YES O(n^5) 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 [X4] [1 0 1 1 0][X4] [0] [X3] [0 0 0 0 0][X3] [0] [g]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [0] [X0] [0 0 0 0 0][X0] [0] [X4] [1 0 0 0 0][X4] [0] [X3] [0 0 0 0 0][X3] [0] [s]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [0] [X0] [0 0 0 0 1][X0] [1] [X9] [X4] [1 0 0 0 0][X9] [1 0 0 0 0][X4] [0] [X8] [X3] [0 0 0 0 0][X8] [0 0 0 0 0][X3] [0] [c]([X7], [X2]) = [0 0 0 0 0][X7] + [0 0 0 0 1][X2] + [1] [X6] [X1] [0 0 0 0 0][X6] [0 0 0 0 0][X1] [1] [X5] [X0] [0 0 0 0 0][X5] [0 0 0 0 1][X0] [0] [X4] [1 0 0 0 1][X4] [0] [X3] [0 0 0 0 0][X3] [0] [f]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [0] [X0] [0 0 0 0 0][X0] [0] Qed