MAYBE
Time: 0.009862
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, n__add(X, Y))),
              fib1(X1, X2) -> n__fib1(X1, X2),
                     fib N -> sel(N, fib1(s 0(), s 0())),
               add(X1, X2) -> n__add(X1, X2),
               add(s X, Y) -> s add(X, Y),
               add(0(), X) -> X,
                activate X -> X,
  activate n__fib1(X1, X2) -> fib1(activate X1, activate X2),
   activate n__add(X1, X2) -> add(activate X1, activate X2)}
 DP:
  DP:
   {   sel#(s N, cons(X, XS)) -> sel#(N, activate XS),
       sel#(s N, cons(X, XS)) -> activate# XS,
                       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#(activate X1, activate X2),
    activate# n__fib1(X1, X2) -> activate# X1,
    activate# n__fib1(X1, X2) -> activate# X2,
     activate# n__add(X1, X2) -> add#(activate X1, activate X2),
     activate# n__add(X1, X2) -> activate# X1,
     activate# n__add(X1, X2) -> activate# X2}
  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, n__add(X, Y))),
               fib1(X1, X2) -> n__fib1(X1, X2),
                      fib N -> sel(N, fib1(s 0(), s 0())),
                add(X1, X2) -> n__add(X1, X2),
                add(s X, Y) -> s add(X, Y),
                add(0(), X) -> X,
                 activate X -> X,
   activate n__fib1(X1, X2) -> fib1(activate X1, activate X2),
    activate n__add(X1, X2) -> add(activate X1, activate X2)}
  UR:
   {              fib1(X, Y) -> cons(X, n__fib1(Y, n__add(X, Y))),
                fib1(X1, X2) -> n__fib1(X1, X2),
                 add(X1, X2) -> n__add(X1, X2),
                 add(s X, Y) -> s add(X, Y),
                 add(0(), X) -> X,
                  activate X -> X,
    activate n__fib1(X1, X2) -> fib1(activate X1, activate X2),
     activate n__add(X1, X2) -> add(activate X1, activate X2),
                     a(x, y) -> x,
                     a(x, y) -> y}
   EDG:
    {(sel#(s N, cons(X, XS)) -> activate# XS, activate# n__add(X1, X2) -> activate# X2)
     (sel#(s N, cons(X, XS)) -> activate# XS, activate# n__add(X1, X2) -> activate# X1)
     (sel#(s N, cons(X, XS)) -> activate# XS, activate# n__add(X1, X2) -> add#(activate X1, activate X2))
     (sel#(s N, cons(X, XS)) -> activate# XS, activate# n__fib1(X1, X2) -> activate# X2)
     (sel#(s N, cons(X, XS)) -> activate# XS, activate# n__fib1(X1, X2) -> activate# X1)
     (sel#(s N, cons(X, XS)) -> activate# XS, activate# n__fib1(X1, X2) -> fib1#(activate X1, activate X2))
     (activate# n__add(X1, X2) -> activate# X1, activate# n__add(X1, X2) -> activate# X2)
     (activate# n__add(X1, X2) -> activate# X1, activate# n__add(X1, X2) -> activate# X1)
     (activate# n__add(X1, X2) -> activate# X1, activate# n__add(X1, X2) -> add#(activate X1, activate X2))
     (activate# n__add(X1, X2) -> activate# X1, activate# n__fib1(X1, X2) -> activate# X2)
     (activate# n__add(X1, X2) -> activate# X1, activate# n__fib1(X1, X2) -> activate# X1)
     (activate# n__add(X1, X2) -> activate# X1, activate# n__fib1(X1, X2) -> fib1#(activate X1, activate X2))
     (activate# n__fib1(X1, X2) -> activate# X2, activate# n__add(X1, X2) -> activate# X2)
     (activate# n__fib1(X1, X2) -> activate# X2, activate# n__add(X1, X2) -> activate# X1)
     (activate# n__fib1(X1, X2) -> activate# X2, activate# n__add(X1, X2) -> add#(activate X1, activate X2))
     (activate# n__fib1(X1, X2) -> activate# X2, activate# n__fib1(X1, X2) -> activate# X2)
     (activate# n__fib1(X1, X2) -> activate# X2, activate# n__fib1(X1, X2) -> activate# X1)
     (activate# n__fib1(X1, X2) -> activate# X2, activate# n__fib1(X1, X2) -> fib1#(activate X1, activate X2))
     (add#(s X, Y) -> add#(X, Y), add#(s X, Y) -> add#(X, Y))
     (activate# n__add(X1, X2) -> activate# X2, activate# n__fib1(X1, X2) -> fib1#(activate X1, activate X2))
     (activate# n__add(X1, X2) -> activate# X2, activate# n__fib1(X1, X2) -> activate# X1)
     (activate# n__add(X1, X2) -> activate# X2, activate# n__fib1(X1, X2) -> activate# X2)
     (activate# n__add(X1, X2) -> activate# X2, activate# n__add(X1, X2) -> add#(activate X1, activate X2))
     (activate# n__add(X1, X2) -> activate# X2, activate# n__add(X1, X2) -> activate# X1)
     (activate# n__add(X1, X2) -> activate# X2, activate# n__add(X1, X2) -> activate# X2)
     (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)
     (activate# n__fib1(X1, X2) -> activate# X1, activate# n__fib1(X1, X2) -> fib1#(activate X1, activate X2))
     (activate# n__fib1(X1, X2) -> activate# X1, activate# n__fib1(X1, X2) -> activate# X1)
     (activate# n__fib1(X1, X2) -> activate# X1, activate# n__fib1(X1, X2) -> activate# X2)
     (activate# n__fib1(X1, X2) -> activate# X1, activate# n__add(X1, X2) -> add#(activate X1, activate X2))
     (activate# n__fib1(X1, X2) -> activate# X1, activate# n__add(X1, X2) -> activate# X1)
     (activate# n__fib1(X1, X2) -> activate# X1, activate# n__add(X1, X2) -> activate# X2)
     (activate# n__add(X1, X2) -> add#(activate X1, activate X2), 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)}
    STATUS:
     arrows: 0.702479
     SCCS (3):
      Scc:
       {sel#(s N, cons(X, XS)) -> sel#(N, activate XS)}
      Scc:
       {activate# n__fib1(X1, X2) -> activate# X1,
        activate# n__fib1(X1, X2) -> activate# X2,
         activate# n__add(X1, X2) -> activate# X1,
         activate# n__add(X1, X2) -> activate# X2}
      Scc:
       {add#(s X, Y) -> add#(X, Y)}
      
