details

property	value
status	complete
benchmark	2.40.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.24624 seconds
cpu usage	15.6854
user time	14.7733
system time	0.912063
max virtual memory	1.9239492E7
max residence set size	2902460.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) 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) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 41 ms] (10) CdtProblem (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (12) BOUNDS(1, 1) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) 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: or(true, y) -> true or(x, true) -> true or(false, false) -> false mem(x, nil) -> false mem(x, set(y)) -> =(x, y) mem(x, union(y, z)) -> or(mem(x, y), mem(x, z)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(z0, true) -> true or(false, false) -> false mem(z0, nil) -> false mem(z0, set(z1)) -> =(z0, z1) mem(z0, union(z1, z2)) -> or(mem(z0, z1), mem(z0, z2)) Tuples: OR(true, z0) -> c OR(z0, true) -> c1 OR(false, false) -> c2 MEM(z0, nil) -> c3 MEM(z0, set(z1)) -> c4 MEM(z0, union(z1, z2)) -> c5(OR(mem(z0, z1), mem(z0, z2)), MEM(z0, z1), MEM(z0, z2)) S tuples: OR(true, z0) -> c OR(z0, true) -> c1 OR(false, false) -> c2 MEM(z0, nil) -> c3 MEM(z0, set(z1)) -> c4 MEM(z0, union(z1, z2)) -> c5(OR(mem(z0, z1), mem(z0, z2)), MEM(z0, z1), MEM(z0, z2)) K tuples:none Defined Rule Symbols: or_2, mem_2 Defined Pair Symbols: OR_2, MEM_2 Compound Symbols: c, c1, c2, c3, c4, c5_3 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: OR(false, false) -> c2 MEM(z0, set(z1)) -> c4 MEM(z0, nil) -> c3 OR(true, z0) -> c OR(z0, true) -> c1 ---------------------------------------- (4) popout

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all output return to Runtime Complexity: TRS Innermost