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:

f3(g1(x), x, y) -> f3(y, y, g1(y))
g1(g1(x)) -> g1(x)

Q is empty.


QTRS
  ↳ DependencyPairsProof

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

f3(g1(x), x, y) -> f3(y, y, g1(y))
g1(g1(x)) -> g1(x)

Q is empty.

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

F3(g1(x), x, y) -> F3(y, y, g1(y))
F3(g1(x), x, y) -> G1(y)

The TRS R consists of the following rules:

f3(g1(x), x, y) -> f3(y, y, g1(y))
g1(g1(x)) -> g1(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:

F3(g1(x), x, y) -> F3(y, y, g1(y))
F3(g1(x), x, y) -> G1(y)

The TRS R consists of the following rules:

f3(g1(x), x, y) -> f3(y, y, g1(y))
g1(g1(x)) -> g1(x)

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

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ DependencyGraphProof
QDP

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

F3(g1(x), x, y) -> F3(y, y, g1(y))

The TRS R consists of the following rules:

f3(g1(x), x, y) -> f3(y, y, g1(y))
g1(g1(x)) -> g1(x)

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