/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(x, h(y)) -> h(f(f(h(a), y), x))



Outermost Strategy.

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

   f(x, h(y)) -> h(f(f(h(a), y), x))



Outermost Strategy.

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

f(f(h(y'''), f(x''', h(y'))), f(h(y''), f(x'', h(y)))) -> f(f(h(y'''), f(x''', h(y'))), f(h(y''), h(f(f(h(a), y), x'')))) with rule f(x'''', h(y1)) -> h(f(f(h(a), y1), x'''')) at position [1,1] and matcher [x'''' / x'', y1 / y]

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

f(f(h(y'''), f(x''', h(y'))), h(f(f(h(a), f(f(h(a), y), x'')), h(y'')))) -> h(f(f(h(a), f(f(h(a), f(f(h(a), y), x'')), h(y''))), f(h(y'''), f(x''', h(y'))))) with rule f(x, h(y1)) -> h(f(f(h(a), y1), x)) at position [] and matcher [x / f(h(y'''), f(x''', h(y'))), y1 / f(f(h(a), f(f(h(a), y), x'')), h(y''))]

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

Context: h([])

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