details

property	value
status	complete
benchmark	Ex15_Luc06_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n029.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.88140511513 seconds
cpu usage	11.635048885
max memory	3.491565568E9

stage attributes

key	value
output-size	4982
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) CpxTrsMatchBoundsProof [FINISHED, 0 ms] (4) BOUNDS(1, n^1) (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: f(n__f(n__a)) -> f(n__g(n__f(n__a))) f(X) -> n__f(X) a -> n__a g(X) -> n__g(X) activate(n__f(X)) -> f(X) activate(n__a) -> a activate(n__g(X)) -> g(activate(X)) activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(n__f(n__a)) -> f(n__g(n__f(n__a))) f(X) -> n__f(X) a -> n__a g(X) -> n__g(X) activate(n__f(X)) -> f(X) activate(n__a) -> a activate(n__g(X)) -> g(activate(X)) activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. The certificate found is represented by the following graph. "[1, 2, 3, 4, 5, 6] {(1,2,[f_1|0, a|0, g_1|0, activate_1|0, n__f_1|1, n__a|1, n__g_1|1, f_1|1, a|1, n__f_1|2, n__a|2]), (1,3,[f_1|1, n__f_1|2]), (1,6,[g_1|1, n__g_1|2]), (2,2,[n__f_1|0, n__a|0, n__g_1|0]), (3,4,[n__g_1|1]), (4,5,[n__f_1|1]), (5,2,[n__a|1]), (6,2,[activate_1|1, f_1|1, n__f_1|1, a|1, n__a|1, n__g_1|1, n__f_1|2, n__a|2]), (6,6,[g_1|1, n__g_1|2]), (6,3,[f_1|1, n__f_1|2])}" ---------------------------------------- (4) BOUNDS(1, n^1) ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Runti Compl Inner Rewri 22807