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TRS Standard pair #516965050
details
property
value
status
complete
benchmark
023.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n135.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.12544798851 seconds
cpu usage
5.367598156
max memory
4.83065856E8
stage attributes
key
value
output-size
1578
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 40 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(id, x) -> x app(plus, 0) -> id app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:s > 0 > plus > app_2 > id and weight map: id=2 plus=1 0=1 s=1 app_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: app(id, x) -> x app(plus, 0) -> id app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES
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