---- CR(R cup S)
---- [Klein and Hirokawa, 2012]
R:
a(b(x),y) -> a(x,b(x))
S:
a(f(x),y) -> f(a(f(y),x))
a(g(x),x) -> g(b(g(x)))
CP_S(R):

CR(S):
see below.

---- CR(R cup S)
---- [Klein and Hirokawa, 2012]
R:
a(g(x),x) -> g(b(g(x)))
S:
a(f(x),y) -> f(a(f(y),x))
CP_S(R):

CR(S):
see below.

---- CR(R)
---- [Hirokawa and Middeldorp, 2011]
R:
a(f(x),y) -> f(a(f(y),x))
CPS'(R):

CP(R):