YES O(n^5) TRS: { concat(leaf(), Y) -> Y, concat(cons(U, V), Y) -> cons(U, concat(V, Y)), lessleaves(X, leaf()) -> false(), lessleaves(leaf(), cons(W, Z)) -> true(), lessleaves(cons(U, V), cons(W, Z)) -> lessleaves(concat(U, V), concat(W, Z)) } DUP: We consider a non-duplicating system. Trs: { concat(leaf(), Y) -> Y, concat(cons(U, V), Y) -> cons(U, concat(V, Y)), lessleaves(X, leaf()) -> false(), lessleaves(leaf(), cons(W, Z)) -> true(), lessleaves(cons(U, V), cons(W, Z)) -> lessleaves(concat(U, V), concat(W, Z)) } Matrix Interpretation: Interpretation class: triangular [0] [0] [true] = [0] [0] [0] [X9] [X4] [1 0 0 1 1][X9] [1 1 0 0 0][X4] [0] [X8] [X3] [0 0 0 0 0][X8] [0 0 0 0 0][X3] [0] [lessleaves]([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 0][X0] [0] [0] [0] [false] = [0] [0] [0] [X9] [X4] [1 0 0 1 0][X9] [1 0 0 0 0][X4] [0] [X8] [X3] [0 0 0 0 0][X8] [0 1 0 0 0][X3] [0] [cons]([X7], [X2]) = [0 0 0 0 0][X7] + [0 0 0 0 0][X2] + [0] [X6] [X1] [0 0 0 1 0][X6] [0 0 0 1 0][X1] [1] [X5] [X0] [0 0 0 0 1][X5] [0 0 0 0 1][X0] [1] [0] [1] [leaf] = [0] [1] [0] [X9] [X4] [1 0 0 1 0][X9] [1 0 0 0 0][X4] [0] [X8] [X3] [0 0 0 0 0][X8] [0 1 0 0 0][X3] [1] [concat]([X7], [X2]) = [0 0 0 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