TRS: {f(s(X), Y) -> h(s(f(h(Y), X)))} POP* + Boolean Semantic Labelling: Normal positions: pi(f_sl=1) = [1,2], pi(f_sl=0) = [1,2] Safe positions: pi(s_sl=1) = [1], pi(s_sl=0) = [1], pi(h_sl=1) = [1], pi(h_sl=0) = [1] Precedence: f_sl=1 > f_sl=0, f_sl=1 > s_sl=1, f_sl=1 > h_sl=1 empty Interpretation: h^(1): 0 | 1 1 | 1 s^(1): 0 | 0 1 | 0 f^(2): 00 | 1 01 | 1 10 | 0 11 | 0 Labelling: h^(1): 0 | 1 1 | 1 s^(1): 0 | 1 1 | 0 f^(2): 00 | 1 01 | 1 10 | 0 11 | 0 Labelled predicative System: {f_sl=1(s_sl=1(;X),Y;) -> h_sl=1(;s_sl=1(;f_sl=0(h_sl=1(;Y),X;))), f_sl=1(s_sl=0(;X),Y;) -> h_sl=1(;s_sl=1(;f_sl=0(h_sl=1(;Y),X;))), f_sl=1(s_sl=1(;X),Y;) -> h_sl=1(;s_sl=1(;f_sl=0(h_sl=1(;Y),X;))), f_sl=1(s_sl=0(;X),Y;) -> h_sl=1(;s_sl=1(;f_sl=0(h_sl=1(;Y),X;)))} Qed