YES O(n^4) TRS: { f(s(X)) -> f(X), g(cons(s(X), Y)) -> s(X), g(cons(0(), Y)) -> g(Y), h(cons(X, Y)) -> h(g(cons(X, Y))) } DUP: We consider a non-duplicating system. Trs: { f(s(X)) -> f(X), g(cons(s(X), Y)) -> s(X), g(cons(0(), Y)) -> g(Y), h(cons(X, Y)) -> h(g(cons(X, Y))) } Matrix Interpretation: Interpretation class: triangular [X3] [1 0 1 0][X3] [0] [X2] [0 0 0 0][X2] [0] [h]([X1]) = [0 0 0 0][X1] + [0] [X0] [0 0 0 0][X0] [0] [0] [0] [0] = [0] [1] [X7] [X3] [1 0 0 1][X7] [1 0 0 0][X3] [0] [X6] [X2] [0 0 0 0][X6] [0 0 0 0][X2] [0] [cons]([X5], [X1]) = [0 0 0 0][X5] + [0 0 0 0][X1] + [1] [X4] [X0] [0 0 0 0][X4] [0 0 0 0][X0] [0] [X3] [1 0 0 0][X3] [0] [X2] [0 0 0 0][X2] [0] [g]([X1]) = [0 0 0 0][X1] + [0] [X0] [0 0 0 0][X0] [1] [X3] [1 0 0 1][X3] [0] [X2] [0 0 0 0][X2] [0] [s]([X1]) = [0 0 0 0][X1] + [0] [X0] [0 0 0 0][X0] [1] [X3] [1 0 0 1][X3] [0] [X2] [0 0 0 0][X2] [0] [f]([X1]) = [0 0 0 0][X1] + [0] [X0] [0 0 0 0][X0] [0] Qed