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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

   a(b(x)) -> b(b(a(a(x))))



Outermost Strategy.

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

   a(b(x)) -> b(b(a(a(x))))



Outermost Strategy.

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

a(a(b(x'))) -> a(b(b(a(a(x'))))) with rule a(b(x'')) -> b(b(a(a(x'')))) at position [0] and matcher [x'' / x']

a(b(b(a(a(x'))))) -> b(b(a(a(b(a(a(x'))))))) with rule a(b(x)) -> b(b(a(a(x)))) at position [] and matcher [x / b(a(a(x')))]

Now an instance of the first term with Matcher [x' / a(a(x'))] occurs in the last term at position [0,0].

Context: b(b([]))

We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
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(2)
NO