(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
rev(a) → a
rev(b) → b
rev(++(x, y)) → ++(rev(y), rev(x))
rev(++(x, x)) → rev(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:
REV(++(x, y)) → REV(y)
REV(++(x, y)) → REV(x)
REV(++(x, x)) → REV(x)
The TRS R consists of the following rules:
rev(a) → a
rev(b) → b
rev(++(x, y)) → ++(rev(y), rev(x))
rev(++(x, x)) → rev(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:
++(x1, x2) = ++(x1, x2)
From the DPs we obtained the following set of size-change graphs:
- REV(++(x, y)) → REV(y) (allowed arguments on rhs = {1})
The graph contains the following edges 1 > 1
- REV(++(x, y)) → REV(x) (allowed arguments on rhs = {1})
The graph contains the following edges 1 > 1
- REV(++(x, x)) → REV(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