YES

TRS:

  fib(0()) -> 0()
  fib(s(0())) -> s(0())
  fib(s(s(0()))) -> s(0())
  fib(s(s(x))) -> sp(g(x))
  g(0()) -> pair(s(0()),0())
  g(s(0())) -> pair(s(0()),s(0()))
  g(s(x)) -> np(g(x))
  sp(pair(x,y)) -> +(x,y)
  np(pair(x,y)) -> pair(+(x,y),x)
  +(x,0()) -> x
  +(x,s(y)) -> s(+(x,y))

max/plus interpretations on N:

  fib_A(x1) = max{9, 0}
  fib#_A(x1) = max{3, 3 + x1}
  0_A = 1
  0#_A = 5
  s_A(x1) = max{6, 3}
  s#_A(x1) = max{0, 4}
  sp_A(x1) = max{5, 9 + x1}
  sp#_A(x1) = max{5, 2 + x1}
  g_A(x1) = max{0, -9}
  g#_A(x1) = max{8, 2}
  pair_A(x1,x2) = max{0, -6 + x1, -7}
  pair#_A(x1,x2) = max{6, 5, 6}
  np_A(x1) = max{0, x1}
  np#_A(x1) = max{1, 7}
  +_A(x1,x2) = max{6, x1, 3}
  +#_A(x1,x2) = max{4, 4, -6}

precedence:

  g = np > 0 = sp = pair > fib = + > s