details

property	value
status	complete
benchmark	thiemann40.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.64908 seconds
cpu usage	19.7246
user time	18.2319
system time	1.4927
max virtual memory	3.7371588E7
max residence set size	3878040.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 9 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 172 ms] (10) BOUNDS(1, n^1) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 36 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) 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: nonZero(0) -> false nonZero(s(x)) -> true p(0) -> 0 p(s(x)) -> x id_inc(x) -> x id_inc(x) -> s(x) random(x) -> rand(x, 0) rand(x, y) -> if(nonZero(x), x, y) if(false, x, y) -> y if(true, x, y) -> rand(p(x), id_inc(y)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: nonZero(0) -> false [1] nonZero(s(x)) -> true [1] p(0) -> 0 [1] p(s(x)) -> x [1] id_inc(x) -> x [1] id_inc(x) -> s(x) [1] random(x) -> rand(x, 0) [1] rand(x, y) -> if(nonZero(x), x, y) [1] if(false, x, y) -> y [1] if(true, x, y) -> rand(p(x), id_inc(y)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: nonZero(0) -> false [1] nonZero(s(x)) -> true [1] p(0) -> 0 [1] p(s(x)) -> x [1] id_inc(x) -> x [1] id_inc(x) -> s(x) [1] random(x) -> rand(x, 0) [1] rand(x, y) -> if(nonZero(x), x, y) [1] if(false, x, y) -> y [1] if(true, x, y) -> rand(p(x), id_inc(y)) [1] The TRS has the following type information: nonZero :: 0:s -> false:true 0 :: 0:s popout

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job log

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actions

all output return to Runtime Complexity: TRS Innermost