YES O(n^4) TRS: { rev(a()) -> a(), rev(b()) -> b(), rev(++(x, y)) -> ++(rev(y), rev(x)), rev(++(x, x)) -> rev(x) } DUP: We consider a non-duplicating system. Trs: { rev(a()) -> a(), rev(b()) -> b(), rev(++(x, y)) -> ++(rev(y), rev(x)), rev(++(x, x)) -> rev(x) } Matrix Interpretation: Interpretation class: triangular [X7] [X3] [1 0 0 0][X7] [1 0 0 0][X3] [0] [X6] [X2] [0 0 0 0][X6] [0 0 0 0][X2] [0] [++]([X5], [X1]) = [0 0 0 0][X5] + [0 0 0 0][X1] + [0] [X4] [X0] [0 0 0 1][X4] [0 0 0 1][X0] [1] [0] [1] [b] = [1] [1] [X3] [1 0 0 1][X3] [0] [X2] [0 0 0 1][X2] [0] [rev]([X1]) = [0 0 0 1][X1] + [0] [X0] [0 0 0 1][X0] [0] [0] [0] [a] = [0] [1] Qed