How expensive is this test? What algorithm is used?

(I'm trying to implement it on the "Prolog surface" and it's relatively complex)

Examples:

?- acyclic_term([1,2,3]).
true.

?- acyclic_term([1,2,3|X]).
true.

?- acyclic_term([1,2,3|foo]).
true.

?- X=[1,2,3|X],acyclic_term(X).
false.