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