Termination w.r.t. Q of the following Term Rewriting System could be proven:

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

app2(f, a) -> app2(f, b)
app2(g, b) -> app2(g, a)

Q is empty.


QTRS
  ↳ Non-Overlap Check

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

app2(f, a) -> app2(f, b)
app2(g, b) -> app2(g, a)

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:

app2(f, a) -> app2(f, b)
app2(g, b) -> app2(g, a)

The set Q consists of the following terms:

app2(f, a)
app2(g, b)


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

APP2(g, b) -> APP2(g, a)
APP2(f, a) -> APP2(f, b)

The TRS R consists of the following rules:

app2(f, a) -> app2(f, b)
app2(g, b) -> app2(g, a)

The set Q consists of the following terms:

app2(f, a)
app2(g, b)

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

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

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

APP2(g, b) -> APP2(g, a)
APP2(f, a) -> APP2(f, b)

The TRS R consists of the following rules:

app2(f, a) -> app2(f, b)
app2(g, b) -> app2(g, a)

The set Q consists of the following terms:

app2(f, a)
app2(g, b)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph contains 0 SCCs with 2 less nodes.