details

property	value
status	complete
benchmark	otto03.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.132316113 seconds
cpu usage	901.096920717
max memory	5.823840256E9

stage attributes

key	value
output-size	15834
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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, 320 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: lt(0, s(x)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) fac(x) -> help(x, 0) help(x, c) -> if(lt(c, x), x, c) if(true, x, c) -> times(s(c), help(x, s(c))) if(false, x, c) -> s(0) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: help(x, []) help([], c) if(true, x, []) The defined contexts are: if([], x1, x2) [] just represents basic- or constructor-terms in the following defined contexts: if([], 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: lt(0, s(x)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) fac(x) -> help(x, 0) help(x, c) -> if(lt(c, x), x, c) if(true, x, c) -> times(s(c), help(x, s(c))) if(false, x, c) -> s(0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- popout

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actions

all output return to Runti Compl Full Rewri 10127