YES

TRS:

  f(x,y,w,w,a()) -> g1(x,x,y,w)
  f(x,y,w,a(),a()) -> g1(y,x,x,w)
  f(x,y,a(),a(),w) -> g2(x,y,y,w)
  f(x,y,a(),w,w) -> g2(y,y,x,w)
  g1(x,x,y,a()) -> h(x,y)
  g1(y,x,x,a()) -> h(x,y)
  g2(x,y,y,a()) -> h(x,y)
  g2(y,y,x,a()) -> h(x,y)
  h(x,x) -> x

max/plus interpretations on N:

  f_A(x1,x2,x3,x4,x5) = max{0, x1, x2, x3, x4, x5}
  f#_A(x1,x2,x3,x4,x5) = max{0, x1, x2, x3, x4, x5}
  a_A = 0
  a#_A = 0
  g1_A(x1,x2,x3,x4) = max{0, x1, x2, x3, x4}
  g1#_A(x1,x2,x3,x4) = max{0, x1, x2, x3, x4}
  g2_A(x1,x2,x3,x4) = max{0, x1, x2, x3, x4}
  g2#_A(x1,x2,x3,x4) = max{0, x1, x2, x3, x4}
  h_A(x1,x2) = max{0, x1, x2}
  h#_A(x1,x2) = max{0, x1, x2}

precedence:

  f > a = g1 = g2 > h