YES

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

CP(R):


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

CR(C): see below.

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