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 LPO with precedence:

  fib > 0 > + > dfib > s
)