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TRS_Conditional 2019-03-28 22.59 pair #432272589
details
property
value
status
complete
benchmark
268.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n158.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.32565 seconds
cpu usage
5.19309
user time
4.97058
system time
0.222512
max virtual memory
3.6973352E7
max residence set size
400384.0
stage attributes
key
value
starexec-result
MAYBE
output
4.94/2.28 MAYBE 4.94/2.29 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 4.94/2.29 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.94/2.29 4.94/2.29 4.94/2.29 Quasi decreasingness of the given CTRS could not be shown: 4.94/2.29 4.94/2.29 (0) CTRS 4.94/2.29 (1) CTRSToQTRSProof [SOUND, 0 ms] 4.94/2.29 (2) QTRS 4.94/2.29 (3) QTRSRRRProof [EQUIVALENT, 25 ms] 4.94/2.29 (4) QTRS 4.94/2.29 (5) AAECC Innermost [EQUIVALENT, 0 ms] 4.94/2.29 (6) QTRS 4.94/2.29 (7) DependencyPairsProof [EQUIVALENT, 0 ms] 4.94/2.29 (8) QDP 4.94/2.29 (9) UsableRulesProof [EQUIVALENT, 0 ms] 4.94/2.29 (10) QDP 4.94/2.29 (11) QReductionProof [EQUIVALENT, 0 ms] 4.94/2.29 (12) QDP 4.94/2.29 (13) NonTerminationLoopProof [COMPLETE, 0 ms] 4.94/2.29 (14) NO 4.94/2.29 4.94/2.29 4.94/2.29 ---------------------------------------- 4.94/2.29 4.94/2.29 (0) 4.94/2.29 Obligation: 4.94/2.29 Conditional term rewrite system: 4.94/2.29 The TRS R consists of the following rules: 4.94/2.29 4.94/2.29 p(q(x)) -> 0 4.94/2.29 c -> c 4.94/2.29 4.94/2.29 The conditional TRS C consists of the following conditional rules: 4.94/2.29 4.94/2.29 a(x) -> b <= p(x) -> 0 4.94/2.29 4.94/2.29 4.94/2.29 ---------------------------------------- 4.94/2.29 4.94/2.29 (1) CTRSToQTRSProof (SOUND) 4.94/2.29 The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. 4.94/2.29 ---------------------------------------- 4.94/2.29 4.94/2.29 (2) 4.94/2.29 Obligation: 4.94/2.29 Q restricted rewrite system: 4.94/2.29 The TRS R consists of the following rules: 4.94/2.29 4.94/2.29 a(x) -> U1(p(x)) 4.94/2.29 U1(0) -> b 4.94/2.29 p(q(x)) -> 0 4.94/2.29 c -> c 4.94/2.29 4.94/2.29 Q is empty. 4.94/2.29 4.94/2.29 ---------------------------------------- 4.94/2.29 4.94/2.29 (3) QTRSRRRProof (EQUIVALENT) 4.94/2.29 Used ordering: 4.94/2.29 Knuth-Bendix order [KBO] with precedence:c > q_1 > a_1 > U1_1 > b > p_1 > 0 4.94/2.29 4.94/2.29 and weight map: 4.94/2.29 4.94/2.29 0=3 4.94/2.29 b=4 4.94/2.29 c=1 4.94/2.29 a_1=2 4.94/2.29 U1_1=1 4.94/2.29 p_1=1 4.94/2.29 q_1=1 4.94/2.29 4.94/2.29 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 4.94/2.29 4.94/2.29 a(x) -> U1(p(x)) 4.94/2.29 U1(0) -> b 4.94/2.29 p(q(x)) -> 0 4.94/2.29 4.94/2.29 4.94/2.29 4.94/2.29 4.94/2.29 ---------------------------------------- 4.94/2.29 4.94/2.29 (4) 4.94/2.29 Obligation: 4.94/2.29 Q restricted rewrite system: 4.94/2.29 The TRS R consists of the following rules: 4.94/2.29 4.94/2.29 c -> c 4.94/2.29 4.94/2.29 Q is empty. 4.94/2.29 4.94/2.29 ---------------------------------------- 4.94/2.29 4.94/2.29 (5) AAECC Innermost (EQUIVALENT) 4.94/2.29 We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none 4.94/2.29 4.94/2.29 The TRS R 2 is 4.94/2.29 c -> c
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