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

linear polynomial interpretations on N:

  f_A(x1,x2,x3,x4,x5) = x1 + x2 + x3 + x5
  f#_A(x1,x2,x3,x4,x5) = x1 + x2 + x5 + 2
  a_A = 1
  a#_A = 0
  g1_A(x1,x2,x3,x4) = x1 + x3
  g1#_A(x1,x2,x3,x4) = x1 + x3 + 1
  g2_A(x1,x2,x3,x4) = x2
  g2#_A(x1,x2,x3,x4) = x1 + x3 + 1
  h_A(x1,x2) = x2
  h#_A(x1,x2) = 0

precedence:

  f > g1 = g2 > a = h