YES

(VAR x y z)
(RULES
  dfib(s(s(x)),y) -> dfib(s(x),dfib(x,y))
  dfib(s(0()),y) -> s(y)
  dfib(0(),y) -> y
  fib(s(s(x))) -> +(fib(x),fib(s(x)))
  fib(s(0())) -> s(0())
  fib(0()) -> 0()
  +(+(x,y),z) -> +(x,+(y,z))
  +(s(x),y) -> s(+(x,y))
  +(0(),x) -> x
)

(COMMENT
Termination is shown by ELPO with interpretations on natural numbers

  +_A(x1,x2) = x2
  0_A = 1
  s_A(x1) = x1
  fib_A(x1) = x1
  dfib_A(x1,x2) = x2
  +#_A(x1,x2) = 0
  0#_A = 0
  s#_A(x1) = 0
  fib#_A(x1) = 0

and precedence:

fib > dfib > + > s > 0
)