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