0.00/0.43 MAYBE 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) -> f1#(rnd1, rnd2) 0.00/0.43 f2#(I0, I1) -> f2#(I0 - 1, I2) [I0 <= 9 /\ 5 <= I0 - 1] 0.00/0.43 f2#(I3, I4) -> f2#(I3, I5) [9 <= I3 - 1] 0.00/0.43 f1#(I6, I7) -> f2#(I7, I8) [-1 <= I7 - 1 /\ 0 <= I6 - 1] 0.00/0.43 R = 0.00/0.43 init(x1, x2) -> f1(rnd1, rnd2) 0.00/0.43 f2(I0, I1) -> f2(I0 - 1, I2) [I0 <= 9 /\ 5 <= I0 - 1] 0.00/0.43 f2(I3, I4) -> f2(I3, I5) [9 <= I3 - 1] 0.00/0.43 f1(I6, I7) -> f2(I7, I8) [-1 <= I7 - 1 /\ 0 <= I6 - 1] 0.00/0.43 0.00/0.43 The dependency graph for this problem is: 0.00/0.43 0 -> 3 0.00/0.43 1 -> 1 0.00/0.43 2 -> 2 0.00/0.43 3 -> 1, 2 0.00/0.43 Where: 0.00/0.43 0) init#(x1, x2) -> f1#(rnd1, rnd2) 0.00/0.43 1) f2#(I0, I1) -> f2#(I0 - 1, I2) [I0 <= 9 /\ 5 <= I0 - 1] 0.00/0.43 2) f2#(I3, I4) -> f2#(I3, I5) [9 <= I3 - 1] 0.00/0.43 3) f1#(I6, I7) -> f2#(I7, I8) [-1 <= I7 - 1 /\ 0 <= I6 - 1] 0.00/0.43 0.00/0.43 We have the following SCCs. 0.00/0.43 { 2 } 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) -> f2#(I0 - 1, I2) [I0 <= 9 /\ 5 <= I0 - 1] 0.00/0.43 R = 0.00/0.43 init(x1, x2) -> f1(rnd1, rnd2) 0.00/0.43 f2(I0, I1) -> f2(I0 - 1, I2) [I0 <= 9 /\ 5 <= I0 - 1] 0.00/0.43 f2(I3, I4) -> f2(I3, I5) [9 <= I3 - 1] 0.00/0.43 f1(I6, I7) -> f2(I7, I8) [-1 <= I7 - 1 /\ 0 <= I6 - 1] 0.00/0.43 0.00/0.43 We use the basic value criterion with the projection function NU: 0.00/0.43 NU[f2#(z1,z2)] = z1 0.00/0.43 0.00/0.43 This gives the following inequalities: 0.00/0.43 I0 <= 9 /\ 5 <= I0 - 1 ==> I0 >! I0 - 1 0.00/0.43 0.00/0.43 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 0.00/0.43 0.00/0.43 DP problem for innermost termination. 0.00/0.43 P = 0.00/0.43 f2#(I3, I4) -> f2#(I3, I5) [9 <= I3 - 1] 0.00/0.43 R = 0.00/0.43 init(x1, x2) -> f1(rnd1, rnd2) 0.00/0.43 f2(I0, I1) -> f2(I0 - 1, I2) [I0 <= 9 /\ 5 <= I0 - 1] 0.00/0.43 f2(I3, I4) -> f2(I3, I5) [9 <= I3 - 1] 0.00/0.43 f1(I6, I7) -> f2(I7, I8) [-1 <= I7 - 1 /\ 0 <= I6 - 1] 0.00/0.43 0.00/3.41 EOF