YES TRS: from(X) -> cons(X,n__from(n__s(X))) sel(0(),cons(X,Y)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) s(X) -> n__s(X) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X max/plus interpretations on N: from_A(x1) = max{4, -4 + x1} from#_A(x1) = max{3, 7} cons_A(x1,x2) = max{4, -4 + x1, 1 + x2} cons#_A(x1,x2) = max{7, 2, 4 + x2} n__from_A(x1) = max{3, -4 + x1} n__from#_A(x1) = max{0, 0} n__s_A(x1) = max{4, 1} n__s#_A(x1) = max{6, 6} sel_A(x1,x2) = max{0, 0, 4 + x2} sel#_A(x1,x2) = max{9, 9, 9} 0_A = 0 0#_A = 0 s_A(x1) = max{4, 3} s#_A(x1) = max{8, 8} activate_A(x1) = max{3, 1 + x1} activate#_A(x1) = max{8, 1} precedence: from = 0 > cons = n__s = sel > activate > n__from = s