2.13/2.21 MAYBE 2.13/2.21 2.13/2.21 DP problem for innermost termination. 2.13/2.21 P = 2.13/2.21 init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 2.13/2.21 f3#(I0, I1, I2, I3, I4) -> f3#(0, 2, I5, I6, I7) [y1 <= I1 - 1 /\ -1 <= I1 - 1 /\ 1 = I0] 2.13/2.21 f3#(I8, I9, I10, I11, I12) -> f3#(0, 0, I13, I14, I15) [-1 <= I9 - 1 /\ 0 <= I16 - 1 /\ I16 <= I9 - 1 /\ I16 <= y3 - 1 /\ I16 <= y2 - 1 /\ 1 = I8] 2.13/2.21 f3#(I17, I18, I19, I20, I21) -> f3#(1, 1, I22, I23, I24) [I25 <= I18 - 1 /\ -1 <= I18 - 1 /\ 0 = I17] 2.13/2.21 f3#(I26, I27, I28, I29, I30) -> f3#(1, I31, I32, I33, I34) [-1 <= I27 - 1 /\ 0 <= I35 - 1 /\ I35 <= I27 - 1 /\ I35 <= I31 - 1 /\ 0 = I26] 2.13/2.21 f2#(I36, I37, I38, I39, I40) -> f3#(1, 1, I41, I42, I43) [I38 <= I37 /\ 0 <= I36 - 1] 2.13/2.21 f2#(I44, I45, I46, I47, I48) -> f3#(1, I49, I50, I51, I52) [0 <= I44 - 1 /\ I47 <= I49 - 1 /\ 0 <= I47 - 1 /\ I46 <= I45] 2.13/2.21 f2#(I53, I54, I55, I56, I57) -> f2#(I58, I54 + 1, I57 - 1, I59, I57) [0 <= I58 - 1 /\ 0 <= I53 - 1 /\ I58 <= I53 /\ I54 <= I55 - 1 /\ -1 <= I57 - 1] 2.13/2.21 f1#(I60, I61, I62, I63, I64) -> f2#(I65, 0, I61 - 1, 0, I61) [0 <= I65 - 1 /\ 0 <= I60 - 1 /\ -1 <= I61 - 1 /\ I65 <= I60] 2.13/2.21 R = 2.13/2.21 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 2.13/2.21 f3(I0, I1, I2, I3, I4) -> f3(0, 2, I5, I6, I7) [y1 <= I1 - 1 /\ -1 <= I1 - 1 /\ 1 = I0] 2.13/2.21 f3(I8, I9, I10, I11, I12) -> f3(0, 0, I13, I14, I15) [-1 <= I9 - 1 /\ 0 <= I16 - 1 /\ I16 <= I9 - 1 /\ I16 <= y3 - 1 /\ I16 <= y2 - 1 /\ 1 = I8] 2.13/2.21 f3(I17, I18, I19, I20, I21) -> f3(1, 1, I22, I23, I24) [I25 <= I18 - 1 /\ -1 <= I18 - 1 /\ 0 = I17] 2.13/2.21 f3(I26, I27, I28, I29, I30) -> f3(1, I31, I32, I33, I34) [-1 <= I27 - 1 /\ 0 <= I35 - 1 /\ I35 <= I27 - 1 /\ I35 <= I31 - 1 /\ 0 = I26] 2.13/2.21 f2(I36, I37, I38, I39, I40) -> f3(1, 1, I41, I42, I43) [I38 <= I37 /\ 0 <= I36 - 1] 2.13/2.21 f2(I44, I45, I46, I47, I48) -> f3(1, I49, I50, I51, I52) [0 <= I44 - 1 /\ I47 <= I49 - 1 /\ 0 <= I47 - 1 /\ I46 <= I45] 2.13/2.21 f2(I53, I54, I55, I56, I57) -> f2(I58, I54 + 1, I57 - 1, I59, I57) [0 <= I58 - 1 /\ 0 <= I53 - 1 /\ I58 <= I53 /\ I54 <= I55 - 1 /\ -1 <= I57 - 1] 2.13/2.21 f1(I60, I61, I62, I63, I64) -> f2(I65, 0, I61 - 1, 0, I61) [0 <= I65 - 1 /\ 0 <= I60 - 1 /\ -1 <= I61 - 1 /\ I65 <= I60] 2.13/2.21 2.13/2.21 The dependency graph for this problem is: 2.13/2.21 0 -> 8 2.13/2.21 1 -> 3, 4 2.13/2.21 2 -> 3 2.13/2.21 3 -> 1 2.13/2.21 4 -> 1, 2 2.13/2.21 5 -> 1 2.13/2.21 6 -> 1, 2 2.13/2.21 7 -> 5, 6, 7 2.13/2.21 8 -> 5, 7 2.13/2.21 Where: 2.13/2.21 0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 2.13/2.21 1) f3#(I0, I1, I2, I3, I4) -> f3#(0, 2, I5, I6, I7) [y1 <= I1 - 1 /\ -1 <= I1 - 1 /\ 1 = I0] 2.13/2.21 