details

property	value
status	complete
benchmark	gcdhard.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n056.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	13.414555788 seconds
cpu usage	48.020819584
max memory	4.394799104E9

stage attributes

key	value
output-size	29656
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

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^1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) 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, 1313 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: minus(0, x) -> 0 minus(s(x), 0) -> s(x) minus(s(x), s(y)) -> minus(x, y) mod(x, 0) -> 0 mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) if(true, x, y) -> x if(false, x, y) -> mod(minus(x, y), y) gcd(x, 0) -> x gcd(0, s(y)) -> s(y) gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) lt(x, 0) -> false lt(0, s(x)) -> true lt(s(x), s(y)) -> lt(x, 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: minus(0, x) -> 0 [1] minus(s(x), 0) -> s(x) [1] minus(s(x), s(y)) -> minus(x, y) [1] mod(x, 0) -> 0 [1] mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) [1] if(true, x, y) -> x [1] if(false, x, y) -> mod(minus(x, y), y) [1] gcd(x, 0) -> x [1] gcd(0, s(y)) -> s(y) [1] gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) [1] lt(x, 0) -> false [1] lt(0, s(x)) -> true [1] lt(s(x), s(y)) -> lt(x, 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: minus(0, x) -> 0 [1] minus(s(x), 0) -> s(x) [1] popout

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actions

all output return to Runti Compl Inner Rewri 22807