TRS: {a(b(x)) -> b(b(a(x)))} POP* + Boolean Semantic Labelling: Normal positions: pi(a_sl=1) = [1], pi(a_sl=0) = [1] Safe positions: pi(b_sl=1) = [1], pi(b_sl=0) = [1] Precedence: a_sl=0 > b_sl=0 empty Interpretation: b^(1): 0 | 0 1 | 0 a^(1): 0 | 0 1 | 0 Labelling: b^(1): 0 | 0 1 | 0 a^(1): 0 | 0 1 | 0 Labelled predicative System: {a_sl=0(b_sl=0(;x);) -> b_sl=0(;b_sl=0(;a_sl=0(x;))), a_sl=0(b_sl=0(;x);) -> b_sl=0(;b_sl=0(;a_sl=0(x;)))} Qed