0.82/1.38 MAYBE 0.82/1.38 0.82/1.38 DP problem for innermost termination. 0.82/1.38 P = 0.82/1.38 init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 0.82/1.38 f2#(I0, I1, I2, I3, I4) -> f2#(I5, I1 + 1, I2 * I1, I2 * I1, I4) [I2 = I3 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 <= I0 /\ 0 <= I2 - 1 /\ 0 <= I1 - 1 /\ I4 <= I2 - 1] 0.82/1.38 f2#(I6, I7, I8, I9, I10) -> f2#(I11, I7 + 1, I8 * I7, I8 * I7, I10) [I8 = I9 /\ 0 <= I11 - 1 /\ 0 <= I6 - 1 /\ I11 <= I6 /\ 0 <= I8 - 1 /\ 0 <= I7 - 1 /\ I8 <= I10 - 1] 0.82/1.38 f1#(I12, I13, I14, I15, I16) -> f2#(I17, 1, 1, 1, I13) [0 <= I17 - 1 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1 /\ I17 <= I12] 0.82/1.38 R = 0.82/1.38 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 0.82/1.38 f2(I0, I1, I2, I3, I4) -> f2(I5, I1 + 1, I2 * I1, I2 * I1, I4) [I2 = I3 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 <= I0 /\ 0 <= I2 - 1 /\ 0 <= I1 - 1 /\ I4 <= I2 - 1] 0.82/1.38 f2(I6, I7, I8, I9, I10) -> f2(I11, I7 + 1, I8 * I7, I8 * I7, I10) [I8 = I9 /\ 0 <= I11 - 1 /\ 0 <= I6 - 1 /\ I11 <= I6 /\ 0 <= I8 - 1 /\ 0 <= I7 - 1 /\ I8 <= I10 - 1] 0.82/1.38 f1(I12, I13, I14, I15, I16) -> f2(I17, 1, 1, 1, I13) [0 <= I17 - 1 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1 /\ I17 <= I12] 0.82/1.38 0.82/1.38 The dependency graph for this problem is: 0.82/1.38 0 -> 3 0.82/1.38 1 -> 1 0.82/1.38 2 -> 1, 2 0.82/1.38 3 -> 1, 2 0.82/1.38 Where: 0.82/1.38 0) init#(x1, x2, x3, x4, x5) -> f1#(rnd1, rnd2, rnd3, rnd4, rnd5) 0.82/1.38 1) f2#(I0, I1, I2, I3, I4) -> f2#(I5, I1 + 1, I2 * I1, I2 * I1, I4) [I2 = I3 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 <= I0 /\ 0 <= I2 - 1 /\ 0 <= I1 - 1 /\ I4 <= I2 - 1] 0.82/1.38 2) f2#(I6, I7, I8, I9, I10) -> f2#(I11, I7 + 1, I8 * I7, I8 * I7, I10) [I8 = I9 /\ 0 <= I11 - 1 /\ 0 <= I6 - 1 /\ I11 <= I6 /\ 0 <= I8 - 1 /\ 0 <= I7 - 1 /\ I8 <= I10 - 1] 0.82/1.38 3) f1#(I12, I13, I14, I15, I16) -> f2#(I17, 1, 1, 1, I13) [0 <= I17 - 1 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1 /\ I17 <= I12] 0.82/1.38 0.82/1.38 We have the following SCCs. 0.82/1.38 { 2 } 0.82/1.38 { 1 } 0.82/1.38 0.82/1.38 DP problem for innermost termination. 0.82/1.38 P = 0.82/1.38 f2#(I0, I1, I2, I3, I4) -> f2#(I5, I1 + 1, I2 * I1, I2 * I1, I4) [I2 = I3 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 <= I0 /\ 0 <= I2 - 1 /\ 0 <= I1 - 1 /\ I4 <= I2 - 1] 0.82/1.38 R = 0.82/1.38 init(x1, x2, x3, x4, x5) -> f1(rnd1, rnd2, rnd3, rnd4, rnd5) 0.82/1.38 f2(I0, I1, I2, I3, I4) -> f2(I5, I1 + 1, I2 * I1, I2 * I1, I4) [I2 = I3 /\ 0 <= I5 - 1 /\ 0 <= I0 - 1 /\ I5 <= I0 /\ 0 <= I2 - 1 /\ 0 <= I1 - 1 /\ I4 <= I2 - 1] 0.82/1.38 f2(I6, I7, I8, I9, I10) -> f2(I11, I7 + 1, I8 * I7, I8 * I7, I10) [I8 = I9 /\ 0 <= I11 - 1 /\ 0 <= I6 - 1 /\ I11 <= I6 /\ 0 <= I8 - 1 /\ 0 <= I7 - 1 /\ I8 <= I10 - 1] 0.82/1.38 f1(I12, I13, I14, I15, I16) -> f2(I17, 1, 1, 1, I13) [0 <= I17 - 1 /\ 0 <= I12 - 1 /\ -1 <= I13 - 1 /\ I17 <= I12] 0.82/1.38 0.82/4.36 EOF