0.97/1.02 MAYBE 0.97/1.02 0.97/1.02 DP problem for innermost termination. 0.97/1.02 P = 0.97/1.02 init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 0.97/1.02 f3#(I0, I1, I2, I3, I4) -> f3#(I0 - 1, I1, I0 - 1 + I1, I3, I4 + 2) [1 <= I3 - 1 /\ I4 + 1 <= I3 - 1 /\ 0 <= I2 - 1 /\ -1 <= I4 - 1 /\ -1 <= y1 - 1 /\ -1 <= y2 - 1 /\ 9 <= y1 * y2 - 1 /\ I4 + 2 <= I3 /\ I0 - 1 <= I0 - 1] 0.97/1.02 f3#(I5, I6, I7, I8, I9) -> f3#(I5, I6 - 1, I5 + I6 - 1, I8, I9 + 2) [1 <= I8 - 1 /\ I9 + 1 <= I8 - 1 /\ 0 <= I7 - 1 /\ -1 <= I9 - 1 /\ -1 <= I10 - 1 /\ -1 <= I11 - 1 /\ I10 * I11 <= 9 /\ I9 + 2 <= I8 /\ I6 - 1 <= I6 - 1] 0.97/1.02 f3#(I12, I13, I14, I15, I16) -> f3#(I12, I13 - 1, I12 + I13 - 1, I15, I16) [I15 <= I16 /\ I13 - 1 <= I13 - 1 /\ -1 <= I15 - 1 /\ 0 <= I14 - 1] 0.97/1.02 f2#(I17, I18, I19, I20, I21) -> f3#(100 * I18, I22, I23, I18, 0) [100 * I18 + I22 = I23 /\ 0 <= 200 * I18 - 13 * I22 /\ 200 * I18 - 13 * I22 <= 12 /\ 0 <= I17 - 1 /\ I22 <= 200 * I18 /\ -1 <= I18 - 1] 0.97/1.02 f1#(I24, I25, I26, I27, I28) -> f2#(I24, I25, I29, I30, I31) [-1 <= I25 - 1 /\ I32 <= 200 * I25 /\ 0 <= I24 - 1] 0.97/1.02 R = 0.97/1.02 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 0.97/1.02 f3(I0, I1, I2, I3, I4) -> f3(I0 - 1, I1, I0 - 1 + I1, I3, I4 + 2) [1 <= I3 - 1 /\ I4 + 1 <= I3 - 1 /\ 0 <= I2 - 1 /\ -1 <= I4 - 1 /\ -1 <= y1 - 1 /\ -1 <= y2 - 1 /\ 9 <= y1 * y2 - 1 /\ I4 + 2 <= I3 /\ I0 - 1 <= I0 - 1] 0.97/1.02 f3(I5, I6, I7, I8, I9) -> f3(I5, I6 - 1, I5 + I6 - 1, I8, I9 + 2) [1 <= I8 - 1 /\ I9 + 1 <= I8 - 1 /\ 0 <= I7 - 1 /\ -1 <= I9 - 1 /\ -1 <= I10 - 1 /\ -1 <= I11 - 1 /\ I10 * I11 <= 9 /\ I9 + 2 <= I8 /\ I6 - 1 <= I6 - 1] 0.97/1.02 f3(I12, I13, I14, I15, I16) -> f3(I12, I13 - 1, I12 + I13 - 1, I15, I16) [I15 <= I16 /\ I13 - 1 <= I13 - 1 /\ -1 <= I15 - 1 /\ 0 <= I14 - 1] 0.97/1.02 f2(I17, I18, I19, I20, I21) -> f3(100 * I18, I22, I23, I18, 0) [100 * I18 + I22 = I23 /\ 0 <= 200 * I18 - 13 * I22 /\ 200 * I18 - 13 * I22 <= 12 /\ 0 <= I17 - 1 /\ I22 <= 200 * I18 /\ -1 <= I18 - 1] 0.97/1.02 f1(I24, I25, I26, I27, I28) -> f2(I24, I25, I29, I30, I31) [-1 <= I25 - 1 /\ I32 <= 200 * I25 /\ 0 <= I24 - 1] 0.97/1.02 0.97/1.02 The dependency graph for this problem is: 0.97/1.02 0 -> 5 0.97/1.02 1 -> 1, 2, 3 0.97/1.02 2 -> 1, 2, 3 0.97/1.02 3 -> 3 0.97/1.02 4 -> 1, 2 0.97/1.02 5 -> 4 0.97/1.02 Where: 0.97/1.02 