1.14/1.19 MAYBE 1.14/1.19 1.14/1.19 DP problem for innermost termination. 1.14/1.19 P = 1.14/1.19 f5#(x1, x2, x3) -> f4#(x1, x2, x3) 1.14/1.19 f4#(I0, I1, I2) -> f1#(I1, I1, I2) 1.14/1.19 f3#(I3, I4, I5) -> f1#(I3, I4, I5) 1.14/1.19 f1#(I6, I7, I8) -> f3#(-1 + I6, -1 + I7, 1 + I8) 1.14/1.19 R = 1.14/1.19 f5(x1, x2, x3) -> f4(x1, x2, x3) 1.14/1.19 f4(I0, I1, I2) -> f1(I1, I1, I2) 1.14/1.19 f3(I3, I4, I5) -> f1(I3, I4, I5) 1.14/1.19 f1(I6, I7, I8) -> f3(-1 + I6, -1 + I7, 1 + I8) 1.14/1.19 f1(I9, I10, I11) -> f2(I9, I10, I11) [1 + I9 <= I10] 1.14/1.19 1.14/1.19 The dependency graph for this problem is: 1.14/1.19 0 -> 1 1.14/1.19 1 -> 3 1.14/1.19 2 -> 3 1.14/1.19 3 -> 2 1.14/1.19 Where: 1.14/1.19 0) f5#(x1, x2, x3) -> f4#(x1, x2, x3) 1.14/1.19 1) f4#(I0, I1, I2) -> f1#(I1, I1, I2) 1.14/1.19 2) f3#(I3, I4, I5) -> f1#(I3, I4, I5) 1.14/1.19 3) f1#(I6, I7, I8) -> f3#(-1 + I6, -1 + I7, 1 + I8) 1.14/1.19 1.14/1.19 We have the following SCCs. 1.14/1.19 { 2, 3 } 1.14/1.19 1.14/1.19 DP problem for innermost termination. 1.14/1.19 P = 1.14/1.19 f3#(I3, I4, I5) -> f1#(I3, I4, I5) 1.14/1.19 f1#(I6, I7, I8) -> f3#(-1 + I6, -1 + I7, 1 + I8) 1.14/1.19 R = 1.14/1.19 f5(x1, x2, x3) -> f4(x1, x2, x3) 1.14/1.19 f4(I0, I1, I2) -> f1(I1, I1, I2) 1.14/1.19 f3(I3, I4, I5) -> f1(I3, I4, I5) 1.14/1.19 f1(I6, I7, I8) -> f3(-1 + I6, -1 + I7, 1 + I8) 1.14/1.19 f1(I9, I10, I11) -> f2(I9, I10, I11) [1 + I9 <= I10] 1.14/1.19 1.14/4.17 EOF