YES
TRS:
 {              g(s(X)) -> s(s(g(X))),
                 g(0()) -> s(0()),
                   f(X) -> cons(X, n__f(g(X))),
                   f(X) -> n__f(X),
  sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)),
   sel(0(), cons(X, Y)) -> X,
            activate(X) -> X,
      activate(n__f(X)) -> f(X)}
 DP:
  Strict:
   {              g#(s(X)) -> g#(X),
                     f#(X) -> g#(X),
    sel#(s(X), cons(Y, Z)) -> sel#(X, activate(Z)),
    sel#(s(X), cons(Y, Z)) -> activate#(Z),
        activate#(n__f(X)) -> f#(X)}
  Weak:
  {              g(s(X)) -> s(s(g(X))),
                  g(0()) -> s(0()),
                    f(X) -> cons(X, n__f(g(X))),
                    f(X) -> n__f(X),
   sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)),
    sel(0(), cons(X, Y)) -> X,
             activate(X) -> X,
       activate(n__f(X)) -> f(X)}
  EDG:
   {(f#(X) -> g#(X), g#(s(X)) -> g#(X))
    (sel#(s(X), cons(Y, Z)) -> activate#(Z), activate#(n__f(X)) -> f#(X))
    (sel#(s(X), cons(Y, Z)) -> sel#(X, activate(Z)), sel#(s(X), cons(Y, Z)) -> sel#(X, activate(Z)))
    (sel#(s(X), cons(Y, Z)) -> sel#(X, activate(Z)), sel#(s(X), cons(Y, Z)) -> activate#(Z))
    (activate#(n__f(X)) -> f#(X), f#(X) -> g#(X))
    (g#(s(X)) -> g#(X), g#(s(X)) -> g#(X))}
   SCCS:
    Scc:
     {sel#(s(X), cons(Y, Z)) -> sel#(X, activate(Z))}
    Scc:
     {g#(s(X)) -> g#(X)}
    SCC:
     Strict:
      {sel#(s(X), cons(Y, Z)) -> sel#(X, activate(Z))}
     Weak:
     {              g(s(X)) -> s(s(g(X))),
                     g(0()) -> s(0()),
                       f(X) -> cons(X, n__f(g(X))),
                       f(X) -> n__f(X),
      sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)),
       sel(0(), cons(X, Y)) -> X,
                activate(X) -> X,
          activate(n__f(X)) -> f(X)}
     SPSC:
      Simple Projection:
       pi(sel#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {g#(s(X)) -> g#(X)}
     Weak:
     {              g(s(X)) -> s(s(g(X))),
                     g(0()) -> s(0()),
                       f(X) -> cons(X, n__f(g(X))),
                       f(X) -> n__f(X),
      sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)),
       sel(0(), cons(X, Y)) -> X,
                activate(X) -> X,
          activate(n__f(X)) -> f(X)}
     SPSC:
      Simple Projection:
       pi(g#) = 0
      Strict:
       {}
      Qed