YES

TRS:

  f(x,y) -> h(x,y)
  f(x,y) -> h(y,x)
  h(x,x) -> x

linear polynomial interpretations on N:

  f_A(x1,x2) = x1 + x2 + 1
  f#_A(x1,x2) = x1 + x2 + 1
  h_A(x1,x2) = x1 + x2
  h#_A(x1,x2) = x1 + x2

precedence:

  h > f