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 conv#(x) -> conv#(x / 2) [x > 0] 0.00/0.17 conv#(x) -> lastbit#(x) [x > 0] 0.00/0.17 lastbit#(I0) -> lastbit#(I0 - 2) [I0 > 1] 0.00/0.17 R = 0.00/0.17 conv(x) -> cons(conv(x / 2), lastbit(x)) [x > 0] 0.00/0.17 conv(0) -> cons(nil, 0) 0.00/0.17 lastbit(I0) -> lastbit(I0 - 2) [I0 > 1] 0.00/0.17 lastbit(1) -> 1 0.00/0.17 lastbit(0) -> 0 0.00/0.17 0.00/0.17 The dependency graph for this problem is: 0.00/0.17 0 -> 0, 1 0.00/0.17 1 -> 2 0.00/0.17 2 -> 2 0.00/0.17 Where: 0.00/0.17 0) conv#(x) -> conv#(x / 2) [x > 0] 0.00/0.17 1) conv#(x) -> lastbit#(x) [x > 0] 0.00/0.17 2) lastbit#(I0) -> lastbit#(I0 - 2) [I0 > 1] 0.00/0.17 0.00/0.17 We have the following SCCs. 0.00/0.17 { 0 } 0.00/0.17 { 2 } 0.00/0.17 0.00/0.17 DP problem for innermost termination. 0.00/0.17 P = 0.00/0.17 lastbit#(I0) -> lastbit#(I0 - 2) [I0 > 1] 0.00/0.17 R = 0.00/0.17 conv(x) -> cons(conv(x / 2), lastbit(x)) [x > 0] 0.00/0.17 conv(0) -> cons(nil, 0) 0.00/0.17 lastbit(I0) -> lastbit(I0 - 2) [I0 > 1] 0.00/0.17 lastbit(1) -> 1 0.00/0.17 lastbit(0) -> 0 0.00/0.17 0.00/0.17 We use the reverse value criterion with the projection function NU: 0.00/0.17 NU[lastbit#(z1)] = z1 0.00/0.17 0.00/0.17 This gives the following inequalities: 0.00/0.17 I0 > 1 ==> I0 > I0 - 2 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. 0.00/0.17 0.00/0.17 DP problem for innermost termination. 0.00/0.17 P = 0.00/0.17 conv#(x) -> conv#(x / 2) [x > 0] 0.00/0.17 R = 0.00/0.17 conv(x) -> cons(conv(x / 2), lastbit(x)) [x > 0] 0.00/0.17 conv(0) -> cons(nil, 0) 0.00/0.17 lastbit(I0) -> lastbit(I0 - 2) [I0 > 1] 0.00/0.17 lastbit(1) -> 1 0.00/0.17 lastbit(0) -> 0 0.00/0.17 0.00/0.17 We use the reverse value criterion with the projection function NU: 0.00/0.17 NU[conv#(z1)] = z1 0.00/0.17 0.00/0.17 This gives the following inequalities: 0.00/0.17 x > 0 ==> x > x / 2 with x >= 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