details

property	value
status	complete
benchmark	#3.37.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n185.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.67458 seconds
cpu usage	3.78814
user time	3.63576
system time	0.152372
max virtual memory	1.8408912E7
max residence set size	236092.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 67 ms] (2) QTRS (3) Overlay + Local Confluence [EQUIVALENT, 0 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) UsableRulesProof [EQUIVALENT, 0 ms] (10) QDP (11) QReductionProof [EQUIVALENT, 0 ms] (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: not(true) -> false not(false) -> true evenodd(x, 0) -> not(evenodd(x, s(0))) evenodd(0, s(0)) -> false evenodd(s(x), s(0)) -> evenodd(x, 0) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(evenodd(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 POL(false) = 0 POL(not(x_1)) = x_1 POL(s(x_1)) = 2*x_1 POL(true) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: evenodd(0, s(0)) -> false ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: not(true) -> false not(false) -> true evenodd(x, 0) -> not(evenodd(x, s(0))) evenodd(s(x), s(0)) -> evenodd(x, 0) Q is empty. ---------------------------------------- (3) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: not(true) -> false not(false) -> true evenodd(x, 0) -> not(evenodd(x, s(0))) evenodd(s(x), s(0)) -> evenodd(x, 0) The set Q consists of the following terms: not(true) not(false) evenodd(x0, 0) evenodd(s(x0), s(0)) ---------------------------------------- (5) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. popout

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all output return to TRS Standard