(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

g(a) → g(b)
bf(a, a)
f(a, a) → g(d)

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:

G(a) → G(b)
G(a) → B
BF(a, a)
F(a, a) → G(d)

The TRS R consists of the following rules:

g(a) → g(b)
bf(a, a)
f(a, a) → g(d)

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 0 SCCs with 4 less nodes.

(4) TRUE