/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination of the given ETRS could be proven:

(0) ETRS
(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
(2) YES


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

   f(g(g(x)), x) -> f(g(x), g(x))
   f(f(x, x), g(x)) -> f(x, h(x))

The set E consists of the following equations:

   f(x, y) == f(y, x)
   f(f(x, y), z) == f(x, f(y, z))


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(1) EDirectTerminationProof (EQUIVALENT)
We use [DA_FALKE] with the following order to prove termination.

Precedence:
g_1 > h_1


Status:
f_2: flat status



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(2)
YES