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(f2(f2(j, a), b), c), d) -> f2(f2(a, b), f2(f2(a, d), c))

Q is empty.


QTRS
  ↳ Non-Overlap Check

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

f2(f2(f2(f2(j, a), b), c), d) -> f2(f2(a, b), f2(f2(a, d), c))

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(f2(f2(f2(j, a), b), c), d) -> f2(f2(a, b), f2(f2(a, d), c))

The set Q consists of the following terms:

f2(f2(f2(f2(j, x0), x1), x2), x3)


Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

F2(f2(f2(f2(j, a), b), c), d) -> F2(a, d)
F2(f2(f2(f2(j, a), b), c), d) -> F2(f2(a, b), f2(f2(a, d), c))
F2(f2(f2(f2(j, a), b), c), d) -> F2(f2(a, d), c)
F2(f2(f2(f2(j, a), b), c), d) -> F2(a, b)

The TRS R consists of the following rules:

f2(f2(f2(f2(j, a), b), c), d) -> f2(f2(a, b), f2(f2(a, d), c))

The set Q consists of the following terms:

f2(f2(f2(f2(j, x0), x1), x2), x3)

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

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

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

F2(f2(f2(f2(j, a), b), c), d) -> F2(a, d)
F2(f2(f2(f2(j, a), b), c), d) -> F2(f2(a, b), f2(f2(a, d), c))
F2(f2(f2(f2(j, a), b), c), d) -> F2(f2(a, d), c)
F2(f2(f2(f2(j, a), b), c), d) -> F2(a, b)

The TRS R consists of the following rules:

f2(f2(f2(f2(j, a), b), c), d) -> f2(f2(a, b), f2(f2(a, d), c))

The set Q consists of the following terms:

f2(f2(f2(f2(j, x0), x1), x2), x3)

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