details

property	value
status	complete
benchmark	LISTUTILITIES_nosorts_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.12927 seconds
cpu usage	12.301
user time	11.4144
system time	0.886598
max virtual memory	1.8775776E7
max residence set size	3438488.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (8) CdtProblem (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 63 ms] (12) CdtProblem (13) CdtKnowledgeProof [FINISHED, 0 ms] (14) BOUNDS(1, 1) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 103 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) TRS for Loop Detection ---------------------------------------- (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: U11(tt, N, X, XS) -> U12(splitAt(activate(N), activate(XS)), activate(X)) U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS) afterNth(N, XS) -> snd(splitAt(N, XS)) and(tt, X) -> activate(X) fst(pair(X, Y)) -> X head(cons(N, XS)) -> N natsFrom(N) -> cons(N, n__natsFrom(s(N))) sel(N, XS) -> head(afterNth(N, XS)) snd(pair(X, Y)) -> Y splitAt(0, XS) -> pair(nil, XS) splitAt(s(N), cons(X, XS)) -> U11(tt, N, X, activate(XS)) tail(cons(N, XS)) -> activate(XS) take(N, XS) -> fst(splitAt(N, XS)) natsFrom(X) -> n__natsFrom(X) activate(n__natsFrom(X)) -> natsFrom(X) activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: U11(tt, z0, z1, z2) -> U12(splitAt(activate(z0), activate(z2)), activate(z1)) U12(pair(z0, z1), z2) -> pair(cons(activate(z2), z0), z1) afterNth(z0, z1) -> snd(splitAt(z0, z1)) and(tt, z0) -> activate(z0) fst(pair(z0, z1)) -> z0 head(cons(z0, z1)) -> z0 natsFrom(z0) -> cons(z0, n__natsFrom(s(z0))) natsFrom(z0) -> n__natsFrom(z0) sel(z0, z1) -> head(afterNth(z0, z1)) snd(pair(z0, z1)) -> z1 splitAt(0, z0) -> pair(nil, z0) splitAt(s(z0), cons(z1, z2)) -> U11(tt, z0, z1, activate(z2)) tail(cons(z0, z1)) -> activate(z1) take(z0, z1) -> fst(splitAt(z0, z1)) activate(n__natsFrom(z0)) -> natsFrom(z0) activate(z0) -> z0 Tuples: U11'(tt, z0, z1, z2) -> c(U12'(splitAt(activate(z0), activate(z2)), activate(z1)), SPLITAT(activate(z0), activate(z2)), ACTIVATE(z0), ACTIVATE(z2), ACTIVATE(z1)) U12'(pair(z0, z1), z2) -> c1(ACTIVATE(z2)) AFTERNTH(z0, z1) -> c2(SND(splitAt(z0, z1)), SPLITAT(z0, z1)) AND(tt, z0) -> c3(ACTIVATE(z0)) FST(pair(z0, z1)) -> c4 HEAD(cons(z0, z1)) -> c5 NATSFROM(z0) -> c6 NATSFROM(z0) -> c7 SEL(z0, z1) -> c8(HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1)) SND(pair(z0, z1)) -> c9 SPLITAT(0, z0) -> c10 SPLITAT(s(z0), cons(z1, z2)) -> c11(U11'(tt, z0, z1, activate(z2)), ACTIVATE(z2)) popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost