YES
TRS:
 {   sel(s(N), cons(X, XS)) -> sel(N, activate(XS)),
      sel(0(), cons(X, XS)) -> X,
                 fib1(X, Y) -> cons(X, n__fib1(Y, add(X, Y))),
               fib1(X1, X2) -> n__fib1(X1, X2),
                     fib(N) -> sel(N, fib1(s(0()), s(0()))),
               add(s(X), Y) -> s(add(X, Y)),
                add(0(), X) -> X,
                activate(X) -> X,
  activate(n__fib1(X1, X2)) -> fib1(X1, X2)}
 DP:
  Strict:
   {   sel#(s(N), cons(X, XS)) -> sel#(N, activate(XS)),
       sel#(s(N), cons(X, XS)) -> activate#(XS),
                   fib1#(X, Y) -> add#(X, Y),
                       fib#(N) -> sel#(N, fib1(s(0()), s(0()))),
                       fib#(N) -> fib1#(s(0()), s(0())),
                 add#(s(X), Y) -> add#(X, Y),
    activate#(n__fib1(X1, X2)) -> fib1#(X1, X2)}
  Weak:
  {   sel(s(N), cons(X, XS)) -> sel(N, activate(XS)),
       sel(0(), cons(X, XS)) -> X,
                  fib1(X, Y) -> cons(X, n__fib1(Y, add(X, Y))),
                fib1(X1, X2) -> n__fib1(X1, X2),
                      fib(N) -> sel(N, fib1(s(0()), s(0()))),
                add(s(X), Y) -> s(add(X, Y)),
                 add(0(), X) -> X,
                 activate(X) -> X,
   activate(n__fib1(X1, X2)) -> fib1(X1, X2)}
  EDG:
   {(activate#(n__fib1(X1, X2)) -> fib1#(X1, X2), fib1#(X, Y) -> add#(X, Y))
    (sel#(s(N), cons(X, XS)) -> activate#(XS), activate#(n__fib1(X1, X2)) -> fib1#(X1, X2))
    (add#(s(X), Y) -> add#(X, Y), add#(s(X), Y) -> add#(X, Y))
    (fib#(N) -> sel#(N, fib1(s(0()), s(0()))), sel#(s(N), cons(X, XS)) -> sel#(N, activate(XS)))
    (fib#(N) -> sel#(N, fib1(s(0()), s(0()))), sel#(s(N), cons(X, XS)) -> activate#(XS))
    (fib1#(X, Y) -> add#(X, Y), add#(s(X), Y) -> add#(X, Y))
    (sel#(s(N), cons(X, XS)) -> sel#(N, activate(XS)), sel#(s(N), cons(X, XS)) -> sel#(N, activate(XS)))
    (sel#(s(N), cons(X, XS)) -> sel#(N, activate(XS)), sel#(s(N), cons(X, XS)) -> activate#(XS))
    (fib#(N) -> fib1#(s(0()), s(0())), fib1#(X, Y) -> add#(X, Y))}
   SCCS:
    Scc:
     {add#(s(X), Y) -> add#(X, Y)}
    Scc:
     {sel#(s(N), cons(X, XS)) -> sel#(N, activate(XS))}
    SCC:
     Strict:
      {add#(s(X), Y) -> add#(X, Y)}
     Weak:
     {   sel(s(N), cons(X, XS)) -> sel(N, activate(XS)),
          sel(0(), cons(X, XS)) -> X,
                     fib1(X, Y) -> cons(X, n__fib1(Y, add(X, Y))),
                   fib1(X1, X2) -> n__fib1(X1, X2),
                         fib(N) -> sel(N, fib1(s(0()), s(0()))),
                   add(s(X), Y) -> s(add(X, Y)),
                    add(0(), X) -> X,
                    activate(X) -> X,
      activate(n__fib1(X1, X2)) -> fib1(X1, X2)}
     SPSC:
      Simple Projection:
       pi(add#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {sel#(s(N), cons(X, XS)) -> sel#(N, activate(XS))}
     Weak:
     {   sel(s(N), cons(X, XS)) -> sel(N, activate(XS)),
          sel(0(), cons(X, XS)) -> X,
                     fib1(X, Y) -> cons(X, n__fib1(Y, add(X, Y))),
                   fib1(X1, X2) -> n__fib1(X1, X2),
                         fib(N) -> sel(N, fib1(s(0()), s(0()))),
                   add(s(X), Y) -> s(add(X, Y)),
                    add(0(), X) -> X,
                    activate(X) -> X,
      activate(n__fib1(X1, X2)) -> fib1(X1, X2)}
     SPSC:
      Simple Projection:
       pi(sel#) = 0
      Strict:
       {}
      Qed