(0) Obligation:
Clauses:
q :- p(s(s(0))).
p(s(X)) :- p(X).
p(0).
p(s(s(s(0)))) :- p(s(s(s(0)))).
Query: q()
(1) PrologToPiTRSViaGraphTransformerProof (SOUND transformation)
Transformed Prolog program to (Pi-)TRS.
(2) Obligation:
Pi-finite rewrite system:
The TRS R consists of the following rules:
qA_in_ → qA_out_
Pi is empty.
(3) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LOPSTR] we result in the following initial DP problem:
Pi DP problem:
P is empty.
The TRS R consists of the following rules:
qA_in_ → qA_out_
Pi is empty.
We have to consider all (P,R,Pi)-chains
(4) Obligation:
Pi DP problem:
P is empty.
The TRS R consists of the following rules:
qA_in_ → qA_out_
Pi is empty.
We have to consider all (P,R,Pi)-chains
(5) PisEmptyProof (EQUIVALENT transformation)
The TRS P is empty. Hence, there is no (P,R,Pi) chain.
(6) YES