(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:Homeomorphic Embedding Order

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