details

property	value
status	complete
benchmark	thiemann24.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.692 seconds
cpu usage	993.273
user time	985.388
system time	7.88569
max virtual memory	5.6805076E7
max residence set size	8586008.0

stage attributes

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

output

WORST_CASE(Omega(n^2), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 261 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 46 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 21 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^2, INF) (20) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: lt(0, s(x)) -> true lt(x, 0) -> false lt(s(x), s(y)) -> lt(x, y) times(0, y) -> 0 times(s(x), y) -> plus(y, times(x, y)) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) fac(x) -> loop(x, s(0), s(0)) loop(x, c, y) -> if(lt(x, c), x, c, y) if(false, x, c, y) -> loop(x, s(c), times(y, s(c))) if(true, x, c, y) -> y S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: lt(0', s(x)) -> true lt(x, 0') -> false lt(s(x), s(y)) -> lt(x, y) times(0', y) -> 0' times(s(x), y) -> plus(y, times(x, y)) plus(0', y) -> y plus(s(x), y) -> s(plus(x, y)) fac(x) -> loop(x, s(0'), s(0')) loop(x, c, y) -> if(lt(x, c), x, c, y) if(false, x, c, y) -> loop(x, s(c), times(y, s(c))) if(true, x, c, y) -> y S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: lt(0', s(x)) -> true lt(x, 0') -> false lt(s(x), s(y)) -> lt(x, y) times(0', y) -> 0' times(s(x), y) -> plus(y, times(x, y)) plus(0', y) -> y plus(s(x), y) -> s(plus(x, y)) fac(x) -> loop(x, s(0'), s(0')) loop(x, c, y) -> if(lt(x, c), x, c, y) if(false, x, c, y) -> loop(x, s(c), times(y, s(c))) popout

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all output return to Runtime Complexity: TRS