Termination w.r.t. Q of the following Term Rewriting System could not be shown:

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

f2(f2(x, a), a) -> f2(f2(f2(a, f2(a, a)), a), x)

Q is empty.


QTRS
  ↳ DependencyPairsProof

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

f2(f2(x, a), a) -> f2(f2(f2(a, f2(a, a)), a), x)

Q is empty.

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

F2(f2(x, a), a) -> F2(a, a)
F2(f2(x, a), a) -> F2(f2(f2(a, f2(a, a)), a), x)
F2(f2(x, a), a) -> F2(a, f2(a, a))
F2(f2(x, a), a) -> F2(f2(a, f2(a, a)), a)

The TRS R consists of the following rules:

f2(f2(x, a), a) -> f2(f2(f2(a, f2(a, a)), a), x)

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

↳ QTRS
  ↳ DependencyPairsProof
QDP
      ↳ DependencyGraphProof

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

F2(f2(x, a), a) -> F2(a, a)
F2(f2(x, a), a) -> F2(f2(f2(a, f2(a, a)), a), x)
F2(f2(x, a), a) -> F2(a, f2(a, a))
F2(f2(x, a), a) -> F2(f2(a, f2(a, a)), a)

The TRS R consists of the following rules:

f2(f2(x, a), a) -> f2(f2(f2(a, f2(a, a)), a), x)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph contains 1 SCC with 3 less nodes.

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ DependencyGraphProof
QDP

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

F2(f2(x, a), a) -> F2(f2(f2(a, f2(a, a)), a), x)

The TRS R consists of the following rules:

f2(f2(x, a), a) -> f2(f2(f2(a, f2(a, a)), a), x)

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