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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307799
details
property
value
status
complete
benchmark
otto13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n098.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.67 seconds
cpu usage
1063.07
user time
1048.55
system time
14.5147
max virtual memory
3.7774616E7
max residence set size
1.4974304E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1062.63/291.55 WORST_CASE(Omega(n^1), O(n^2)) 1062.84/291.57 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1062.84/291.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1062.84/291.57 1062.84/291.57 1062.84/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1062.84/291.57 1062.84/291.57 (0) CpxTRS 1062.84/291.57 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 1062.84/291.57 (2) CpxTRS 1062.84/291.57 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1062.84/291.57 (4) CpxWeightedTrs 1062.84/291.57 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1062.84/291.57 (6) CpxTypedWeightedTrs 1062.84/291.57 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 1062.84/291.57 (8) CpxTypedWeightedCompleteTrs 1062.84/291.57 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1062.84/291.57 (10) CpxRNTS 1062.84/291.57 (11) CompleteCoflocoProof [FINISHED, 1171 ms] 1062.84/291.57 (12) BOUNDS(1, n^2) 1062.84/291.57 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1062.84/291.57 (14) CpxTRS 1062.84/291.57 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1062.84/291.57 (16) typed CpxTrs 1062.84/291.57 (17) OrderProof [LOWER BOUND(ID), 0 ms] 1062.84/291.57 (18) typed CpxTrs 1062.84/291.57 (19) RewriteLemmaProof [LOWER BOUND(ID), 299 ms] 1062.84/291.57 (20) BEST 1062.84/291.57 (21) proven lower bound 1062.84/291.57 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 1062.84/291.57 (23) BOUNDS(n^1, INF) 1062.84/291.57 (24) typed CpxTrs 1062.84/291.57 (25) RewriteLemmaProof [LOWER BOUND(ID), 85 ms] 1062.84/291.57 (26) typed CpxTrs 1062.84/291.57 (27) RewriteLemmaProof [LOWER BOUND(ID), 21 ms] 1062.84/291.57 (28) typed CpxTrs 1062.84/291.57 1062.84/291.57 1062.84/291.57 ---------------------------------------- 1062.84/291.57 1062.84/291.57 (0) 1062.84/291.57 Obligation: 1062.84/291.57 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1062.84/291.57 1062.84/291.57 1062.84/291.57 The TRS R consists of the following rules: 1062.84/291.57 1062.84/291.57 le(0, y, z) -> greater(y, z) 1062.84/291.57 le(s(x), 0, z) -> false 1062.84/291.57 le(s(x), s(y), 0) -> false 1062.84/291.57 le(s(x), s(y), s(z)) -> le(x, y, z) 1062.84/291.57 greater(x, 0) -> first 1062.84/291.57 greater(0, s(y)) -> second 1062.84/291.57 greater(s(x), s(y)) -> greater(x, y) 1062.84/291.57 double(0) -> 0 1062.84/291.57 double(s(x)) -> s(s(double(x))) 1062.84/291.57 triple(x) -> if(le(x, x, double(x)), x, 0, 0) 1062.84/291.57 if(false, x, y, z) -> true 1062.84/291.57 if(first, x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z)) 1062.84/291.57 if(second, x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z) 1062.84/291.57 1062.84/291.57 S is empty. 1062.84/291.57 Rewrite Strategy: FULL 1062.84/291.57 ---------------------------------------- 1062.84/291.57 1062.84/291.57 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 1062.84/291.57 Converted rc-obligation to irc-obligation. 1062.84/291.57 1062.84/291.57 The duplicating contexts are: 1062.84/291.57 triple([]) 1062.84/291.57 if(first, [], y, z) 1062.84/291.57 if(first, x, [], z) 1062.84/291.57 if(first, x, y, []) 1062.84/291.57 if(second, [], y, z) 1062.84/291.57 if(second, x, [], z) 1062.84/291.57 if(second, x, y, []) 1062.84/291.57 1062.84/291.57 1062.84/291.57 The defined contexts are: 1062.84/291.57 if([], s(x1), x2, s(x3)) 1062.84/291.57 if([], s(x1), s(x2), x3) 1062.84/291.57 if([], x1, 0, 0) 1062.84/291.57 le(x0, x1, []) 1062.84/291.57 greater(x0, []) 1062.84/291.57 1062.84/291.57 1062.84/291.57 [] just represents basic- or constructor-terms in the following defined contexts: 1062.84/291.57 if([], s(x1), x2, s(x3)) 1062.84/291.57 if([], s(x1), s(x2), x3) 1062.84/291.57 1062.84/291.57 1062.84/291.57 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 1062.84/291.57 ---------------------------------------- 1062.84/291.57 1062.84/291.57 (2) 1062.84/291.57 Obligation: 1062.84/291.57 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 1062.84/291.57 1062.84/291.57 1062.84/291.57 The TRS R consists of the following rules:
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