YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given ETRS could be proven:

(0) ETRS
(1) EDirectTerminationProof [EQUIVALENT, 194 ms]
(2) YES


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

   ac1(a, ac2(b, c)) -> ac1(b, f(ac2(a, c)))
   ac2(a, ac1(b, c)) -> ac2(b, f(ac1(a, c)))

The set E consists of the following equations:

   ac1(x, y) == ac1(y, x)
   ac2(x, y) == ac2(y, x)
   ac1(ac1(x, y), z) == ac1(x, ac1(y, z))
   ac2(ac2(x, y), z) == ac2(x, ac2(y, z))


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

Precedence:
ac1_2 > b > a > c
ac1_2 > f_1
ac2_2 > f_1


Status:
ac1_2: flat status
ac2_2: flat status



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(2)
YES