YES O(n^4) TRS: { g(a()) -> g(b()), b() -> f(a(), a()), f(a(), a()) -> g(d())} DUP: We consider a non-duplicating system. Trs: { g(a()) -> g(b()), b() -> f(a(), a()), f(a(), a()) -> g(d())} Matrix Interpretation: Interpretation class: triangular [0] [0] [d] = [0] [0] [X7] [X3] [1 1 0 0][X7] [1 0 0 0][X3] [0] [X6] [X2] [0 0 0 0][X6] [0 0 0 0][X2] [0] [f]([X5], [X1]) = [0 0 0 0][X5] + [0 0 0 0][X1] + [0] [X4] [X0] [0 0 0 0][X4] [0 0 0 0][X0] [0] [0] [1] [a] = [3] [1] [3] [0] [b] = [0] [2] [X3] [1 1 3 2][X3] [0] [X2] [0 0 0 0][X2] [0] [g]([X1]) = [0 0 1 0][X1] + [0] [X0] [0 0 0 0][X0] [0] Qed