      
      
      SCC (1):
       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, n__add(X, Y))),
                    fib1(X1, X2) -> n__fib1(X1, X2),
                           fib N -> sel(N, fib1(s 0(), s 0())),
                     add(X1, X2) -> n__add(X1, X2),
                     add(s X, Y) -> s add(X, Y),
                     add(0(), X) -> X,
                      activate X -> X,
        activate n__fib1(X1, X2) -> fib1(activate X1, activate X2),
         activate n__add(X1, X2) -> add(activate X1, activate X2)}
       Open
      
      SCC (4):
       Strict:
        {activate# n__fib1(X1, X2) -> activate# X1,
         activate# n__fib1(X1, X2) -> activate# X2,
          activate# n__add(X1, X2) -> activate# X1,
          activate# n__add(X1, X2) -> activate# 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, n__add(X, Y))),
                    fib1(X1, X2) -> n__fib1(X1, X2),
                           fib N -> sel(N, fib1(s 0(), s 0())),
                     add(X1, X2) -> n__add(X1, X2),
                     add(s X, Y) -> s add(X, Y),
                     add(0(), X) -> X,
                      activate X -> X,
        activate n__fib1(X1, X2) -> fib1(activate X1, activate X2),
         activate n__add(X1, X2) -> add(activate X1, activate X2)}
       Open
      
      SCC (1):
       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, n__add(X, Y))),
                    fib1(X1, X2) -> n__fib1(X1, X2),
                           fib N -> sel(N, fib1(s 0(), s 0())),
                     add(X1, X2) -> n__add(X1, X2),
                     add(s X, Y) -> s add(X, Y),
                     add(0(), X) -> X,
                      activate X -> X,
        activate n__fib1(X1, X2) -> fib1(activate X1, activate X2),
         activate n__add(X1, X2) -> add(activate X1, activate X2)}
       Open