42, I43) -> f5#(I44, I45, I46, I47) [I44 <= I41 /\ 0 <= y1 - 1 /\ I45 <= I41 /\ 0 <= I40 - 1 /\ 0 <= I41 - 1 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ I42 + 2 <= I41] 2.80/2.87 f1#(I48, I49, I50, I51) -> f5#(I52, I53, I54, I55) [-1 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I48 - 1 /\ I53 + 1 <= I48 /\ 0 <= I49 - 1 /\ I52 + 1 <= I48] 2.80/2.87 f4#(I56, I57, I58, I59) -> f4#(I60, I61, I58 - 1, I59 + 1) [0 <= I58 - 1 /\ 0 <= I62 - 1 /\ -1 <= I59 - 1 /\ I60 - 2 <= I56 /\ I60 - 2 <= I57 /\ I61 - 2 <= I56 /\ I61 - 2 <= I57 /\ 1 <= I56 - 1 /\ 1 <= I57 - 1 /\ 3 <= I60 - 1 /\ 3 <= I61 - 1] 2.80/2.87 f4#(I63, I64, I65, I66) -> f4#(I67, I68, I65 - 1, I66 + 1) [3 <= I68 - 1 /\ 3 <= I67 - 1 /\ 1 <= I64 - 1 /\ 1 <= I63 - 1 /\ I68 - 2 <= I64 /\ I68 - 2 <= I63 /\ I67 - 2 <= I64 /\ I67 - 2 <= I63 /\ 0 <= I65 - 1 /\ -1 <= I66 - 1] 2.80/2.87 f4#(I69, I70, I71, I72) -> f4#(I73, I74, I71 - 1, I72 + 1) [0 <= I74 - 1 /\ 0 <= I73 - 1 /\ 1 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I71 - 1 /\ -1 <= I72 - 1] 2.80/2.87 f4#(I75, I76, I77, I78) -> f4#(I79, I80, I77 - 1, I78 + 1) [0 <= I77 - 1 /\ 0 <= I81 - 1 /\ -1 <= I78 - 1 /\ 0 <= I75 - 1 /\ 1 <= I76 - 1 /\ 0 <= I79 - 1 /\ 0 <= I80 - 1] 2.80/2.87 f4#(I82, I83, I84, I85) -> f4#(I86, I87, I84 - 1, I85 + 1) [0 <= I84 - 1 /\ 0 <= I88 - 1 /\ -1 <= I85 - 1 /\ I86 <= I82 /\ I87 + 2 <= I83 /\ 0 <= I82 - 1 /\ 2 <= I83 - 1 /\ 0 <= I86 - 1 /\ 0 <= I87 - 1] 2.80/2.87 f4#(I89, I90, I91, I92) -> f4#(I93, I94, I91 - 1, I92 + 1) [0 <= I94 - 1 /\ 0 <= I93 - 1 /\ 2 <= I90 - 1 /\ 0 <= I89 - 1 /\ I94 + 2 <= I90 /\ I93 <= I89 /\ 0 <= I91 - 1 /\ -1 <= I92 - 1] 2.80/2.87 f1#(I95, I96, I97, I98) -> f4#(I99, I100, I101, 1) [1 <= I100 - 1 /\ 1 <= I99 - 1 /\ 0 <= I95 - 1 /\ I100 - 1 <= I95 /\ I99 - 1 <= I95 /\ -1 <= I96 - 1 /\ 0 <= I101 - 1] 2.80/2.87 f3#(I102, I103, I104, I105) -> f2#(I106, I107, I104, I108) [I104 + 2 <= I103 /\ 1 <= I107 - 1 /\ 0 <= I106 - 1 /\ 1 <= I103 - 1 /\ 0 <= I102 - 1 /\ I107 <= I103 /\ I106 + 1 <= I103 /\ I106 <= I102] 2.80/2.87 f1#(I109, I110, I111, I112) -> f2#(I113, I114, I115, I116) [0 <= I114 - 1 /\ 0 <= I113 - 1 /\ 0 <= I109 - 1 /\ I113 <= I109] 2.80/2.87 R = 2.80/2.87 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 2.80/2.87 f6(I0, I1, I2, I3) -> f6(I4, I5, I6, I7) [2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I4 - 2 <= I0] 2.80/2.87 f6(I8, I9, I10, I11) -> f6(I12, I13, I14, I15) [-1 <= I12 - 1 /\ 1 <= I8 - 1 /\ I12 + 2 <= I8] 2.80/2.87 f5(I16, I17, I18, I19) -> f6(I20, I21, I22, I23) [2 <= I20 - 1 /\ 2 <= I17 - 1 /\ 2 <= I16 - 1 /\ I20 <= I17 /\ I20 <= I16] 2.80/2.87 f5(I24, I25, I26, I27) -> f5(I28, I29, I30, I31) [-1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1] 2.80/2.87 f5(I32, I33, I34, I35) -> f5(I36, I37, I38, I39) [-1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 1 <= I33 - 1 /\ 1 <= I32 - 1 /\ I37 + 2 <= I33 /\ I37 + 2 <= I32 /\ I36 + 2 <= I33 /\ I36 + 2 <= I32] 2.80/2.87 f2(I40, I41, I42, I43) -> f5(I44, I45, I46, I47) [I44 <= I41 /\ 0 <= y1 - 1 /\ I45 <= I41 /\ 0 <= I40 - 1 /\ 0 <= I41 - 1 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ I42 + 2 <= I41] 2.80/2.87 f1(I48, I49, I50, I51) -> f5(I52, I53, I54, I55) [-1 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I48 - 1 /\ I53 + 1 <= I48 /\ 0 <= I49 - 1 /\ I52 + 1 <= I48] 2.80/2.87 f4(I56, I57, I58, I59) -> f4(I60, I61, I58 - 1, I59 + 1) [0 <= I58 - 1 /\ 0 <= I62 - 1 /\ -1 <= I59 - 1 /\ I60 - 2 <= I56 /\ I60 - 2 <= I57 /\ I61 - 2 <= I56 /\ I61 - 2 <= I57 /\ 1 <= I56 - 1 /\ 1 <= I57 - 1 /\ 3 <= I60 - 1 /\ 3 <= I61 - 1] 2.80/2.87 f4(I63, I64, I65, I66) -> f4(I67, I68, I65 - 1, I66 + 1) [3 <= I68 - 1 /\ 3 <= I67 - 1 /\ 1 <= I64 - 1 /\ 1 <= I63 - 1 /\ I68 - 2 <= I64 /\ I68 - 2 <= I63 /\ I67 - 2 <= I64 /\ I67 - 2 <= I63 /\ 0 <= I65 - 1 /\ -1 <= I66 - 1] 2.80/2.87 f4(I69, I70, I71, I72) -> f4(I73, I74, I71 - 1, I72 + 1) [0 <= I74 - 1 /\ 0 <= I73 - 1 /\ 1 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I71 - 1 /\ -1 <= I72 - 1] 2.80/2.87 f4(I75, I76, I77, I78) -> f4(I79, I80, I77 - 1, I78 + 1) [0 <= I77 - 1 /\ 0 <= I81 - 1 /\ -1 <= I78 - 1 /\ 0 <= I75 - 1 /\ 1 <= I76 - 1 /\ 0 <= I79 - 1 /\ 0 <= I80 - 1] 2.80/2.87 f4(I82, I83, I84, I85) -> f4(I86, I87, I84 - 1, I85 + 1) [0 <= I84 - 1 /\ 0 <= I88 - 1 /\ -1 <= I85 - 1 /\ I86 <= I82 /\ I87 + 2 <= I83 /\ 0 <= I82 - 1 /\ 2 <= I83 - 1 /\ 0 <= I86 - 1 /\ 0 <= I87 - 1] 2.80/2.87 f4(I89, I90, I91, I92) -> f4(I93, I94, I91 - 1, I92 + 1) [0 <= I94 - 1 /\ 0 <= I93 - 1 /\ 2 <= I90 - 1 /\ 0 <= I89 - 1 /\ I94 + 2 <= I90 /\ I93 <= I89 /\ 0 <= I91 - 1 /\ -1 <= I92 - 1] 2.80/2.87 f1(I95, I96, I97, I98) -> f4(I99, I100, I101, 1) [1 <= I100 - 1 /\ 1 <= I99 - 1 /\ 0 <= I95 - 1 /\ I100 - 1 <= I95 /\ I99 - 1 <= I95 /\ -1 <= I96 - 1 /\ 0 <= I101 - 1] 2.80/2.87 