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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

   h(f(f(x))) -> h(f(g(f(x))))
   f(g(f(x))) -> f(f(x))



Outermost Strategy.

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

   h(f(f(x))) -> h(f(g(f(x))))
   f(g(f(x))) -> f(f(x))



Outermost Strategy.

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

h(f(g(f(x')))) -> h(f(f(x'))) with rule f(g(f(x''))) -> f(f(x'')) at position [0] and matcher [x'' / x']

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

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