YES

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

CP(R):


critical-pair-closing system C:
b() -> c()

CR(C): see below.

---- CR(R)
---- R : linear and strongly closed [Huet, 1980]
R:
b() -> c()
CP(R):