---- CR(R cup S)
---- [Klein and Hirokawa, 2012]
R:
f(x,x) -> s(s(x))
S:
infty() -> s(infty())
CP_S(R):

CR(S):
see below.

---- CR(R)
---- [Hirokawa and Middeldorp, 2011]
R:
infty() -> s(infty())
CPS'(R):

CP(R):