YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1,x2) = x1
  f#_A(x1,x2) = x1
  a_A = 0
  a#_A = 2
  b_A = 0
  b#_A = 3
  c_A = 4
  c#_A = 1
  d_A = 1
  d#_A = 0

precedence:

  b > a > c > f > d