1.53/1.58 MAYBE 1.53/1.58 1.53/1.58 DP problem for innermost termination. 1.53/1.58 P = 1.53/1.58 init#(x1, x2) -> f1#(rnd1, rnd2) 1.53/1.58 f2#(I0, I1) -> f2#(I0 - 1, I1 + 1) [0 <= I1 - 1 /\ I1 + 1 <= 2 * I0 - 1 /\ 1 <= I0 - 1 /\ I1 <= I0 - 1] 1.53/1.58 f2#(I2, I3) -> f2#(I2 + 1, I3 + 1) [0 <= I3 - 1 /\ 2 * I2 <= I3 + 1 /\ 1 <= I2 - 1 /\ I3 <= I2 - 1] 1.53/1.58 f2#(I4, I5) -> f2#(I4 + 1, I5) [-1 <= I4 - 1 /\ 2 <= I5 - 1 - (I4 + 1) - 1 /\ I4 <= 4 /\ I4 <= I5 /\ 0 <= I5 - 1] 1.53/1.58 f2#(I6, I7) -> f2#(I6 + 2, I7 - 1) [-1 <= I6 - 1 /\ I7 - 1 - (I6 + 1) <= 2 /\ I6 <= 4 /\ I6 <= I7 /\ 0 <= I7 - 1] 1.53/1.58 f2#(I8, I9) -> f2#(I8 - 1, I9 - 1) [I8 <= I9 /\ 0 <= I9 - 1 /\ 4 <= I8 - 1] 1.53/1.58 f1#(I10, I11) -> f2#(I11, I11) [-1 <= I11 - 1 /\ 0 <= I10 - 1] 1.53/1.58 R = 1.53/1.58 init(x1, x2) -> f1(rnd1, rnd2) 1.53/1.58 f2(I0, I1) -> f2(I0 - 1, I1 + 1) [0 <= I1 - 1 /\ I1 + 1 <= 2 * I0 - 1 /\ 1 <= I0 - 1 /\ I1 <= I0 - 1] 1.53/1.58 f2(I2, I3) -> f2(I2 + 1, I3 + 1) [0 <= I3 - 1 /\ 2 * I2 <= I3 + 1 /\ 1 <= I2 - 1 /\ I3 <= I2 - 1] 1.53/1.58 f2(I4, I5) -> f2(I4 + 1, I5) [-1 <= I4 - 1 /\ 2 <= I5 - 1 - (I4 + 1) - 1 /\ I4 <= 4 /\ I4 <= I5 /\ 0 <= I5 - 1] 1.53/1.58 f2(I6, I7) -> f2(I6 + 2, I7 - 1) [-1 <= I6 - 1 /\ I7 - 1 - (I6 + 1) <= 2 /\ I6 <= 4 /\ I6 <= I7 /\ 0 <= I7 - 1] 1.53/1.58 f2(I8, I9) -> f2(I8 - 1, I9 - 1) [I8 <= I9 /\ 0 <= I9 - 1 /\ 4 <= I8 - 1] 1.53/1.58 f1(I10, I11) -> f2(I11, I11) [-1 <= I11 - 1 /\ 0 <= I10 - 1] 1.53/1.58 1.53/1.58 The dependency graph for this problem is: 1.53/1.58 0 -> 6 1.53/1.58 1 -> 1, 4, 5 1.53/1.58 2 -> 1.53/1.58 3 -> 3, 4, 5 1.53/1.58 4 -> 1, 4, 5 1.53/1.58 5 -> 3, 4, 5 1.53/1.58 6 -> 4, 5 1.53/1.58 Where: 1.53/1.58 0) init#(x1, x2) -> f1#(rnd1, rnd2) 1.53/1.58 1) f2#(I0, I1) -> f2#(I0 - 1, I1 + 1) [0 <= I1 - 1 /\ I1 + 1 <= 2 * I0 - 1 /\ 1 <= I0 - 1 /\ I1 <= I0 - 1] 