/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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:

   f(g(x), x, y) -> f(y, y, g(y))
   g(g(x)) -> g(x)



Outermost Strategy.

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

   f(g(x), x, y) -> f(y, y, g(y))
   g(g(x)) -> g(x)



Outermost Strategy.

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

f(g(g(x')), g(g(x')), g(g(x''))) -> f(g(g(x')), g(x'), g(g(x''))) with rule g(g(x''')) -> g(x''') at position [1] and matcher [x''' / x']

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

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