MAYBE
Time: 0.002320
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:
  DP:
   {   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)}
  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)}
  UR:
   {              fib1(X, Y) -> cons(X, n__fib1(Y, add(X, Y))),
                fib1(X1, X2) -> n__fib1(X1, X2),
                 add(s X, Y) -> s add(X, Y),
                 add(0(), X) -> X,
                  activate X -> X,
    activate n__fib1(X1, X2) -> fib1(X1, X2),
                     a(x, y) -> x,
                     a(x, y) -> y}
   EDG:
    {(sel#(s N, cons(X, XS)) -> activate# XS, activate# n__fib1(X1, X2) -> fib1#(X1, X2))
     (activate# n__fib1(X1, X2) -> fib1#(X1, X2), fib1#(X, 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, 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))}
    STATUS:
     arrows: 0.816327
     SCCS (2):
      Scc:
       {sel#(s N, cons(X, XS)) -> sel#(N, activate XS)}
      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, 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)}
       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, 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)}
       Open