YES

TRS:

  f(0(),y) -> y
  f(x,0()) -> x
  f(i(x),y) -> i(x)
  f(f(x,y),z) -> f(x,f(y,z))
  f(g(x,y),z) -> g(f(x,z),f(y,z))
  f(1(),g(x,y)) -> x
  f(2(),g(x,y)) -> y

max/plus interpretations on N:

  f_A(x1,x2) = max{0, x1, x2}
  f#_A(x1,x2) = max{0, x1, x2}
  0_A = 0
  0#_A = 0
  i_A(x1) = max{0, x1}
  i#_A(x1) = max{0, x1}
  g_A(x1,x2) = max{0, x1, x2}
  g#_A(x1,x2) = max{0, x1, x2}
  1_A = 0
  1#_A = 0
  2_A = 0
  2#_A = 0

precedence:

  i > f = 0 = 1 = 2 > g