YES

# strong closedness (Huet 1980)

Consider the left-linear TRS R:

  f(g(g(x))) -> a()
  f(g(h(x))) -> b()
  f(h(g(x))) -> b()
  f(h(h(x))) -> c()
  g(x) -> h(x)
  a() -> b()
  b() -> c()

R is linear and every critical pair is strongly closed