(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: Combined order from the following AFS and order.
.1(
x1,
x2) =
.1(
x1)
.(
x1,
x2) =
.(
x1,
x2)
Lexicographic path order with status [LPO].
Quasi-Precedence:
.^11 > .2
Status:
.^11: [1]
.2: [1,2]
The following usable rules [FROCOS05] were oriented:
.(.(x, y), z) → .(x, .(y, z))
(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