details

property	value
status	complete
benchmark	random-222.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n106.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.93947 seconds
cpu usage	14.8614
user time	14.2518
system time	0.609508
max virtual memory	6.2385776E7
max residence set size	1748976.0

stage attributes

key	value
starexec-result	YES

output

14.67/5.85 YES 14.67/5.88 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 14.67/5.88 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.67/5.88 14.67/5.88 14.67/5.88 Termination w.r.t. Q of the given QTRS could be proven: 14.67/5.88 14.67/5.88 (0) QTRS 14.67/5.88 (1) QTRSRRRProof [EQUIVALENT, 40 ms] 14.67/5.88 (2) QTRS 14.67/5.88 (3) DependencyPairsProof [EQUIVALENT, 10 ms] 14.67/5.88 (4) QDP 14.67/5.88 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 14.67/5.88 (6) AND 14.67/5.88 (7) QDP 14.67/5.88 (8) UsableRulesProof [EQUIVALENT, 0 ms] 14.67/5.88 (9) QDP 14.67/5.88 (10) DependencyGraphProof [EQUIVALENT, 0 ms] 14.67/5.88 (11) QDP 14.67/5.88 (12) UsableRulesProof [EQUIVALENT, 1 ms] 14.67/5.88 (13) QDP 14.67/5.88 (14) MRRProof [EQUIVALENT, 2 ms] 14.67/5.88 (15) QDP 14.67/5.88 (16) PisEmptyProof [EQUIVALENT, 0 ms] 14.67/5.88 (17) YES 14.67/5.88 (18) QDP 14.67/5.88 (19) UsableRulesProof [EQUIVALENT, 0 ms] 14.67/5.88 (20) QDP 14.67/5.88 (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] 14.67/5.88 (22) YES 14.67/5.88 14.67/5.88 14.67/5.88 ---------------------------------------- 14.67/5.88 14.67/5.88 (0) 14.67/5.88 Obligation: 14.67/5.88 Q restricted rewrite system: 14.67/5.88 The TRS R consists of the following rules: 14.67/5.88 14.67/5.88 a(b(a(a(x1)))) -> a(b(b(b(x1)))) 14.67/5.88 b(b(a(a(x1)))) -> a(b(a(b(x1)))) 14.67/5.88 b(a(a(b(x1)))) -> b(a(b(a(x1)))) 14.67/5.88 14.67/5.88 Q is empty. 14.67/5.88 14.67/5.88 ---------------------------------------- 14.67/5.88 14.67/5.88 (1) QTRSRRRProof (EQUIVALENT) 14.67/5.88 Used ordering: 14.67/5.88 Polynomial interpretation [POLO]: 14.67/5.88 14.67/5.88 POL(a(x_1)) = 1 + x_1 14.67/5.88 POL(b(x_1)) = x_1 14.67/5.88 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 14.67/5.88 14.67/5.88 a(b(a(a(x1)))) -> a(b(b(b(x1)))) 14.67/5.88 14.67/5.88 14.67/5.88 14.67/5.88 14.67/5.88 ---------------------------------------- 14.67/5.88 14.67/5.88 (2) 14.67/5.88 Obligation: 14.67/5.88 Q restricted rewrite system: 14.67/5.88 The TRS R consists of the following rules: 14.67/5.88 14.67/5.88 b(b(a(a(x1)))) -> a(b(a(b(x1)))) 14.67/5.88 b(a(a(b(x1)))) -> b(a(b(a(x1)))) 14.67/5.88 14.67/5.88 Q is empty. 14.67/5.88 14.67/5.88 ---------------------------------------- 14.67/5.88 14.67/5.88 (3) DependencyPairsProof (EQUIVALENT) 14.67/5.88 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 14.67/5.88 ---------------------------------------- 14.67/5.88 14.67/5.88 (4) 14.67/5.88 Obligation: 14.67/5.88 Q DP problem: 14.67/5.88 The TRS P consists of the following rules: 14.67/5.88 14.67/5.88 B(b(a(a(x1)))) -> B(a(b(x1))) 14.67/5.88 B(b(a(a(x1)))) -> B(x1) 14.67/5.88 B(a(a(b(x1)))) -> B(a(b(a(x1)))) 14.67/5.88 B(a(a(b(x1)))) -> B(a(x1)) 14.67/5.88 14.67/5.88 The TRS R consists of the following rules: 14.67/5.88 14.67/5.88 b(b(a(a(x1)))) -> a(b(a(b(x1)))) 14.67/5.88 b(a(a(b(x1)))) -> b(a(b(a(x1)))) 14.67/5.88 14.67/5.88 Q is empty. 14.67/5.88 We have to consider all minimal (P,Q,R)-chains. 14.67/5.88 ---------------------------------------- 14.67/5.88 14.67/5.88 (5) DependencyGraphProof (EQUIVALENT) 14.67/5.88 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node. 14.67/5.88 ---------------------------------------- popout

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