details

property	value
status	complete
benchmark	2.42.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.16719 seconds
cpu usage	16.4345
user time	15.1007
system time	1.33386
max virtual memory	1.8812024E7
max residence set size	3543176.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) DependencyGraphProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsTAProof [FINISHED, 0 ms] (8) BOUNDS(1, n^1) (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (10) TRS for Loop Detection (11) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: flatten(nil) -> nil flatten(unit(x)) -> flatten(x) flatten(++(x, y)) -> ++(flatten(x), flatten(y)) flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y)) flatten(flatten(x)) -> flatten(x) rev(nil) -> nil rev(unit(x)) -> unit(x) rev(++(x, y)) -> ++(rev(y), rev(x)) rev(rev(x)) -> x ++(x, nil) -> x ++(nil, y) -> y ++(++(x, y), z) -> ++(x, ++(y, z)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DependencyGraphProof (UPPER BOUND(ID)) The following rules are not reachable from basic terms in the dependency graph and can be removed: rev(++(x, y)) -> ++(rev(y), rev(x)) rev(rev(x)) -> x ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: flatten(nil) -> nil flatten(unit(x)) -> flatten(x) flatten(++(x, y)) -> ++(flatten(x), flatten(y)) flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y)) flatten(flatten(x)) -> flatten(x) rev(nil) -> nil rev(unit(x)) -> unit(x) ++(x, nil) -> x ++(nil, y) -> y ++(++(x, y), z) -> ++(x, ++(y, z)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) NestedDefinedSymbolProof (UPPER BOUND(ID)) The TRS does not nest defined symbols. Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: flatten(++(x, y)) -> ++(flatten(x), flatten(y)) flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y)) flatten(flatten(x)) -> flatten(x) ++(++(x, y), z) -> ++(x, ++(y, z)) ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: flatten(nil) -> nil popout

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all output return to Runtime Complexity: TRS