(0) Obligation:
Clauses:p(.(A, [])) :- l(.(A, [])).
r(1).
l([]).
l(.(H, T)) :- ','(r(H), l(T)).
Queries:
p(a).
(1) PrologToPrologProblemTransformerProof (SOUND transformation)
Built Prolog problem from termination graph.
(2) Obligation:
Clauses:p1(.(1, [])).
Queries:
p1(a).
(3) PrologToPiTRSProof (SOUND transformation)
We use the technique of [LOPSTR]. With regard to the inferred argument filtering the predicates were used in the following modes:Transforming Prolog into the following Term Rewriting System:
Pi-finite rewrite system:
The TRS R consists of the following rules:
p1_in_a(.(1, [])) → p1_out_a(.(1, []))
The argument filtering Pi contains the following mapping:
p1_in_a(x1) = p1_in_a
p1_out_a(x1) = p1_out_a(x1)
Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog
(4) Obligation:
Pi-finite rewrite system:The TRS R consists of the following rules:
p1_in_a(.(1, [])) → p1_out_a(.(1, []))
The argument filtering Pi contains the following mapping:
p1_in_a(x1) = p1_in_a
p1_out_a(x1) = p1_out_a(x1)
(5) 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:
p1_in_a(.(1, [])) → p1_out_a(.(1, []))
The argument filtering Pi contains the following mapping:
p1_in_a(x1) = p1_in_a
p1_out_a(x1) = p1_out_a(x1)
We have to consider all (P,R,Pi)-chains
(6) Obligation:
Pi DP problem:P is empty.
The TRS R consists of the following rules:
p1_in_a(.(1, [])) → p1_out_a(.(1, []))
The argument filtering Pi contains the following mapping:
p1_in_a(x1) = p1_in_a
p1_out_a(x1) = p1_out_a(x1)
We have to consider all (P,R,Pi)-chains