Example:

obtain_cyclic(L) :- L=[1,2,3,4,5|T],L=[1,2|T].

:- begin_tests(cyclic).

test(01) :- obtain_cyclic(L),cyclic_term(L).
test(02) :- obtain_cyclic([1|L]),cyclic_term(L).
test(03) :- obtain_cyclic([1,2|L]),cyclic_term(L).
test(04) :- obtain_cyclic([1,2,3|L]),cyclic_term(L).
test(05) :- obtain_cyclic([1,2,3,4|L]),cyclic_term(L).
test(06) :- obtain_cyclic([1,2,3,4,5|L]),cyclic_term(L).
test(07) :- obtain_cyclic([1,2,3,4,5,3|L]),cyclic_term(L).
test(08) :- obtain_cyclic([1,2,3,4,5,3,4|L]),cyclic_term(L).
test(09) :- obtain_cyclic([1,2,3,4,5,3,4,5|L]),cyclic_term(L).
test(10) :- obtain_cyclic([1,2,3,4,5,3,4,5,3|L]),cyclic_term(L).
test(11) :- obtain_cyclic([1,2,3,4,5,3,4,5,3,4|L]),cyclic_term(L).
test(12) :- obtain_cyclic([1,2,3,4,5,3,4,5,3,4,5|L]),cyclic_term(L).

:- end_tests(cyclic).

rt(cyclic) :- run_tests(cyclic).

And so:

?- rt(_).
% PL-Unit: cyclic ............ done
% All 12 tests passed
true.

What is the cost of detecting that a term is cyclic (a rational tree)?

Another example, a list which contains itself:

?- list_to_ord_set([X,Y,Z],X).
X = [X, Y, Z].

?- list_to_ord_set([X,Y,Z],X),X=[W|_],W=[WW|_],WW=[WWW|_].
X = W, W = WW, WW = WWW, WWW = [WWW, Y, Z].