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:

app2(app2(map_1, f), app2(app2(cons, h), t)) -> app2(app2(cons, app2(f, h)), app2(app2(map_1, f), t))
app2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(f, h), c)), app2(app2(app2(map_2, f), c), t))
app2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(app2(f, g), h), c)), app2(app2(app2(app2(map_3, f), g), c), t))

Q is empty.


↳ QTRS
  ↳ Non-Overlap Check

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

app2(app2(map_1, f), app2(app2(cons, h), t)) -> app2(app2(cons, app2(f, h)), app2(app2(map_1, f), t))
app2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(f, h), c)), app2(app2(app2(map_2, f), c), t))
app2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(app2(f, g), h), c)), app2(app2(app2(app2(map_3, f), g), c), t))

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(app2(map_1, f), app2(app2(cons, h), t)) -> app2(app2(cons, app2(f, h)), app2(app2(map_1, f), t))
app2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(f, h), c)), app2(app2(app2(map_2, f), c), t))
app2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(app2(f, g), h), c)), app2(app2(app2(app2(map_3, f), g), c), t))

The set Q consists of the following terms:

app2(app2(map_1, x0), app2(app2(cons, x1), x2))
app2(app2(app2(map_2, x0), x1), app2(app2(cons, x2), x3))
app2(app2(app2(app2(map_3, x0), g), x1), app2(app2(cons, x2), x3))


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

APP2(app2(map_1, f), app2(app2(cons, h), t)) -> APP2(app2(map_1, f), t)
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(app2(app2(map_2, f), c), t)
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(app2(cons, app2(app2(app2(f, g), h), c)), app2(app2(app2(app2(map_3, f), g), c), t))
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(f, h)
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(app2(app2(f, g), h), c)
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(app2(f, g), h)
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(app2(f, h), c)
APP2(app2(map_1, f), app2(app2(cons, h), t)) -> APP2(cons, app2(f, h))
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(cons, app2(app2(f, h), c))
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(app2(cons, app2(app2(f, h), c)), app2(app2(app2(map_2, f), c), t))
APP2(app2(map_1, f), app2(app2(cons, h), t)) -> APP2(app2(cons, app2(f, h)), app2(app2(map_1, f), t))
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(cons, app2(app2(app2(f, g), h), c))
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(app2(app2(app2(map_3, f), g), c), t)
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(f, g)
APP2(app2(map_1, f), app2(app2(cons, h), t)) -> APP2(f, h)

The TRS R consists of the following rules:

app2(app2(map_1, f), app2(app2(cons, h), t)) -> app2(app2(cons, app2(f, h)), app2(app2(map_1, f), t))
app2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(f, h), c)), app2(app2(app2(map_2, f), c), t))
app2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(app2(f, g), h), c)), app2(app2(app2(app2(map_3, f), g), c), t))

The set Q consists of the following terms:

app2(app2(map_1, x0), app2(app2(cons, x1), x2))
app2(app2(app2(map_2, x0), x1), app2(app2(cons, x2), x3))
app2(app2(app2(app2(map_3, x0), g), x1), app2(app2(cons, x2), x3))

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(app2(map_1, f), app2(app2(cons, h), t)) -> APP2(app2(map_1, f), t)
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(app2(app2(map_2, f), c), t)
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(app2(cons, app2(app2(app2(f, g), h), c)), app2(app2(app2(app2(map_3, f), g), c), t))
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(f, h)
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(app2(app2(f, g), h), c)
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(app2(f, g), h)
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(app2(f, h), c)
APP2(app2(map_1, f), app2(app2(cons, h), t)) -> APP2(cons, app2(f, h))
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(cons, app2(app2(f, h), c))
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(app2(cons, app2(app2(f, h), c)), app2(app2(app2(map_2, f), c), t))
APP2(app2(map_1, f), app2(app2(cons, h), t)) -> APP2(app2(cons, app2(f, h)), app2(app2(map_1, f), t))
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(cons, app2(app2(app2(f, g), h), c))
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(app2(app2(app2(map_3, f), g), c), t)
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(f, g)
APP2(app2(map_1, f), app2(app2(cons, h), t)) -> APP2(f, h)

The TRS R consists of the following rules:

app2(app2(map_1, f), app2(app2(cons, h), t)) -> app2(app2(cons, app2(f, h)), app2(app2(map_1, f), t))
app2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(f, h), c)), app2(app2(app2(map_2, f), c), t))
app2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(app2(f, g), h), c)), app2(app2(app2(app2(map_3, f), g), c), t))

The set Q consists of the following terms:

app2(app2(map_1, x0), app2(app2(cons, x1), x2))
app2(app2(app2(map_2, x0), x1), app2(app2(cons, x2), x3))
app2(app2(app2(app2(map_3, x0), g), x1), app2(app2(cons, x2), x3))

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph contains 1 SCC with 7 less nodes.

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

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

APP2(app2(map_1, f), app2(app2(cons, h), t)) -> APP2(app2(map_1, f), t)
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(app2(app2(map_2, f), c), t)
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(f, h)
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(app2(app2(f, g), h), c)
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(app2(f, g), h)
APP2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> APP2(app2(app2(app2(map_3, f), g), c), t)
APP2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> APP2(app2(f, h), c)
APP2(app2(map_1, f), app2(app2(cons, h), t)) -> APP2(f, h)

The TRS R consists of the following rules:

app2(app2(map_1, f), app2(app2(cons, h), t)) -> app2(app2(cons, app2(f, h)), app2(app2(map_1, f), t))
app2(app2(app2(map_2, f), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(f, h), c)), app2(app2(app2(map_2, f), c), t))
app2(app2(app2(app2(map_3, f), g), c), app2(app2(cons, h), t)) -> app2(app2(cons, app2(app2(app2(f, g), h), c)), app2(app2(app2(app2(map_3, f), g), c), t))

The set Q consists of the following terms:

app2(app2(map_1, x0), app2(app2(cons, x1), x2))
app2(app2(app2(map_2, x0), x1), app2(app2(cons, x2), x3))
app2(app2(app2(app2(map_3, x0), g), x1), app2(app2(cons, x2), x3))

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