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

Q is empty.


↳ QTRS
  ↳ Non-Overlap Check

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

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

Q is empty.

The TRS is non-overlapping. Hence, we can switch to innermost.

↳ QTRS
  ↳ Non-Overlap Check
    ↳ QTRS
      ↳ DependencyPairsProof

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

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

The set Q consists of the following terms:

f2(a, f2(f2(a, a), x0))


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

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

The TRS R consists of the following rules:

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

The set Q consists of the following terms:

f2(a, f2(f2(a, a), x0))

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

↳ QTRS
  ↳ Non-Overlap Check
    ↳ QTRS
      ↳ DependencyPairsProof
        ↳ QDP
          ↳ DependencyGraphProof

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

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

The TRS R consists of the following rules:

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

The set Q consists of the following terms:

f2(a, f2(f2(a, a), x0))

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

↳ QTRS
  ↳ Non-Overlap Check
    ↳ QTRS
      ↳ DependencyPairsProof
        ↳ QDP
          ↳ DependencyGraphProof
            ↳ QDP

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

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

The TRS R consists of the following rules:

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

The set Q consists of the following terms:

f2(a, f2(f2(a, a), x0))

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