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TRS Standard pair #516964580
details
property
value
status
complete
benchmark
jones4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n076.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.02900099754 seconds
cpu usage
5.25758645
max memory
4.72240128E8
stage attributes
key
value
output-size
1500
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 34 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES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(m, n, s(r)) -> p(m, r, n) p(m, s(n), 0) -> p(0, n, m) p(m, 0, 0) -> m Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:0 > s_1 > p_3 and weight map: 0=2 s_1=1 p_3=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: p(m, n, s(r)) -> p(m, r, n) p(m, s(n), 0) -> p(0, n, m) p(m, 0, 0) -> m ---------------------------------------- (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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