Consider following rules:

1) append([], Y, Y).
2) append([H|X], Y, [H|Z]) :- append(X, Y, Z).
3) prefix(X, Z) :- append(X, Y, Z).
4) suffix(Y, Z) :- append(X, Y, Z).

and the query

suffix([c, d, e], [a, b, c, d, e]).     

which we can easily see is 'YES' since the first list is indeed a
suffix of the second list.

Now we will trace it.

Rules 1, 2, and 3 definitely do not apply.  Let's try rule 4, plugging
in what we know for the given variables:

4)  suffix([c, d, e], [a, b, c, d, e]) :- append(X, [c, d, e], [a, b, c, d, e]).
    by letting Y = [c, d, e] and Z = [a, b, c, d, e]

So our suffix query is true if the right hand side (the append) is true.  Now
we need to test the append clause the same way.  Rule 1 does not apply since
[c, d, e] is not equal to [a, b, c, d, e], though it would be possible to make
X = [].  Let's try rule 2, again plugging in what we know for the given
variables:

2)  append([a|X], [c, d, e], [a|b, c, d, e]) :- append(X, [c, d, e], [b, c, d, e]).
    by letting H = a, Y = [c, d, e], and Z = [b, c, d, e]

So our left hand side append is true if the right hand side append is true.  Now
we need to test the right hand side append.  Rule 1 does not apply since
[c, d, e] is not equal to [b, c, d, e], though it would be possible to make
X = [].  Let's try rule 2, again plugging in what we know for the given
variables:

2)  append([b|X], [c, d, e], [b|c, d, e]) :- append(X, [c, d, e], [c, d, e]).
    by letting H = b, Y = [c, d, e], and Z = [c, d, e]

So our left hand side append is true if the right hand side append is true.  Now
we need to test the right hand side append.  Guess what, rule 1 applies!  Here it
is, again plugging in what we know for the given variables:

1)  append([], [c, d, e], [c, d, e]).
    by letting X = [] and Y = [c, d, e]

This means the preceding two appends are true and ultimately the original suffix is
true also, and we get the answer 'yes'.