(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
*(x, +(y, z)) → +(*(x, y), *(x, 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)
*1(x, +(y, z)) → *1(x, z)
The TRS R consists of the following rules:
*(x, +(y, z)) → +(*(x, y), *(x, z))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
(3) QDPSizeChangeProof (EQUIVALENT transformation)
We used the following order and afs together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem.
Order:Homeomorphic Embedding Order
AFS:
+(x1, x2) = +(x1, x2)
From the DPs we obtained the following set of size-change graphs:
- *1(x, +(y, z)) → *1(x, y) (allowed arguments on rhs = {1, 2})
The graph contains the following edges 1 >= 1, 2 > 2
- *1(x, +(y, z)) → *1(x, z) (allowed arguments on rhs = {1, 2})
The graph contains the following edges 1 >= 1, 2 > 2
We oriented the following set of usable rules [AAECC05,FROCOS05].
none
(4) TRUE