/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 ms]
(2) NO


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

   f(s(x), x) -> f(s(x), round(x))
   round(0) -> 0
   round(0) -> s(0)
   round(s(0)) -> s(0)
   round(s(s(x))) -> s(s(round(x)))



Outermost Strategy.

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

   f(s(x), x) -> f(s(x), round(x))
   round(0) -> 0
   round(0) -> s(0)
   round(s(0)) -> s(0)
   round(s(s(x))) -> s(s(round(x)))



Outermost Strategy.

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

f(s(0), round(0)) -> f(s(0), 0) with rule round(0) -> 0 at position [1] and matcher [ ]

f(s(0), 0) -> f(s(0), round(0)) with rule f(s(x), x) -> f(s(x), round(x)) at position [] and matcher [x / 0]

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