details

property	value
status	complete
benchmark	z026.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n072.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.37835 seconds
cpu usage	13.735
user time	13.0961
system time	0.638927
max virtual memory	7.8897416E7
max residence set size	1657500.0

stage attributes

key	value
starexec-result	YES

output

13.06/4.18 YES 13.52/4.31 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 13.52/4.31 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.52/4.31 13.52/4.31 13.52/4.31 Termination w.r.t. Q of the given QTRS could be proven: 13.52/4.31 13.52/4.31 (0) QTRS 13.52/4.31 (1) FlatCCProof [EQUIVALENT, 0 ms] 13.52/4.31 (2) QTRS 13.52/4.31 (3) RootLabelingProof [EQUIVALENT, 0 ms] 13.52/4.31 (4) QTRS 13.52/4.31 (5) DependencyPairsProof [EQUIVALENT, 29 ms] 13.52/4.31 (6) QDP 13.52/4.31 (7) QDPOrderProof [EQUIVALENT, 212 ms] 13.52/4.31 (8) QDP 13.52/4.31 (9) PisEmptyProof [EQUIVALENT, 0 ms] 13.52/4.31 (10) YES 13.52/4.31 13.52/4.31 13.52/4.31 ---------------------------------------- 13.52/4.31 13.52/4.31 (0) 13.52/4.31 Obligation: 13.52/4.31 Q restricted rewrite system: 13.52/4.31 The TRS R consists of the following rules: 13.52/4.31 13.52/4.31 a(b(b(x1))) -> b(a(a(x1))) 13.52/4.31 a(a(b(x1))) -> b(b(a(x1))) 13.52/4.31 13.52/4.31 Q is empty. 13.52/4.31 13.52/4.31 ---------------------------------------- 13.52/4.31 13.52/4.31 (1) FlatCCProof (EQUIVALENT) 13.52/4.31 We used flat context closure [ROOTLAB] 13.52/4.31 As Q is empty the flat context closure was sound AND complete. 13.52/4.31 13.52/4.31 ---------------------------------------- 13.52/4.31 13.52/4.31 (2) 13.52/4.31 Obligation: 13.52/4.31 Q restricted rewrite system: 13.52/4.31 The TRS R consists of the following rules: 13.52/4.31 13.52/4.31 a(a(b(b(x1)))) -> a(b(a(a(x1)))) 13.52/4.31 b(a(b(b(x1)))) -> b(b(a(a(x1)))) 13.52/4.31 a(a(a(b(x1)))) -> a(b(b(a(x1)))) 13.52/4.31 b(a(a(b(x1)))) -> b(b(b(a(x1)))) 13.52/4.31 13.52/4.31 Q is empty. 13.52/4.31 13.52/4.31 ---------------------------------------- 13.52/4.31 13.52/4.31 (3) RootLabelingProof (EQUIVALENT) 13.52/4.31 We used plain root labeling [ROOTLAB] with the following heuristic: 13.52/4.31 LabelAll: All function symbols get labeled 13.52/4.31 13.52/4.31 As Q is empty the root labeling was sound AND complete. 13.52/4.31 13.52/4.31 ---------------------------------------- 13.52/4.31 13.52/4.31 (4) 13.52/4.31 Obligation: 13.52/4.31 Q restricted rewrite system: 13.52/4.31 The TRS R consists of the following rules: 13.52/4.31 13.52/4.31 a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) 13.52/4.31 a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> a_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) 13.52/4.31 b_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) 13.52/4.31 b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) 13.52/4.31 a_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) 13.52/4.31 a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) 13.52/4.31 b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) 13.52/4.31 b_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) 13.52/4.31 13.52/4.31 Q is empty. 13.52/4.31 13.52/4.31 ---------------------------------------- 13.52/4.31 13.52/4.31 (5) DependencyPairsProof (EQUIVALENT) 13.52/4.31 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 13.52/4.31 ---------------------------------------- 13.52/4.31 13.52/4.31 (6) 13.52/4.31 Obligation: 13.52/4.31 Q DP problem: 13.52/4.31 The TRS P consists of the following rules: 13.52/4.31 13.52/4.31 A_{A_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> B_{A_1}(a_{a_1}(a_{a_1}(x1))) 13.52/4.31 A_{A_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> A_{A_1}(a_{a_1}(x1)) 13.52/4.31 A_{A_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> A_{A_1}(x1) 13.52/4.31 A_{A_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> B_{A_1}(a_{a_1}(a_{b_1}(x1))) 13.52/4.31 A_{A_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> A_{A_1}(a_{b_1}(x1)) 13.52/4.31 B_{A_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> B_{A_1}(a_{a_1}(a_{a_1}(x1))) 13.52/4.31 B_{A_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> A_{A_1}(a_{a_1}(x1)) 13.52/4.31 B_{A_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))) -> A_{A_1}(x1) 13.52/4.31 B_{A_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> B_{A_1}(a_{a_1}(a_{b_1}(x1))) 13.52/4.31 B_{A_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))) -> A_{A_1}(a_{b_1}(x1)) 13.52/4.31 A_{A_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> B_{A_1}(a_{a_1}(x1)) popout

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all output return to SRS_Standard 2019-03-29 03.29