details

property	value
status	complete
benchmark	random-87.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.23057 seconds
cpu usage	13.1034
user time	12.4029
system time	0.700476
max virtual memory	2.10123E7
max residence set size	1807584.0

stage attributes

key	value
starexec-result	YES

output

12.75/4.10 YES 12.75/4.15 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 12.75/4.15 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.75/4.15 12.75/4.15 12.75/4.15 Termination w.r.t. Q of the given QTRS could be proven: 12.75/4.15 12.75/4.15 (0) QTRS 12.75/4.15 (1) RootLabelingProof [EQUIVALENT, 0 ms] 12.75/4.15 (2) QTRS 12.75/4.15 (3) QTRSRRRProof [EQUIVALENT, 8 ms] 12.75/4.15 (4) QTRS 12.75/4.15 (5) DependencyPairsProof [EQUIVALENT, 0 ms] 12.75/4.15 (6) QDP 12.75/4.15 (7) DependencyGraphProof [EQUIVALENT, 1 ms] 12.75/4.15 (8) AND 12.75/4.15 (9) QDP 12.75/4.15 (10) UsableRulesProof [EQUIVALENT, 0 ms] 12.75/4.15 (11) QDP 12.75/4.15 (12) QDPOrderProof [EQUIVALENT, 6 ms] 12.75/4.15 (13) QDP 12.75/4.15 (14) PisEmptyProof [EQUIVALENT, 0 ms] 12.75/4.15 (15) YES 12.75/4.15 (16) QDP 12.75/4.15 (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] 12.75/4.15 (18) YES 12.75/4.15 12.75/4.15 12.75/4.15 ---------------------------------------- 12.75/4.15 12.75/4.15 (0) 12.75/4.15 Obligation: 12.75/4.15 Q restricted rewrite system: 12.75/4.15 The TRS R consists of the following rules: 12.75/4.15 12.75/4.15 a(a(b(a(x1)))) -> a(b(a(a(x1)))) 12.75/4.15 b(a(b(b(x1)))) -> b(b(a(b(x1)))) 12.75/4.15 a(b(a(b(x1)))) -> a(b(b(b(x1)))) 12.75/4.15 12.75/4.15 Q is empty. 12.75/4.15 12.75/4.15 ---------------------------------------- 12.75/4.15 12.75/4.15 (1) RootLabelingProof (EQUIVALENT) 12.75/4.15 We used plain root labeling [ROOTLAB] with the following heuristic: 12.75/4.15 LabelAll: All function symbols get labeled 12.75/4.15 12.75/4.15 As Q is empty the root labeling was sound AND complete. 12.75/4.15 12.75/4.15 ---------------------------------------- 12.75/4.15 12.75/4.15 (2) 12.75/4.15 Obligation: 12.75/4.15 Q restricted rewrite system: 12.75/4.15 The TRS R consists of the following rules: 12.75/4.15 12.75/4.15 a_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(x1)))) -> a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) 12.75/4.15 a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1)))) -> a_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) 12.75/4.15 b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> b_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) 12.75/4.15 b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) 12.75/4.15 a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))) 12.75/4.15 a_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))) 12.75/4.15 12.75/4.15 Q is empty. 12.75/4.15 12.75/4.15 ---------------------------------------- 12.75/4.15 12.75/4.15 (3) QTRSRRRProof (EQUIVALENT) 12.75/4.15 Used ordering: 12.75/4.15 Polynomial interpretation [POLO]: 12.75/4.15 12.75/4.15 POL(a_{a_1}(x_1)) = x_1 12.75/4.15 POL(a_{b_1}(x_1)) = x_1 12.75/4.15 POL(b_{a_1}(x_1)) = 1 + x_1 12.75/4.15 POL(b_{b_1}(x_1)) = x_1 12.75/4.15 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 12.75/4.15 12.75/4.15 a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))) 12.75/4.15 a_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))) 12.75/4.15 12.75/4.15 12.75/4.15 12.75/4.15 12.75/4.15 ---------------------------------------- 12.75/4.15 12.75/4.15 (4) 12.75/4.15 Obligation: 12.75/4.15 Q restricted rewrite system: 12.75/4.15 The TRS R consists of the following rules: 12.75/4.15 12.75/4.15 a_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(x1)))) -> a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) 12.75/4.15 a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1)))) -> a_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) 12.75/4.15 b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> b_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) 12.75/4.15 b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) 12.75/4.15 12.75/4.15 Q is empty. 12.75/4.15 12.75/4.15 ---------------------------------------- 12.75/4.15 12.75/4.15 (5) DependencyPairsProof (EQUIVALENT) popout

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all output return to SRS_Standard 2019-03-29 03.29