details

property	value
status	complete
benchmark	4.05.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	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.494 seconds
cpu usage	344.524
user time	339.227
system time	5.2977
max virtual memory	1.8946632E7
max residence set size	8723548.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 6 ms] (2) CpxTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (4) CdtProblem (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 45 ms] (10) CdtProblem (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (12) BOUNDS(1, 1) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 948 ms] (20) proven lower bound (21) LowerBoundPropagationProof [FINISHED, 0 ms] (22) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: *(x, +(y, z)) -> +(*(x, y), *(x, z)) *(+(x, y), z) -> +(*(x, z), *(y, z)) *(x, 1) -> x *(1, y) -> y S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS does not nest defined symbols, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: *(x, +(y, z)) -> +(*(x, y), *(x, z)) *(+(x, y), z) -> +(*(x, z), *(y, z)) *(x, 1) -> x *(1, y) -> y S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (4) Obligation: Complexity Dependency Tuples Problem Rules: *(z0, +(z1, z2)) -> +(*(z0, z1), *(z0, z2)) *(+(z0, z1), z2) -> +(*(z0, z2), *(z1, z2)) *(z0, 1) -> z0 *(1, z0) -> z0 Tuples: *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) *'(+(z0, z1), z2) -> c1(*'(z0, z2), *'(z1, z2)) *'(z0, 1) -> c2 *'(1, z0) -> c3 S tuples: *'(z0, +(z1, z2)) -> c(*'(z0, z1), *'(z0, z2)) *'(+(z0, z1), z2) -> c1(*'(z0, z2), *'(z1, z2)) *'(z0, 1) -> c2 *'(1, z0) -> c3 K tuples:none Defined Rule Symbols: *_2 Defined Pair Symbols: *'_2 popout

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all output return to Runtime Complexity: TRS