(0) Obligation:

Clauses:

p(b).
p(a) :- p1(X).
p1(b) :- !.
p1(a) :- p1(X).

Queries:

p(g).

(1) PrologToPrologProblemTransformerProof (SOUND transformation)

Built Prolog problem from termination graph.

(2) Obligation:

Clauses:

p11(b).
p11(a).

Queries:

p11(g).

(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:

p11_in_g(b) → p11_out_g(b)
p11_in_g(a) → p11_out_g(a)

The argument filtering Pi contains the following mapping:
p11_in_g(x1)  =  p11_in_g(x1)
b  =  b
p11_out_g(x1)  =  p11_out_g
a  =  a

Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

(4) Obligation:

Pi-finite rewrite system:
The TRS R consists of the following rules:

p11_in_g(b) → p11_out_g(b)
p11_in_g(a) → p11_out_g(a)

The argument filtering Pi contains the following mapping:
p11_in_g(x1)  =  p11_in_g(x1)
b  =  b
p11_out_g(x1)  =  p11_out_g
a  =  a

(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:

p11_in_g(b) → p11_out_g(b)
p11_in_g(a) → p11_out_g(a)

The argument filtering Pi contains the following mapping:
p11_in_g(x1)  =  p11_in_g(x1)
b  =  b
p11_out_g(x1)  =  p11_out_g
a  =  a

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:

p11_in_g(b) → p11_out_g(b)
p11_in_g(a) → p11_out_g(a)

The argument filtering Pi contains the following mapping:
p11_in_g(x1)  =  p11_in_g(x1)
b  =  b
p11_out_g(x1)  =  p11_out_g
a  =  a

We have to consider all (P,R,Pi)-chains

(7) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,R,Pi) chain.

(8) TRUE