details

property	value
status	complete
benchmark	z012.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n159.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.51466 seconds
cpu usage	21.852
user time	21.1383
system time	0.713729
max virtual memory	2.047076E7
max residence set size	2039868.0

stage attributes

key	value
starexec-result	YES

output

21.19/6.36 YES 21.52/6.39 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 21.52/6.39 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 21.52/6.39 21.52/6.39 21.52/6.39 Termination w.r.t. Q of the given QTRS could be proven: 21.52/6.39 21.52/6.39 (0) QTRS 21.52/6.39 (1) QTRSRRRProof [EQUIVALENT, 37 ms] 21.52/6.39 (2) QTRS 21.52/6.39 (3) DependencyPairsProof [EQUIVALENT, 24 ms] 21.52/6.39 (4) QDP 21.52/6.39 (5) MRRProof [EQUIVALENT, 7 ms] 21.52/6.39 (6) QDP 21.52/6.39 (7) PisEmptyProof [EQUIVALENT, 0 ms] 21.52/6.39 (8) YES 21.52/6.39 21.52/6.39 21.52/6.39 ---------------------------------------- 21.52/6.39 21.52/6.39 (0) 21.52/6.39 Obligation: 21.52/6.39 Q restricted rewrite system: 21.52/6.39 The TRS R consists of the following rules: 21.52/6.39 21.52/6.39 a(x1) -> b(x1) 21.52/6.39 a(b(x1)) -> b(c(a(x1))) 21.52/6.39 b(x1) -> c(x1) 21.52/6.39 c(b(x1)) -> a(x1) 21.52/6.39 21.52/6.39 Q is empty. 21.52/6.39 21.52/6.39 ---------------------------------------- 21.52/6.39 21.52/6.39 (1) QTRSRRRProof (EQUIVALENT) 21.52/6.39 Used ordering: 21.52/6.39 Polynomial interpretation [POLO]: 21.52/6.39 21.52/6.39 POL(a(x_1)) = 1 + x_1 21.52/6.39 POL(b(x_1)) = 1 + x_1 21.52/6.39 POL(c(x_1)) = x_1 21.52/6.39 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 21.52/6.39 21.52/6.39 b(x1) -> c(x1) 21.52/6.39 21.52/6.39 21.52/6.39 21.52/6.39 21.52/6.39 ---------------------------------------- 21.52/6.39 21.52/6.39 (2) 21.52/6.39 Obligation: 21.52/6.39 Q restricted rewrite system: 21.52/6.39 The TRS R consists of the following rules: 21.52/6.39 21.52/6.39 a(x1) -> b(x1) 21.52/6.39 a(b(x1)) -> b(c(a(x1))) 21.52/6.39 c(b(x1)) -> a(x1) 21.52/6.39 21.52/6.39 Q is empty. 21.52/6.39 21.52/6.39 ---------------------------------------- 21.52/6.39 21.52/6.39 (3) DependencyPairsProof (EQUIVALENT) 21.52/6.39 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 21.52/6.39 ---------------------------------------- 21.52/6.39 21.52/6.39 (4) 21.52/6.39 Obligation: 21.52/6.39 Q DP problem: 21.52/6.39 The TRS P consists of the following rules: 21.52/6.39 21.52/6.39 A(b(x1)) -> C(a(x1)) 21.52/6.39 A(b(x1)) -> A(x1) 21.52/6.39 C(b(x1)) -> A(x1) 21.52/6.39 21.52/6.39 The TRS R consists of the following rules: 21.52/6.39 21.52/6.39 a(x1) -> b(x1) 21.52/6.39 a(b(x1)) -> b(c(a(x1))) 21.52/6.39 c(b(x1)) -> a(x1) 21.52/6.39 21.52/6.39 Q is empty. 21.52/6.39 We have to consider all minimal (P,Q,R)-chains. 21.52/6.39 ---------------------------------------- 21.52/6.39 21.52/6.39 (5) MRRProof (EQUIVALENT) 21.52/6.39 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 21.52/6.39 21.52/6.39 Strictly oriented dependency pairs: 21.52/6.39 21.52/6.39 A(b(x1)) -> C(a(x1)) 21.52/6.39 A(b(x1)) -> A(x1) 21.52/6.39 C(b(x1)) -> A(x1) 21.52/6.39 21.52/6.39 21.52/6.39 Used ordering: Polynomial interpretation [POLO]: 21.52/6.39 21.52/6.39 POL(A(x_1)) = 3 + 2*x_1 21.52/6.39 POL(C(x_1)) = 2*x_1 popout

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all output return to SRS_Standard 2019-03-29 03.29