Termination w.r.t. Q proof of /home/nowonder/forschung/aprove/satrung/aprove/lpar14/nonterminSLASHCSRSLASHEx4_7_77

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:

zeros -> cons₂(0, zeros)
tail₁(cons₂(X, XS)) -> XS

Q is empty.

↳ QTRS

  ↳ Non-Overlap Check

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

zeros -> cons₂(0, zeros)
tail₁(cons₂(X, XS)) -> XS

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:

zeros -> cons₂(0, zeros)
tail₁(cons₂(X, XS)) -> XS

The set Q consists of the following terms:

zeros
tail₁(cons₂(x0, x1))

Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

ZEROS -> ZEROS

The TRS R consists of the following rules:

zeros -> cons₂(0, zeros)
tail₁(cons₂(X, XS)) -> XS

The set Q consists of the following terms:

zeros
tail₁(cons₂(x0, x1))

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

↳ QTRS

  ↳ Non-Overlap Check

    ↳ QTRS

      ↳ DependencyPairsProof

        ↳ QDP

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

ZEROS -> ZEROS

The TRS R consists of the following rules:

zeros -> cons₂(0, zeros)
tail₁(cons₂(X, XS)) -> XS

The set Q consists of the following terms:

zeros
tail₁(cons₂(x0, x1))

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