f3(I102, I103, I104, I105) -> f2(I106, I107, I104, I108) [I104 + 2 <= I103 /\ 1 <= I107 - 1 /\ 0 <= I106 - 1 /\ 1 <= I103 - 1 /\ 0 <= I102 - 1 /\ I107 <= I103 /\ I106 + 1 <= I103 /\ I106 <= I102] 2.80/2.87 f1(I109, I110, I111, I112) -> f2(I113, I114, I115, I116) [0 <= I114 - 1 /\ 0 <= I113 - 1 /\ 0 <= I109 - 1 /\ I113 <= I109] 2.80/2.87 2.80/2.87 The dependency graph for this problem is: 2.80/2.87 0 -> 7, 14, 16 2.80/2.87 1 -> 1, 2 2.80/2.87 2 -> 1, 2 2.80/2.87 3 -> 1, 2 2.80/2.87 4 -> 3, 4, 5 2.80/2.87 5 -> 3, 4, 5 2.80/2.87 6 -> 3, 4, 5 2.80/2.87 7 -> 3, 4, 5 2.80/2.87 8 -> 8, 9, 10, 11, 12, 13 2.80/2.87 9 -> 8, 9, 10, 11, 12, 13 2.80/2.87 10 -> 8, 9, 10, 11, 12, 13 2.80/2.87 11 -> 8, 9, 10, 11, 12, 13 2.80/2.87 12 -> 8, 9, 10, 11, 12, 13 2.80/2.87 13 -> 8, 9, 10, 11, 12, 13 2.80/2.87 14 -> 8, 9, 10, 11, 12, 13 2.80/2.87 15 -> 6 2.80/2.87 16 -> 6 2.80/2.87 Where: 2.80/2.87 0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 2.80/2.87 1) f6#(I0, I1, I2, I3) -> f6#(I4, I5, I6, I7) [2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I4 - 2 <= I0] 2.80/2.87 2) f6#(I8, I9, I10, I11) -> f6#(I12, I13, I14, I15) [-1 <= I12 - 1 /\ 1 <= I8 - 1 /\ I12 + 2 <= I8] 2.80/2.87 3) f5#(I16, I17, I18, I19) -> f6#(I20, I21, I22, I23) [2 <= I20 - 1 /\ 2 <= I17 - 1 /\ 2 <= I16 - 1 /\ I20 <= I17 /\ I20 <= I16] 2.80/2.87 4) f5#(I24, I25, I26, I27) -> f5#(I28, I29, I30, I31) [-1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1] 2.80/2.87 5) f5#(I32, I33, I34, I35) -> f5#(I36, I37, I38, I39) [-1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 1 <= I33 - 1 /\ 1 <= I32 - 1 /\ I37 + 2 <= I33 /\ I37 + 2 <= I32 /\ I36 + 2 <= I33 /\ I36 + 2 <= I32] 2.80/2.87 6) f2#(I40, I41, I42, I43) -> f5#(I44, I45, I46, I47) [I44 <= I41 /\ 0 <= y1 - 1 /\ I45 <= I41 /\ 0 <= I40 - 1 /\ 0 <= I41 - 1 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ I42 + 2 <= I41] 2.80/2.87 7) f1#(I48, I49, I50, I51) -> f5#(I52, I53, I54, I55) [-1 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I48 - 1 /\ I53 + 1 <= I48 /\ 0 <= I49 - 1 /\ I52 + 1 <= I48] 2.80/2.87 8) f4#(I56, I57, I58, I59) -> f4#(I60, I61, I58 - 1, I59 + 1) [0 <= I58 - 1 /\ 0 <= I62 - 1 /\ -1 <= I59 - 1 /\ I60 - 2 <= I56 /\ I60 - 2 <= I57 /\ I61 - 2 <= I56 /\ I61 - 2 <= I57 /\ 1 <= I56 - 1 /\ 1 <= I57 - 1 /\ 3 <= I60 - 1 /\ 3 <= I61 - 1] 2.80/2.87 9) f4#(I63, I64, I65, I66) -> f4#(I67, I68, I65 - 1, I66 + 1) [3 <= I68 - 1 /\ 3 <= I67 - 1 /\ 1 <= I64 - 1 /\ 1 <= I63 - 1 /\ I68 - 2 <= I64 /\ I68 - 2 <= I63 /\ I67 - 2 <= I64 /\ I67 - 2 <= I63 /\ 0 <= I65 - 1 /\ -1 <= I66 - 1] 2.80/2.87 10) f4#(I69, I70, I71, I72) -> f4#(I73, I74, I71 - 1, I72 + 1) [0 <= I74 - 1 /\ 0 <= I73 - 1 /\ 1 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I71 - 1 /\ -1 <= I72 - 1] 2.80/2.87 11) f4#(I75, I76, I77, I78) -> f4#(I79, I80, I77 - 1, I78 + 1) [0 <= I77 - 1 /\ 0 <= I81 - 1 /\ -1 <= I78 - 1 /\ 0 <= I75 - 1 /\ 1 <= I76 - 1 /\ 0 <= I79 - 1 /\ 0 <= I80 - 1] 2.80/2.87 12) f4#(I82, I83, I84, I85) -> f4#(I86, I87, I84 - 1, I85 + 1) [0 <= I84 - 1 /\ 0 <= I88 - 1 /\ -1 <= I85 - 1 /\ I86 <= I82 /\ I87 + 2 <= I83 /\ 0 <= I82 - 1 /\ 2 <= I83 - 1 /\ 0 <= I86 - 1 /\ 0 <= I87 - 1] 2.80/2.87 13) f4#(I89, I90, I91, I92) -> f4#(I93, I94, I91 - 1, I92 + 1) [0 <= I94 - 1 /\ 0 <= I93 - 1 /\ 2 <= I90 - 1 /\ 0 <= I89 - 1 /\ I94 + 2 <= I90 /\ I93 <= I89 /\ 0 <= I91 - 1 /\ -1 <= I92 - 1] 2.80/2.87 14) f1#(I95, I96, I97, I98) -> f4#(I99, I100, I101, 1) [1 <= I100 - 1 /\ 1 <= I99 - 1 /\ 0 <= I95 - 1 /\ I100 - 1 <= I95 /\ I99 - 1 <= I95 /\ -1 <= I96 - 1 /\ 0 <= I101 - 1] 2.80/2.87 15) f3#(I102, I103, I104, I105) -> f2#(I106, I107, I104, I108) [I104 + 2 <= I103 /\ 1 <= I107 - 1 /\ 0 <= I106 - 1 /\ 1 <= I103 - 1 /\ 0 <= I102 - 1 /\ I107 <= I103 /\ I106 + 1 <= I103 /\ I106 <= I102] 2.80/2.87 16) f1#(I109, I110, I111, I112) -> f2#(I113, I114, I115, I116) [0 <= I114 - 1 /\ 0 <= I113 - 1 /\ 0 <= I109 - 1 /\ I113 <= I109] 2.80/2.87 2.80/2.87 We have the following SCCs. 2.80/2.87 { 8, 9, 10, 11, 12, 13 } 2.80/2.87 { 4, 5 } 2.80/2.87 { 1, 2 } 2.80/2.87 2.80/2.87 DP problem for innermost termination. 2.80/2.87 P = 2.80/2.87 f6#(I0, I1, I2, I3) -> f6#(I4, I5, I6, I7) [2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I4 - 2 <= I0] 2.80/2.87 f6#(I8, I9, I10, I11) -> f6#(I12, I13, I14, I15) [-1 <= I12 - 1 /\ 1 <= I8 - 1 /\ I12 + 2 <= I8] 2.80/2.87 R = 2.80/2.87 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 2.80/2.87 f6(I0, I1, I2, I3) -> f6(I4, I5, I6, I7) [2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I4 - 2 <= I0] 2.80/2.87 f6(I8, I9, I10, I11) -> f6(I12, I13, I14, I15) [-1 <= I12 - 1 /\ 1 <= I8 - 1 /\ I12 + 2 <= I8] 2.80/2.87 f5(I16, I17, I18, I19) -> f6(I20, I21, I22, I23) [2 <= I20 - 1 /\ 2 <= I17 - 1 /\ 2 <= I16 - 1 /\ I20 <= I17 /\ I20 <= I16] 2.80/2.87 f5(I24, I25, I26, I27) -> f5(I28, I29, I30, I31) [-1 <= I29 - 1 /\ -1 <= I28 - 1 /\ 2 <= I25 - 1 /\ 2 <= I24 - 1] 2.80/2.87 f5(I32, I33, I34, I35) -> f5(I36, I37, I38, I39) [-1 <= I37 - 1 /\ -1 <= I36 - 1 /\ 1 <= I33 - 1 /\ 1 <= I32 - 1 /\ I37 + 2 <= I33 /\ I37 + 2 <= I32 /\ I36 + 2 <= I33 /\ I36 + 2 <= I32] 2.80/2.87 f2(I40, I41, I42, I43) -> f5(I44, I45, I46, I47) [I44 <= I41 /\ 0 <= y1 - 1 /\ I45 <= I41 /\ 0 <= I40 - 1 /\ 0 <= I41 - 1 /\ 0 <= I44 - 1 /\ 0 <= I45 - 1 /\ I42 + 2 <= I41] 2.80/2.87 f1(I48, I49, I50, I51) -> f5(I52, I53, I54, I55) [-1 <= I53 - 1 /\ -1 <= I52 - 1 /\ 0 <= I48 - 1 /\ I53 + 1 <= I48 /\ 0 <= I49 - 1 /\ I52 + 1 <= I48] 2.80/2.87 f4(I56, I57, I58, I59) -> f4(I60, I61, I58 - 1, I59 + 1) [0 <= I58 - 1 /\ 0 <= I62 - 1 /\ -1 <= I59 - 1 /\ I60 - 2 <= I56 /\ I60 - 2 <= I57 /\ I61 - 2 <= I56 /\ I61 - 2 <= I57 /\ 1 <= I56 - 1 /\ 1 <= I57 - 1 /\ 3 <= I60 - 1 /\ 3 <= I61 - 1] 2.80/2.87 f4(I63, I64, I65, I66) -> f4(I67, I68, I65 - 1, I66 + 1) [3 <= I68 - 1 /\ 3 <= I67 - 1 /\ 1 <= I64 - 1 /\ 1 <= I63 - 1 /\ I68 - 2 <= I64 /\ I68 - 2 <= I63 /\ I67 - 2 <= I64 /\ I67 - 2 <= I63 /\ 0 <= I65 - 1 /\ -1 <= I66 - 1] 2.80/2.87 f4(I69, I70, I71, I72) -> f4(I73, I74, I71 - 1, I72 + 1) [0 <= I74 - 1 /\ 0 <= I73 - 1 /\ 1 <= I70 - 1 /\ 0 <= I69 - 1 /\ 0 <= I71 - 1 /\ -1 <= I72 - 1] 2.80/2.87 f4(I75, I76, I77, I78) -> f4(I79, I80, I77 - 1, I78 + 1) [0 <= I77 - 1 /\ 0 <= I81 - 1 /\ -1 <= I78 - 1 /\ 0 <= I75 - 1 /\ 1 <= I76 - 1 /\ 0 <= I79 - 1 /\ 0 <= I80 - 1] 2.80/2.87 f4(I82, I83, I84, I85) -> f4(I86, I87, I84 - 1, I85 + 1) [0 <= I84 - 1 /\ 0 <= I88 - 1 /\ -1 <= I85 - 1 /\ I86 <= I82 /\ I87 + 2 <= I83 /\ 0 <= I82 - 1 /\ 2 <= I83 - 1 /\ 0 <= I86 - 1 /\ 0 <= I87 - 1] 2.80/2.87 f4(I89, I90, I91, I92) -> f4(I93, I94, I91 - 1, I92 + 1) [0 <= I94 - 1 /\ 0 <= I93 - 1 /\ 2 <= I90 - 1 /\ 0 <= I89 - 1 /\ I94 + 2 <= I90 /\ I93 <= I89 /\ 0 <= I91 - 1 /\ -1 <= I92 - 1] 2.80/2.87 f1(I95, I96, I97, I98) -> f4(I99, I100, I101, 1) [1 <= I100 - 1 /\ 1 <= I99 - 1 /\ 0 <= I95 - 1 /\ I100 - 1 <= I95 /\ I99 - 1 <= I95 /\ -1 <= I96 - 1 /\ 0 <= I101 - 1] 2.80/2.87 f3(I102, I103, I104, I105) -> f2(I106, I107, I104, I108) [I104 + 2 <= I103 /\ 1 <= I107 - 1 /\ 0 <= I106 - 1 /\ 1 <= I103 - 1 /\ 0 <= I102 - 1 /\ I107 <= I103 /\ I106 + 1 <= I103 /\ I106 <= I102] 2.80/2.87 f1(I109, I110, I111, I112) -> f2(I113, I114, I115, I116) [0 <= I114 - 1 /\ 0 <= I113 - 1 /\ 0 <= I109 - 1 /\ I113 <= I109] 2.80/2.87 2.80/5.85 EOF