/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 763 ms]
(2) NO


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

   f(f(f(a, x), y), z) -> f(f(x, z), f(y, z))
   f(f(b, x), y) -> x
   f(c, y) -> y



Outermost Strategy.

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

   f(f(f(a, x), y), z) -> f(f(x, z), f(y, z))
   f(f(b, x), y) -> x
   f(c, y) -> y



Outermost Strategy.

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

f(f(f(f(b, f(f(a, a), b)), y'), f(f(b, f(a, f(f(b, f(f(a, a), b)), y'''))), y'')), y'''') -> f(f(f(f(b, f(f(a, a), b)), y'), f(a, f(f(b, f(f(a, a), b)), y'''))), y'''') with rule f(f(b, x'), y''1) -> x' at position [0,1] and matcher [x' / f(a, f(f(b, f(f(a, a), b)), y''')), y''1 / y'']

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

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

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

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

Now an instance of the first term with Matcher [y' / y''', y'' / y'''', y'''' / f(y'''', f(f(b, f(a, f(f(b, f(f(a, a), b)), y'''))), y''''))] 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