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:

f1(g1(a)) -> a
f1(f1(x)) -> b
g1(x) -> f1(g1(x))

Q is empty.


QTRS
  ↳ DependencyPairsProof

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

f1(g1(a)) -> a
f1(f1(x)) -> b
g1(x) -> f1(g1(x))

Q is empty.

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

G1(x) -> F1(g1(x))
G1(x) -> G1(x)

The TRS R consists of the following rules:

f1(g1(a)) -> a
f1(f1(x)) -> b
g1(x) -> f1(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:

G1(x) -> F1(g1(x))
G1(x) -> G1(x)

The TRS R consists of the following rules:

f1(g1(a)) -> a
f1(f1(x)) -> b
g1(x) -> f1(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:

G1(x) -> G1(x)

The TRS R consists of the following rules:

f1(g1(a)) -> a
f1(f1(x)) -> b
g1(x) -> f1(g1(x))

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