details

property	value
status	complete
benchmark	random-26.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n032.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.50118 seconds
cpu usage	10.3698
user time	9.76268
system time	0.607066
max virtual memory	2.014E7
max residence set size	1699844.0

stage attributes

key	value
starexec-result	YES

output

9.93/3.40 YES 10.24/3.46 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 10.24/3.46 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.24/3.46 10.24/3.46 10.24/3.46 Termination w.r.t. Q of the given QTRS could be proven: 10.24/3.46 10.24/3.46 (0) QTRS 10.24/3.46 (1) FlatCCProof [EQUIVALENT, 0 ms] 10.24/3.46 (2) QTRS 10.24/3.46 (3) RootLabelingProof [EQUIVALENT, 0 ms] 10.24/3.46 (4) QTRS 10.24/3.46 (5) QTRSRRRProof [EQUIVALENT, 64 ms] 10.24/3.46 (6) QTRS 10.24/3.46 (7) DependencyPairsProof [EQUIVALENT, 8 ms] 10.24/3.46 (8) QDP 10.24/3.46 (9) QDPOrderProof [EQUIVALENT, 17 ms] 10.24/3.46 (10) QDP 10.24/3.46 (11) DependencyGraphProof [EQUIVALENT, 0 ms] 10.24/3.46 (12) TRUE 10.24/3.46 10.24/3.46 10.24/3.46 ---------------------------------------- 10.24/3.46 10.24/3.46 (0) 10.24/3.46 Obligation: 10.24/3.46 Q restricted rewrite system: 10.24/3.46 The TRS R consists of the following rules: 10.24/3.46 10.24/3.46 a(b(b(a(x1)))) -> b(a(b(a(x1)))) 10.24/3.46 a(b(b(b(x1)))) -> a(a(b(a(x1)))) 10.24/3.46 a(a(a(a(x1)))) -> b(b(b(a(x1)))) 10.24/3.46 10.24/3.46 Q is empty. 10.24/3.46 10.24/3.46 ---------------------------------------- 10.24/3.46 10.24/3.46 (1) FlatCCProof (EQUIVALENT) 10.24/3.46 We used flat context closure [ROOTLAB] 10.24/3.46 As Q is empty the flat context closure was sound AND complete. 10.24/3.46 10.24/3.46 ---------------------------------------- 10.24/3.46 10.24/3.46 (2) 10.24/3.46 Obligation: 10.24/3.46 Q restricted rewrite system: 10.24/3.46 The TRS R consists of the following rules: 10.24/3.46 10.24/3.46 a(b(b(b(x1)))) -> a(a(b(a(x1)))) 10.24/3.46 a(a(b(b(a(x1))))) -> a(b(a(b(a(x1))))) 10.24/3.46 b(a(b(b(a(x1))))) -> b(b(a(b(a(x1))))) 10.24/3.46 a(a(a(a(a(x1))))) -> a(b(b(b(a(x1))))) 10.24/3.46 b(a(a(a(a(x1))))) -> b(b(b(b(a(x1))))) 10.24/3.46 10.24/3.46 Q is empty. 10.24/3.46 10.24/3.46 ---------------------------------------- 10.24/3.46 10.24/3.46 (3) RootLabelingProof (EQUIVALENT) 10.24/3.46 We used plain root labeling [ROOTLAB] with the following heuristic: 10.24/3.46 LabelAll: All function symbols get labeled 10.24/3.46 10.24/3.46 As Q is empty the root labeling was sound AND complete. 10.24/3.46 10.24/3.46 ---------------------------------------- 10.24/3.46 10.24/3.46 (4) 10.24/3.46 Obligation: 10.24/3.46 Q restricted rewrite system: 10.24/3.46 The TRS R consists of the following rules: 10.24/3.46 10.24/3.46 a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(x1)))) 10.24/3.46 a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1)))) 10.24/3.46 a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1))))) -> a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(x1))))) 10.24/3.46 a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1))))) -> a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1))))) 10.24/3.46 b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1))))) -> b_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(x1))))) 10.24/3.46 b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1))))) -> b_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1))))) 10.24/3.46 a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1))))) 10.24/3.46 a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1))))) 10.24/3.46 b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1))))) 10.24/3.46 b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1))))) 10.24/3.46 10.24/3.46 Q is empty. 10.24/3.46 10.24/3.46 ---------------------------------------- 10.24/3.46 10.24/3.46 (5) QTRSRRRProof (EQUIVALENT) 10.24/3.46 Used ordering: 10.24/3.46 Polynomial interpretation [POLO]: 10.24/3.46 10.24/3.46 POL(a_{a_1}(x_1)) = 1 + x_1 10.24/3.46 POL(a_{b_1}(x_1)) = 1 + x_1 10.24/3.46 POL(b_{a_1}(x_1)) = x_1 10.24/3.46 POL(b_{b_1}(x_1)) = 1 + x_1 10.24/3.46 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 10.24/3.46 10.24/3.46 a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1)))) 10.24/3.46 a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1))))) -> a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(x1))))) 10.24/3.46 a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1))))) -> a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(a_{b_1}(x1))))) 10.24/3.46 a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1))))) popout

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all output return to SRS_Standard 2019-03-29 03.29