YES(?,O(n^2)) 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] [true] = [1] [X3] [X1] [1 3][X3] [1 3][X1] [0] [lessleaves]([X2], [X0]) = [0 0][X2] + [0 0][X0] + [1] [0] [false] = [0] [X3] [X1] [1 1][X3] [1 0][X1] [1] [cons]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [3] [1] [leaf] = [0] [X3] [X1] [1 1][X3] [1 0][X1] [0] [concat]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [0] Qed