(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
app(app(app(uncurry, f), x), y) → app(app(f, x), y)
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:
APP(app(app(uncurry, f), x), y) → APP(app(f, x), y)
APP(app(app(uncurry, f), x), y) → APP(f, x)
The TRS R consists of the following rules:
app(app(app(uncurry, f), x), y) → app(app(f, x), y)
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:Lexicographic path order with status [LPO].
Quasi-Precedence:
[app2, uncurry]
Status:
app2: [2,1]
uncurry: []
AFS:
app(x1, x2) = app(x1, x2)
uncurry = uncurry
From the DPs we obtained the following set of size-change graphs:
- APP(app(app(uncurry, f), x), y) → APP(app(f, x), y) (allowed arguments on rhs = {1, 2})
The graph contains the following edges 1 > 1, 2 >= 2
- APP(app(app(uncurry, f), x), y) → APP(f, x) (allowed arguments on rhs = {1, 2})
The graph contains the following edges 1 > 1, 1 > 2
We oriented the following set of usable rules [AAECC05,FROCOS05].
app(app(app(uncurry, f), x), y) → app(app(f, x), y)
(4) TRUE