YES

TRS:

  f(a(),b()) -> f(a(),c())
  f(c(),d()) -> f(b(),d())

max/plus interpretations on N:

  f_A(x1,x2) = max{0, 2, 1}
  f#_A(x1,x2) = max{1, 2 + x1, 5}
  a_A = 0
  a#_A = 0
  b_A = 1
  b#_A = 5
  c_A = 4
  c#_A = 4
  d_A = 1
  d#_A = 5

precedence:

  c > d > b > f > a