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

CR(S):
see below.

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

CP(R):