MAYBE

Problem:
 f(X) -> cons(X,n__f(n__g(X)))
 g(0()) -> s(0())
 g(s(X)) -> s(s(g(X)))
 sel(0(),cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
 f(X) -> n__f(X)
 g(X) -> n__g(X)
 activate(n__f(X)) -> f(activate(X))
 activate(n__g(X)) -> g(activate(X))
 activate(X) -> X

Proof:
 Open