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TRS Conditional pair #516978499
details
property
value
status
complete
benchmark
lucMarMes.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
Mixed_CTRS_2014
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.67549300194 seconds
cpu usage
7.112545249
max memory
5.5597056E8
stage attributes
key
value
output-size
4183
starexec-result
MAYBE
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could not be shown: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 36 ms] (4) QTRS (5) Overlay + Local Confluence [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) UsableRulesProof [EQUIVALENT, 0 ms] (10) QDP (11) QReductionProof [EQUIVALENT, 0 ms] (12) QDP (13) NonTerminationLoopProof [COMPLETE, 0 ms] (14) NO ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R is empty. The conditional TRS C consists of the following conditional rules: a -> b <= f(a) -> b ---------------------------------------- (1) CTRSToQTRSProof (SOUND) The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a -> U1(f(a)) U1(b) -> b Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(U1(x_1)) = 2*x_1 POL(a) = 0 POL(b) = 2 POL(f(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: U1(b) -> b ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a -> U1(f(a)) 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 -> U1(f(a)) The set Q consists of the following terms:
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