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 LPO with precedence:

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