details

property	value
status	complete
benchmark	ex1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n181.star.cs.uiowa.edu
space	Mixed_outermost

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.83191 seconds
cpu usage	5.02099
user time	4.7979
system time	0.223089
max virtual memory	1.847466E7
max residence set size	378528.0

stage attributes

key	value
starexec-result	YES

output

4.78/1.77 YES 4.78/1.78 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 4.78/1.78 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.78/1.78 4.78/1.78 4.78/1.78 Outermost Termination of the given OTRS could be proven: 4.78/1.78 4.78/1.78 (0) OTRS 4.78/1.78 (1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms] 4.78/1.78 (2) QTRS 4.78/1.78 (3) QTRSRRRProof [EQUIVALENT, 33 ms] 4.78/1.78 (4) QTRS 4.78/1.78 (5) QTRSRRRProof [EQUIVALENT, 16 ms] 4.78/1.78 (6) QTRS 4.78/1.78 (7) AAECC Innermost [EQUIVALENT, 0 ms] 4.78/1.78 (8) QTRS 4.78/1.78 (9) DependencyPairsProof [EQUIVALENT, 0 ms] 4.78/1.78 (10) QDP 4.78/1.78 (11) DependencyGraphProof [EQUIVALENT, 0 ms] 4.78/1.78 (12) QDP 4.78/1.78 (13) UsableRulesProof [EQUIVALENT, 0 ms] 4.78/1.78 (14) QDP 4.78/1.78 (15) QReductionProof [EQUIVALENT, 0 ms] 4.78/1.78 (16) QDP 4.78/1.78 (17) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms] 4.78/1.78 (18) YES 4.78/1.78 4.78/1.78 4.78/1.78 ---------------------------------------- 4.78/1.78 4.78/1.78 (0) 4.78/1.78 Obligation: 4.78/1.78 Term rewrite system R: 4.78/1.78 The TRS R consists of the following rules: 4.78/1.78 4.78/1.78 f(g(a)) -> a 4.78/1.78 f(f(x)) -> b 4.78/1.78 g(x) -> f(g(x)) 4.78/1.78 4.78/1.78 4.78/1.78 4.78/1.78 Outermost Strategy. 4.78/1.78 4.78/1.78 ---------------------------------------- 4.78/1.78 4.78/1.78 (1) Raffelsieper-Zantema-Transformation (SOUND) 4.78/1.78 We applied the Raffelsieper-Zantema transformation to transform the outermost TRS to a standard TRS. 4.78/1.78 ---------------------------------------- 4.78/1.78 4.78/1.78 (2) 4.78/1.78 Obligation: 4.78/1.78 Q restricted rewrite system: 4.78/1.78 The TRS R consists of the following rules: 4.78/1.78 4.78/1.78 down(f(g(a))) -> up(a) 4.78/1.78 down(f(f(x))) -> up(b) 4.78/1.78 down(g(x)) -> up(f(g(x))) 4.78/1.78 top(up(x)) -> top(down(x)) 4.78/1.78 down(f(a)) -> f_flat(down(a)) 4.78/1.78 down(f(b)) -> f_flat(down(b)) 4.78/1.78 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 4.78/1.78 down(f(g(f(y6)))) -> f_flat(down(g(f(y6)))) 4.78/1.78 down(f(g(g(y7)))) -> f_flat(down(g(g(y7)))) 4.78/1.78 down(f(g(b))) -> f_flat(down(g(b))) 4.78/1.78 down(f(g(fresh_constant))) -> f_flat(down(g(fresh_constant))) 4.78/1.78 f_flat(up(x_1)) -> up(f(x_1)) 4.78/1.78 g_flat(up(x_1)) -> up(g(x_1)) 4.78/1.78 4.78/1.78 Q is empty. 4.78/1.78 4.78/1.78 ---------------------------------------- 4.78/1.78 4.78/1.78 (3) QTRSRRRProof (EQUIVALENT) 4.78/1.78 Used ordering: 4.78/1.78 Polynomial interpretation [POLO]: 4.78/1.78 4.78/1.78 POL(a) = 0 4.78/1.78 POL(b) = 0 4.78/1.78 POL(down(x_1)) = 2 + 2*x_1 4.78/1.78 POL(f(x_1)) = x_1 4.78/1.78 POL(f_flat(x_1)) = x_1 4.78/1.78 POL(fresh_constant) = 0 4.78/1.78 POL(g(x_1)) = x_1 4.78/1.78 POL(g_flat(x_1)) = 1 + 2*x_1 4.78/1.78 POL(top(x_1)) = 2*x_1 4.78/1.78 POL(up(x_1)) = 2 + 2*x_1 4.78/1.78 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 4.78/1.78 4.78/1.78 g_flat(up(x_1)) -> up(g(x_1)) 4.78/1.78 4.78/1.78 4.78/1.78 4.78/1.78 4.78/1.78 ---------------------------------------- 4.78/1.78 4.78/1.78 (4) 4.78/1.78 Obligation: 4.78/1.78 Q restricted rewrite system: 4.78/1.78 The TRS R consists of the following rules: 4.78/1.78 popout

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all output return to TRS_Outermost 2019-04-01 06.45