YES Problem: f(empty(),l) -> l f(cons(x,k),l) -> g(k,l,cons(x,k)) g(a,b,c) -> f(a,cons(b,c)) Proof: DP Processor: DPs: f#(cons(x,k),l) -> g#(k,l,cons(x,k)) g#(a,b,c) -> f#(a,cons(b,c)) TRS: f(empty(),l) -> l f(cons(x,k),l) -> g(k,l,cons(x,k)) g(a,b,c) -> f(a,cons(b,c)) Arctic Interpretation Processor: dimension: 1 interpretation: [g#](x0, x1, x2) = 1x0 + -11x1 + -1x2 + -2, [f#](x0, x1) = x0 + -8x1 + -4, [g](x0, x1, x2) = 6x0 + 4x2 + 4, [cons](x0, x1) = 2x1 + 0, [f](x0, x1) = 5x0 + 1x1 + -16, [empty] = 0 orientation: f#(cons(x,k),l) = 2k + -8l + 0 >= 1k + -11l + -1 = g#(k,l,cons(x,k)) g#(a,b,c) = 1a + -11b + -1c + -2 >= a + -6c + -4 = f#(a,cons(b,c)) f(empty(),l) = 1l + 5 >= l = l f(cons(x,k),l) = 7k + 1l + 5 >= 6k + 4 = g(k,l,cons(x,k)) g(a,b,c) = 6a + 4c + 4 >= 5a + 3c + 1 = f(a,cons(b,c)) problem: DPs: TRS: f(empty(),l) -> l f(cons(x,k),l) -> g(k,l,cons(x,k)) g(a,b,c) -> f(a,cons(b,c)) Qed