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TRS Standard pair #516965660
details
property
value
status
complete
benchmark
z11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n062.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.32983016968 seconds
cpu usage
6.276993419
max memory
4.78507008E8
stage attributes
key
value
output-size
10278
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 88 ms] (2) QTRS (3) Overlay + Local Confluence [EQUIVALENT, 0 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) ATransformationProof [EQUIVALENT, 0 ms] (13) QDP (14) QReductionProof [EQUIVALENT, 0 ms] (15) QDP (16) MRRProof [EQUIVALENT, 5 ms] (17) QDP (18) DependencyGraphProof [EQUIVALENT, 0 ms] (19) TRUE (20) QDP (21) UsableRulesProof [EQUIVALENT, 0 ms] (22) QDP (23) ATransformationProof [EQUIVALENT, 0 ms] (24) QDP (25) QReductionProof [EQUIVALENT, 0 ms] (26) QDP (27) MRRProof [EQUIVALENT, 6 ms] (28) QDP (29) DependencyGraphProof [EQUIVALENT, 0 ms] (30) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(f, 0) -> a(s, 0) a(d, 0) -> 0 a(d, a(s, x)) -> a(s, a(s, a(d, a(p, a(s, x))))) a(f, a(s, x)) -> a(d, a(f, a(p, a(s, x)))) a(p, a(s, x)) -> x Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(a(x_1, x_2)) = 2*x_1 + x_2 POL(d) = 0 POL(f) = 1 POL(p) = 0 POL(s) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a(f, 0) -> a(s, 0) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(d, 0) -> 0 a(d, a(s, x)) -> a(s, a(s, a(d, a(p, a(s, x))))) a(f, a(s, x)) -> a(d, a(f, a(p, a(s, x)))) a(p, a(s, x)) -> x Q is empty. ---------------------------------------- (3) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ----------------------------------------
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