YES

---- CR(R)
---- R : left-linear, C : CR and CP-closing, and Cdup/R : SN
R:
0(1(2(3(4(x))))) -> 0(2(1(3(4(x)))))
0(5(1(2(4(3(x)))))) -> 0(5(2(1(4(3(x))))))
0(5(2(4(1(3(x)))))) -> 0(1(5(2(4(3(x))))))
0(5(3(1(2(4(x)))))) -> 0(1(5(3(2(4(x))))))
0(5(4(1(3(2(x)))))) -> 0(5(4(3(1(2(x))))))

CP(R):


critical-pair-closing system C:


CR(C): see below.

---- CR(R)
---- R is empty.