(0) Obligation:
Clauses:thief(john).
thief(X) :- ','(thief(X), !).
Queries:
thief(g).
(1) PrologToDTProblemTransformerProof (SOUND transformation)
Built DT problem from termination graph.
(2) Obligation:
Triples:thief1(T7) :- thief1(T7).
Clauses:
thiefc1(john).
thiefc1(john).
thiefc1(T7) :- thiefc1(T7).
Afs:
thief1(x1) = thief1(x1)
(3) TriplesToPiDPProof (SOUND transformation)
We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:thief1_in: (b)
Transforming TRIPLES into the following Term Rewriting System:
Pi DP problem:
The TRS P consists of the following rules:
THIEF1_IN_G(T7) → U1_G(T7, thief1_in_g(T7))
THIEF1_IN_G(T7) → THIEF1_IN_G(T7)
R is empty.
Pi is empty.
We have to consider all (P,R,Pi)-chains
Infinitary Constructor Rewriting Termination of PiDP implies Termination of TRIPLES
(4) Obligation:
Pi DP problem:The TRS P consists of the following rules:
THIEF1_IN_G(T7) → U1_G(T7, thief1_in_g(T7))
THIEF1_IN_G(T7) → THIEF1_IN_G(T7)
R is empty.
Pi is empty.
We have to consider all (P,R,Pi)-chains
(5) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LOPSTR] contains 1 SCC with 1 less node.(6) Obligation:
Pi DP problem:The TRS P consists of the following rules:
THIEF1_IN_G(T7) → THIEF1_IN_G(T7)
R is empty.
Pi is empty.
We have to consider all (P,R,Pi)-chains
(7) PiDPToQDPProof (EQUIVALENT transformation)
Transforming (infinitary) constructor rewriting Pi-DP problem [LOPSTR] into ordinary QDP problem [LPAR04] by application of Pi.(8) Obligation:
Q DP problem:The TRS P consists of the following rules:
THIEF1_IN_G(T7) → THIEF1_IN_G(T7)
R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.
(9) NonTerminationProof (EQUIVALENT transformation)
We used the non-termination processor [FROCOS05] to show that the DP problem is infinite.Found a loop by semiunifying a rule from P directly.
s = THIEF1_IN_G(T7) evaluates to t =THIEF1_IN_G(T7)
Thus s starts an infinite chain as s semiunifies with t with the following substitutions:
- Matcher: [ ]
- Semiunifier: [ ]
Rewriting sequence
The DP semiunifies directly so there is only one rewrite step from THIEF1_IN_G(T7) to THIEF1_IN_G(T7).