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SRS Standard pair #516968884
details
property
value
status
complete
benchmark
z025.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n136.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
4.91349315643 seconds
cpu usage
11.285021355
max memory
1.239781376E9
stage attributes
key
value
output-size
4145
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 16 ms] (4) QTRS (5) Overlay + Local Confluence [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 1 ms] (8) QDP (9) UsableRulesProof [EQUIVALENT, 0 ms] (10) QDP (11) QReductionProof [EQUIVALENT, 0 ms] (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(x1)) -> a(b(x1)) a(a(a(x1))) -> b(a(a(b(x1)))) b(b(b(b(x1)))) -> a(x1) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(x1)) -> b(a(x1)) a(a(a(x1))) -> b(a(a(b(x1)))) b(b(b(b(x1)))) -> a(x1) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a(x_1)) = 3 + x_1 POL(b(x_1)) = 1 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a(a(a(x1))) -> b(a(a(b(x1)))) b(b(b(b(x1)))) -> a(x1) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(x1)) -> b(a(x1)) Q is empty. ---------------------------------------- (5) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (6) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(x1)) -> b(a(x1))
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