Termination w.r.t. Q proof of /home/nowonder/forschung/aprove/satrung/aprove/lpar14/variousSLASH20.trs

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:

s1₁(s1₁(s0₁(s0₁(x)))) -> s0₁(s0₁(s0₁(s1₁(s1₁(s1₁(x))))))

Q is empty.

↳ QTRS

  ↳ Non-Overlap Check

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

s1₁(s1₁(s0₁(s0₁(x)))) -> s0₁(s0₁(s0₁(s1₁(s1₁(s1₁(x))))))

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:

s1₁(s1₁(s0₁(s0₁(x)))) -> s0₁(s0₁(s0₁(s1₁(s1₁(s1₁(x))))))

The set Q consists of the following terms:

s1₁(s1₁(s0₁(s0₁(x0))))

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

S1₁(s1₁(s0₁(s0₁(x)))) -> S1₁(x)
S1₁(s1₁(s0₁(s0₁(x)))) -> S1₁(s1₁(x))
S1₁(s1₁(s0₁(s0₁(x)))) -> S1₁(s1₁(s1₁(x)))

The TRS R consists of the following rules:

s1₁(s1₁(s0₁(s0₁(x)))) -> s0₁(s0₁(s0₁(s1₁(s1₁(s1₁(x))))))

The set Q consists of the following terms:

s1₁(s1₁(s0₁(s0₁(x0))))

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:

S1₁(s1₁(s0₁(s0₁(x)))) -> S1₁(x)
S1₁(s1₁(s0₁(s0₁(x)))) -> S1₁(s1₁(x))
S1₁(s1₁(s0₁(s0₁(x)))) -> S1₁(s1₁(s1₁(x)))

The TRS R consists of the following rules:

s1₁(s1₁(s0₁(s0₁(x)))) -> s0₁(s0₁(s0₁(s1₁(s1₁(s1₁(x))))))

The set Q consists of the following terms:

s1₁(s1₁(s0₁(s0₁(x0))))

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