0.87/0.89 MAYBE 0.87/0.89 0.87/0.89 DP problem for innermost termination. 0.87/0.89 P = 0.87/0.89 init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 0.87/0.89 f2#(I0, I1, I2, I3, I4) -> f2#(I5, I6, I7, I3, I4 + 1) [0 <= I2 - 1 /\ 1 <= I0 + 1 + y1 /\ -1 <= I3 - 1 /\ -1 <= I4 - 1 /\ I4 <= I3 - 1 /\ -1 <= I0 - 1 /\ -1 <= y1 - 1 /\ I0 = I1 /\ I0 + 1 + y1 = I5 /\ I0 + 1 + y1 = I6 /\ 10 - (I0 + 1 + y1) = I7] 0.87/0.89 f2#(I8, I9, I10, I11, I12) -> f2#(I8 + 1, I8 + 1, 10 - (I8 + 1), I11, I12) [I8 = I9 /\ -1 <= I11 - 1 /\ I11 <= I12 /\ 0 <= I10 - 1 /\ -1 <= I8 - 1 /\ I8 <= I8 + 1 - 1] 0.87/0.89 f1#(I13, I14, I15, I16, I17) -> f2#(I18, I19, I20, I14, 3) [-1 <= I18 - 1 /\ 2 <= I14 - 1 /\ -1 <= I21 - 1 /\ -1 <= I19 - 1 /\ 0 <= I13 - 1 /\ I21 - I19 = I20] 0.87/0.89 f1#(I22, I23, I24, I25, I26) -> f2#(I27, 0, I28, 2, 2) [2 = I23 /\ 0 <= I22 - 1 /\ -1 <= I27 - 1 /\ -1 <= I28 - 1] 0.87/0.89 f1#(I29, I30, I31, I32, I33) -> f2#(I34, 0, 0, 1, 1) [1 = I30 /\ -1 <= I34 - 1 /\ 0 <= I29 - 1] 0.87/0.89 f1#(I35, I36, I37, I38, I39) -> f2#(0, 0, 0, 0, 0) [0 = I36 /\ 0 <= I35 - 1] 0.87/0.89 R = 0.87/0.89 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 0.87/0.89 f2(I0, I1, I2, I3, I4) -> f2(I5, I6, I7, I3, I4 + 1) [0 <= I2 - 1 /\ 1 <= I0 + 1 + y1 /\ -1 <= I3 - 1 /\ -1 <= I4 - 1 /\ I4 <= I3 - 1 /\ -1 <= I0 - 1 /\ -1 <= y1 - 1 /\ I0 = I1 /\ I0 + 1 + y1 = I5 /\ I0 + 1 + y1 = I6 /\ 10 - (I0 + 1 + y1) = I7] 0.87/0.89 f2(I8, I9, I10, I11, I12) -> f2(I8 + 1, I8 + 1, 10 - (I8 + 1), I11, I12) [I8 = I9 /\ -1 <= I11 - 1 /\ I11 <= I12 /\ 0 <= I10 - 1 /\ -1 <= I8 - 1 /\ I8 <= I8 + 1 - 1] 0.87/0.89 f1(I13, I14, I15, I16, I17) -> f2(I18, I19, I20, I14, 3) [-1 <= I18 - 1 /\ 2 <= I14 - 1 /\ -1 <= I21 - 1 /\ -1 <= I19 - 1 /\ 0 <= I13 - 1 /\ I21 - I19 = I20] 0.87/0.89 f1(I22, I23, I24, I25, I26) -> f2(I27, 0, I28, 2, 2) [2 = I23 /\ 0 <= I22 - 1 /\ -1 <= I27 - 1 /\ -1 <= I28 - 1] 0.87/0.89 f1(I29, I30, I31, I32, I33) -> f2(I34, 0, 0, 1, 1) [1 = I30 /\ -1 <= I34 - 1 /\ 0 <= I29 - 1] 0.87/0.89 f1(I35, I36, I37, I38, I39) -> f2(0, 0, 0, 0, 0) [0 = I36 /\ 0 <= I35 - 1] 0.87/0.89 0.87/0.89 The dependency graph for this problem is: 0.87/0.89 0 -> 3, 4, 5, 6 0.87/0.89 1 -> 1, 2 0.87/0.89 2 -> 2 0.87/0.89 3 -> 1, 2 0.87/0.89 4 -> 2 0.87/0.89 5 -> 0.87/0.89 6 -> 0.87/0.89 Where: 0.87/0.89 