details

property	value
status	complete
benchmark	sym-1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n153.star.cs.uiowa.edu
space	Waldmann_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.17818 seconds
cpu usage	5.54468
user time	5.27096
system time	0.273717
max virtual memory	1.9141892E7
max residence set size	650504.0

stage attributes

key	value
starexec-result	YES

output

5.37/2.12 YES 5.37/2.14 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 5.37/2.14 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.37/2.14 5.37/2.14 5.37/2.14 Termination w.r.t. Q of the given QTRS could be proven: 5.37/2.14 5.37/2.14 (0) QTRS 5.37/2.14 (1) FlatCCProof [EQUIVALENT, 0 ms] 5.37/2.14 (2) QTRS 5.37/2.14 (3) RootLabelingProof [EQUIVALENT, 0 ms] 5.37/2.14 (4) QTRS 5.37/2.14 (5) QTRSRRRProof [EQUIVALENT, 3 ms] 5.37/2.14 (6) QTRS 5.37/2.14 (7) QTRSRRRProof [EQUIVALENT, 0 ms] 5.37/2.14 (8) QTRS 5.37/2.14 (9) RisEmptyProof [EQUIVALENT, 2 ms] 5.37/2.14 (10) YES 5.37/2.14 5.37/2.14 5.37/2.14 ---------------------------------------- 5.37/2.14 5.37/2.14 (0) 5.37/2.14 Obligation: 5.37/2.14 Q restricted rewrite system: 5.37/2.14 The TRS R consists of the following rules: 5.37/2.14 5.37/2.14 a(a(x1)) -> a(b(a(x1))) 5.37/2.14 b(b(x1)) -> a(a(x1)) 5.37/2.14 a(b(b(a(x1)))) -> x1 5.37/2.14 5.37/2.14 Q is empty. 5.37/2.14 5.37/2.14 ---------------------------------------- 5.37/2.14 5.37/2.14 (1) FlatCCProof (EQUIVALENT) 5.37/2.14 We used flat context closure [ROOTLAB] 5.37/2.14 As Q is empty the flat context closure was sound AND complete. 5.37/2.14 5.37/2.14 ---------------------------------------- 5.37/2.14 5.37/2.14 (2) 5.37/2.14 Obligation: 5.37/2.14 Q restricted rewrite system: 5.37/2.14 The TRS R consists of the following rules: 5.37/2.14 5.37/2.14 a(a(x1)) -> a(b(a(x1))) 5.37/2.14 a(b(b(x1))) -> a(a(a(x1))) 5.37/2.14 b(b(b(x1))) -> b(a(a(x1))) 5.37/2.14 a(a(b(b(a(x1))))) -> a(x1) 5.37/2.14 b(a(b(b(a(x1))))) -> b(x1) 5.37/2.14 5.37/2.14 Q is empty. 5.37/2.14 5.37/2.14 ---------------------------------------- 5.37/2.14 5.37/2.14 (3) RootLabelingProof (EQUIVALENT) 5.37/2.14 We used plain root labeling [ROOTLAB] with the following heuristic: 5.37/2.14 LabelAll: All function symbols get labeled 5.37/2.14 5.37/2.14 As Q is empty the root labeling was sound AND complete. 5.37/2.14 5.37/2.14 ---------------------------------------- 5.37/2.14 5.37/2.14 (4) 5.37/2.14 Obligation: 5.37/2.14 Q restricted rewrite system: 5.37/2.14 The TRS R consists of the following rules: 5.37/2.14 5.37/2.14 a_{a_1}(a_{a_1}(x1)) -> a_{b_1}(b_{a_1}(a_{a_1}(x1))) 5.37/2.14 a_{a_1}(a_{b_1}(x1)) -> a_{b_1}(b_{a_1}(a_{b_1}(x1))) 5.37/2.14 a_{b_1}(b_{b_1}(b_{a_1}(x1))) -> a_{a_1}(a_{a_1}(a_{a_1}(x1))) 5.37/2.14 a_{b_1}(b_{b_1}(b_{b_1}(x1))) -> a_{a_1}(a_{a_1}(a_{b_1}(x1))) 5.37/2.14 b_{b_1}(b_{b_1}(b_{a_1}(x1))) -> b_{a_1}(a_{a_1}(a_{a_1}(x1))) 5.37/2.14 b_{b_1}(b_{b_1}(b_{b_1}(x1))) -> b_{a_1}(a_{a_1}(a_{b_1}(x1))) 5.37/2.14 a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1))))) -> a_{a_1}(x1) 5.37/2.14 a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1))))) -> a_{b_1}(x1) 5.37/2.14 b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1))))) -> b_{a_1}(x1) 5.37/2.14 b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1))))) -> b_{b_1}(x1) 5.37/2.14 5.37/2.14 Q is empty. 5.37/2.14 5.37/2.14 ---------------------------------------- 5.37/2.14 5.37/2.14 (5) QTRSRRRProof (EQUIVALENT) 5.37/2.14 Used ordering: 5.37/2.14 Polynomial interpretation [POLO]: 5.37/2.14 5.37/2.14 POL(a_{a_1}(x_1)) = 1 + x_1 5.37/2.14 POL(a_{b_1}(x_1)) = 1 + x_1 5.37/2.14 POL(b_{a_1}(x_1)) = x_1 5.37/2.14 POL(b_{b_1}(x_1)) = 3 + x_1 5.37/2.14 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 5.37/2.14 5.37/2.14 a_{b_1}(b_{b_1}(b_{a_1}(x1))) -> a_{a_1}(a_{a_1}(a_{a_1}(x1))) 5.37/2.14 a_{b_1}(b_{b_1}(b_{b_1}(x1))) -> a_{a_1}(a_{a_1}(a_{b_1}(x1))) 5.37/2.14 b_{b_1}(b_{b_1}(b_{a_1}(x1))) -> b_{a_1}(a_{a_1}(a_{a_1}(x1))) 5.37/2.14 b_{b_1}(b_{b_1}(b_{b_1}(x1))) -> b_{a_1}(a_{a_1}(a_{b_1}(x1))) 5.37/2.14 a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1))))) -> a_{a_1}(x1) 5.37/2.14 a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1))))) -> a_{b_1}(x1) popout

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all output return to SRS_Standard 2019-03-29 03.29