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:

h1(f1(f1(x))) -> h1(f1(g1(f1(x))))
f1(g1(f1(x))) -> f1(f1(x))

Q is empty.


QTRS
  ↳ DependencyPairsProof

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

h1(f1(f1(x))) -> h1(f1(g1(f1(x))))
f1(g1(f1(x))) -> f1(f1(x))

Q is empty.

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

H1(f1(f1(x))) -> H1(f1(g1(f1(x))))
H1(f1(f1(x))) -> F1(g1(f1(x)))
F1(g1(f1(x))) -> F1(f1(x))

The TRS R consists of the following rules:

h1(f1(f1(x))) -> h1(f1(g1(f1(x))))
f1(g1(f1(x))) -> f1(f1(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:

H1(f1(f1(x))) -> H1(f1(g1(f1(x))))
H1(f1(f1(x))) -> F1(g1(f1(x)))
F1(g1(f1(x))) -> F1(f1(x))

The TRS R consists of the following rules:

h1(f1(f1(x))) -> h1(f1(g1(f1(x))))
f1(g1(f1(x))) -> f1(f1(x))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph contains 1 SCC with 2 less nodes.

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ DependencyGraphProof
QDP

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

H1(f1(f1(x))) -> H1(f1(g1(f1(x))))

The TRS R consists of the following rules:

h1(f1(f1(x))) -> h1(f1(g1(f1(x))))
f1(g1(f1(x))) -> f1(f1(x))

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