/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 41 ms]
(2) NO


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

   f(g(x), s(0), y) -> f(g(s(0)), y, g(x))
   g(s(x)) -> s(g(x))
   g(0) -> 0



Outermost Strategy.

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

   f(g(x), s(0), y) -> f(g(s(0)), y, g(x))
   g(s(x)) -> s(g(x))
   g(0) -> 0



Outermost Strategy.

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

f(g(s(0)), g(s(0)), g(s(0))) -> f(g(s(0)), s(g(0)), g(s(0))) with rule g(s(x')) -> s(g(x')) at position [1] and matcher [x' / 0]

f(g(s(0)), s(g(0)), g(s(0))) -> f(g(s(0)), s(0), g(s(0))) with rule g(0) -> 0 at position [1,0] and matcher [ ]

f(g(s(0)), s(0), g(s(0))) -> f(g(s(0)), g(s(0)), g(s(0))) with rule f(g(x), s(0), y) -> f(g(s(0)), y, g(x)) at position [] and matcher [x / s(0), y / g(s(0))]

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