YES

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

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

  fib_A(x1) = 0
  0_A = 0
  s_A(x1) = x1
  +_A(x1,x2) = x1
  dfib_A(x1) = 1
  -_A(x1,x2) = x1
  p_A(x1) = x1
  0#_A = 0
  +#_A(x1,x2) = x2
  -#_A(x1,x2) = x2
  p#_A(x1) = x1

and precedence:

p > dfib > fib > + > s > - > 0
)