details

property	value
status	complete
benchmark	mod.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.55 seconds
cpu usage	306.195
user time	304.535
system time	1.66011
max virtual memory	1.8281072E7
max residence set size	5168344.0

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 277 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), 32 ms] (14) typed CpxTrs ---------------------------------------- (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: minus(0, y) -> 0 minus(s(x), y) -> if(gt(s(x), y), x, y) if(true, x, y) -> s(minus(x, y)) if(false, x, y) -> 0 mod(x, 0) -> 0 mod(x, s(y)) -> if1(lt(x, s(y)), x, s(y)) if1(true, x, y) -> x if1(false, x, y) -> mod(minus(x, y), y) gt(0, y) -> false gt(s(x), 0) -> true gt(s(x), s(y)) -> gt(x, y) lt(x, 0) -> false lt(0, s(x)) -> true lt(s(x), s(y)) -> lt(x, 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^1, INF). The TRS R consists of the following rules: minus(0', y) -> 0' minus(s(x), y) -> if(gt(s(x), y), x, y) if(true, x, y) -> s(minus(x, y)) if(false, x, y) -> 0' mod(x, 0') -> 0' mod(x, s(y)) -> if1(lt(x, s(y)), x, s(y)) if1(true, x, y) -> x if1(false, x, y) -> mod(minus(x, y), y) gt(0', y) -> false gt(s(x), 0') -> true gt(s(x), s(y)) -> gt(x, y) lt(x, 0') -> false lt(0', s(x)) -> true lt(s(x), s(y)) -> lt(x, y) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: minus(0', y) -> 0' minus(s(x), y) -> if(gt(s(x), y), x, y) if(true, x, y) -> s(minus(x, y)) if(false, x, y) -> 0' mod(x, 0') -> 0' mod(x, s(y)) -> if1(lt(x, s(y)), x, s(y)) if1(true, x, y) -> x if1(false, x, y) -> mod(minus(x, y), y) gt(0', y) -> false gt(s(x), 0') -> true popout

output may be truncated. 'popout' for the full output.

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all output return to Runtime Complexity: TRS