27.01/26.63 MAYBE 27.01/26.63 27.01/26.63 DP problem for innermost termination. 27.01/26.63 P = 27.01/26.63 f5#(x1, x2) -> f4#(x1, x2) 27.01/26.63 f4#(I0, I1) -> f2#(I0, I1) 27.01/26.63 f3#(I2, I3) -> f1#(I2, I3) [1 <= I3] 27.01/26.63 f3#(I4, I5) -> f1#(I4, I5) [1 + I5 <= 0] 27.01/26.63 f2#(I6, I7) -> f3#(I6, I7) [1 <= I6] 27.01/26.63 f2#(I8, I9) -> f3#(I8, I9) [1 + I8 <= 0] 27.01/26.63 f1#(I10, I11) -> f2#(I10, -1 + I11) [2 - I11 <= I10 /\ I11 <= I10] 27.01/26.63 f1#(I12, I13) -> f2#(-1 + I12, I13) [1 + I13 <= I12 /\ I13 <= 1 - I12] 27.01/26.63 f1#(I14, I15) -> f2#(I14, 1 + I15) [1 + I14 <= -1 * I15 /\ I14 <= I15] 27.01/26.63 f1#(I16, I17) -> f2#(1 + I16, I17) [1 + I16 <= I17 /\ -1 * I16 <= I17] 27.01/26.63 R = 27.01/26.63 f5(x1, x2) -> f4(x1, x2) 27.01/26.63 f4(I0, I1) -> f2(I0, I1) 27.01/26.63 f3(I2, I3) -> f1(I2, I3) [1 <= I3] 27.01/26.63 f3(I4, I5) -> f1(I4, I5) [1 + I5 <= 0] 27.01/26.63 f2(I6, I7) -> f3(I6, I7) [1 <= I6] 27.01/26.63 f2(I8, I9) -> f3(I8, I9) [1 + I8 <= 0] 27.01/26.63 f1(I10, I11) -> f2(I10, -1 + I11) [2 - I11 <= I10 /\ I11 <= I10] 27.01/26.63 f1(I12, I13) -> f2(-1 + I12, I13) [1 + I13 <= I12 /\ I13 <= 1 - I12] 27.01/26.63 f1(I14, I15) -> f2(I14, 1 + I15) [1 + I14 <= -1 * I15 /\ I14 <= I15] 27.01/26.63 f1(I16, I17) -> f2(1 + I16, I17) [1 + I16 <= I17 /\ -1 * I16 <= I17] 27.01/26.63 27.01/26.63 The dependency graph for this problem is: 27.01/26.63 0 -> 1 27.01/26.63 1 -> 4, 5 27.01/26.63 2 -> 6, 8, 9 27.01/26.63 3 -> 6, 7, 8 27.01/26.63 4 -> 2, 3 27.01/26.63 5 -> 2, 3 27.01/26.63 6 -> 4 27.01/26.63 7 -> 4, 5 27.01/26.63 8 -> 5 27.01/26.63 9 -> 4, 5 27.01/26.63 Where: 27.01/26.63 0) f5#(x1, x2) -> f4#(x1, x2) 27.01/26.63 1) f4#(I0, I1) -> f2#(I0, I1) 27.01/26.63 2) f3#(I2, I3) -> f1#(I2, I3) [1 <= I3] 27.01/26.63 3) f3#(I4, I5) -> f1#(I4, I5) [1 + I5 <= 0] 27.01/26.63 4) f2#(I6, I7) -> f3#(I6, I7) [1 <= I6] 27.01/26.63 5) f2#(I8, I9) -> f3#(I8, I9) [1 + I8 <= 0] 27.01/26.63 6) f1#(I10, I11) -> f2#(I10, -1 + I11) [2 - I11 <= I10 /\ I11 <= I10] 27.01/26.63 7) f1#(I12, I13) -> f2#(-1 + I12, I13) [1 + I13 <= I12 /\ I13 <= 1 - I12] 27.01/26.63 8) f1#(I14, I15) -> f2#(I14, 1 + I15) [1 + I14 <= -1 * I15 /\ I14 <= I15] 27.01/26.63 9) f1#(I16, I17) -> f2#(1 + I16, I17) [1 + I16 <= I17 /\ -1 * I16 <= I17] 27.01/26.63 27.01/26.63 We have the following SCCs. 27.01/26.63 { 2, 3, 4, 5, 6, 7, 8, 9 } 27.01/26.63 27.01/26.63 DP problem for innermost termination. 27.01/26.63 P = 27.01/26.63 f3#(I2, I3) -> f1#(I2, I3) [1 <= I3] 27.01/26.63 f3#(I4, I5) -> f1#(I4, I5) [1 + I5 <= 0] 27.01/26.63 f2#(I6, I7) -> f3#(I6, I7) [1 <= I6] 27.01/26.63 f2#(I8, I9) -> f3#(I8, I9) [1 + I8 <= 0] 27.01/26.63 f1#(I10, I11) -> f2#(I10, -1 + I11) [2 - I11 <= I10 /\ I11 <= I10] 27.01/26.63 f1#(I12, I13) -> f2#(-1 + I12, I13) [1 + I13 <= I12 /\ I13 <= 1 - I12] 27.01/26.63 f1#(I14, I15) -> f2#(I14, 1 + I15) [1 + I14 <= -1 * I15 /\ I14 <= I15] 27.01/26.63 f1#(I16, I17) -> f2#(1 + I16, I17) [1 + I16 <= I17 /\ -1 * I16 <= I17] 27.01/26.63 R = 27.01/26.63 f5(x1, x2) -> f4(x1, x2) 27.01/26.63 f4(I0, I1) -> f2(I0, I1) 27.01/26.63 f3(I2, I3) -> f1(I2, I3) [1 <= I3] 27.01/26.63 f3(I4, I5) -> f1(I4, I5) [1 + I5 <= 0] 27.01/26.63 f2(I6, I7) -> f3(I6, I7) [1 <= I6] 27.01/26.63 f2(I8, I9) -> f3(I8, I9) [1 + I8 <= 0] 27.01/26.63 f1(I10, I11) -> f2(I10, -1 + I11) [2 - I11 <= I10 /\ I11 <= I10] 27.01/26.63 f1(I12, I13) -> f2(-1 + I12, I13) [1 + I13 <= I12 /\ I13 <= 1 - I12] 27.01/26.63 f1(I14, I15) -> f2(I14, 1 + I15) [1 + I14 <= -1 * I15 /\ I14 <= I15] 27.01/26.63 f1(I16, I17) -> f2(1 + I16, I17) [1 + I16 <= I17 /\ -1 * I16 <= I17] 27.01/26.63 27.01/29.60 EOF