(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
app(app(fmap, fnil), x) → nil
app(app(fmap, app(app(fcons, f), t)), x) → app(app(cons, app(f, x)), app(app(fmap, t), x))
Q is empty.
(1) Overlay + Local Confluence (EQUIVALENT transformation)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
app(app(fmap, fnil), x) → nil
app(app(fmap, app(app(fcons, f), t)), x) → app(app(cons, app(f, x)), app(app(fmap, t), x))
The set Q consists of the following terms:
app(app(fmap, fnil), x0)
app(app(fmap, app(app(fcons, x0), x1)), x2)
(3) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
APP(app(fmap, app(app(fcons, f), t)), x) → APP(app(cons, app(f, x)), app(app(fmap, t), x))
APP(app(fmap, app(app(fcons, f), t)), x) → APP(cons, app(f, x))
APP(app(fmap, app(app(fcons, f), t)), x) → APP(f, x)
APP(app(fmap, app(app(fcons, f), t)), x) → APP(app(fmap, t), x)
APP(app(fmap, app(app(fcons, f), t)), x) → APP(fmap, t)
The TRS R consists of the following rules:
app(app(fmap, fnil), x) → nil
app(app(fmap, app(app(fcons, f), t)), x) → app(app(cons, app(f, x)), app(app(fmap, t), x))
The set Q consists of the following terms:
app(app(fmap, fnil), x0)
app(app(fmap, app(app(fcons, x0), x1)), x2)
We have to consider all minimal (P,Q,R)-chains.
(5) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
(6) Obligation:
Q DP problem:
The TRS P consists of the following rules:
APP(app(fmap, app(app(fcons, f), t)), x) → APP(app(fmap, t), x)
APP(app(fmap, app(app(fcons, f), t)), x) → APP(f, x)
The TRS R consists of the following rules:
app(app(fmap, fnil), x) → nil
app(app(fmap, app(app(fcons, f), t)), x) → app(app(cons, app(f, x)), app(app(fmap, t), x))
The set Q consists of the following terms:
app(app(fmap, fnil), x0)
app(app(fmap, app(app(fcons, x0), x1)), x2)
We have to consider all minimal (P,Q,R)-chains.