(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
ap(ap(g, x), y) → y
ap(f, x) → ap(f, app(g, 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:
ap(ap(g, x), y) → y
ap(f, x) → ap(f, app(g, x))
The set Q consists of the following terms:
ap(ap(g, x0), x1)
ap(f, x0)
(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:
AP(f, x) → AP(f, app(g, x))
The TRS R consists of the following rules:
ap(ap(g, x), y) → y
ap(f, x) → ap(f, app(g, x))
The set Q consists of the following terms:
ap(ap(g, x0), x1)
ap(f, x0)
We have to consider all minimal (P,Q,R)-chains.