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TRS Standard pair #516965760
details
property
value
status
complete
benchmark
pair2simple1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
Endrullis_06
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.1590950489 seconds
cpu usage
5.527965397
max memory
4.78068736E8
stage attributes
key
value
output-size
1434
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 91 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: p(a(x0), p(a(b(x1)), x2)) -> p(a(b(a(x2))), p(a(a(x1)), x2)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: [p_2, b_1] > a_1 Status: p_2: [2,1] a_1: multiset status b_1: [1] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: p(a(x0), p(a(b(x1)), x2)) -> p(a(b(a(x2))), p(a(a(x1)), x2)) ---------------------------------------- (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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