details

property	value
status	complete
benchmark	member.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	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.60527 seconds
cpu usage	14.3293
user time	13.0407
system time	1.28862
max virtual memory	1.8745484E7
max residence set size	3848116.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 163 ms] (2) CpxRelTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 3 ms] (4) CdtProblem (5) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (6) CdtProblem (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 3 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms] (12) CdtProblem (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (14) BOUNDS(1, 1) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (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), 284 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 27 ms] (24) proven lower bound (25) LowerBoundPropagationProof [FINISHED, 0 ms] (26) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: member(x', Cons(x, xs)) -> member[Ite][True][Ite](!EQ(x', x), x', Cons(x, xs)) member(x, Nil) -> False notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(x, xs) -> member(x, xs) The (relative) TRS S consists of the following rules: !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True member[Ite][True][Ite](False, x', Cons(x, xs)) -> member(x', xs) member[Ite][True][Ite](True, x, xs) -> True Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: member(x', Cons(x, xs)) -> member[Ite][True][Ite](!EQ(x', x), x', Cons(x, xs)) member(x, Nil) -> False notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(x, xs) -> member(x, xs) The (relative) TRS S consists of the following rules: !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True member[Ite][True][Ite](False, x', Cons(x, xs)) -> member(x', xs) member[Ite][True][Ite](True, x, xs) -> True Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS Innermost