details

property	value
status	complete
benchmark	#4.33.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	Strategy_removed_AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.655 seconds
cpu usage	1067.79
user time	1058.09
system time	9.69873
max virtual memory	3.7307168E7
max residence set size	1.0762304E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).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), 221 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), 43 ms] (14) proven lower bound (15) LowerBoundPropagationProof [FINISHED, 0 ms] (16) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) sum(cons(0, x), y) -> sum(x, y) sum(nil, y) -> y weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0, x))) weight(cons(n, nil)) -> 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^2, INF). The TRS R consists of the following rules: sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) sum(cons(0', x), y) -> sum(x, y) sum(nil, y) -> y weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0', x))) weight(cons(n, nil)) -> n S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules: sum(cons(s(n), x), cons(m, y)) -> sum(cons(n, x), cons(s(m), y)) sum(cons(0', x), y) -> sum(x, y) sum(nil, y) -> y weight(cons(n, cons(m, x))) -> weight(sum(cons(n, cons(m, x)), cons(0', x))) weight(cons(n, nil)) -> n Types: sum :: cons:nil -> cons:nil -> cons:nil cons :: s:0' -> cons:nil -> cons:nil s :: s:0' -> s:0' 0' :: s:0' nil :: cons:nil weight :: cons:nil -> s:0' hole_cons:nil1_0 :: cons:nil hole_s:0'2_0 :: s:0' gen_cons:nil3_0 :: Nat -> cons:nil gen_s:0'4_0 :: Nat -> s:0' ---------------------------------------- (5) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: sum, weight They will be analysed ascendingly in the following order: sum < weight 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