YES O(n^5) TRS: { .(x, 1()) -> x, .(x, i(x)) -> 1(), .(y, .(i(y), z)) -> z, .(1(), x) -> x, .(i(x), x) -> 1(), .(i(y), .(y, z)) -> z, i(1()) -> 1(), i(i(x)) -> x } DUP: We consider a non-duplicating system. Trs: { .(x, 1()) -> x, .(x, i(x)) -> 1(), .(y, .(i(y), z)) -> z, .(1(), x) -> x, .(i(x), x) -> 1(), .(i(y), .(y, z)) -> z, i(1()) -> 1(), i(i(x)) -> x } Matrix Interpretation: Interpretation class: triangular [X4] [1 1 0 0 0][X4] [0] [X3] [0 1 0 0 0][X3] [1] [i]([X2]) = [0 0 1 0 0][X2] + [0] [X1] [0 0 0 1 0][X1] [0] [X0] [0 0 0 0 1][X0] [0] [0] [1] [1] = [0] [0] [0] [X9] [X4] [1 0 0 0 0][X9] [1 0 0 0 0][X4] [1] [X8] [X3] [0 1 0 0 0][X8] [0 1 0 0 0][X3] [0] [.]([X7], [X2]) = [0 0 1 0 0][X7] + [0 0 1 0 0][X2] + [0] [X6] [X1] [0 0 0 1 0][X6] [0 0 0 1 0][X1] [0] [X5] [X0] [0 0 0 0 1][X5] [0 0 0 0 1][X0] [0] Qed