(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
app(app(apply, f), x) → app(f, x)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(app(x1, x2)) = 1 + 2·x1 + 2·x2
POL(apply) = 0
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
app(app(apply, f), x) → app(f, x)
(2) Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.
(3) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(4) YES