YES

---- CR(R)
---- R : left-linear, C : CR and CP-closing, and Cdup/R : SN
R:
F(G(x,A(),B())) -> x
G(F(H(C(),D())),x,y) -> H(K1(x),K2(y))
K1(A()) -> C()
K2(B()) -> D()

CP(R):
F(H(K1(A()),K2(B()))) -> F(H(C(),D()))

critical-pair-closing system C:
F(G(x,A(),B())) -> x
K1(A()) -> C()
K2(B()) -> D()

CR(C): see below.

---- CR(R)
---- R : linear and strongly closed [Huet, 1980]
R:
F(G(x,A(),B())) -> x
K1(A()) -> C()
K2(B()) -> D()
CP(R):