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:

app(app(map_1, f), app(app(cons, h), t)) → app(app(cons, app(f, h)), app(app(map_1, f), t))
app(app(app(map_2, f), c), app(app(cons, h), t)) → app(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t))
app(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → app(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t))

Q is empty.


↳ QTRS
  ↳ DependencyPairsProof

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

app(app(map_1, f), app(app(cons, h), t)) → app(app(cons, app(f, h)), app(app(map_1, f), t))
app(app(app(map_2, f), c), app(app(cons, h), t)) → app(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t))
app(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → app(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t))

Q is empty.

Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(app(app(app(map_3, f), g), c), t)
APP(app(map_1, f), app(app(cons, h), t)) → APP(app(map_1, f), t)
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(app(f, g), h)
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t))
APP(app(map_1, f), app(app(cons, h), t)) → APP(f, h)
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t))
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(app(app(f, g), h), c)
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(f, g)
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(f, h)
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(cons, app(app(f, h), c))
APP(app(map_1, f), app(app(cons, h), t)) → APP(app(cons, app(f, h)), app(app(map_1, f), t))
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(cons, app(app(app(f, g), h), c))
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(app(app(map_2, f), c), t)
APP(app(map_1, f), app(app(cons, h), t)) → APP(cons, app(f, h))
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(app(f, h), c)

The TRS R consists of the following rules:

app(app(map_1, f), app(app(cons, h), t)) → app(app(cons, app(f, h)), app(app(map_1, f), t))
app(app(app(map_2, f), c), app(app(cons, h), t)) → app(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t))
app(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → app(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t))

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:

APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(app(app(app(map_3, f), g), c), t)
APP(app(map_1, f), app(app(cons, h), t)) → APP(app(map_1, f), t)
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(app(f, g), h)
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t))
APP(app(map_1, f), app(app(cons, h), t)) → APP(f, h)
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t))
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(app(app(f, g), h), c)
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(f, g)
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(f, h)
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(cons, app(app(f, h), c))
APP(app(map_1, f), app(app(cons, h), t)) → APP(app(cons, app(f, h)), app(app(map_1, f), t))
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(cons, app(app(app(f, g), h), c))
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(app(app(map_2, f), c), t)
APP(app(map_1, f), app(app(cons, h), t)) → APP(cons, app(f, h))
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(app(f, h), c)

The TRS R consists of the following rules:

app(app(map_1, f), app(app(cons, h), t)) → app(app(cons, app(f, h)), app(app(map_1, f), t))
app(app(app(map_2, f), c), app(app(cons, h), t)) → app(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t))
app(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → app(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 7 less nodes.

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ DependencyGraphProof
        ↳ QDP

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

APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(app(app(app(map_3, f), g), c), t)
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(app(f, g), h)
APP(app(map_1, f), app(app(cons, h), t)) → APP(app(map_1, f), t)
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(app(app(map_2, f), c), t)
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(app(f, h), c)
APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → APP(app(app(f, g), h), c)
APP(app(map_1, f), app(app(cons, h), t)) → APP(f, h)
APP(app(app(map_2, f), c), app(app(cons, h), t)) → APP(f, h)

The TRS R consists of the following rules:

app(app(map_1, f), app(app(cons, h), t)) → app(app(cons, app(f, h)), app(app(map_1, f), t))
app(app(app(map_2, f), c), app(app(cons, h), t)) → app(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t))
app(app(app(app(map_3, f), g), c), app(app(cons, h), t)) → app(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t))

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