details

property	value
status	complete
benchmark	random-141.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n173.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.41274 seconds
cpu usage	13.6204
user time	12.9482
system time	0.672236
max virtual memory	2.033672E7
max residence set size	1703156.0

stage attributes

key	value
starexec-result	YES

output

13.05/4.27 YES 13.30/4.35 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 13.30/4.35 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.30/4.35 13.30/4.35 13.30/4.35 Termination w.r.t. Q of the given QTRS could be proven: 13.30/4.35 13.30/4.35 (0) QTRS 13.30/4.35 (1) FlatCCProof [EQUIVALENT, 0 ms] 13.30/4.35 (2) QTRS 13.30/4.35 (3) RootLabelingProof [EQUIVALENT, 0 ms] 13.30/4.35 (4) QTRS 13.30/4.35 (5) QTRSRRRProof [EQUIVALENT, 30 ms] 13.30/4.35 (6) QTRS 13.30/4.35 (7) QTRSRRRProof [EQUIVALENT, 0 ms] 13.30/4.35 (8) QTRS 13.30/4.35 (9) DependencyPairsProof [EQUIVALENT, 0 ms] 13.30/4.35 (10) QDP 13.30/4.35 (11) DependencyGraphProof [EQUIVALENT, 0 ms] 13.30/4.35 (12) QDP 13.30/4.35 (13) QDPOrderProof [EQUIVALENT, 78 ms] 13.30/4.35 (14) QDP 13.30/4.35 (15) PisEmptyProof [EQUIVALENT, 0 ms] 13.30/4.35 (16) YES 13.30/4.35 13.30/4.35 13.30/4.35 ---------------------------------------- 13.30/4.35 13.30/4.35 (0) 13.30/4.35 Obligation: 13.30/4.35 Q restricted rewrite system: 13.30/4.35 The TRS R consists of the following rules: 13.30/4.35 13.30/4.35 a(a(a(a(x1)))) -> b(a(b(b(x1)))) 13.30/4.35 b(b(a(b(x1)))) -> a(b(b(b(x1)))) 13.30/4.35 a(a(b(a(x1)))) -> a(a(a(a(x1)))) 13.30/4.35 13.30/4.35 Q is empty. 13.30/4.35 13.30/4.35 ---------------------------------------- 13.30/4.35 13.30/4.35 (1) FlatCCProof (EQUIVALENT) 13.30/4.35 We used flat context closure [ROOTLAB] 13.30/4.35 As Q is empty the flat context closure was sound AND complete. 13.30/4.35 13.30/4.35 ---------------------------------------- 13.30/4.35 13.30/4.35 (2) 13.30/4.35 Obligation: 13.30/4.35 Q restricted rewrite system: 13.30/4.35 The TRS R consists of the following rules: 13.30/4.35 13.30/4.35 a(a(b(a(x1)))) -> a(a(a(a(x1)))) 13.30/4.35 a(a(a(a(a(x1))))) -> a(b(a(b(b(x1))))) 13.30/4.35 b(a(a(a(a(x1))))) -> b(b(a(b(b(x1))))) 13.30/4.35 a(b(b(a(b(x1))))) -> a(a(b(b(b(x1))))) 13.30/4.35 b(b(b(a(b(x1))))) -> b(a(b(b(b(x1))))) 13.30/4.35 13.30/4.35 Q is empty. 13.30/4.35 13.30/4.35 ---------------------------------------- 13.30/4.35 13.30/4.35 (3) RootLabelingProof (EQUIVALENT) 13.30/4.35 We used plain root labeling [ROOTLAB] with the following heuristic: 13.30/4.35 LabelAll: All function symbols get labeled 13.30/4.35 13.30/4.35 As Q is empty the root labeling was sound AND complete. 13.30/4.35 13.30/4.35 ---------------------------------------- 13.30/4.35 13.30/4.35 (4) 13.30/4.35 Obligation: 13.30/4.35 Q restricted rewrite system: 13.30/4.35 The TRS R consists of the following rules: 13.30/4.35 13.30/4.35 a_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1)))) 13.30/4.35 a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1)))) 13.30/4.35 a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> a_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1))))) 13.30/4.35 a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> a_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1))))) 13.30/4.35 b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1))))) 13.30/4.35 b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1))))) 13.30/4.35 a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1))))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))) 13.30/4.35 a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1))))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))) 13.30/4.35 b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1))))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))) 13.30/4.35 b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1))))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))) 13.30/4.35 13.30/4.35 Q is empty. 13.30/4.35 13.30/4.35 ---------------------------------------- 13.30/4.35 13.30/4.35 (5) QTRSRRRProof (EQUIVALENT) 13.30/4.35 Used ordering: 13.30/4.35 Polynomial interpretation [POLO]: 13.30/4.35 13.30/4.35 POL(a_{a_1}(x_1)) = 1 + x_1 13.30/4.35 POL(a_{b_1}(x_1)) = x_1 13.30/4.35 POL(b_{a_1}(x_1)) = 2 + x_1 13.30/4.35 POL(b_{b_1}(x_1)) = x_1 13.30/4.35 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 13.30/4.35 popout

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