4.37/4.66 MAYBE 4.37/4.66 4.37/4.66 DP problem for innermost termination. 4.37/4.66 P = 4.37/4.66 init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 4.37/4.66 f3#(I0, I1, I2, I3) -> f2#(I4, I5, I6, I3) [-1 <= I3 - 1 /\ 0 <= I2 - 1 /\ I4 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I4 - 1 /\ I3 - I1 - 2 * y1 <= 1 /\ 0 <= I3 - I1 - 2 * y1 /\ I1 + y1 = I5 /\ I3 - (I1 + y1) = I6] 4.37/4.66 f2#(I7, I8, I9, I10) -> f3#(I7, I8, I9, I10) [-1 <= I10 - 1 /\ 0 <= I9 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1] 4.37/4.66 f1#(I12, I13, I14, I15) -> f2#(I16, 0, I13, I13) [0 <= I16 - 1 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1 /\ I16 <= I12] 4.37/4.66 R = 4.37/4.66 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 4.37/4.66 f3(I0, I1, I2, I3) -> f2(I4, I5, I6, I3) [-1 <= I3 - 1 /\ 0 <= I2 - 1 /\ I4 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I4 - 1 /\ I3 - I1 - 2 * y1 <= 1 /\ 0 <= I3 - I1 - 2 * y1 /\ I1 + y1 = I5 /\ I3 - (I1 + y1) = I6] 4.37/4.66 f2(I7, I8, I9, I10) -> f3(I7, I8, I9, I10) [-1 <= I10 - 1 /\ 0 <= I9 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1] 4.37/4.66 f1(I12, I13, I14, I15) -> f2(I16, 0, I13, I13) [0 <= I16 - 1 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1 /\ I16 <= I12] 4.37/4.66 4.37/4.66 The dependency graph for this problem is: 4.37/4.66 0 -> 3 4.37/4.66 1 -> 2 4.37/4.66 2 -> 1 4.37/4.66 3 -> 2 4.37/4.66 Where: 4.37/4.66 0) init#(x1, x2, x3, x4) -> f1#(rnd1, rnd2, rnd3, rnd4) 4.37/4.66 1) f3#(I0, I1, I2, I3) -> f2#(I4, I5, I6, I3) [-1 <= I3 - 1 /\ 0 <= I2 - 1 /\ I4 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I4 - 1 /\ I3 - I1 - 2 * y1 <= 1 /\ 0 <= I3 - I1 - 2 * y1 /\ I1 + y1 = I5 /\ I3 - (I1 + y1) = I6] 4.37/4.66 2) f2#(I7, I8, I9, I10) -> f3#(I7, I8, I9, I10) [-1 <= I10 - 1 /\ 0 <= I9 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1] 4.37/4.66 3) f1#(I12, I13, I14, I15) -> f2#(I16, 0, I13, I13) [0 <= I16 - 1 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1 /\ I16 <= I12] 4.37/4.66 4.37/4.66 We have the following SCCs. 4.37/4.66 { 1, 2 } 4.37/4.66 4.37/4.66 DP problem for innermost termination. 4.37/4.66 P = 4.37/4.66 f3#(I0, I1, I2, I3) -> f2#(I4, I5, I6, I3) [-1 <= I3 - 1 /\ 0 <= I2 - 1 /\ I4 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I4 - 1 /\ I3 - I1 - 2 * y1 <= 1 /\ 0 <= I3 - I1 - 2 * y1 /\ I1 + y1 = I5 /\ I3 - (I1 + y1) = I6] 4.37/4.66 f2#(I7, I8, I9, I10) -> f3#(I7, I8, I9, I10) [-1 <= I10 - 1 /\ 0 <= I9 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1] 4.37/4.66 R = 4.37/4.66 init(x1, x2, x3, x4) -> f1(rnd1, rnd2, rnd3, rnd4) 4.37/4.66 f3(I0, I1, I2, I3) -> f2(I4, I5, I6, I3) [-1 <= I3 - 1 /\ 0 <= I2 - 1 /\ I4 <= I0 /\ 0 <= I0 - 1 /\ 0 <= I4 - 1 /\ I3 - I1 - 2 * y1 <= 1 /\ 0 <= I3 - I1 - 2 * y1 /\ I1 + y1 = I5 /\ I3 - (I1 + y1) = I6] 4.37/4.66 f2(I7, I8, I9, I10) -> f3(I7, I8, I9, I10) [-1 <= I10 - 1 /\ 0 <= I9 - 1 /\ I11 <= I7 /\ 0 <= I7 - 1 /\ 0 <= I11 - 1] 4.37/4.66 f1(I12, I13, I14, I15) -> f2(I16, 0, I13, I13) [0 <= I16 - 1 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1 /\ I16 <= I12] 4.37/4.66 4.37/7.64 EOF