YES

TRS:

  g(x,y) -> x
  g(x,y) -> y
  f(s(x),y,y) -> f(y,x,s(x))

linear polynomial interpretations on N:

  g_A(x1,x2) = x1 + x2
  g#_A(x1,x2) = x1 + x2
  f_A(x1,x2,x3) = x1 + x3
  f#_A(x1,x2,x3) = x1 + x2
  s_A(x1) = x1 + 1
  s#_A(x1) = 0

precedence:

  f > g = s