(0) Obligation:

Clauses:

list([]).
list(X) :- ','(no(empty(X)), ','(tail(X, T), list(T))).
tail([], []).
tail(.(X, Xs), Xs).
empty(X).
no(X) :- ','(X, ','(!, failure(a))).
no(X1).
failure(b).

Query: list(g)

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph DT10.

(2) Obligation:

Triples:


Clauses:


Afs:

(3) TPisEmptyProof (EQUIVALENT transformation)

There are no more dependency triples. Hence, the dependency triple problem trivially terminates.

(4) YES