/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 48 ms]
(2) NO


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

   app(app(const, x), y) -> x
   app(app(app(subst, f), g), x) -> app(app(f, x), app(g, x))
   app(app(fix, f), x) -> app(app(f, app(fix, f)), x)



Outermost Strategy.

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

   app(app(const, x), y) -> x
   app(app(app(subst, f), g), x) -> app(app(f, x), app(g, x))
   app(app(fix, f), x) -> app(app(f, app(fix, f)), x)



Outermost Strategy.

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

app(app(app(fix, subst), x'), x) -> app(app(app(subst, app(fix, subst)), x'), x) with rule app(app(fix, f'), x'') -> app(app(f', app(fix, f')), x'') at position [0] and matcher [f' / subst, x'' / x']

app(app(app(subst, app(fix, subst)), x'), x) -> app(app(app(fix, subst), x), app(x', x)) with rule app(app(app(subst, f), g), x'') -> app(app(f, x''), app(g, x'')) at position [] and matcher [f / app(fix, subst), g / x', x'' / x]

Now an instance of the first term with Matcher [x' / x, x / app(x', x)] 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