details

property	value
status	complete
benchmark	thiemann34.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	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	292.557828903 seconds
cpu usage	1094.23659598
max memory	1.3151711232E10

stage attributes

key	value
output-size	22916
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

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^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (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), 1 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 807 ms] (10) BOUNDS(1, n^2) (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^2). The TRS R consists of the following rules: gt(s(x), 0) -> true gt(0, y) -> false gt(s(x), s(y)) -> gt(x, y) divides(x, y) -> div(x, y, y) div(0, 0, z) -> true div(0, s(x), z) -> false div(s(x), 0, s(z)) -> div(s(x), s(z), s(z)) div(s(x), s(y), z) -> div(x, y, z) prime(x) -> test(x, s(s(0))) test(x, y) -> if1(gt(x, y), x, y) if1(true, x, y) -> if2(divides(x, y), x, y) if1(false, x, y) -> true if2(true, x, y) -> false if2(false, x, y) -> test(x, s(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^2). The TRS R consists of the following rules: gt(s(x), 0) -> true [1] gt(0, y) -> false [1] gt(s(x), s(y)) -> gt(x, y) [1] divides(x, y) -> div(x, y, y) [1] div(0, 0, z) -> true [1] div(0, s(x), z) -> false [1] div(s(x), 0, s(z)) -> div(s(x), s(z), s(z)) [1] div(s(x), s(y), z) -> div(x, y, z) [1] prime(x) -> test(x, s(s(0))) [1] test(x, y) -> if1(gt(x, y), x, y) [1] if1(true, x, y) -> if2(divides(x, y), x, y) [1] if1(false, x, y) -> true [1] if2(true, x, y) -> false [1] if2(false, x, y) -> test(x, s(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: 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