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