YES

TRS:

  f(f(x,y,z),u,f(x,y,v)) -> f(x,y,f(z,u,v))
  f(x,y,y) -> y
  f(x,y,g(y)) -> x
  f(x,x,y) -> x
  f(g(x),x,y) -> y

linear polynomial interpretations on N:

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

precedence:

  f > g