Let $$

R

and $$

S

be binary relations defined as follows.

$$

R

is defined on $=\{,,,,,,,,\}$

A

$=$

$\{$

a

$,$

b

$,$

c

$,$

d

$,$

e

$,$

f

$,$

g

$,$

h

$,$

i

$\}$

by the following arrow diagram.

$$

S

is defined on $\backslash$times $$

Z

$\backslash$times

Z

by $(,)(,)$

$($

w

$,$

x

$)$

S

$($

y

$,$

z

$)$

if and only if $+$

w

$+$

x

$$

y

$$

z

is even.