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