Termination w.r.t. Q proof of /tmp/tmpx1erjH/25.trs

Termination w.r.t. Q of the following Term Rewriting System could be proven:

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

g(a) → g(b)
b → f(a, a)
f(a, a) → g(d)

Q is empty.

↳ QTRS

  ↳ Overlay + Local Confluence

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

g(a) → g(b)
b → f(a, a)
f(a, a) → g(d)

Q is empty.

The TRS is overlay and locally confluent. By [19] we can switch to innermost.

↳ QTRS

  ↳ Overlay + Local Confluence

    ↳ QTRS

      ↳ DependencyPairsProof

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

g(a) → g(b)
b → f(a, a)
f(a, a) → g(d)

The set Q consists of the following terms:

g(a)
b
f(a, a)

Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

g(a) → g(b)
b → f(a, a)
f(a, a) → g(d)

The set Q consists of the following terms:

g(a)
b
f(a, a)

We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ Overlay + Local Confluence

    ↳ QTRS

      ↳ DependencyPairsProof

        ↳ QDP

          ↳ DependencyGraphProof

Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

g(a) → g(b)
b → f(a, a)
f(a, a) → g(d)

The set Q consists of the following terms:

g(a)
b
f(a, a)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 0 SCCs with 4 less nodes.