YES O(n^3) TRS: { a__f(X1, X2, X3) -> f(X1, X2, X3), a__f(a(), X, X) -> a__f(X, a__b(), b()), a__b() -> b(), a__b() -> a(), mark(b()) -> a__b(), mark(a()) -> a(), mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) } DUP: We consider a non-duplicating system. Trs: { a__f(X1, X2, X3) -> f(X1, X2, X3), a__f(a(), X, X) -> a__f(X, a__b(), b()), a__b() -> b(), a__b() -> a(), mark(b()) -> a__b(), mark(a()) -> a(), mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) } Matrix Interpretation: Interpretation class: triangular [X8] [X5] [X2] [1 2 0][X8] [1 0 0][X5] [1 2 0][X2] [0] [f]([X7], [X4], [X1]) = [0 0 0][X7] + [0 0 0][X4] + [0 0 0][X1] + [0] [X6] [X3] [X0] [0 0 1][X6] [0 0 1][X3] [0 0 0][X0] [2] [X2] [1 0 1][X2] [1] [mark]([X1]) = [0 0 0][X1] + [2] [X0] [0 0 1][X0] [3] [0] [a] = [2] [1] [0] [b] = [0] [1] [1] [a__b] = [2] [1] [X8] [X5] [X2] [1 2 0][X8] [1 0 0][X5] [1 2 0][X2] [1] [a__f]([X7], [X4], [X1]) = [0 0 0][X7] + [0 0 0][X4] + [0 0 0][X1] + [0] [X6] [X3] [X0] [0 0 1][X6] [0 0 1][X3] [0 0 0][X0] [2] Qed