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Runti Compl Full Rewri 10127 pair #381902423
details
property
value
status
complete
benchmark
4.10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.485154152 seconds
cpu usage
359.470667075
max memory
1.1533504512E10
stage attributes
key
value
output-size
11845
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 8 ms] (6) CdtProblem (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 30 ms] (12) CdtProblem (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 13 ms] (14) CdtProblem (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (16) BOUNDS(1, 1) (17) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxTRS (19) SlicingProof [LOWER BOUND(ID), 0 ms] (20) CpxTRS (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) typed CpxTrs (23) OrderProof [LOWER BOUND(ID), 0 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 658 ms] (26) proven lower bound (27) LowerBoundPropagationProof [FINISHED, 0 ms] (28) 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)) -> *(otimes(x, y), z) *(1, y) -> y *(+(x, y), z) -> oplus(*(x, z), *(y, z)) *(x, oplus(y, z)) -> oplus(*(x, y), *(x, z)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The TRS does not nest defined symbols. Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: *(x, *(y, z)) -> *(otimes(x, y), z) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: *(1, y) -> y *(+(x, y), z) -> oplus(*(x, z), *(y, z)) *(x, oplus(y, z)) -> oplus(*(x, y), *(x, z)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS does not nest defined symbols, we have rc = irc. ---------------------------------------- (4) 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: *(1, y) -> y *(+(x, y), z) -> oplus(*(x, z), *(y, z)) *(x, oplus(y, z)) -> oplus(*(x, y), *(x, z))
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