YES

TRS:

  f(0()) -> 0()
  f(s(0())) -> s(0())
  f(s(s(x))) -> p(h(g(x)))
  g(0()) -> pair(s(0()),s(0()))
  g(s(x)) -> h(g(x))
  h(x) -> pair(+(p(x),q(x)),p(x))
  p(pair(x,y)) -> x
  q(pair(x,y)) -> y
  +(x,0()) -> x
  +(x,s(y)) -> s(+(x,y))
  f(s(s(x))) -> +(p(g(x)),q(g(x)))
  g(s(x)) -> pair(+(p(g(x)),q(g(x))),p(g(x)))

max/plus interpretations on N:

  f_A(x1) = max{7, 8}
  f#_A(x1) = max{8, 9 + x1}
  0_A = 8
  0#_A = 9
  s_A(x1) = max{1, 7}
  s#_A(x1) = max{0, 3}
  p_A(x1) = max{8, -2 + x1}
  p#_A(x1) = max{2, 0}
  h_A(x1) = max{10, x1}
  h#_A(x1) = max{12, 14}
  g_A(x1) = max{1, 10}
  g#_A(x1) = max{1, 15}
  pair_A(x1,x2) = max{10, 2 + x1, 2 + x2}
  pair#_A(x1,x2) = max{14, 14, 14}
  +_A(x1,x2) = max{8, x1, 7}
  +#_A(x1,x2) = max{11, 11, 4}
  q_A(x1) = max{1, -2 + x1}
  q#_A(x1) = max{13, 4}

precedence:

  f > h > 0 = + = q > s > p = pair > g