0.00/0.17 YES 0.00/0.17 0.00/0.17 DP problem for innermost termination. 0.00/0.17 P = 0.00/0.17 eval#(x, y) -> eval#(y, y) [x > 0 && x > y] 0.00/0.17 eval#(I0, I1) -> eval#(I0 - 1, I1) [I0 > 0 && I1 >= I0] 0.00/0.17 R = 0.00/0.17 eval(x, y) -> eval(y, y) [x > 0 && x > y] 0.00/0.17 eval(I0, I1) -> eval(I0 - 1, I1) [I0 > 0 && I1 >= I0] 0.00/0.17 0.00/0.17 The dependency graph for this problem is: 0.00/0.17 0 -> 1 0.00/0.17 1 -> 1 0.00/0.17 Where: 0.00/0.17 0) eval#(x, y) -> eval#(y, y) [x > 0 && x > y] 0.00/0.17 1) eval#(I0, I1) -> eval#(I0 - 1, I1) [I0 > 0 && I1 >= I0] 0.00/0.17 0.00/0.17 We have the following SCCs. 0.00/0.17 { 1 } 0.00/0.17 0.00/0.17 DP problem for innermost termination. 0.00/0.17 P = 0.00/0.17 eval#(I0, I1) -> eval#(I0 - 1, I1) [I0 > 0 && I1 >= I0] 0.00/0.17 R = 0.00/0.17 eval(x, y) -> eval(y, y) [x > 0 && x > y] 0.00/0.17 eval(I0, I1) -> eval(I0 - 1, I1) [I0 > 0 && I1 >= I0] 0.00/0.17 0.00/0.17 We use the reverse value criterion with the projection function NU: 0.00/0.17 NU[eval#(z1,z2)] = z1 0.00/0.17 0.00/0.17 This gives the following inequalities: 0.00/0.17 I0 > 0 && I1 >= I0 ==> I0 > I0 - 1 with I0 >= 0 0.00/0.17 0.00/0.17 All dependency pairs are strictly oriented, so the entire dependency pair problem may be removed. 0.00/3.15 EOF