YES

---- CR(R)
---- R : left-linear, C : CR and CP-closing, and Cdup/R : SN
R:
b(a(b(b(x)))) -> b(b(b(a(b(x)))))
b(a(a(b(b(x))))) -> b(a(b(b(a(a(b(x)))))))
b(a(a(a(b(b(x)))))) -> b(a(a(b(b(a(a(a(b(x)))))))))

CP(R):
b(a(b(b(b(b(a(b(___y1)))))))) -> b(b(b(a(b(a(b(b(___y1))))))))
b(a(a(b(b(b(b(a(b(___y3))))))))) -> b(a(b(b(a(a(b(a(b(b(___y3))))))))))
b(a(a(a(b(b(b(b(a(b(___y5)))))))))) ->
  b(a(a(b(b(a(a(a(b(a(b(b(___y5))))))))))))
b(a(b(b(a(b(b(a(a(b(___y7)))))))))) -> b(b(b(a(b(a(a(b(b(___y7)))))))))
b(a(a(b(b(a(b(b(a(a(b(___y9))))))))))) ->
  b(a(b(b(a(a(b(a(a(b(b(___y9)))))))))))
b(a(a(a(b(b(a(b(b(a(a(b(___y11)))))))))))) ->
  b(a(a(b(b(a(a(a(b(a(a(b(b(___y11)))))))))))))
b(a(b(b(a(a(b(b(a(a(a(b(___y13)))))))))))) ->
  b(b(b(a(b(a(a(a(b(b(___y13))))))))))
b(a(a(b(b(a(a(b(b(a(a(a(b(___y15))))))))))))) ->
  b(a(b(b(a(a(b(a(a(a(b(b(___y15))))))))))))
b(a(a(a(b(b(a(a(b(b(a(a(a(b(___y17)))))))))))))) ->
  b(a(a(b(b(a(a(a(b(a(a(a(b(b(___y17))))))))))))))

critical-pair-closing system C:
b(a(b(b(x)))) -> b(b(b(a(b(x)))))
b(a(a(b(b(x))))) -> b(a(b(b(a(a(b(x)))))))
b(a(a(a(b(b(x)))))) -> b(a(a(b(b(a(a(a(b(x)))))))))

CR(C): see below.

---- CR(R)
---- R : linear and strongly closed [Huet, 1980]
R:
b(a(b(b(x)))) -> b(b(b(a(b(x)))))
b(a(a(b(b(x))))) -> b(a(b(b(a(a(b(x)))))))
b(a(a(a(b(b(x)))))) -> b(a(a(b(b(a(a(a(b(x)))))))))
CP(R):
b(a(b(b(b(b(a(b(___y19)))))))) -> b(b(b(a(b(a(b(b(___y19))))))))
b(a(a(b(b(b(b(a(b(___y21))))))))) -> b(a(b(b(a(a(b(a(b(b(___y21))))))))))
b(a(a(a(b(b(b(b(a(b(___y23)))))))))) ->
  b(a(a(b(b(a(a(a(b(a(b(b(___y23))))))))))))
b(a(b(b(a(b(b(a(a(b(___y25)))))))))) -> b(b(b(a(b(a(a(b(b(___y25)))))))))
b(a(a(b(b(a(b(b(a(a(b(___y27))))))))))) ->
  b(a(b(b(a(a(b(a(a(b(b(___y27)))))))))))
b(a(a(a(b(b(a(b(b(a(a(b(___y29)))))))))))) ->
  b(a(a(b(b(a(a(a(b(a(a(b(b(___y29)))))))))))))
b(a(b(b(a(a(b(b(a(a(a(b(___y31)))))))))))) ->
  b(b(b(a(b(a(a(a(b(b(___y31))))))))))
b(a(a(b(b(a(a(b(b(a(a(a(b(___y33))))))))))))) ->
  b(a(b(b(a(a(b(a(a(a(b(b(___y33))))))))))))
b(a(a(a(b(b(a(a(b(b(a(a(a(b(___y35)))))))))))))) ->
  b(a(a(b(b(a(a(a(b(a(a(a(b(b(___y35))))))))))))))