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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 34 ms]
(2) QTRS
(3) RisEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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

   +(*(x, y), *(x, z)) -> *(x, +(y, z))
   +(+(x, y), z) -> +(x, +(y, z))
   +(*(x, y), +(*(x, z), u)) -> +(*(x, +(y, z)), u)

Q is empty.

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(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Knuth-Bendix order [KBO] with precedence:u > *_2 > +_2

and weight map:

   u=1
   *_2=0
   +_2=0

The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   +(*(x, y), *(x, z)) -> *(x, +(y, z))
   +(+(x, y), z) -> +(x, +(y, z))
   +(*(x, y), +(*(x, z), u)) -> +(*(x, +(y, z)), u)




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(2)
Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.

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(3) RisEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
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(4)
YES