details

property	value
status	complete
benchmark	gcd_triple.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n078.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.481338978 seconds
cpu usage	311.643352877
max memory	5.462556672E9

stage attributes

key	value
output-size	4535
starexec-result	WORST_CASE(Omega(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), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: min(x, 0) -> 0 min(0, y) -> 0 min(s(x), s(y)) -> s(min(x, y)) max(x, 0) -> x max(0, y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0) -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y), z) -> gcd(-(max(x, y), min(x, y)), s(min(x, y)), z) gcd(x, s(y), s(z)) -> gcd(x, -(max(y, z), min(y, z)), s(min(y, z))) gcd(s(x), y, s(z)) -> gcd(-(max(x, z), min(x, z)), y, s(min(x, z))) gcd(x, 0, 0) -> x gcd(0, y, 0) -> y gcd(0, 0, z) -> z S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: min(x, 0) -> 0 min(0, y) -> 0 min(s(x), s(y)) -> s(min(x, y)) max(x, 0) -> x max(0, y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0) -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y), z) -> gcd(-(max(x, y), min(x, y)), s(min(x, y)), z) gcd(x, s(y), s(z)) -> gcd(x, -(max(y, z), min(y, z)), s(min(y, z))) gcd(s(x), y, s(z)) -> gcd(-(max(x, z), min(x, z)), y, s(min(x, z))) gcd(x, 0, 0) -> x gcd(0, y, 0) -> y gcd(0, 0, z) -> z S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence -(s(x), s(y)) ->^+ -(x, y) gives rise to a decreasing loop by considering the right hand sides subterm at position []. The pumping substitution is [x / s(x), y / s(y)]. The result substitution is [ ]. popout

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all output return to Runti Compl Full Rewri 10127