YES

TRS:

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

max/plus interpretations on N:

  f_A(x1,x2,x3) = max{2, 1 + x1, 1 + x2, x3}
  f#_A(x1,x2,x3) = max{2, 1 + x1, 1 + x2, x3}
  g_A(x1) = max{2, 1 + x1}
  g#_A(x1) = max{2, 1 + x1}

precedence:

  f > g