YES O(n^3) TRS: { ++(x, nil()) -> x, ++(++(x, y), z) -> ++(x, ++(y, z)), ++(nil(), y) -> y, ++(.(x, y), z) -> .(x, ++(y, z)) } DUP: We consider a non-duplicating system. Trs: { ++(x, nil()) -> x, ++(++(x, y), z) -> ++(x, ++(y, z)), ++(nil(), y) -> y, ++(.(x, y), z) -> .(x, ++(y, z)) } Matrix Interpretation: Interpretation class: triangular [X5] [X2] [1 0 0][X5] [1 0 0][X2] [0] [.]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [0] [X3] [X0] [0 0 0][X3] [0 0 1][X0] [1] [1] [nil] = [0] [0] [X5] [X2] [1 0 1][X5] [1 0 0][X2] [0] [++]([X4], [X1]) = [0 1 0][X4] + [0 1 0][X1] + [0] [X3] [X0] [0 0 1][X3] [0 0 1][X0] [1] Qed