YES

TRS:

  fib(0()) -> 0()
  fib(s(0())) -> s(0())
  fib(s(s(x))) -> +(fib(s(x)),fib(x))
  +(x,0()) -> x
  +(x,s(y)) -> s(+(x,y))

max/plus interpretations on N:

  fib_A(x1) = max{0, x1}
  fib#_A(x1) = max{0, x1}
  0_A = 0
  0#_A = 0
  s_A(x1) = max{0, x1}
  s#_A(x1) = max{0, x1}
  +_A(x1,x2) = max{0, x1, x2}
  +#_A(x1,x2) = max{0, x1, x2}

precedence:

  fib > + > s > 0