YES

---- CR(R)
---- R : left-linear, C : CR and CP-closing, and Cdup/R : SN
R:
Ap(Ap(Ap(S(),x),y),z) -> Ap(Ap(x,z),Ap(y,z))
Ap(Ap(K(),x),y) -> x
Ap(I(),x) -> x

CP(R):


critical-pair-closing system C:


CR(C): see below.

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