0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 0.97/1.02 1) f3#(I0, I1, I2, I3, I4) -> f3#(I0 - 1, I1, I0 - 1 + I1, I3, I4 + 2) [1 <= I3 - 1 /\ I4 + 1 <= I3 - 1 /\ 0 <= I2 - 1 /\ -1 <= I4 - 1 /\ -1 <= y1 - 1 /\ -1 <= y2 - 1 /\ 9 <= y1 * y2 - 1 /\ I4 + 2 <= I3 /\ I0 - 1 <= I0 - 1] 0.97/1.02 2) f3#(I5, I6, I7, I8, I9) -> f3#(I5, I6 - 1, I5 + I6 - 1, I8, I9 + 2) [1 <= I8 - 1 /\ I9 + 1 <= I8 - 1 /\ 0 <= I7 - 1 /\ -1 <= I9 - 1 /\ -1 <= I10 - 1 /\ -1 <= I11 - 1 /\ I10 * I11 <= 9 /\ I9 + 2 <= I8 /\ I6 - 1 <= I6 - 1] 0.97/1.02 3) f3#(I12, I13, I14, I15, I16) -> f3#(I12, I13 - 1, I12 + I13 - 1, I15, I16) [I15 <= I16 /\ I13 - 1 <= I13 - 1 /\ -1 <= I15 - 1 /\ 0 <= I14 - 1] 0.97/1.02 4) f2#(I17, I18, I19, I20, I21) -> f3#(100 * I18, I22, I23, I18, 0) [100 * I18 + I22 = I23 /\ 0 <= 200 * I18 - 13 * I22 /\ 200 * I18 - 13 * I22 <= 12 /\ 0 <= I17 - 1 /\ I22 <= 200 * I18 /\ -1 <= I18 - 1] 0.97/1.02 5) f1#(I24, I25, I26, I27, I28) -> f2#(I24, I25, I29, I30, I31) [-1 <= I25 - 1 /\ I32 <= 200 * I25 /\ 0 <= I24 - 1] 0.97/1.02 0.97/1.02 We have the following SCCs. 0.97/1.02 { 1, 2 } 0.97/1.02 { 3 } 0.97/1.02 0.97/1.02 DP problem for innermost termination. 0.97/1.02 P = 0.97/1.02 f3#(I12, I13, I14, I15, I16) -> f3#(I12, I13 - 1, I12 + I13 - 1, I15, I16) [I15 <= I16 /\ I13 - 1 <= I13 - 1 /\ -1 <= I15 - 1 /\ 0 <= I14 - 1] 0.97/1.02 R = 0.97/1.02 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 0.97/1.02 f3(I0, I1, I2, I3, I4) -> f3(I0 - 1, I1, I0 - 1 + I1, I3, I4 + 2) [1 <= I3 - 1 /\ I4 + 1 <= I3 - 1 /\ 0 <= I2 - 1 /\ -1 <= I4 - 1 /\ -1 <= y1 - 1 /\ -1 <= y2 - 1 /\ 9 <= y1 * y2 - 1 /\ I4 + 2 <= I3 /\ I0 - 1 <= I0 - 1] 0.97/1.02 f3(I5, I6, I7, I8, I9) -> f3(I5, I6 - 1, I5 + I6 - 1, I8, I9 + 2) [1 <= I8 - 1 /\ I9 + 1 <= I8 - 1 /\ 0 <= I7 - 1 /\ -1 <= I9 - 1 /\ -1 <= I10 - 1 /\ -1 <= I11 - 1 /\ I10 * I11 <= 9 /\ I9 + 2 <= I8 /\ I6 - 1 <= I6 - 1] 0.97/1.02 f3(I12, I13, I14, I15, I16) -> f3(I12, I13 - 1, I12 + I13 - 1, I15, I16) [I15 <= I16 /\ I13 - 1 <= I13 - 1 /\ -1 <= I15 - 1 /\ 0 <= I14 - 1] 0.97/1.02 f2(I17, I18, I19, I20, I21) -> f3(100 * I18, I22, I23, I18, 0) [100 * I18 + I22 = I23 /\ 0 <= 200 * I18 - 13 * I22 /\ 200 * I18 - 13 * I22 <= 12 /\ 0 <= I17 - 1 /\ I22 <= 200 * I18 /\ -1 <= I18 - 1] 0.97/1.02 f1(I24, I25, I26, I27, I28) -> f2(I24, I25, I29, I30, I31) [-1 <= I25 - 1 /\ I32 <= 200 * I25 /\ 0 <= I24 - 1] 0.97/1.02 0.97/3.99 EOF