Is dependent co-arising an "IF AND ONLY IF A THEN B" relation? &quot;IF AND ONLY IF A THEN B&quot; means if you get B you get A, if you get A you get B, if you don't get B you don't get A, and if you don't get A you don't get B.
Does dependent co-arising have the same relation I've mentioned above?

&quot;From ignorance as a requisite condition come fabrications. From fabrications as a requisite condition comes consciousness. From consciousness as a requisite condition comes name-&amp;-form...&quot;


&quot;Now from the remainderless fading &amp; cessation of that very ignorance comes the cessation of fabrications. From the cessation of fabrications comes the cessation of consciousness. From the cessation of consciousness comes the cessation of name-&amp;-form...&quot;

If the answer is &quot;yes&quot; to the above question, as we know an Arahant has ceased the craving without remainder. Then do consciousness, name-&amp;-form, six sense media, contact, and feeling not  present in an Arahant? If these present as effects of past birth's causes, how one can escape from this cycle?
If the answer is &quot;no&quot; to my first question, then is there another dependent co-arising which applies to Arahants? (I suppose there's no such)
I know that dependent co-arising is very complex and hard to understand. But, I've got totally confused here. Please someone help me.
OP: Does dependent co-arising have the same relation I've mentioned above?

Yes.

OP: If the answer is &quot;yes&quot; to the above question, as we know an Arahant has ceased the craving without remainder. Then do
consciousness, name-&amp;-form, six sense media, contact, and feeling not
present in an Arahant?

Please see the quote from SN 22.48 below on the five (non-clinging) aggregates and the five clinging aggregates.
In an Arahant, ignorance ceases, hence the five clinging aggregates also cease, thus collapsing dependent origination nidanas. This means that the nidanas of consciousness, name-and-form, six sense media, contact and feeling  that are tainted with clinging, cease in an Arahant.
However, the five (non-clinging) aggregates remain and continue functioning. This is also implied by Nibbana element with fuel remaining in Iti 44. This is also supported by Ven. Thanissaro's commentary quoted below.
When the Arahant passes away, the five (non-clinging) aggregates cease. This is also implied by Nibbana element without fuel remaining in Iti 44.

OP: If these present as effects of past birth's causes, how one can escape from this cycle?

I don't quite understand this question. From my understanding, the way to escape suffering is by uprooting ignorance through cultivating wisdom through the Noble Eightfold Path.
From SN 22.48 (trans. Ven. Bodhi):

“And what, bhikkhus, are the five aggregates? Whatever kind of form
there is, whether past, future, or present, internal or external,
gross or subtle, inferior or superior, far or near: this is called the
form aggregate. Whatever kind of feeling there is … this is called the
feeling aggregate. Whatever kind of perception there is … this is
called the perception aggregate. Whatever kind of volitional
formations there are … these are called the volitional formations
aggregate. Whatever kind of consciousness there is, whether past,
future, or present, internal or external, gross or subtle, inferior or
superior, far or near: this is called the consciousness aggregate.
These, bhikkhus, are called the five aggregates.
“And what, bhikkhus, are the five aggregates subject to clinging?
Whatever kind of form there is, whether past, future, or present … far
or near, that is tainted, that can be clung to: this is called the
form aggregate subject to clinging. Whatever kind of feeling there is
… that is tainted, that can be clung to: this is called the feeling
aggregate subject to clinging. Whatever kind of perception there is …
that is tainted, that can be clung to: this is called the perception
aggregate subject to clinging. Whatever kind of volitional formations
there are … that are tainted, that can be clung to: these are called
the volitional formations aggregate subject to clinging. Whatever kind
of consciousness there is, whether past, future, or present, internal
or external, gross or subtle, inferior or superior, far or near, that
is tainted, that can be clung to: this is called the consciousness
aggregate subject to clinging. These, bhikkhus, are called the five
aggregates subject to clinging.”

From Iti 44 (trans. Ven. Thanissaro):

This was said by the Blessed One, said by the Arahant, so I have
heard: &quot;Monks, there are these two forms of the Unbinding property.
Which two? The Unbinding property with fuel remaining, &amp; the Unbinding
property with no fuel remaining.
And what is the Unbinding property with fuel remaining? There is the
case where a monk is an arahant whose fermentations have ended, who
has reached fulfillment, finished the task, laid down the burden,
attained the true goal, ended the fetter of becoming, and is released
through right gnosis. His five sense faculties still remain and, owing
to their being intact, he is cognizant of the agreeable &amp; the
disagreeable, and is sensitive to pleasure &amp; pain. His ending of
passion, aversion, &amp; delusion is termed the Unbinding property with
fuel remaining.
And what is the Unbinding property with no fuel remaining? There is
the case where a monk is an arahant whose fermentations have ended,
who has reached fulfillment, finished the task, laid down the burden,
attained the true goal, ended the fetter of becoming, and is released
through right gnosis. For him, all that is sensed, being unrelished,
will grow cold right here. This is termed the Unbinding property with
no fuel remaining.&quot;

Commentary on Iti 44 by Ven. Thanissaro:

With fuel remaining (sa-upadisesa) and with no fuel remaining
(anupadisesa): The analogy here is to a fire. In the first case, the
flames are out, but the embers are still glowing. In the second, the
fire is so thoroughly out that the embers have grown cold. The &quot;fuel&quot;
here is the five aggregates. While the arahant is
still alive, he/she still experiences the five aggregates, but they do
not burn with the fires of passion, aversion, or delusion. When the
arahant passes away, there is no longer any experience of aggregates
here or anywhere else.


From comments:

OP: Five non-clinging aggregates are also conditioned. What is the cause for five non-clinging aggregates? Does that cause lie within the
dependent co-arising?

The origin of the five (non-clinging) aggregates can be found in SN 35.145:

&quot;Now what, monks, is old kamma? The eye is to be seen as old kamma,
fabricated &amp; willed, capable of being felt. The ear... The nose... The
tongue... The body... The intellect is to be seen as old kamma,
fabricated &amp; willed, capable of being felt. This is called old kamma.
&quot;And what is new kamma? Whatever kamma one does now with the body,
with speech, or with the intellect: This is called new kamma.

If the next question is &quot;whose old kamma is it?&quot;, the answer comes from SN 12.17.