1.31/1.34 MAYBE 1.31/1.34 1.31/1.34 DP problem for innermost termination. 1.31/1.34 P = 1.31/1.34 init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 1.31/1.34 f7#(I0, I1, I2, I3) -> f3#(I4, I5, I6, I7) [-1 <= I6 - 1 /\ 1 <= I5 - 1 /\ 2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I0 /\ I4 <= I0] 1.31/1.34 f8#(I8, I9, I10, I11) -> f7#(I12, I13, I14, I15) [I9 + 4 <= I8 /\ 2 <= I12 - 1 /\ 2 <= I8 - 1 /\ I12 <= I8] 1.31/1.34 f6#(I16, I17, I18, I19) -> f7#(I20, I21, I22, I23) [2 <= I20 - 1 /\ 0 <= I17 - 1 /\ 2 <= I16 - 1] 1.31/1.34 f6#(I24, I25, I26, I27) -> f7#(I28, I29, I30, I31) [4 <= I28 - 1 /\ 0 <= I25 - 1 /\ 2 <= I24 - 1] 1.31/1.34 f6#(I32, I33, I34, I35) -> f3#(I36, I37, I38, I39) [-1 <= I38 - 1 /\ 1 <= I37 - 1 /\ 1 <= I36 - 1 /\ 0 <= I33 - 1 /\ 2 <= I32 - 1 /\ I37 - 1 <= I33 /\ I37 + 1 <= I32 /\ I36 - 1 <= I33 /\ I36 + 1 <= I32] 1.31/1.34 f6#(I40, I41, I42, I43) -> f6#(I44, I45, I46, I47) [-1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 0 <= I41 - 1 /\ 2 <= I40 - 1 /\ I45 + 1 <= I41 /\ I45 + 3 <= I40 /\ I44 <= I41 /\ I44 + 2 <= I40] 1.31/1.34 f1#(I48, I49, I50, I51) -> f6#(I52, I53, I54, I55) [3 <= I52 - 1 /\ 1 <= I53 - 1] 1.31/1.34 f5#(I56, I57, I58, I59) -> f5#(I60, I61, I62, I63) [-1 <= I61 - 1 /\ 0 <= I60 - 1 /\ 0 <= I57 - 1 /\ 2 <= I56 - 1 /\ I61 + 1 <= I57 /\ I61 + 3 <= I56 /\ I60 <= I57 /\ I60 + 2 <= I56] 1.31/1.34 f1#(I64, I65, I66, I67) -> f5#(I68, I69, I70, I71) [3 <= I68 - 1 /\ 1 <= I69 - 1] 1.31/1.34 f4#(I72, I73, I74, I75) -> f4#(I76, I77, I78, I79) [-1 <= I77 - 1 /\ 0 <= I76 - 1 /\ 0 <= I73 - 1 /\ 2 <= I72 - 1 /\ I77 + 1 <= I73 /\ I77 + 3 <= I72 /\ I76 <= I73 /\ I76 + 2 <= I72] 1.31/1.34 f1#(I80, I81, I82, I83) -> f4#(I84, I85, I86, I87) [3 <= I84 - 1 /\ 1 <= I85 - 1] 1.31/1.34 f3#(I88, I89, I90, I91) -> f3#(I92, I93, I94, I95) [-1 <= I94 - 1 /\ 0 <= I93 - 1 /\ 0 <= I92 - 1 /\ 0 <= I90 - 1 /\ 0 <= I89 - 1 /\ 2 <= I88 - 1 /\ I93 <= I89] 1.31/1.34 f1#(I96, I97, I98, I99) -> f3#(I100, I101, I102, I103) [4 <= I101 - 1 /\ -1 <= I102 - 1 /\ 3 <= I100 - 1] 1.31/1.34 f2#(I104, I105, I106, I107) -> f2#(I108, I109, I110, I111) [-1 <= I111 - 1 /\ -1 <= I110 - 1 /\ 0 <= I109 - 1 /\ -1 <= I108 - 1 /\ 0 <= I107 - 1 /\ 0 <= I106 - 1 /\ 0 <= I105 - 1 /\ 0 <= I104 - 1 /\ I111 + 1 <= I105 /\ I110 + 1 <= I105 /\ I109 <= I107 /\ I109 <= I106 /\ I109 <= I104 /\ I108 + 1 <= I105] 1.31/1.34 f1#(I112, I113, I114, I115) -> f2#(I116, I117, I118, I119) [3 <= I118 - 1 /\ 3 <= I119 - 1 /\ 3 <= I117 - 1 /\ 3 <= I116 - 1] 1.31/1.34 R = 1.31/1.34 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 1.31/1.34 f7(I0, I1, I2, I3) -> f3(I4, I5, I6, I7) [-1 <= I6 - 1 /\ 1 <= I5 - 1 /\ 2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I0 /\ I4 <= I0] 1.31/1.34 f8(I8, I9, I10, I11) -> f7(I12, I13, I14, I15) [I9 + 4 <= I8 /\ 2 <= I12 - 1 /\ 2 <= I8 - 1 /\ I12 <= I8] 1.31/1.34 f6(I16, I17, I18, I19) -> f7(I20, I21, I22, I23) [2 <= I20 - 1 /\ 0 <= I17 - 1 /\ 2 <= I16 - 1] 1.31/1.34 f6(I24, I25, I26, I27) -> f7(I28, I29, I30, I31) [4 <= I28 - 1 /\ 0 <= I25 - 1 /\ 2 <= I24 - 1] 1.31/1.34 f6(I32, I33, I34, I35) -> f3(I36, I37, I38, I39) [-1 <= I38 - 1 /\ 1 <= I37 - 1 /\ 1 <= I36 - 1 /\ 0 <= I33 - 1 /\ 2 <= I32 - 1 /\ I37 - 1 <= I33 /\ I37 + 1 <= I32 /\ I36 - 1 <= I33 /\ I36 + 1 <= I32] 1.31/1.34 f6(I40, I41, I42, I43) -> f6(I44, I45, I46, I47) [-1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 0 <= I41 - 1 /\ 2 <= I40 - 1 /\ I45 + 1 <= I41 /\ I45 + 3 <= I40 /\ I44 <= I41 /\ I44 + 2 <= I40] 1.31/1.34 f1(I48, I49, I50, I51) -> f6(I52, I53, I54, I55) [3 <= I52 - 1 /\ 1 <= I53 - 1] 1.31/1.34 f5(I56, I57, I58, I59) -> f5(I60, I61, I62, I63) [-1 <= I61 - 1 /\ 0 <= I60 - 1 /\ 0 <= I57 - 1 /\ 2 <= I56 - 1 /\ I61 + 1 <= I57 /\ I61 + 3 <= I56 /\ I60 <= I57 /\ I60 + 2 <= I56] 1.31/1.34 f1(I64, I65, I66, I67) -> f5(I68, I69, I70, I71) [3 <= I68 - 1 /\ 1 <= I69 - 1] 1.31/1.34 f4(I72, I73, I74, I75) -> f4(I76, I77, I78, I79) [-1 <= I77 - 1 /\ 0 <= I76 - 1 /\ 0 <= I73 - 1 /\ 2 <= I72 - 1 /\ I77 + 1 <= I73 /\ I77 + 3 <= I72 /\ I76 <= I73 /\ I76 + 2 <= I72] 1.31/1.34 f1(I80, I81, I82, I83) -> f4(I84, I85, I86, I87) [3 <= I84 - 1 /\ 1 <= I85 - 1] 1.31/1.34 f3(I88, I89, I90, I91) -> f3(I92, I93, I94, I95) [-1 <= I94 - 1 /\ 0 <= I93 - 1 /\ 0 <= I92 - 1 /\ 0 <= I90 - 1 /\ 0 <= I89 - 1 /\ 2 <= I88 - 1 /\ I93 <= I89] 1.31/1.34 f1(I96, I97, I98, I99) -> f3(I100, I101, I102, I103) [4 <= I101 - 1 /\ -1 <= I102 - 1 /\ 3 <= I100 - 1] 1.31/1.34 f2(I104, I105, I106, I107) -> f2(I108, I109, I110, I111) [-1 <= I111 - 1 /\ -1 <= I110 - 1 /\ 0 <= I109 - 1 /\ -1 <= I108 - 1 /\ 0 <= I107 - 1 /\ 0 <= I106 - 1 /\ 0 <= I105 - 1 /\ 0 <= I104 - 1 /\ I111 + 1 <= I105 /\ I110 + 1 <= I105 /\ I109 <= I107 /\ I109 <= I106 /\ I109 <= I104 /\ I108 + 1 <= I105] 1.31/1.34 f1(I112, I113, I114, I115) -> f2(I116, I117, I118, I119) [3 <= I118 - 1 /\ 3 <= I119 - 1 /\ 3 <= I117 - 1 /\ 3 <= I116 - 1] 1.31/1.34 1.31/1.34 The dependency graph for this problem is: 1.31/1.34 0 -> 7, 9, 11, 13, 15 1.31/1.34 1 -> 12 1.31/1.34 2 -> 1 1.31/1.34 3 -> 1 1.31/1.34 4 -> 1 1.31/1.34 5 -> 12 1.31/1.34 6 -> 3, 4, 5, 6 1.31/1.34 7 -> 3, 4, 5, 6 1.31/1.34 8 -> 8 1.31/1.34 9 -> 8 1.31/1.34 10 -> 10 1.31/1.34 11 -> 10 1.31/1.34 12 -> 12 1.31/1.34 13 -> 12 1.31/1.34 14 -> 14 1.31/1.34 15 -> 14 1.31/1.34 Where: 1.31/1.34 0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 1.31/1.34 1) f7#(I0, I1, I2, I3) -> f3#(I4, I5, I6, I7) [-1 <= I6 - 1 /\ 1 <= I5 - 1 /\ 2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I0 /\ I4 <= I0] 1.31/1.34 2) f8#(I8, I9, I10, I11) -> f7#(I12, I13, I14, I15) [I9 + 4 <= I8 /\ 2 <= I12 - 1 /\ 2 <= I8 - 1 /\ I12 <= I8] 1.31/1.34 3) f6#(I16, I17, I18, I19) -> f7#(I20, I21, I22, I23) [2 <= I20 - 1 /\ 0 <= I17 - 1 /\ 2 <= I16 - 1] 1.31/1.34 4) f6#(I24, I25, I26, I27) -> f7#(I28, I29, I30, I31) [4 <= I28 - 1 /\ 0 <= I25 - 1 /\ 2 <= I24 - 1] 1.31/1.34 5) f6#(I32, I33, I34, I35) -> f3#(I36, I37, I38, I39) [-1 <= I38 - 1 /\ 1 <= I37 - 1 /\ 1 <= I36 - 1 /\ 0 <= I33 - 1 /\ 2 <= I32 - 1 /\ I37 - 1 <= I33 /\ I37 + 1 <= I32 /\ I36 - 1 <= I33 /\ I36 + 1 <= I32] 1.31/1.34 6) f6#(I40, I41, I42, I43) -> f6#(I44, I45, I46, I47) [-1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 0 <= I41 - 1 /\ 2 <= I40 - 1 /\ I45 + 1 <= I41 /\ I45 + 3 <= I40 /\ I44 <= I41 /\ I44 + 2 <= I40] 1.31/1.34 7) f1#(I48, I49, I50, I51) -> f6#(I52, I53, I54, I55) [3 <= I52 - 1 /\ 1 <= I53 - 1] 1.31/1.34 8) f5#(I56, I57, I58, I59) -> f5#(I60, I61, I62, I63) [-1 <= I61 - 1 /\ 0 <= I60 - 1 /\ 0 <= I57 - 1 /\ 2 <= I56 - 1 /\ I61 + 1 <= I57 /\ I61 + 3 <= I56 /\ I60 <= I57 /\ I60 + 2 <= I56] 1.31/1.34 9) f1#(I64, I65, I66, I67) -> f5#(I68, I69, I70, I71) [3 <= I68 - 1 /\ 1 <= I69 - 1] 1.31/1.34 10) f4#(I72, I73, I74, I75) -> f4#(I76, I77, I78, I79) [-1 <= I77 - 1 /\ 0 <= I76 - 1 /\ 0 <= I73 - 1 /\ 2 <= I72 - 1 /\ I77 + 1 <= I73 /\ I77 + 3 <= I72 /\ I76 <= I73 /\ I76 + 2 <= I72] 1.31/1.34 11) f1#(I80, I81, I82, I83) -> f4#(I84, I85, I86, I87) [3 <= I84 - 1 /\ 1 <= I85 - 1] 1.31/1.34 12) f3#(I88, I89, I90, I91) -> f3#(I92, I93, I94, I95) [-1 <= I94 - 1 /\ 0 <= I93 - 1 /\ 0 <= I92 - 1 /\ 0 <= I90 - 1 /\ 0 <= I89 - 1 /\ 2 <= I88 - 1 /\ I93 <= I89] 1.31/1.34 13) f1#(I96, I97, I98, I99) -> f3#(I100, I101, I102, I103) [4 <= I101 - 1 /\ -1 <= I102 - 1 /\ 3 <= I100 - 1] 1.31/1.34 14) f2#(I104, I105, I106, I107) -> f2#(I108, I109, I110, I111) [-1 <= I111 - 1 /\ -1 <= I110 - 1 /\ 0 <= I109 - 1 /\ -1 <= I108 - 1 /\ 0 <= I107 - 1 /\ 0 <= I106 - 1 /\ 0 <= I105 - 1 /\ 0 <= I104 - 1 /\ I111 + 1 <= I105 /\ I110 + 1 <= I105 /\ I109 <= I107 /\ I109 <= I106 /\ I109 <= I104 /\ I108 + 1 <= I105] 1.31/1.34 15) f1#(I112, I113, I114, I115) -> f2#(I116, I117, I118, I119) [3 <= I118 - 1 /\ 3 <= I119 - 1 /\ 3 <= I117 - 1 /\ 3 <= I116 - 1] 1.31/1.34 1.31/1.34 We have the following SCCs. 1.31/1.34 { 6 } 1.31/1.34 { 8 } 1.31/1.34 { 10 } 1.31/1.34 { 12 } 1.31/1.34 { 14 } 1.31/1.34 1.31/1.34 DP problem for innermost termination. 1.31/1.34 P = 1.31/1.34 f2#(I104, I105, I106, I107) -> f2#(I108, I109, I110, I111) [-1 <= I111 - 1 /\ -1 <= I110 - 1 /\ 0 <= I109 - 1 /\ -1 <= I108 - 1 /\ 0 <= I107 - 1 /\ 0 <= I106 - 1 /\ 0 <= I105 - 1 /\ 0 <= I104 - 1 /\ I111 + 1 <= I105 /\ I110 + 1 <= I105 /\ I109 <= I107 /\ I109 <= I106 /\ I109 <= I104 /\ I108 + 1 <= I105] 1.31/1.34 R = 1.31/1.34 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 1.31/1.34 f7(I0, I1, I2, I3) -> f3(I4, I5, I6, I7) [-1 <= I6 - 1 /\ 1 <= I5 - 1 /\ 2 <= I4 - 1 /\ 2 <= I0 - 1 /\ I5 + 1 <= I0 /\ I4 <= I0] 1.31/1.34 