1.53/1.58 2) f2#(I2, I3) -> f2#(I2 + 1, I3 + 1) [0 <= I3 - 1 /\ 2 * I2 <= I3 + 1 /\ 1 <= I2 - 1 /\ I3 <= I2 - 1] 1.53/1.58 3) f2#(I4, I5) -> f2#(I4 + 1, I5) [-1 <= I4 - 1 /\ 2 <= I5 - 1 - (I4 + 1) - 1 /\ I4 <= 4 /\ I4 <= I5 /\ 0 <= I5 - 1] 1.53/1.58 4) f2#(I6, I7) -> f2#(I6 + 2, I7 - 1) [-1 <= I6 - 1 /\ I7 - 1 - (I6 + 1) <= 2 /\ I6 <= 4 /\ I6 <= I7 /\ 0 <= I7 - 1] 1.53/1.58 5) f2#(I8, I9) -> f2#(I8 - 1, I9 - 1) [I8 <= I9 /\ 0 <= I9 - 1 /\ 4 <= I8 - 1] 1.53/1.58 6) f1#(I10, I11) -> f2#(I11, I11) [-1 <= I11 - 1 /\ 0 <= I10 - 1] 1.53/1.58 1.53/1.58 We have the following SCCs. 1.53/1.58 { 1, 3, 4, 5 } 1.53/1.58 1.53/1.58 DP problem for innermost termination. 1.53/1.58 P = 1.53/1.58 f2#(I0, I1) -> f2#(I0 - 1, I1 + 1) [0 <= I1 - 1 /\ I1 + 1 <= 2 * I0 - 1 /\ 1 <= I0 - 1 /\ I1 <= I0 - 1] 1.53/1.58 f2#(I4, I5) -> f2#(I4 + 1, I5) [-1 <= I4 - 1 /\ 2 <= I5 - 1 - (I4 + 1) - 1 /\ I4 <= 4 /\ I4 <= I5 /\ 0 <= I5 - 1] 1.53/1.58 f2#(I6, I7) -> f2#(I6 + 2, I7 - 1) [-1 <= I6 - 1 /\ I7 - 1 - (I6 + 1) <= 2 /\ I6 <= 4 /\ I6 <= I7 /\ 0 <= I7 - 1] 1.53/1.58 f2#(I8, I9) -> f2#(I8 - 1, I9 - 1) [I8 <= I9 /\ 0 <= I9 - 1 /\ 4 <= I8 - 1] 1.53/1.58 R = 1.53/1.58 init(x1, x2) -> f1(rnd1, rnd2) 1.53/1.58 f2(I0, I1) -> f2(I0 - 1, I1 + 1) [0 <= I1 - 1 /\ I1 + 1 <= 2 * I0 - 1 /\ 1 <= I0 - 1 /\ I1 <= I0 - 1] 1.53/1.58 f2(I2, I3) -> f2(I2 + 1, I3 + 1) [0 <= I3 - 1 /\ 2 * I2 <= I3 + 1 /\ 1 <= I2 - 1 /\ I3 <= I2 - 1] 1.53/1.58 f2(I4, I5) -> f2(I4 + 1, I5) [-1 <= I4 - 1 /\ 2 <= I5 - 1 - (I4 + 1) - 1 /\ I4 <= 4 /\ I4 <= I5 /\ 0 <= I5 - 1] 1.53/1.58 f2(I6, I7) -> f2(I6 + 2, I7 - 1) [-1 <= I6 - 1 /\ I7 - 1 - (I6 + 1) <= 2 /\ I6 <= 4 /\ I6 <= I7 /\ 0 <= I7 - 1] 1.53/1.58 f2(I8, I9) -> f2(I8 - 1, I9 - 1) [I8 <= I9 /\ 0 <= I9 - 1 /\ 4 <= I8 - 1] 1.53/1.58 f1(I10, I11) -> f2(I11, I11) [-1 <= I11 - 1 /\ 0 <= I10 - 1] 1.53/1.58 1.53/4.56 EOF