0.00/0.43 YES 0.00/0.43 0.00/0.43 DP problem for innermost termination. 0.00/0.43 P = 0.00/0.43 init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 0.00/0.43 f2#(I0, I1, I2) -> f2#(I3, I1 + 1, I2) [0 <= I3 - 1 /\ 0 <= I0 - 1 /\ I3 <= I0 /\ -1 <= I2 - 1 /\ I1 <= I2 - 1] 0.00/0.43 f1#(I4, I5, I6) -> f2#(I7, 0, I5) [0 <= I7 - 1 /\ 0 <= I4 - 1 /\ -1 <= I5 - 1 /\ I7 <= I4] 0.00/0.43 R = 0.00/0.43 init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 0.00/0.43 f2(I0, I1, I2) -> f2(I3, I1 + 1, I2) [0 <= I3 - 1 /\ 0 <= I0 - 1 /\ I3 <= I0 /\ -1 <= I2 - 1 /\ I1 <= I2 - 1] 0.00/0.43 f1(I4, I5, I6) -> f2(I7, 0, I5) [0 <= I7 - 1 /\ 0 <= I4 - 1 /\ -1 <= I5 - 1 /\ I7 <= I4] 0.00/0.43 0.00/0.43 The dependency graph for this problem is: 0.00/0.43 0 -> 2 0.00/0.43 1 -> 1 0.00/0.43 2 -> 1 0.00/0.43 Where: 0.00/0.43 0) init#(x1, x2, x3) -> f1#(rnd1, rnd2, rnd3) 0.00/0.43 1) f2#(I0, I1, I2) -> f2#(I3, I1 + 1, I2) [0 <= I3 - 1 /\ 0 <= I0 - 1 /\ I3 <= I0 /\ -1 <= I2 - 1 /\ I1 <= I2 - 1] 0.00/0.43 2) f1#(I4, I5, I6) -> f2#(I7, 0, I5) [0 <= I7 - 1 /\ 0 <= I4 - 1 /\ -1 <= I5 - 1 /\ I7 <= I4] 0.00/0.43 0.00/0.43 We have the following SCCs. 0.00/0.43 { 1 } 0.00/0.43 0.00/0.43 DP problem for innermost termination. 0.00/0.43 P = 0.00/0.43 f2#(I0, I1, I2) -> f2#(I3, I1 + 1, I2) [0 <= I3 - 1 /\ 0 <= I0 - 1 /\ I3 <= I0 /\ -1 <= I2 - 1 /\ I1 <= I2 - 1] 0.00/0.43 R = 0.00/0.43 init(x1, x2, x3) -> f1(rnd1, rnd2, rnd3) 0.00/0.43 f2(I0, I1, I2) -> f2(I3, I1 + 1, I2) [0 <= I3 - 1 /\ 0 <= I0 - 1 /\ I3 <= I0 /\ -1 <= I2 - 1 /\ I1 <= I2 - 1] 0.00/0.43 f1(I4, I5, I6) -> f2(I7, 0, I5) [0 <= I7 - 1 /\ 0 <= I4 - 1 /\ -1 <= I5 - 1 /\ I7 <= I4] 0.00/0.43 0.00/0.43 We use the reverse value criterion with the projection function NU: 0.00/0.43 NU[f2#(z1,z2,z3)] = z3 - 1 + -1 * z2 0.00/0.43 0.00/0.43 This gives the following inequalities: 0.00/0.43 0 <= I3 - 1 /\ 0 <= I0 - 1 /\ I3 <= I0 /\ -1 <= I2 - 1 /\ I1 <= I2 - 1 ==> I2 - 1 + -1 * I1 > I2 - 1 + -1 * (I1 + 1) with I2 - 1 + -1 * I1 >= 0 0.00/0.43 0.00/0.43 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 0.00/3.41 EOF