Termination w.r.t. Q proof of /tmp/tmpX-E2FK/quadruple1.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:

p(p(b(a(x0)), x1), p(x2, x3)) → p(p(x3, a(x2)), p(b(a(x1)), b(x0)))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

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

p(p(b(a(x0)), x1), p(x2, x3)) → p(p(x3, a(x2)), p(b(a(x1)), b(x0)))

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:

P(p(b(a(x0)), x1), p(x2, x3)) → P(x3, a(x2))
P(p(b(a(x0)), x1), p(x2, x3)) → P(b(a(x1)), b(x0))
P(p(b(a(x0)), x1), p(x2, x3)) → P(p(x3, a(x2)), p(b(a(x1)), b(x0)))

The TRS R consists of the following rules:

p(p(b(a(x0)), x1), p(x2, x3)) → p(p(x3, a(x2)), p(b(a(x1)), b(x0)))

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:

P(p(b(a(x0)), x1), p(x2, x3)) → P(x3, a(x2))
P(p(b(a(x0)), x1), p(x2, x3)) → P(b(a(x1)), b(x0))
P(p(b(a(x0)), x1), p(x2, x3)) → P(p(x3, a(x2)), p(b(a(x1)), b(x0)))

The TRS R consists of the following rules:

p(p(b(a(x0)), x1), p(x2, x3)) → p(p(x3, a(x2)), p(b(a(x1)), b(x0)))

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 2 less nodes.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ QDP

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

P(p(b(a(x0)), x1), p(x2, x3)) → P(p(x3, a(x2)), p(b(a(x1)), b(x0)))

The TRS R consists of the following rules:

p(p(b(a(x0)), x1), p(x2, x3)) → p(p(x3, a(x2)), p(b(a(x1)), b(x0)))

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