2) f3#(I8, I9, I10, I11, I12) -> f3#(0, 0, I13, I14, I15) [-1 <= I9 - 1 /\ 0 <= I16 - 1 /\ I16 <= I9 - 1 /\ I16 <= y3 - 1 /\ I16 <= y2 - 1 /\ 1 = I8] 2.13/2.21 3) f3#(I17, I18, I19, I20, I21) -> f3#(1, 1, I22, I23, I24) [I25 <= I18 - 1 /\ -1 <= I18 - 1 /\ 0 = I17] 2.13/2.21 4) f3#(I26, I27, I28, I29, I30) -> f3#(1, I31, I32, I33, I34) [-1 <= I27 - 1 /\ 0 <= I35 - 1 /\ I35 <= I27 - 1 /\ I35 <= I31 - 1 /\ 0 = I26] 2.13/2.21 5) f2#(I36, I37, I38, I39, I40) -> f3#(1, 1, I41, I42, I43) [I38 <= I37 /\ 0 <= I36 - 1] 2.13/2.21 6) f2#(I44, I45, I46, I47, I48) -> f3#(1, I49, I50, I51, I52) [0 <= I44 - 1 /\ I47 <= I49 - 1 /\ 0 <= I47 - 1 /\ I46 <= I45] 2.13/2.21 7) f2#(I53, I54, I55, I56, I57) -> f2#(I58, I54 + 1, I57 - 1, I59, I57) [0 <= I58 - 1 /\ 0 <= I53 - 1 /\ I58 <= I53 /\ I54 <= I55 - 1 /\ -1 <= I57 - 1] 2.13/2.21 8) f1#(I60, I61, I62, I63, I64) -> f2#(I65, 0, I61 - 1, 0, I61) [0 <= I65 - 1 /\ 0 <= I60 - 1 /\ -1 <= I61 - 1 /\ I65 <= I60] 2.13/2.21 2.13/2.21 We have the following SCCs. 2.13/2.21 { 7 } 2.13/2.21 { 1, 2, 3, 4 } 2.13/2.21 2.13/2.21 DP problem for innermost termination. 2.13/2.21 P = 2.13/2.21 f3#(I0, I1, I2, I3, I4) -> f3#(0, 2, I5, I6, I7) [y1 <= I1 - 1 /\ -1 <= I1 - 1 /\ 1 = I0] 2.13/2.21 f3#(I8, I9, I10, I11, I12) -> f3#(0, 0, I13, I14, I15) [-1 <= I9 - 1 /\ 0 <= I16 - 1 /\ I16 <= I9 - 1 /\ I16 <= y3 - 1 /\ I16 <= y2 - 1 /\ 1 = I8] 2.13/2.21 f3#(I17, I18, I19, I20, I21) -> f3#(1, 1, I22, I23, I24) [I25 <= I18 - 1 /\ -1 <= I18 - 1 /\ 0 = I17] 2.13/2.21 f3#(I26, I27, I28, I29, I30) -> f3#(1, I31, I32, I33, I34) [-1 <= I27 - 1 /\ 0 <= I35 - 1 /\ I35 <= I27 - 1 /\ I35 <= I31 - 1 /\ 0 = I26] 2.13/2.21 R = 2.13/2.21 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 2.13/2.21 f3(I0, I1, I2, I3, I4) -> f3(0, 2, I5, I6, I7) [y1 <= I1 - 1 /\ -1 <= I1 - 1 /\ 1 = I0] 2.13/2.21 f3(I8, I9, I10, I11, I12) -> f3(0, 0, I13, I14, I15) [-1 <= I9 - 1 /\ 0 <= I16 - 1 /\ I16 <= I9 - 1 /\ I16 <= y3 - 1 /\ I16 <= y2 - 1 /\ 1 = I8] 2.13/2.21 f3(I17, I18, I19, I20, I21) -> f3(1, 1, I22, I23, I24) [I25 <= I18 - 1 /\ -1 <= I18 - 1 /\ 0 = I17] 2.13/2.21 f3(I26, I27, I28, I29, I30) -> f3(1, I31, I32, I33, I34) [-1 <= I27 - 1 /\ 0 <= I35 - 1 /\ I35 <= I27 - 1 /\ I35 <= I31 - 1 /\ 0 = I26] 2.13/2.21 f2(I36, I37, I38, I39, I40) -> f3(1, 1, I41, I42, I43) [I38 <= I37 /\ 0 <= I36 - 1] 2.13/2.21 f2(I44, I45, I46, I47, I48) -> f3(1, I49, I50, I51, I52) [0 <= I44 - 1 /\ I47 <= I49 - 1 /\ 0 <= I47 - 1 /\ I46 <= I45] 2.13/2.21 f2(I53, I54, I55, I56, I57) -> f2(I58, I54 + 1, I57 - 1, I59, I57) [0 <= I58 - 1 /\ 0 <= I53 - 1 /\ I58 <= I53 /\ I54 <= I55 - 1 /\ -1 <= I57 - 1] 2.13/2.21 f1(I60, I61, I62, I63, I64) -> f2(I65, 0, I61 - 1, 0, I61) [0 <= I65 - 1 /\ 0 <= I60 - 1 /\ -1 <= I61 - 1 /\ I65 <= I60] 2.13/2.21 2.13/2.21 EOF