(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
and(not(not(x)), y, not(z)) → and(y, band(x, z), 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:
AND(not(not(x)), y, not(z)) → AND(y, band(x, z), x)
The TRS R consists of the following rules:
and(not(not(x)), y, not(z)) → and(y, band(x, z), 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:
not(x1) = not(x1)
band(x1, x2) = x2
From the DPs we obtained the following set of size-change graphs:
- AND(not(not(x)), y, not(z)) → AND(y, band(x, z), x) (allowed arguments on rhs = {1, 2, 3})
The graph contains the following edges 2 >= 1, 3 > 2, 1 > 3
We oriented the following set of usable rules [AAECC05,FROCOS05].
none
(4) TRUE