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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307665
details
property
value
status
complete
benchmark
4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n079.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.52 seconds
cpu usage
884.479
user time
881.388
system time
3.09125
max virtual memory
3.8048132E7
max residence set size
5253052.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
884.20/291.46 WORST_CASE(Omega(n^1), O(n^1)) 884.20/291.47 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 884.20/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 884.20/291.47 884.20/291.47 884.20/291.47 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 884.20/291.47 884.20/291.47 (0) CpxTRS 884.20/291.47 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 884.20/291.47 (2) CpxTRS 884.20/291.47 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 884.20/291.47 (4) CpxWeightedTrs 884.20/291.47 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 884.20/291.47 (6) CpxTypedWeightedTrs 884.20/291.47 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 884.20/291.47 (8) CpxTypedWeightedCompleteTrs 884.20/291.47 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms] 884.20/291.47 (10) CpxRNTS 884.20/291.47 (11) CompleteCoflocoProof [FINISHED, 216 ms] 884.20/291.47 (12) BOUNDS(1, n^1) 884.20/291.47 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 884.20/291.47 (14) CpxTRS 884.20/291.47 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 884.20/291.47 (16) typed CpxTrs 884.20/291.47 (17) OrderProof [LOWER BOUND(ID), 0 ms] 884.20/291.47 (18) typed CpxTrs 884.20/291.47 (19) RewriteLemmaProof [LOWER BOUND(ID), 270 ms] 884.20/291.47 (20) BEST 884.20/291.47 (21) proven lower bound 884.20/291.47 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 884.20/291.47 (23) BOUNDS(n^1, INF) 884.20/291.47 (24) typed CpxTrs 884.20/291.47 884.20/291.47 884.20/291.47 ---------------------------------------- 884.20/291.47 884.20/291.47 (0) 884.20/291.47 Obligation: 884.20/291.47 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 884.20/291.47 884.20/291.47 884.20/291.47 The TRS R consists of the following rules: 884.20/291.47 884.20/291.47 cond(true, x, y) -> cond(gr(x, y), y, x) 884.20/291.47 gr(0, x) -> false 884.20/291.47 gr(s(x), 0) -> true 884.20/291.47 gr(s(x), s(y)) -> gr(x, y) 884.20/291.47 884.20/291.47 S is empty. 884.20/291.47 Rewrite Strategy: FULL 884.20/291.47 ---------------------------------------- 884.20/291.47 884.20/291.47 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 884.20/291.47 Converted rc-obligation to irc-obligation. 884.20/291.47 884.20/291.47 The duplicating contexts are: 884.20/291.47 cond(true, [], y) 884.20/291.47 cond(true, x, []) 884.20/291.47 884.20/291.47 884.20/291.47 The defined contexts are: 884.20/291.47 cond([], x1, x2) 884.20/291.47 884.20/291.47 884.20/291.47 [] just represents basic- or constructor-terms in the following defined contexts: 884.20/291.47 cond([], x1, x2) 884.20/291.47 884.20/291.47 884.20/291.47 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 884.20/291.47 ---------------------------------------- 884.20/291.47 884.20/291.47 (2) 884.20/291.47 Obligation: 884.20/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 884.20/291.47 884.20/291.47 884.20/291.47 The TRS R consists of the following rules: 884.20/291.47 884.20/291.47 cond(true, x, y) -> cond(gr(x, y), y, x) 884.20/291.47 gr(0, x) -> false 884.20/291.47 gr(s(x), 0) -> true 884.20/291.47 gr(s(x), s(y)) -> gr(x, y) 884.20/291.47 884.20/291.47 S is empty. 884.20/291.47 Rewrite Strategy: INNERMOST 884.20/291.47 ---------------------------------------- 884.20/291.47 884.20/291.47 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 884.20/291.47 Transformed relative TRS to weighted TRS 884.20/291.47 ---------------------------------------- 884.20/291.47 884.20/291.47 (4) 884.20/291.47 Obligation: 884.20/291.47 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 884.20/291.47 884.20/291.47 884.20/291.47 The TRS R consists of the following rules: 884.20/291.47 884.20/291.47 cond(true, x, y) -> cond(gr(x, y), y, x) [1] 884.20/291.47 gr(0, x) -> false [1]
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