0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 0.87/0.89 1) f2#(I0, I1, I2, I3, I4) -> f2#(I5, I6, I7, I3, I4 + 1) [0 <= I2 - 1 /\ 1 <= I0 + 1 + y1 /\ -1 <= I3 - 1 /\ -1 <= I4 - 1 /\ I4 <= I3 - 1 /\ -1 <= I0 - 1 /\ -1 <= y1 - 1 /\ I0 = I1 /\ I0 + 1 + y1 = I5 /\ I0 + 1 + y1 = I6 /\ 10 - (I0 + 1 + y1) = I7] 0.87/0.89 2) f2#(I8, I9, I10, I11, I12) -> f2#(I8 + 1, I8 + 1, 10 - (I8 + 1), I11, I12) [I8 = I9 /\ -1 <= I11 - 1 /\ I11 <= I12 /\ 0 <= I10 - 1 /\ -1 <= I8 - 1 /\ I8 <= I8 + 1 - 1] 0.87/0.89 3) f1#(I13, I14, I15, I16, I17) -> f2#(I18, I19, I20, I14, 3) [-1 <= I18 - 1 /\ 2 <= I14 - 1 /\ -1 <= I21 - 1 /\ -1 <= I19 - 1 /\ 0 <= I13 - 1 /\ I21 - I19 = I20] 0.87/0.89 4) f1#(I22, I23, I24, I25, I26) -> f2#(I27, 0, I28, 2, 2) [2 = I23 /\ 0 <= I22 - 1 /\ -1 <= I27 - 1 /\ -1 <= I28 - 1] 0.87/0.89 5) f1#(I29, I30, I31, I32, I33) -> f2#(I34, 0, 0, 1, 1) [1 = I30 /\ -1 <= I34 - 1 /\ 0 <= I29 - 1] 0.87/0.89 6) f1#(I35, I36, I37, I38, I39) -> f2#(0, 0, 0, 0, 0) [0 = I36 /\ 0 <= I35 - 1] 0.87/0.89 0.87/0.89 We have the following SCCs. 0.87/0.89 { 1 } 0.87/0.89 { 2 } 0.87/0.89 0.87/0.89 DP problem for innermost termination. 0.87/0.89 P = 0.87/0.89 f2#(I8, I9, I10, I11, I12) -> f2#(I8 + 1, I8 + 1, 10 - (I8 + 1), I11, I12) [I8 = I9 /\ -1 <= I11 - 1 /\ I11 <= I12 /\ 0 <= I10 - 1 /\ -1 <= I8 - 1 /\ I8 <= I8 + 1 - 1] 0.87/0.89 R = 0.87/0.89 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 0.87/0.89 f2(I0, I1, I2, I3, I4) -> f2(I5, I6, I7, I3, I4 + 1) [0 <= I2 - 1 /\ 1 <= I0 + 1 + y1 /\ -1 <= I3 - 1 /\ -1 <= I4 - 1 /\ I4 <= I3 - 1 /\ -1 <= I0 - 1 /\ -1 <= y1 - 1 /\ I0 = I1 /\ I0 + 1 + y1 = I5 /\ I0 + 1 + y1 = I6 /\ 10 - (I0 + 1 + y1) = I7] 0.87/0.89 f2(I8, I9, I10, I11, I12) -> f2(I8 + 1, I8 + 1, 10 - (I8 + 1), I11, I12) [I8 = I9 /\ -1 <= I11 - 1 /\ I11 <= I12 /\ 0 <= I10 - 1 /\ -1 <= I8 - 1 /\ I8 <= I8 + 1 - 1] 0.87/0.89 f1(I13, I14, I15, I16, I17) -> f2(I18, I19, I20, I14, 3) [-1 <= I18 - 1 /\ 2 <= I14 - 1 /\ -1 <= I21 - 1 /\ -1 <= I19 - 1 /\ 0 <= I13 - 1 /\ I21 - I19 = I20] 0.87/0.89 f1(I22, I23, I24, I25, I26) -> f2(I27, 0, I28, 2, 2) [2 = I23 /\ 0 <= I22 - 1 /\ -1 <= I27 - 1 /\ -1 <= I28 - 1] 0.87/0.89 f1(I29, I30, I31, I32, I33) -> f2(I34, 0, 0, 1, 1) [1 = I30 /\ -1 <= I34 - 1 /\ 0 <= I29 - 1] 0.87/0.89 f1(I35, I36, I37, I38, I39) -> f2(0, 0, 0, 0, 0) [0 = I36 /\ 0 <= I35 - 1] 0.87/0.89 0.87/3.87 EOF