/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 136 ms]
(2) NO


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

   +(x, +(y, z)) -> +(+(x, y), z)
   *(x, +(y, z)) -> +(*(x, y), *(x, z))
   +(+(x, *(y, z)), *(y, u)) -> +(x, *(y, +(z, u)))



Outermost Strategy.

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

   +(x, +(y, z)) -> +(+(x, y), z)
   *(x, +(y, z)) -> +(*(x, y), *(x, z))
   +(+(x, *(y, z)), *(y, u)) -> +(x, *(y, +(z, u)))



Outermost Strategy.

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

+(+(x'', *(y, z)), *(y, u)) -> +(x'', *(y, +(z, u))) with rule +(+(x, *(y', z')), *(y', u')) -> +(x, *(y', +(z', u'))) at position [] and matcher [x / x'', y' / y, z' / z, u' / u]

+(x'', *(y, +(z, u))) -> +(x'', +(*(y, z), *(y, u))) with rule *(x', +(y', z')) -> +(*(x', y'), *(x', z')) at position [1] and matcher [x' / y, y' / z, z' / u]

+(x'', +(*(y, z), *(y, u))) -> +(+(x'', *(y, z)), *(y, u)) with rule +(x, +(y', z')) -> +(+(x, y'), z') at position [] and matcher [x / x'', y' / *(y, z), z' / *(y, u)]

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