/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 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, z), *(y, z))
   *(x, +(y, f(z))) -> *(g(x, z), +(y, y))



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, z), *(y, z))
   *(x, +(y, f(z))) -> *(g(x, z), +(y, y))



Outermost Strategy.

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

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

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