YES

# strong closedness (Huet 1980)

Consider the left-linear TRS R:

  a() -> c()
  b() -> c()
  f(a(),b()) -> d()
  f(x,c()) -> f(c(),c())
  f(c(),x) -> f(c(),c())
  d() -> f(a(),c())
  d() -> f(c(),b())

R is linear and every critical pair is strongly closed