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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308390
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
n068.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.578 seconds
cpu usage
400.004
user time
391.935
system time
8.06901
max virtual memory
1.8945292E7
max residence set size
1.1318744E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
399.88/291.52 WORST_CASE(Omega(n^1), O(n^3)) 399.88/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 399.88/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 399.88/291.53 399.88/291.53 399.88/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 399.88/291.53 399.88/291.53 (0) CpxTRS 399.88/291.53 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 399.88/291.53 (2) CpxTRS 399.88/291.53 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 399.88/291.53 (4) CpxTRS 399.88/291.53 (5) CpxTrsToCdtProof [UPPER BOUND(ID), 3 ms] 399.88/291.53 (6) CdtProblem 399.88/291.53 (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 399.88/291.53 (8) CdtProblem 399.88/291.53 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 399.88/291.53 (10) CdtProblem 399.88/291.53 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 37 ms] 399.88/291.53 (12) CdtProblem 399.88/291.53 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 399.88/291.53 (14) BOUNDS(1, 1) 399.88/291.53 (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 399.88/291.53 (16) CpxTRS 399.88/291.53 (17) SlicingProof [LOWER BOUND(ID), 0 ms] 399.88/291.53 (18) CpxTRS 399.88/291.53 (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 399.88/291.53 (20) typed CpxTrs 399.88/291.53 (21) OrderProof [LOWER BOUND(ID), 0 ms] 399.88/291.53 (22) typed CpxTrs 399.88/291.53 (23) RewriteLemmaProof [LOWER BOUND(ID), 674 ms] 399.88/291.53 (24) proven lower bound 399.88/291.53 (25) LowerBoundPropagationProof [FINISHED, 0 ms] 399.88/291.53 (26) BOUNDS(n^1, INF) 399.88/291.53 399.88/291.53 399.88/291.53 ---------------------------------------- 399.88/291.53 399.88/291.53 (0) 399.88/291.53 Obligation: 399.88/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 399.88/291.53 399.88/291.53 399.88/291.53 The TRS R consists of the following rules: 399.88/291.53 399.88/291.53 *(x, *(y, z)) -> *(otimes(x, y), z) 399.88/291.53 *(1, y) -> y 399.88/291.53 *(+(x, y), z) -> oplus(*(x, z), *(y, z)) 399.88/291.53 *(x, oplus(y, z)) -> oplus(*(x, y), *(x, z)) 399.88/291.53 399.88/291.53 S is empty. 399.88/291.53 Rewrite Strategy: FULL 399.88/291.53 ---------------------------------------- 399.88/291.53 399.88/291.53 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 399.88/291.53 The TRS does not nest defined symbols. 399.88/291.53 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 399.88/291.53 *(x, *(y, z)) -> *(otimes(x, y), z) 399.88/291.53 399.88/291.53 ---------------------------------------- 399.88/291.53 399.88/291.53 (2) 399.88/291.53 Obligation: 399.88/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^3). 399.88/291.53 399.88/291.53 399.88/291.53 The TRS R consists of the following rules: 399.88/291.53 399.88/291.53 *(1, y) -> y 399.88/291.53 *(+(x, y), z) -> oplus(*(x, z), *(y, z)) 399.88/291.53 *(x, oplus(y, z)) -> oplus(*(x, y), *(x, z)) 399.88/291.53 399.88/291.53 S is empty. 399.88/291.53 Rewrite Strategy: FULL 399.88/291.53 ---------------------------------------- 399.88/291.53 399.88/291.53 (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) 399.88/291.53 Converted rc-obligation to irc-obligation. 399.88/291.53 399.88/291.53 As the TRS does not nest defined symbols, we have rc = irc. 399.88/291.53 ---------------------------------------- 399.88/291.53 399.88/291.53 (4) 399.88/291.53 Obligation: 399.88/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^3). 399.88/291.53 399.88/291.53 399.88/291.53 The TRS R consists of the following rules: 399.88/291.53 399.88/291.53 *(1, y) -> y 399.88/291.53 *(+(x, y), z) -> oplus(*(x, z), *(y, z)) 399.88/291.53 *(x, oplus(y, z)) -> oplus(*(x, y), *(x, z)) 399.88/291.53 399.88/291.53 S is empty. 399.88/291.53 Rewrite Strategy: INNERMOST 399.88/291.53 ---------------------------------------- 399.88/291.53 399.88/291.53 (5) CpxTrsToCdtProof (UPPER BOUND(ID)) 399.88/291.53 Converted Cpx (relative) TRS to CDT 399.88/291.53 ----------------------------------------
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