f8(I8, I9, I10, I11) -> f7(I12, I13, I14, I15) [I9 + 4 <= I8 /\ 2 <= I12 - 1 /\ 2 <= I8 - 1 /\ I12 <= I8] 1.31/1.34 f6(I16, I17, I18, I19) -> f7(I20, I21, I22, I23) [2 <= I20 - 1 /\ 0 <= I17 - 1 /\ 2 <= I16 - 1] 1.31/1.34 f6(I24, I25, I26, I27) -> f7(I28, I29, I30, I31) [4 <= I28 - 1 /\ 0 <= I25 - 1 /\ 2 <= I24 - 1] 1.31/1.34 f6(I32, I33, I34, I35) -> f3(I36, I37, I38, I39) [-1 <= I38 - 1 /\ 1 <= I37 - 1 /\ 1 <= I36 - 1 /\ 0 <= I33 - 1 /\ 2 <= I32 - 1 /\ I37 - 1 <= I33 /\ I37 + 1 <= I32 /\ I36 - 1 <= I33 /\ I36 + 1 <= I32] 1.31/1.34 f6(I40, I41, I42, I43) -> f6(I44, I45, I46, I47) [-1 <= I45 - 1 /\ 0 <= I44 - 1 /\ 0 <= I41 - 1 /\ 2 <= I40 - 1 /\ I45 + 1 <= I41 /\ I45 + 3 <= I40 /\ I44 <= I41 /\ I44 + 2 <= I40] 1.31/1.34 f1(I48, I49, I50, I51) -> f6(I52, I53, I54, I55) [3 <= I52 - 1 /\ 1 <= I53 - 1] 1.31/1.34 f5(I56, I57, I58, I59) -> f5(I60, I61, I62, I63) [-1 <= I61 - 1 /\ 0 <= I60 - 1 /\ 0 <= I57 - 1 /\ 2 <= I56 - 1 /\ I61 + 1 <= I57 /\ I61 + 3 <= I56 /\ I60 <= I57 /\ I60 + 2 <= I56] 1.31/1.34 f1(I64, I65, I66, I67) -> f5(I68, I69, I70, I71) [3 <= I68 - 1 /\ 1 <= I69 - 1] 1.31/1.34 f4(I72, I73, I74, I75) -> f4(I76, I77, I78, I79) [-1 <= I77 - 1 /\ 0 <= I76 - 1 /\ 0 <= I73 - 1 /\ 2 <= I72 - 1 /\ I77 + 1 <= I73 /\ I77 + 3 <= I72 /\ I76 <= I73 /\ I76 + 2 <= I72] 1.31/1.34 f1(I80, I81, I82, I83) -> f4(I84, I85, I86, I87) [3 <= I84 - 1 /\ 1 <= I85 - 1] 1.31/1.34 f3(I88, I89, I90, I91) -> f3(I92, I93, I94, I95) [-1 <= I94 - 1 /\ 0 <= I93 - 1 /\ 0 <= I92 - 1 /\ 0 <= I90 - 1 /\ 0 <= I89 - 1 /\ 2 <= I88 - 1 /\ I93 <= I89] 1.31/1.34 f1(I96, I97, I98, I99) -> f3(I100, I101, I102, I103) [4 <= I101 - 1 /\ -1 <= I102 - 1 /\ 3 <= I100 - 1] 1.31/1.34 f2(I104, I105, I106, I107) -> f2(I108, I109, I110, I111) [-1 <= I111 - 1 /\ -1 <= I110 - 1 /\ 0 <= I109 - 1 /\ -1 <= I108 - 1 /\ 0 <= I107 - 1 /\ 0 <= I106 - 1 /\ 0 <= I105 - 1 /\ 0 <= I104 - 1 /\ I111 + 1 <= I105 /\ I110 + 1 <= I105 /\ I109 <= I107 /\ I109 <= I106 /\ I109 <= I104 /\ I108 + 1 <= I105] 1.31/1.34 f1(I112, I113, I114, I115) -> f2(I116, I117, I118, I119) [3 <= I118 - 1 /\ 3 <= I119 - 1 /\ 3 <= I117 - 1 /\ 3 <= I116 - 1] 1.31/1.34 1.31/4.32 EOF