details

property	value
status	complete
benchmark	aprove2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	11.0279 seconds
cpu usage	39.4163
user time	37.4576
system time	1.95869
max virtual memory	1.8899808E7
max residence set size	4147316.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 496 ms] (10) BOUNDS(1, n^1) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 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: ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) div(x, y) -> ify(ge(y, s(0)), x, y) ify(false, x, y) -> divByZeroError ify(true, x, y) -> if(ge(x, y), x, y) if(false, x, y) -> 0 if(true, x, y) -> s(div(minus(x, y), 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: ge(x, 0) -> true [1] ge(0, s(x)) -> false [1] ge(s(x), s(y)) -> ge(x, y) [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] div(x, y) -> ify(ge(y, s(0)), x, y) [1] ify(false, x, y) -> divByZeroError [1] ify(true, x, y) -> if(ge(x, y), x, y) [1] if(false, x, y) -> 0 [1] if(true, x, y) -> s(div(minus(x, y), 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: ge(x, 0) -> true [1] ge(0, s(x)) -> false [1] ge(s(x), s(y)) -> ge(x, y) [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] div(x, y) -> ify(ge(y, s(0)), x, y) [1] ify(false, x, y) -> divByZeroError [1] ify(true, x, y) -> if(ge(x, y), x, y) [1] if(false, x, y) -> 0 [1] if(true, x, y) -> s(div(minus(x, y), y)) [1] The TRS has the following type information: ge :: 0:s:divByZeroError -> 0:s:divByZeroError -> true:false 0 :: 0:s:divByZeroError popout

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actions

all output return to Runtime Complexity: TRS Innermost