details

property	value
status	complete
benchmark	dup13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n103.star.cs.uiowa.edu
space	Trafo_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	59.6722 seconds
cpu usage	231.503
user time	226.366
system time	5.13761
max virtual memory	4.0236252E7
max residence set size	8294460.0

stage attributes

key	value
starexec-result	YES

output

230.73/59.46 YES 231.09/59.57 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 231.09/59.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 231.09/59.57 231.09/59.57 231.09/59.57 Termination w.r.t. Q of the given QTRS could be proven: 231.09/59.57 231.09/59.57 (0) QTRS 231.09/59.57 (1) RootLabelingProof [EQUIVALENT, 0 ms] 231.09/59.57 (2) QTRS 231.09/59.57 (3) QTRSRRRProof [EQUIVALENT, 14 ms] 231.09/59.57 (4) QTRS 231.09/59.57 (5) DependencyPairsProof [EQUIVALENT, 71 ms] 231.09/59.57 (6) QDP 231.09/59.57 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 231.09/59.57 (8) QDP 231.09/59.57 (9) QDPOrderProof [EQUIVALENT, 1717 ms] 231.09/59.57 (10) QDP 231.09/59.57 (11) QDPOrderProof [EQUIVALENT, 3673 ms] 231.09/59.57 (12) QDP 231.09/59.57 (13) DependencyGraphProof [EQUIVALENT, 0 ms] 231.09/59.57 (14) TRUE 231.09/59.57 231.09/59.57 231.09/59.57 ---------------------------------------- 231.09/59.57 231.09/59.57 (0) 231.09/59.57 Obligation: 231.09/59.57 Q restricted rewrite system: 231.09/59.57 The TRS R consists of the following rules: 231.09/59.57 231.09/59.57 a(a(a(a(x1)))) -> a(a(b(b(b(b(b(b(x1)))))))) 231.09/59.57 b(b(a(a(x1)))) -> b(b(b(b(c(c(x1)))))) 231.09/59.57 a(a(b(b(b(b(c(c(x1)))))))) -> a(a(a(a(a(a(b(b(x1)))))))) 231.09/59.57 231.09/59.57 Q is empty. 231.09/59.57 231.09/59.57 ---------------------------------------- 231.09/59.57 231.09/59.57 (1) RootLabelingProof (EQUIVALENT) 231.09/59.57 We used plain root labeling [ROOTLAB] with the following heuristic: 231.09/59.57 LabelAll: All function symbols get labeled 231.09/59.57 231.09/59.57 As Q is empty the root labeling was sound AND complete. 231.09/59.57 231.09/59.57 ---------------------------------------- 231.09/59.57 231.09/59.57 (2) 231.09/59.57 Obligation: 231.09/59.57 Q restricted rewrite system: 231.09/59.57 The TRS R consists of the following rules: 231.09/59.57 231.09/59.57 a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))))) 231.09/59.57 a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))))) 231.09/59.57 a_{a_1}(a_{a_1}(a_{a_1}(a_{c_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))))) 231.09/59.57 b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{a_1}(x1)))))) 231.09/59.57 b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{b_1}(x1)))))) 231.09/59.57 b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{c_1}(x1)))))) 231.09/59.57 a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{a_1}(x1)))))))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))))))) 231.09/59.57 a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{b_1}(x1)))))))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))))))) 231.09/59.57 a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{c_1}(x1)))))))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{c_1}(x1)))))))) 231.09/59.57 231.09/59.57 Q is empty. 231.09/59.57 231.09/59.57 ---------------------------------------- 231.09/59.57 231.09/59.57 (3) QTRSRRRProof (EQUIVALENT) 231.09/59.57 Used ordering: 231.09/59.57 Polynomial interpretation [POLO]: 231.09/59.57 231.09/59.57 POL(a_{a_1}(x_1)) = x_1 231.09/59.57 POL(a_{b_1}(x_1)) = x_1 231.09/59.57 POL(a_{c_1}(x_1)) = 1 + x_1 231.09/59.57 POL(b_{a_1}(x_1)) = x_1 231.09/59.57 POL(b_{b_1}(x_1)) = x_1 231.09/59.57 POL(b_{c_1}(x_1)) = x_1 231.09/59.57 POL(c_{a_1}(x_1)) = x_1 231.09/59.57 POL(c_{b_1}(x_1)) = x_1 231.09/59.57 POL(c_{c_1}(x_1)) = x_1 231.09/59.57 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 231.09/59.57 231.09/59.57 a_{a_1}(a_{a_1}(a_{a_1}(a_{c_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))))) 231.09/59.57 b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{c_1}(x1)))))) 231.09/59.57 231.09/59.57 231.09/59.57 231.09/59.57 231.09/59.57 ---------------------------------------- 231.09/59.57 231.09/59.57 (4) 231.09/59.57 Obligation: 231.09/59.57 Q restricted rewrite system: 231.09/59.57 The TRS R consists of the following rules: 231.09/59.57 231.09/59.57 a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))))) 231.09/59.57 a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))))) 231.09/59.57 b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{a_1}(x1)))))) 231.09/59.57 b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{b_1}(x1)))))) 231.09/59.57 a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{a_1}(x1)))))))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))))))) 231.09/59.57 a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{b_1}(x1)))))))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))))))) popout

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all output return to SRS_Standard 2019-03-29 03.29