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

Q is empty.


↳ QTRS
  ↳ DependencyPairsProof

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

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

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

The TRS R consists of the following rules:

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

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

↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ QDPOrderProof

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

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

The TRS R consists of the following rules:

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

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].


The following pairs can be oriented strictly and are deleted.


P(a(x0), p(x1, p(x2, x3))) → P(x0, p(a(x3), x3))
P(a(x0), p(x1, p(x2, x3))) → P(a(x3), x3)
The remaining pairs can at least be oriented weakly.

P(a(x0), p(x1, p(x2, x3))) → P(x1, p(x0, p(a(x3), x3)))
Used ordering: Polynomial interpretation [25,35]:

POL(P(x1, x2)) = (11/4)x_2   
POL(a(x1)) = 11/4 + (5/4)x_1   
POL(p(x1, x2)) = 5/4 + (13/4)x_2   
The value of delta used in the strict ordering is 715/64.
The following usable rules [17] were oriented:

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



↳ QTRS
  ↳ DependencyPairsProof
    ↳ QDP
      ↳ QDPOrderProof
        ↳ QDP

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

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

The TRS R consists of the following rules:

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

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