TRS: {f(0(), 1(), x) -> f(x, x, x)} POP* + Boolean Semantic Labelling: Normal positions: pi(f_sl=1) = [1,2,3], pi(f_sl=0) = [1,2,3] Safe positions: Precedence: f_sl=1 > f_sl=0 empty Interpretation: f^(3): 000 | 0 001 | 0 010 | 0 011 | 0 100 | 0 101 | 0 110 | 0 111 | 0 0^(0): | 0 1^(0): | 1 Labelling: f^(3): 000 | 0 001 | 0 010 | 1 011 | 1 100 | 0 101 | 0 110 | 0 111 | 0 0^(0): | 0 1^(0): | 0 Labelled predicative System: {f_sl=1(0_sl=0(),1_sl=0(),x;) -> f_sl=0(x,x,x;), f_sl=1(0_sl=0(),1_sl=0(),x;) -> f_sl=0(x,x,x;)} Qed