details

property	value
status	complete
benchmark	evenodd.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.97393 seconds
cpu usage	14.0747
user time	12.6702
system time	1.40451
max virtual memory	1.8873936E7
max residence set size	3886228.0

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/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) CpxTrsMatchBoundsTAProof [FINISHED, 0 ms] (4) BOUNDS(1, n^1) (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTRS (7) SlicingProof [LOWER BOUND(ID), 0 ms] (8) CpxTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 139 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: odd(Cons(x, xs)) -> even(xs) odd(Nil) -> False even(Cons(x, xs)) -> odd(xs) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False even(Nil) -> True evenodd(x) -> even(x) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (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: odd(Cons(x, xs)) -> even(xs) odd(Nil) -> False even(Cons(x, xs)) -> odd(xs) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False even(Nil) -> True evenodd(x) -> even(x) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsMatchBoundsTAProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 1. The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: final states : [1, 2, 3, 4] transitions: Cons0(0, 0) -> 0 Nil0() -> 0 False0() -> 0 True0() -> 0 odd0(0) -> 1 even0(0) -> 2 notEmpty0(0) -> 3 evenodd0(0) -> 4 even1(0) -> 1 False1() -> 1 odd1(0) -> 2 True1() -> 3 False1() -> 3 True1() -> 2 even1(0) -> 4 even1(0) -> 2 False1() -> 2 odd1(0) -> 1 odd1(0) -> 4 True1() -> 1 True1() -> 4 False1() -> 4 popout

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all output return to Runtime Complexity: TRS Innermost