details

property	value
status	complete
benchmark	cade09.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.631 seconds
cpu usage	1067.91
user time	1054.39
system time	13.5235
max virtual memory	3.7831844E7
max residence set size	1.4341332E7

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^2)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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, 479 ms] (10) BOUNDS(1, n^2) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 283 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 136 ms] (24) typed CpxTrs ---------------------------------------- (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: f(true, x, y) -> f(gt(x, y), x, round(s(y))) round(0) -> 0 round(s(0)) -> s(s(0)) round(s(s(x))) -> s(s(round(x))) gt(0, v) -> false gt(s(u), 0) -> true gt(s(u), s(v)) -> gt(u, v) 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: f(true, x, y) -> f(gt(x, y), x, round(s(y))) [1] round(0) -> 0 [1] round(s(0)) -> s(s(0)) [1] round(s(s(x))) -> s(s(round(x))) [1] gt(0, v) -> false [1] gt(s(u), 0) -> true [1] gt(s(u), s(v)) -> gt(u, v) [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: f(true, x, y) -> f(gt(x, y), x, round(s(y))) [1] round(0) -> 0 [1] round(s(0)) -> s(s(0)) [1] round(s(s(x))) -> s(s(round(x))) [1] gt(0, v) -> false [1] gt(s(u), 0) -> true [1] gt(s(u), s(v)) -> gt(u, v) [1] The TRS has the following type information: f :: true:false -> s:0 -> s:0 -> f true :: true:false gt :: s:0 -> s:0 -> true:false round :: s:0 -> s:0 s :: s:0 -> s:0 popout

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actions

all output return to Runtime Complexity: TRS Innermost