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.