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


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NO
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 53 ms]
(2) NO


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

   app(app(app(if, true), x), y) -> x
   app(app(app(if, false), x), y) -> y
   app(app(app(until, p), f), x) -> app(app(app(if, app(p, x)), x), app(app(app(until, p), f), app(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(app(if, true), x), y) -> x
   app(app(app(if, false), x), y) -> y
   app(app(app(until, p), f), x) -> app(app(app(if, app(p, x)), x), app(app(app(until, p), f), app(f, x)))



Outermost Strategy.

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

app(app(app(until, p), f), x) -> app(app(app(if, app(p, x)), x), app(app(app(until, p), f), app(f, x))) with rule app(app(app(until, p'), f'), x') -> app(app(app(if, app(p', x')), x'), app(app(app(until, p'), f'), app(f', x'))) at position [] and matcher [p' / p, f' / f, x' / x]

Now an instance of the first term with Matcher [x / app(f, x)] occurs in the last term at position [1].

Context: app(app(app(if, app(p, x)), x), [])

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