details

property	value
status	complete
benchmark	ack_prolog.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.511 seconds
cpu usage	1058.55
user time	1047.37
system time	11.1792
max virtual memory	5.6105728E7
max residence set size	1.5214884E7

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 702 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: ack_in(0, n) -> ack_out(s(n)) ack_in(s(m), 0) -> u11(ack_in(m, s(0))) u11(ack_out(n)) -> ack_out(n) ack_in(s(m), s(n)) -> u21(ack_in(s(m), n), m) u21(ack_out(n), m) -> u22(ack_in(m, n)) u22(ack_out(n)) -> ack_out(n) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: ack_in(0', n) -> ack_out(s(n)) ack_in(s(m), 0') -> u11(ack_in(m, s(0'))) u11(ack_out(n)) -> ack_out(n) ack_in(s(m), s(n)) -> u21(ack_in(s(m), n), m) u21(ack_out(n), m) -> u22(ack_in(m, n)) u22(ack_out(n)) -> ack_out(n) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules: ack_in(0', n) -> ack_out(s(n)) ack_in(s(m), 0') -> u11(ack_in(m, s(0'))) u11(ack_out(n)) -> ack_out(n) ack_in(s(m), s(n)) -> u21(ack_in(s(m), n), m) u21(ack_out(n), m) -> u22(ack_in(m, n)) u22(ack_out(n)) -> ack_out(n) Types: ack_in :: 0':s -> 0':s -> ack_out 0' :: 0':s ack_out :: 0':s -> ack_out s :: 0':s -> 0':s u11 :: ack_out -> ack_out u21 :: ack_out -> 0':s -> ack_out u22 :: ack_out -> ack_out hole_ack_out1_0 :: ack_out hole_0':s2_0 :: 0':s gen_0':s3_0 :: Nat -> 0':s ---------------------------------------- (5) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: ack_in, u21 They will be analysed ascendingly in the following order: ack_in = u21 popout

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

job log

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actions

all output return to Runtime Complexity: TRS Innermost