details

property	value
status	complete
benchmark	cade14.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.512 seconds
cpu usage	1109.28
user time	1098.37
system time	10.9153
max virtual memory	3.811878E7
max residence set size	1.0227224E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 541 ms] (12) BOUNDS(1, n^2) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: diff(x, y) -> cond1(equal(x, y), x, y) cond1(true, x, y) -> 0 cond1(false, x, y) -> cond2(gt(x, y), x, y) cond2(true, x, y) -> s(diff(x, s(y))) cond2(false, x, y) -> s(diff(s(x), y)) gt(0, v) -> false gt(s(u), 0) -> true gt(s(u), s(v)) -> gt(u, v) equal(0, 0) -> true equal(s(x), 0) -> false equal(0, s(y)) -> false equal(s(x), s(y)) -> equal(x, y) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: diff([], y) diff(x, []) cond1(false, [], y) cond1(false, x, []) The defined contexts are: cond2([], x1, x2) cond1([], x1, x2) [] just represents basic- or constructor-terms in the following defined contexts: cond2([], x1, x2) cond1([], x1, x2) As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: diff(x, y) -> cond1(equal(x, y), x, y) cond1(true, x, y) -> 0 cond1(false, x, y) -> cond2(gt(x, y), x, y) cond2(true, x, y) -> s(diff(x, s(y))) cond2(false, x, y) -> s(diff(s(x), y)) gt(0, v) -> false gt(s(u), 0) -> true gt(s(u), s(v)) -> gt(u, v) equal(0, 0) -> true equal(s(x), 0) -> false equal(0, s(y)) -> false equal(s(x), s(y)) -> equal(x, y) S is empty. popout

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all output return to Runtime Complexity: TRS