details

property	value
status	complete
benchmark	18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.3638 seconds
cpu usage	12.5514
user time	11.688
system time	0.863424
max virtual memory	1.8807944E7
max residence set size	2907220.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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), 5 ms] (2) CdtProblem (3) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 32 ms] (6) CdtProblem (7) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (8) BOUNDS(1, 1) (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTRS (11) SlicingProof [LOWER BOUND(ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 487 ms] (18) proven lower bound (19) LowerBoundPropagationProof [FINISHED, 0 ms] (20) BOUNDS(n^1, INF) ---------------------------------------- (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: *(x, +(y, z)) -> +(*(x, y), *(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: *(z0, +(z1, z2)) -> +(*(z0, z1), *(z0, z2)) Tuples: *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) S tuples: *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) K tuples:none Defined Rule Symbols: *_2 Defined Pair Symbols: *'_2 Compound Symbols: c_2 ---------------------------------------- (3) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: *(z0, +(z1, z2)) -> +(*(z0, z1), *(z0, z2)) ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) S tuples: *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) K tuples:none Defined Rule Symbols:none Defined Pair Symbols: *'_2 Compound Symbols: c_2 ---------------------------------------- (5) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) We considered the (Usable) Rules:none And the Tuples: *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) popout

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all output return to Runtime Complexity: TRS Innermost