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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

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



Outermost Strategy.

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

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



Outermost Strategy.

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

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

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

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