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{1, 3 + x1, 4 + x2, -1, -1, 1}
  f#_A(x1,x2,x3,x4,x5) = max{5, 5, 4 + x2, 5, 0, 5}
  a_A = 1
  a#_A = 0
  g1_A(x1,x2,x3,x4) = max{4, 2, 2 + x2, x3, 1}
  g1#_A(x1,x2,x3,x4) = max{3, -1, -1, -1, 1}
  g2_A(x1,x2,x3,x4) = max{2, 3 + x1, -1, x3, 1}
  g2#_A(x1,x2,x3,x4) = max{3, 3, 4 + x2, 5, 3}
  h_A(x1,x2) = max{3, x1, 1}
  h#_A(x1,x2) = max{2, -2, -2}

precedence:

  f > a = g1 = g2 > h