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TRS Stand 20472 pair #381712446
details
property
value
status
complete
benchmark
21.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n029.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.62885189056 seconds
cpu usage
3.59155501
max memory
2.25247232E8
stage attributes
key
value
output-size
2725
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 33 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4)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 ---------------------------------------- (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. ---------------------------------------- (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)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. Q is empty.
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