(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
a(b(a(x))) → b(a(b(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:
A(b(a(x))) → A(b(x))
The TRS R consists of the following rules:
a(b(a(x))) → b(a(b(x)))
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:
a(x1) = a(x1)
b(x1) = x1
From the DPs we obtained the following set of size-change graphs:
- A(b(a(x))) → A(b(x)) (allowed arguments on rhs = {1})
The graph contains the following edges 1 > 1
We oriented the following set of usable rules [AAECC05,FROCOS05].
none
(4) TRUE