(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
a(f, a(f, x)) → a(x, g)
a(x, g) → a(f, a(g, a(f, x)))
Q is empty.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
Q DP problem:
The TRS P consists of the following rules:
A(f, a(f, x)) → A(x, g)
A(x, g) → A(f, a(g, a(f, x)))
A(x, g) → A(g, a(f, x))
A(x, g) → A(f, x)
The TRS R consists of the following rules:
a(f, a(f, x)) → a(x, g)
a(x, g) → a(f, a(g, a(f, x)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
(3) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
A(x, g) → A(f, a(g, a(f, x)))
A(f, a(f, x)) → A(x, g)
A(x, g) → A(f, x)
The TRS R consists of the following rules:
a(f, a(f, x)) → a(x, g)
a(x, g) → a(f, a(g, a(f, x)))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.