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