details

property	value
status	complete
benchmark	un06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n136.star.cs.uiowa.edu
space	Trafo_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	8.66604 seconds
cpu usage	30.4019
user time	29.1704
system time	1.23146
max virtual memory	4.1099632E7
max residence set size	3284996.0

stage attributes

key	value
starexec-result	YES

output

30.08/8.56 YES 30.25/8.61 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 30.25/8.61 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 30.25/8.61 30.25/8.61 30.25/8.61 Termination w.r.t. Q of the given QTRS could be proven: 30.25/8.61 30.25/8.61 (0) QTRS 30.25/8.61 (1) DependencyPairsProof [EQUIVALENT, 15 ms] 30.25/8.61 (2) QDP 30.25/8.61 (3) DependencyGraphProof [EQUIVALENT, 5 ms] 30.25/8.61 (4) AND 30.25/8.61 (5) QDP 30.25/8.61 (6) QDPSizeChangeProof [EQUIVALENT, 0 ms] 30.25/8.61 (7) YES 30.25/8.61 (8) QDP 30.25/8.61 (9) QDPOrderProof [EQUIVALENT, 447 ms] 30.25/8.61 (10) QDP 30.25/8.61 (11) PisEmptyProof [EQUIVALENT, 0 ms] 30.25/8.61 (12) YES 30.25/8.61 30.25/8.61 30.25/8.61 ---------------------------------------- 30.25/8.61 30.25/8.61 (0) 30.25/8.61 Obligation: 30.25/8.61 Q restricted rewrite system: 30.25/8.61 The TRS R consists of the following rules: 30.25/8.61 30.25/8.61 b(b(x1)) -> b(a(b(a(a(b(x1)))))) 30.25/8.61 b(b(a(b(x1)))) -> b(a(b(b(x1)))) 30.25/8.61 b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(a(b(b(x1)))))) 30.25/8.61 b(b(a(a(b(x1))))) -> b(a(a(b(b(x1))))) 30.25/8.61 30.25/8.61 Q is empty. 30.25/8.61 30.25/8.61 ---------------------------------------- 30.25/8.61 30.25/8.61 (1) DependencyPairsProof (EQUIVALENT) 30.25/8.61 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 30.25/8.61 ---------------------------------------- 30.25/8.61 30.25/8.61 (2) 30.25/8.61 Obligation: 30.25/8.61 Q DP problem: 30.25/8.61 The TRS P consists of the following rules: 30.25/8.61 30.25/8.61 B(b(x1)) -> B(a(b(a(a(b(x1)))))) 30.25/8.61 B(b(x1)) -> B(a(a(b(x1)))) 30.25/8.61 B(b(a(b(x1)))) -> B(a(b(b(x1)))) 30.25/8.61 B(b(a(b(x1)))) -> B(b(x1)) 30.25/8.61 B(a(a(a(b(a(a(b(x1)))))))) -> B(a(a(a(b(b(x1)))))) 30.25/8.61 B(a(a(a(b(a(a(b(x1)))))))) -> B(b(x1)) 30.25/8.61 B(b(a(a(b(x1))))) -> B(a(a(b(b(x1))))) 30.25/8.61 B(b(a(a(b(x1))))) -> B(b(x1)) 30.25/8.61 30.25/8.61 The TRS R consists of the following rules: 30.25/8.61 30.25/8.61 b(b(x1)) -> b(a(b(a(a(b(x1)))))) 30.25/8.61 b(b(a(b(x1)))) -> b(a(b(b(x1)))) 30.25/8.61 b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(a(b(b(x1)))))) 30.25/8.61 b(b(a(a(b(x1))))) -> b(a(a(b(b(x1))))) 30.25/8.61 30.25/8.61 Q is empty. 30.25/8.61 We have to consider all minimal (P,Q,R)-chains. 30.25/8.61 ---------------------------------------- 30.25/8.61 30.25/8.61 (3) DependencyGraphProof (EQUIVALENT) 30.25/8.61 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 5 less nodes. 30.25/8.61 ---------------------------------------- 30.25/8.61 30.25/8.61 (4) 30.25/8.61 Complex Obligation (AND) 30.25/8.61 30.25/8.61 ---------------------------------------- 30.25/8.61 30.25/8.61 (5) 30.25/8.61 Obligation: 30.25/8.61 Q DP problem: 30.25/8.61 The TRS P consists of the following rules: 30.25/8.61 30.25/8.61 B(b(a(a(b(x1))))) -> B(b(x1)) 30.25/8.61 B(b(a(b(x1)))) -> B(b(x1)) 30.25/8.61 30.25/8.61 The TRS R consists of the following rules: 30.25/8.61 30.25/8.61 b(b(x1)) -> b(a(b(a(a(b(x1)))))) 30.25/8.61 b(b(a(b(x1)))) -> b(a(b(b(x1)))) 30.25/8.61 b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(a(b(b(x1)))))) 30.25/8.61 b(b(a(a(b(x1))))) -> b(a(a(b(b(x1))))) 30.25/8.61 30.25/8.61 Q is empty. 30.25/8.61 We have to consider all minimal (P,Q,R)-chains. 30.25/8.61 ---------------------------------------- 30.25/8.61 30.25/8.61 (6) QDPSizeChangeProof (EQUIVALENT) 30.25/8.61 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 30.25/8.61 30.25/8.61 From the DPs we obtained the following set of size-change graphs: 30.25/8.61 *B(b(a(a(b(x1))))) -> B(b(x1)) popout

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