(0) Obligation:

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

*(x, *(y, z)) → *(*(x, y), z)
*(x, x) → x

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(x, y)

The TRS R consists of the following rules:

*(x, *(y, z)) → *(*(x, y), z)
*(x, x) → x

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(x, y)
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, x2)

Tags:
*1 has argument tags [2,2,1] and root tag 0

Comparison: MAX
Underlying order for the size change arcs and the rules of R:
Recursive path order with status [RPO].
Quasi-Precedence:
[*^12, *2]

Status:
*^12: [2,1]
*2: [2,1]


The following usable rules [FROCOS05] were oriented:

*(x, *(y, z)) → *(*(x, y), z)
*(x, x) → x

(4) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following rules:

*(x, *(y, z)) → *(*(x, y), z)
*(x, x) → x

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