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	n038.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.470202923 seconds
cpu usage	342.408749325
max memory	8.838455296E9

stage attributes

key	value
output-size	8485
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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), 0 ms] (2) CpxTRS (3) CpxTrsToCdtProof [UPPER BOUND(ID), 10 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)), 27 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), 989 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 popout

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all output return to Runti Compl Full Rewri 10127