details

property	value
status	complete
benchmark	ex4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n068.star.cs.uiowa.edu
space	Mixed_outermost

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.0039 seconds
cpu usage	5.14451
user time	4.91344
system time	0.231069
max virtual memory	1.8675372E7
max residence set size	511616.0

stage attributes

key	value
starexec-result	YES

output

4.90/1.93 YES 4.90/1.95 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 4.90/1.95 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.90/1.95 4.90/1.95 4.90/1.95 Outermost Termination of the given OTRS could be proven: 4.90/1.95 4.90/1.95 (0) OTRS 4.90/1.95 (1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms] 4.90/1.95 (2) QTRS 4.90/1.95 (3) QTRSRRRProof [EQUIVALENT, 29 ms] 4.90/1.95 (4) QTRS 4.90/1.95 (5) AAECC Innermost [EQUIVALENT, 0 ms] 4.90/1.95 (6) QTRS 4.90/1.95 (7) DependencyPairsProof [EQUIVALENT, 0 ms] 4.90/1.95 (8) QDP 4.90/1.95 (9) DependencyGraphProof [EQUIVALENT, 0 ms] 4.90/1.95 (10) AND 4.90/1.95 (11) QDP 4.90/1.95 (12) UsableRulesProof [EQUIVALENT, 0 ms] 4.90/1.95 (13) QDP 4.90/1.95 (14) QReductionProof [EQUIVALENT, 0 ms] 4.90/1.95 (15) QDP 4.90/1.95 (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] 4.90/1.95 (17) YES 4.90/1.95 (18) QDP 4.90/1.95 (19) UsableRulesProof [EQUIVALENT, 0 ms] 4.90/1.95 (20) QDP 4.90/1.95 (21) QReductionProof [EQUIVALENT, 0 ms] 4.90/1.95 (22) QDP 4.90/1.95 (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] 4.90/1.95 (24) YES 4.90/1.95 (25) QDP 4.90/1.95 (26) UsableRulesProof [EQUIVALENT, 0 ms] 4.90/1.95 (27) QDP 4.90/1.95 (28) QReductionProof [EQUIVALENT, 0 ms] 4.90/1.95 (29) QDP 4.90/1.95 (30) QDPOrderProof [EQUIVALENT, 28 ms] 4.90/1.95 (31) QDP 4.90/1.95 (32) PisEmptyProof [EQUIVALENT, 0 ms] 4.90/1.95 (33) YES 4.90/1.95 4.90/1.95 4.90/1.95 ---------------------------------------- 4.90/1.95 4.90/1.95 (0) 4.90/1.95 Obligation: 4.90/1.95 Term rewrite system R: 4.90/1.95 The TRS R consists of the following rules: 4.90/1.95 4.90/1.95 f(h(x)) -> f(i(x)) 4.90/1.95 f(i(x)) -> a 4.90/1.95 i(x) -> h(x) 4.90/1.95 4.90/1.95 4.90/1.95 4.90/1.95 Outermost Strategy. 4.90/1.95 4.90/1.95 ---------------------------------------- 4.90/1.95 4.90/1.95 (1) Raffelsieper-Zantema-Transformation (SOUND) 4.90/1.95 We applied the Raffelsieper-Zantema transformation to transform the outermost TRS to a standard TRS. 4.90/1.95 ---------------------------------------- 4.90/1.95 4.90/1.95 (2) 4.90/1.95 Obligation: 4.90/1.95 Q restricted rewrite system: 4.90/1.95 The TRS R consists of the following rules: 4.90/1.95 4.90/1.95 down(f(h(x))) -> up(f(i(x))) 4.90/1.95 down(f(i(x))) -> up(a) 4.90/1.95 down(i(x)) -> up(h(x)) 4.90/1.95 top(up(x)) -> top(down(x)) 4.90/1.95 down(h(y1)) -> h_flat(down(y1)) 4.90/1.95 down(f(f(y4))) -> f_flat(down(f(y4))) 4.90/1.95 down(f(a)) -> f_flat(down(a)) 4.90/1.95 down(f(fresh_constant)) -> f_flat(down(fresh_constant)) 4.90/1.95 f_flat(up(x_1)) -> up(f(x_1)) 4.90/1.95 h_flat(up(x_1)) -> up(h(x_1)) 4.90/1.95 i_flat(up(x_1)) -> up(i(x_1)) 4.90/1.95 4.90/1.95 Q is empty. 4.90/1.95 4.90/1.95 ---------------------------------------- 4.90/1.95 4.90/1.95 (3) QTRSRRRProof (EQUIVALENT) 4.90/1.95 Used ordering: 4.90/1.95 Polynomial interpretation [POLO]: 4.90/1.95 4.90/1.95 POL(a) = 0 4.90/1.95 POL(down(x_1)) = 2 + 2*x_1 4.90/1.95 POL(f(x_1)) = 2 + 2*x_1 4.90/1.95 POL(f_flat(x_1)) = 2 + 2*x_1 4.90/1.95 POL(fresh_constant) = 1 4.90/1.95 POL(h(x_1)) = x_1 4.90/1.95 POL(h_flat(x_1)) = x_1 4.90/1.95 POL(i(x_1)) = x_1 4.90/1.95 POL(i_flat(x_1)) = 1 + 2*x_1 4.90/1.95 POL(top(x_1)) = x_1 4.90/1.95 POL(up(x_1)) = 2 + 2*x_1 popout

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all output return to TRS_Outermost 2019-04-01 06.45