YES

TRS:

  fib(N) -> sel(N,fib1(s(0()),s(0())))
  fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
  add(0(),X) -> X
  add(s(X),Y) -> s(add(X,Y))
  sel(0(),cons(X,XS)) -> X
  sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
  fib1(X1,X2) -> n__fib1(X1,X2)
  activate(n__fib1(X1,X2)) -> fib1(X1,X2)
  activate(X) -> X

max/plus interpretations on N:

  fib_A(x1) = max{14, 11}
  fib#_A(x1) = max{17, 12 + x1}
  sel_A(x1,x2) = max{14, 13, 3 + x2}
  sel#_A(x1,x2) = max{16, 17, 6 + x2}
  fib1_A(x1,x2) = max{5, -3 + x1, -3 + x2}
  fib1#_A(x1,x2) = max{17, 1 + x1, -2 + x2}
  s_A(x1) = max{12, 13}
  s#_A(x1) = max{17, -4}
  0_A = 1
  0#_A = 0
  cons_A(x1,x2) = max{1, -3 + x1, 3 + x2}
  cons#_A(x1,x2) = max{17, -3, 3 + x2}
  n__fib1_A(x1,x2) = max{1, -6 + x1, -6 + x2}
  n__fib1#_A(x1,x2) = max{17, -3, 1}
  add_A(x1,x2) = max{5, x1, x2}
  add#_A(x1,x2) = max{0, 17, -3}
  activate_A(x1) = max{11, 3 + x1}
  activate#_A(x1) = max{17, 8 + x1}

precedence:

  fib > sel = 0 > activate > fib1 > cons = n__fib1 = add > s