/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 33 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:

   +(p1, p1) -> p2
   +(p1, +(p2, p2)) -> p5
   +(p5, p5) -> p10
   +(+(x, y), z) -> +(x, +(y, z))
   +(p1, +(p1, x)) -> +(p2, x)
   +(p1, +(p2, +(p2, x))) -> +(p5, x)
   +(p2, p1) -> +(p1, p2)
   +(p2, +(p1, x)) -> +(p1, +(p2, x))
   +(p2, +(p2, p2)) -> +(p1, p5)
   +(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
   +(p5, p1) -> +(p1, p5)
   +(p5, +(p1, x)) -> +(p1, +(p5, x))
   +(p5, p2) -> +(p2, p5)
   +(p5, +(p2, x)) -> +(p2, +(p5, x))
   +(p5, +(p5, x)) -> +(p10, x)
   +(p10, p1) -> +(p1, p10)
   +(p10, +(p1, x)) -> +(p1, +(p10, x))
   +(p10, p2) -> +(p2, p10)
   +(p10, +(p2, x)) -> +(p2, +(p10, x))
   +(p10, p5) -> +(p5, p10)
   +(p10, +(p5, x)) -> +(p5, +(p10, x))

Q is empty.

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(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Knuth-Bendix order [KBO] with precedence:p10 > p2 > p1 > p5 > +_2

and weight map:

   p1=2
   p2=2
   p5=3
   p10=4
   +_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:

   +(p1, p1) -> p2
   +(p1, +(p2, p2)) -> p5
   +(p5, p5) -> p10
   +(+(x, y), z) -> +(x, +(y, z))
   +(p1, +(p1, x)) -> +(p2, x)
   +(p1, +(p2, +(p2, x))) -> +(p5, x)
   +(p2, p1) -> +(p1, p2)
   +(p2, +(p1, x)) -> +(p1, +(p2, x))
   +(p2, +(p2, p2)) -> +(p1, p5)
   +(p2, +(p2, +(p2, x))) -> +(p1, +(p5, x))
   +(p5, p1) -> +(p1, p5)
   +(p5, +(p1, x)) -> +(p1, +(p5, x))
   +(p5, p2) -> +(p2, p5)
   +(p5, +(p2, x)) -> +(p2, +(p5, x))
   +(p5, +(p5, x)) -> +(p10, x)
   +(p10, p1) -> +(p1, p10)
   +(p10, +(p1, x)) -> +(p1, +(p10, x))
   +(p10, p2) -> +(p2, p10)
   +(p10, +(p2, x)) -> +(p2, +(p10, x))
   +(p10, p5) -> +(p5, p10)
   +(p10, +(p5, x)) -> +(p5, +(p10, x))




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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