(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
.(.(x, y), z) → .(x, .(y, z))
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:
.1(.(x, y), z) → .1(x, .(y, z))
.1(.(x, y), z) → .1(y, z)
The TRS R consists of the following rules:
.(.(x, y), z) → .(x, .(y, z))
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.
.1(.(x, y), z) → .1(x, .(y, z))
.1(.(x, y), z) → .1(y, z)
The remaining pairs can at least be oriented weakly.
Used ordering: SCNP Order with the following components:
Level mapping:
Top level AFS:
.1(
x0,
x1,
x2) =
.1(
x0,
x1)
Tags:
.1 has argument tags [0,3,3] and root tag 0
Comparison: MS
Underlying order for the size change arcs and the rules of R:
Combined order from the following AFS and order.
.1(
x1,
x2) =
.1
.(
x1,
x2) =
.(
x1,
x2)
Recursive path order with status [RPO].
Quasi-Precedence:
[.^1, .2]
Status:
.^1: multiset
.2: multiset
The following usable rules [FROCOS05] were oriented:
none
(4) Obligation:
Q DP problem:
P is empty.
The TRS R consists of the following rules:
.(.(x, y), z) → .(x, .(y, z))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
(5) PisEmptyProof (EQUIVALENT transformation)
The TRS P is empty. Hence, there is no (P,Q,R) chain.
(6) TRUE