details

property	value
status	complete
benchmark	13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n035.star.cs.uiowa.edu
space	Zantema_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	11.3597 seconds
cpu usage	38.5949
user time	37.2194
system time	1.3755
max virtual memory	4.1934304E7
max residence set size	4042816.0

stage attributes

key	value
starexec-result	YES

output

30.58/8.69 YES 38.30/10.68 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 38.30/10.68 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 38.30/10.68 38.30/10.68 38.30/10.68 Termination w.r.t. Q of the given QTRS could be proven: 38.30/10.68 38.30/10.68 (0) QTRS 38.30/10.68 (1) QTRSRRRProof [EQUIVALENT, 44 ms] 38.30/10.68 (2) QTRS 38.30/10.68 (3) DependencyPairsProof [EQUIVALENT, 18 ms] 38.30/10.68 (4) QDP 38.30/10.68 (5) QDPOrderProof [EQUIVALENT, 159 ms] 38.30/10.68 (6) QDP 38.30/10.68 (7) QDPOrderProof [EQUIVALENT, 267 ms] 38.30/10.68 (8) QDP 38.30/10.68 (9) DependencyGraphProof [EQUIVALENT, 0 ms] 38.30/10.68 (10) TRUE 38.30/10.68 38.30/10.68 38.30/10.68 ---------------------------------------- 38.30/10.68 38.30/10.68 (0) 38.30/10.68 Obligation: 38.30/10.68 Q restricted rewrite system: 38.30/10.68 The TRS R consists of the following rules: 38.30/10.68 38.30/10.68 a(a(a(b(b(x1))))) -> b(b(b(x1))) 38.30/10.68 b(a(a(a(b(x1))))) -> a(a(a(b(a(a(a(x1))))))) 38.30/10.68 a(a(a(x1))) -> a(a(x1)) 38.30/10.68 b(b(x1)) -> a(b(a(x1))) 38.30/10.68 38.30/10.68 Q is empty. 38.30/10.68 38.30/10.68 ---------------------------------------- 38.30/10.68 38.30/10.68 (1) QTRSRRRProof (EQUIVALENT) 38.30/10.68 Used ordering: 38.30/10.68 Polynomial interpretation [POLO]: 38.30/10.68 38.30/10.68 POL(a(x_1)) = 1 + x_1 38.30/10.68 POL(b(x_1)) = 3 + x_1 38.30/10.68 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 38.30/10.68 38.30/10.68 a(a(a(x1))) -> a(a(x1)) 38.30/10.68 b(b(x1)) -> a(b(a(x1))) 38.30/10.68 38.30/10.68 38.30/10.68 38.30/10.68 38.30/10.68 ---------------------------------------- 38.30/10.68 38.30/10.68 (2) 38.30/10.68 Obligation: 38.30/10.68 Q restricted rewrite system: 38.30/10.68 The TRS R consists of the following rules: 38.30/10.68 38.30/10.68 a(a(a(b(b(x1))))) -> b(b(b(x1))) 38.30/10.68 b(a(a(a(b(x1))))) -> a(a(a(b(a(a(a(x1))))))) 38.30/10.68 38.30/10.68 Q is empty. 38.30/10.68 38.30/10.68 ---------------------------------------- 38.30/10.68 38.30/10.68 (3) DependencyPairsProof (EQUIVALENT) 38.30/10.68 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 38.30/10.68 ---------------------------------------- 38.30/10.68 38.30/10.68 (4) 38.30/10.68 Obligation: 38.30/10.68 Q DP problem: 38.30/10.68 The TRS P consists of the following rules: 38.30/10.68 38.30/10.68 A(a(a(b(b(x1))))) -> B(b(b(x1))) 38.30/10.68 B(a(a(a(b(x1))))) -> A(a(a(b(a(a(a(x1))))))) 38.30/10.68 B(a(a(a(b(x1))))) -> A(a(b(a(a(a(x1)))))) 38.30/10.68 B(a(a(a(b(x1))))) -> A(b(a(a(a(x1))))) 38.30/10.68 B(a(a(a(b(x1))))) -> B(a(a(a(x1)))) 38.30/10.68 B(a(a(a(b(x1))))) -> A(a(a(x1))) 38.30/10.68 B(a(a(a(b(x1))))) -> A(a(x1)) 38.30/10.68 B(a(a(a(b(x1))))) -> A(x1) 38.30/10.68 38.30/10.68 The TRS R consists of the following rules: 38.30/10.68 38.30/10.68 a(a(a(b(b(x1))))) -> b(b(b(x1))) 38.30/10.68 b(a(a(a(b(x1))))) -> a(a(a(b(a(a(a(x1))))))) 38.30/10.69 38.30/10.69 Q is empty. 38.30/10.69 We have to consider all minimal (P,Q,R)-chains. 38.30/10.69 ---------------------------------------- 38.30/10.69 38.30/10.69 (5) QDPOrderProof (EQUIVALENT) 38.30/10.69 We use the reduction pair processor [LPAR04,JAR06]. 38.30/10.69 38.30/10.69 38.30/10.69 The following pairs can be oriented strictly and are deleted. 38.30/10.69 38.30/10.69 B(a(a(a(b(x1))))) -> A(a(b(a(a(a(x1)))))) 38.30/10.69 B(a(a(a(b(x1))))) -> A(b(a(a(a(x1))))) 38.30/10.69 B(a(a(a(b(x1))))) -> B(a(a(a(x1)))) popout

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all output return to SRS_Standard 2019-03-29 03.29