details

property	value
status	complete
benchmark	2.29.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	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.95588 seconds
cpu usage	23.5566
user time	22.0902
system time	1.46632
max virtual memory	1.8916976E7
max residence set size	3884328.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 152 ms] (12) BOUNDS(1, n^1) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxTRS (15) SlicingProof [LOWER BOUND(ID), 0 ms] (16) CpxTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 3787 ms] (22) proven lower bound (23) LowerBoundPropagationProof [FINISHED, 0 ms] (24) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)), s(x)) prime1(x, 0) -> false prime1(x, s(0)) -> true prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))) divp(x, y) -> =(rem(x, y), 0) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS does not nest defined symbols, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)), s(x)) prime1(x, 0) -> false prime1(x, s(0)) -> true prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))) divp(x, y) -> =(rem(x, y), 0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: prime(0) -> false [1] prime(s(0)) -> false [1] prime(s(s(x))) -> prime1(s(s(x)), s(x)) [1] prime1(x, 0) -> false [1] prime1(x, s(0)) -> true [1] prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))) [1] divp(x, y) -> =(rem(x, y), 0) [1] Rewrite Strategy: INNERMOST popout

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all output return to Runtime Complexity: TRS