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

Q is empty.


↳ QTRS
  ↳ DependencyPairsProof

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

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

Q is empty.

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ QDPAfsSolverProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using an argument filtering and a montonic ordering, at least one Dependency Pair of this SCC can be strictly oriented.

F2(a, f2(a, x)) -> F2(b, x)
F2(c, f2(c, x)) -> F2(a, x)
F2(b, f2(b, x)) -> F2(c, x)
Used argument filtering: F2(x1, x2)  =  x2
f2(x1, x2)  =  f1(x2)
a  =  a
c  =  c
b  =  b
Used ordering: Precedence:
trivial



↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ QDPAfsSolverProof
        ↳ QDP

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

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

The TRS R consists of the following rules:

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

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