/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Outermost Termination of the given OTRS could be disproven:

(0) OTRS
(1) OutermostNonTerminationProof [COMPLETE, 221 ms]
(2) NO


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(0)
Obligation:
Term rewrite system R:
The TRS R consists of the following rules:

   ap(ap(f, x), x) -> ap(ap(x, ap(f, x)), ap(ap(cons, x), nil))
   ap(ap(ap(foldr, g), h), nil) -> h
   ap(ap(ap(foldr, g), h), ap(ap(cons, x), xs)) -> ap(ap(g, x), ap(ap(ap(foldr, g), h), xs))



Outermost Strategy.

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(1) OutermostNonTerminationProof (COMPLETE)
Term rewrite system R:
The TRS R consists of the following rules:

   ap(ap(f, x), x) -> ap(ap(x, ap(f, x)), ap(ap(cons, x), nil))
   ap(ap(ap(foldr, g), h), nil) -> h
   ap(ap(ap(foldr, g), h), ap(ap(cons, x), xs)) -> ap(ap(g, x), ap(ap(ap(foldr, g), h), xs))



Outermost Strategy.

---------- Loop: ----------

ap(ap(ap(f, foldr), foldr), ap(ap(ap(foldr, ap(f, foldr)), ap(ap(cons, foldr), nil)), nil)) -> ap(ap(ap(f, foldr), foldr), ap(ap(cons, foldr), nil)) with rule ap(ap(ap(foldr, g), h), nil) -> h at position [1] and matcher [g / ap(f, foldr), h / ap(ap(cons, foldr), nil)]

ap(ap(ap(f, foldr), foldr), ap(ap(cons, foldr), nil)) -> ap(ap(ap(foldr, ap(f, foldr)), ap(ap(cons, foldr), nil)), ap(ap(cons, foldr), nil)) with rule ap(ap(f, x'), x') -> ap(ap(x', ap(f, x')), ap(ap(cons, x'), nil)) at position [0] and matcher [x' / foldr]

ap(ap(ap(foldr, ap(f, foldr)), ap(ap(cons, foldr), nil)), ap(ap(cons, foldr), nil)) -> ap(ap(ap(f, foldr), foldr), ap(ap(ap(foldr, ap(f, foldr)), ap(ap(cons, foldr), nil)), nil)) with rule ap(ap(ap(foldr, g), h), ap(ap(cons, x), xs)) -> ap(ap(g, x), ap(ap(ap(foldr, g), h), xs)) at position [] and matcher [g / ap(f, foldr), h / ap(ap(cons, foldr), nil), x / foldr, xs / nil]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [].

Context: []

We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
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(2)
NO