0.66/0.69 MAYBE 0.66/0.69 0.66/0.69 DP problem for innermost termination. 0.66/0.69 P = 0.66/0.69 init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 0.66/0.69 f2#(I0, I1, I2, I3) -> f2#(I4, I5, I2, I3 + 1) [0 <= I1 - 1 /\ 0 <= I2 - 1 /\ -1 <= I3 - 1 /\ I3 <= I2 - 1 /\ I3 + 1 <= I2 /\ -1 <= y1 - 1 /\ I0 - 1 - y1 = I4 /\ I0 - 1 - y1 = I5] 0.66/0.69 f2#(I6, I7, I8, I9) -> f2#(I6 - 1, I6 - 1, I8, I9) [0 <= I7 - 1 /\ I8 <= I9 /\ I6 - 1 <= I6 - 1 /\ -1 <= I8 - 1] 0.66/0.69 f1#(I10, I11, I12, I13) -> f2#(I14, I15, I11, 2) [0 <= I10 - 1 /\ -1 <= I14 - 1 /\ 1 <= I11 - 1 /\ -1 <= I15 - 1] 0.66/0.69 f1#(I16, I17, I18, I19) -> f2#(I20, 0, 1, 1) [1 = I17 /\ -1 <= I20 - 1 /\ 0 <= I16 - 1] 0.66/0.69 f1#(I21, I22, I23, I24) -> f2#(0, 0, 0, 0) [0 = I22 /\ 0 <= I21 - 1] 0.66/0.69 R = 0.66/0.69 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 0.66/0.69 f2(I0, I1, I2, I3) -> f2(I4, I5, I2, I3 + 1) [0 <= I1 - 1 /\ 0 <= I2 - 1 /\ -1 <= I3 - 1 /\ I3 <= I2 - 1 /\ I3 + 1 <= I2 /\ -1 <= y1 - 1 /\ I0 - 1 - y1 = I4 /\ I0 - 1 - y1 = I5] 0.66/0.69 f2(I6, I7, I8, I9) -> f2(I6 - 1, I6 - 1, I8, I9) [0 <= I7 - 1 /\ I8 <= I9 /\ I6 - 1 <= I6 - 1 /\ -1 <= I8 - 1] 0.66/0.69 f1(I10, I11, I12, I13) -> f2(I14, I15, I11, 2) [0 <= I10 - 1 /\ -1 <= I14 - 1 /\ 1 <= I11 - 1 /\ -1 <= I15 - 1] 0.66/0.69 f1(I16, I17, I18, I19) -> f2(I20, 0, 1, 1) [1 = I17 /\ -1 <= I20 - 1 /\ 0 <= I16 - 1] 0.66/0.69 f1(I21, I22, I23, I24) -> f2(0, 0, 0, 0) [0 = I22 /\ 0 <= I21 - 1] 0.66/0.69 0.66/0.69 The dependency graph for this problem is: 0.66/0.69 0 -> 3, 4, 5 0.66/0.69 1 -> 1, 2 0.66/0.69 2 -> 2 0.66/0.69 3 -> 1, 2 0.66/0.69 4 -> 0.66/0.69 5 -> 0.66/0.69 Where: 0.66/0.69 0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 0.66/0.69 1) f2#(I0, I1, I2, I3) -> f2#(I4, I5, I2, I3 + 1) [0 <= I1 - 1 /\ 0 <= I2 - 1 /\ -1 <= I3 - 1 /\ I3 <= I2 - 1 /\ I3 + 1 <= I2 /\ -1 <= y1 - 1 /\ I0 - 1 - y1 = I4 /\ I0 - 1 - y1 = I5] 0.66/0.69 2) f2#(I6, I7, I8, I9) -> f2#(I6 - 1, I6 - 1, I8, I9) [0 <= I7 - 1 /\ I8 <= I9 /\ I6 - 1 <= I6 - 1 /\ -1 <= I8 - 1] 0.66/0.69 3) f1#(I10, I11, I12, I13) -> f2#(I14, I15, I11, 2) [0 <= I10 - 1 /\ -1 <= I14 - 1 /\ 1 <= I11 - 1 /\ -1 <= I15 - 1] 0.66/0.69 4) f1#(I16, I17, I18, I19) -> f2#(I20, 0, 1, 1) [1 = I17 /\ -1 <= I20 - 1 /\ 0 <= I16 - 1] 0.66/0.69 5) f1#(I21, I22, I23, I24) -> f2#(0, 0, 0, 0) [0 = I22 /\ 0 <= I21 - 1] 0.66/0.69 0.66/0.69 We have the following SCCs. 0.66/0.69 { 1 } 0.66/0.69 { 2 } 0.66/0.69 0.66/0.69 DP problem for innermost termination. 0.66/0.69 P = 0.66/0.69 f2#(I6, I7, I8, I9) -> f2#(I6 - 1, I6 - 1, I8, I9) [0 <= I7 - 1 /\ I8 <= I9 /\ I6 - 1 <= I6 - 1 /\ -1 <= I8 - 1] 0.66/0.69 R = 0.66/0.69 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 0.66/0.69 f2(I0, I1, I2, I3) -> f2(I4, I5, I2, I3 + 1) [0 <= I1 - 1 /\ 0 <= I2 - 1 /\ -1 <= I3 - 1 /\ I3 <= I2 - 1 /\ I3 + 1 <= I2 /\ -1 <= y1 - 1 /\ I0 - 1 - y1 = I4 /\ I0 - 1 - y1 = I5] 0.66/0.69 f2(I6, I7, I8, I9) -> f2(I6 - 1, I6 - 1, I8, I9) [0 <= I7 - 1 /\ I8 <= I9 /\ I6 - 1 <= I6 - 1 /\ -1 <= I8 - 1] 0.66/0.69 f1(I10, I11, I12, I13) -> f2(I14, I15, I11, 2) [0 <= I10 - 1 /\ -1 <= I14 - 1 /\ 1 <= I11 - 1 /\ -1 <= I15 - 1] 0.66/0.69 f1(I16, I17, I18, I19) -> f2(I20, 0, 1, 1) [1 = I17 /\ -1 <= I20 - 1 /\ 0 <= I16 - 1] 0.66/0.69 f1(I21, I22, I23, I24) -> f2(0, 0, 0, 0) [0 = I22 /\ 0 <= I21 - 1] 0.66/0.69 0.66/3.67 EOF