YES O(n^5) TRS: { __(X, nil()) -> X, __(__(X, Y), Z) -> __(X, __(Y, Z)), __(nil(), X) -> X, U12(tt()) -> tt(), U11(tt()) -> U12(tt()), isNePal(__(I, __(P, I))) -> U11(tt()) } DUP: We consider a non-duplicating system. Trs: { __(X, nil()) -> X, __(__(X, Y), Z) -> __(X, __(Y, Z)), __(nil(), X) -> X, U12(tt()) -> tt(), U11(tt()) -> U12(tt()), isNePal(__(I, __(P, I))) -> U11(tt()) } Matrix Interpretation: Interpretation class: triangular [X4] [1 1 0 0 0][X4] [0] [X3] [0 0 0 0 0][X3] [1] [isNePal]([X2]) = [0 0 0 0 0][X2] + [1] [X1] [0 0 0 0 0][X1] [1] [X0] [0 0 0 0 0][X0] [0] [X4] [1 1 0 0 0][X4] [1] [X3] [0 1 0 0 0][X3] [0] [U11]([X2]) = [0 0 1 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [1] [X0] [0 0 0 0 0][X0] [0] [0] [1] [tt] = [1] [0] [0] [X4] [1 0 1 0 0][X4] [0] [X3] [0 0 0 0 0][X3] [1] [U12]([X2]) = [0 0 0 0 0][X2] + [1] [X1] [0 0 0 0 0][X1] [1] [X0] [0 0 0 0 0][X0] [0] [0] [0] [nil] = [0] [0] [0] [X9] [X4] [1 1 0 0 0][X9] [1 0 0 0 0][X4] [1] [X8] [X3] [0 1 0 0 0][X8] [0 1 0 0 0][X3] [1] [__]([X7], [X2]) = [0 0 1 0 0][X7] + [0 0 1 0 0][X2] + [0] [X6] [X1] [0 0 0 1 0][X6] [0 0 0 1 0][X1] [0] [X5] [X0] [0 0 0 0 1][X5] [0 0 0 0 1][X0] [0] Qed