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(g1(X), Y) -> f2(X, f2(g1(X), Y))

Q is empty.


QTRS
  ↳ Non-Overlap Check

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

f2(g1(X), Y) -> f2(X, f2(g1(X), Y))

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(g1(X), Y) -> f2(X, f2(g1(X), Y))

The set Q consists of the following terms:

f2(g1(x0), x1)


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

F2(g1(X), Y) -> F2(X, f2(g1(X), Y))
F2(g1(X), Y) -> F2(g1(X), Y)

The TRS R consists of the following rules:

f2(g1(X), Y) -> f2(X, f2(g1(X), Y))

The set Q consists of the following terms:

f2(g1(x0), x1)

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

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

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

F2(g1(X), Y) -> F2(X, f2(g1(X), Y))
F2(g1(X), Y) -> F2(g1(X), Y)

The TRS R consists of the following rules:

f2(g1(X), Y) -> f2(X, f2(g1(X), Y))

The set Q consists of the following terms:

f2(g1(x0), x1)

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(g1(X), Y) -> F2(X, f2(g1(X), Y))
Used argument filtering: F2(x1, x2)  =  x1
g1(x1)  =  g1(x1)
f2(x1, x2)  =  f
Used ordering: Quasi Precedence: trivial


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

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

F2(g1(X), Y) -> F2(g1(X), Y)

The TRS R consists of the following rules:

f2(g1(X), Y) -> f2(X, f2(g1(X), Y))

The set Q consists of the following terms:

f2(g1(x0), x1)

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