(0) Obligation:
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.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
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.
(3) QDPOrderProof (EQUIVALENT transformation)
We use the reduction pair processor [LPAR04].
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.
Used ordering: Combined order from the following AFS and order.
P(
x1,
x2) =
x2
p(
x1,
x2) =
p(
x2)
Recursive path order with status [RPO].
Quasi-Precedence:
trivial
Status:
trivial
The following usable rules [FROCOS05] were oriented:
p(a(x0), p(x1, p(x2, x3))) → p(x1, p(x0, p(a(x3), x3)))
(4) Obligation:
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.