MAYBE
Time: 0.121755
TRS:
 {sel(s N, cons(X, XS)) -> sel(N, XS),
  sel(0(), cons(X, XS)) -> X,
             fib1(X, Y) -> cons(X, fib1(Y, add(X, Y))),
                  fib N -> sel(N, fib1(s 0(), s 0())),
            add(s X, Y) -> s add(X, Y),
            add(0(), X) -> X}
 DP:
  DP:
   {sel#(s N, cons(X, XS)) -> sel#(N, XS),
               fib1#(X, Y) -> fib1#(Y, add(X, Y)),
               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)}
  TRS:
  {sel(s N, cons(X, XS)) -> sel(N, XS),
   sel(0(), cons(X, XS)) -> X,
              fib1(X, Y) -> cons(X, fib1(Y, add(X, Y))),
                   fib N -> sel(N, fib1(s 0(), s 0())),
             add(s X, Y) -> s add(X, Y),
             add(0(), X) -> X}
  EDG:
   {(fib1#(X, Y) -> fib1#(Y, add(X, Y)), fib1#(X, Y) -> add#(X, Y))
    (fib1#(X, Y) -> fib1#(Y, add(X, Y)), fib1#(X, Y) -> fib1#(Y, add(X, Y)))
    (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, XS))
    (fib# N -> fib1#(s 0(), s 0()), fib1#(X, Y) -> fib1#(Y, add(X, Y)))
    (fib# N -> fib1#(s 0(), s 0()), fib1#(X, Y) -> add#(X, Y))
    (fib1#(X, Y) -> add#(X, Y), add#(s X, Y) -> add#(X, Y))
    (sel#(s N, cons(X, XS)) -> sel#(N, XS), sel#(s N, cons(X, XS)) -> sel#(N, XS))}
   STATUS:
    arrows: 0.777778
    SCCS (3):
     Scc:
      {fib1#(X, Y) -> fib1#(Y, add(X, Y))}
     Scc:
      {add#(s X, Y) -> add#(X, Y)}
     Scc:
      {sel#(s N, cons(X, XS)) -> sel#(N, XS)}
     
     
     
     SCC (1):
      Strict:
       {fib1#(X, Y) -> fib1#(Y, add(X, Y))}
      Weak:
      {sel(s N, cons(X, XS)) -> sel(N, XS),
       sel(0(), cons(X, XS)) -> X,
                  fib1(X, Y) -> cons(X, fib1(Y, add(X, Y))),
                       fib N -> sel(N, fib1(s 0(), s 0())),
                 add(s X, Y) -> s add(X, Y),
                 add(0(), X) -> X}
      Open
     
     SCC (1):
      Strict:
       {add#(s X, Y) -> add#(X, Y)}
      Weak:
      {sel(s N, cons(X, XS)) -> sel(N, XS),
       sel(0(), cons(X, XS)) -> X,
                  fib1(X, Y) -> cons(X, fib1(Y, add(X, Y))),
                       fib N -> sel(N, fib1(s 0(), s 0())),
                 add(s X, Y) -> s add(X, Y),
                 add(0(), X) -> X}
      Open
     SCC (1):
      Strict:
       {sel#(s N, cons(X, XS)) -> sel#(N, XS)}
      Weak:
      {sel(s N, cons(X, XS)) -> sel(N, XS),
       sel(0(), cons(X, XS)) -> X,
                  fib1(X, Y) -> cons(X, fib1(Y, add(X, Y))),
                       fib N -> sel(N, fib1(s 0(), s 0())),
                 add(s X, Y) -> s add(X, Y),
                 add(0(), X) -> X}
      Open