YES(?,O(n^2)) TRS: { concat(leaf(), y) -> y, concat(cons(u, v), y) -> cons(u, concat(v, y)), less_leaves(x, leaf()) -> false(), less_leaves(leaf(), cons(w, z)) -> true(), less_leaves(cons(u, v), cons(w, z)) -> less_leaves(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)), less_leaves(x, leaf()) -> false(), less_leaves(leaf(), cons(w, z)) -> true(), less_leaves(cons(u, v), cons(w, z)) -> less_leaves(concat(u, v), concat(w, z)) } Matrix Interpretation: Interpretation class: triangular [0] [true] = [1] [X3] [X1] [1 3][X3] [1 3][X1] [0] [less_leaves]([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