YES

# strong closedness (Huet 1980)

Consider the left-linear TRS R:

  W(W(x)) -> W(x)
  B(I(x)) -> W(x)
  W(B(x)) -> B(x)
  F(H(x),y) -> F(H(x),G(y))
  F(x,I(y)) -> F(G(x),I(y))
  G(x) -> x

R is linear and every critical pair is strongly closed