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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307722
details
property
value
status
complete
benchmark
#3.1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n046.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.87704 seconds
cpu usage
22.5757
user time
21.2184
system time
1.35736
max virtual memory
1.90148E7
max residence set size
3673584.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
22.50/6.82 WORST_CASE(Omega(n^1), O(n^1)) 22.50/6.83 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 22.50/6.83 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 22.50/6.83 22.50/6.83 22.50/6.83 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 22.50/6.83 22.50/6.83 (0) CpxTRS 22.50/6.83 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 22.50/6.83 (2) CpxTRS 22.50/6.83 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 22.50/6.83 (4) CpxWeightedTrs 22.50/6.83 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 22.50/6.83 (6) CpxTypedWeightedTrs 22.50/6.83 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 22.50/6.83 (8) CpxTypedWeightedCompleteTrs 22.50/6.83 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 9 ms] 22.50/6.83 (10) CpxRNTS 22.50/6.83 (11) CompleteCoflocoProof [FINISHED, 240 ms] 22.50/6.83 (12) BOUNDS(1, n^1) 22.50/6.83 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 22.50/6.83 (14) CpxTRS 22.50/6.83 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 22.50/6.83 (16) typed CpxTrs 22.50/6.83 (17) OrderProof [LOWER BOUND(ID), 0 ms] 22.50/6.83 (18) typed CpxTrs 22.50/6.83 (19) RewriteLemmaProof [LOWER BOUND(ID), 289 ms] 22.50/6.83 (20) BEST 22.50/6.83 (21) proven lower bound 22.50/6.83 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 22.50/6.83 (23) BOUNDS(n^1, INF) 22.50/6.83 (24) typed CpxTrs 22.50/6.83 22.50/6.83 22.50/6.83 ---------------------------------------- 22.50/6.83 22.50/6.83 (0) 22.50/6.83 Obligation: 22.50/6.83 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 22.50/6.83 22.50/6.83 22.50/6.83 The TRS R consists of the following rules: 22.50/6.83 22.50/6.83 minus(x, 0) -> x 22.50/6.83 minus(s(x), s(y)) -> minus(x, y) 22.50/6.83 quot(0, s(y)) -> 0 22.50/6.83 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 22.50/6.83 22.50/6.83 S is empty. 22.50/6.83 Rewrite Strategy: FULL 22.50/6.83 ---------------------------------------- 22.50/6.83 22.50/6.83 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 22.50/6.83 Converted rc-obligation to irc-obligation. 22.50/6.83 22.50/6.83 The duplicating contexts are: 22.50/6.83 quot(s(x), s([])) 22.50/6.83 22.50/6.83 22.50/6.83 The defined contexts are: 22.50/6.83 quot([], s(x1)) 22.50/6.83 minus([], x1) 22.50/6.83 22.50/6.83 22.50/6.83 [] just represents basic- or constructor-terms in the following defined contexts: 22.50/6.83 quot([], s(x1)) 22.50/6.83 22.50/6.83 22.50/6.83 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 22.50/6.83 ---------------------------------------- 22.50/6.83 22.50/6.83 (2) 22.50/6.83 Obligation: 22.50/6.83 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 22.50/6.83 22.50/6.83 22.50/6.83 The TRS R consists of the following rules: 22.50/6.83 22.50/6.83 minus(x, 0) -> x 22.50/6.83 minus(s(x), s(y)) -> minus(x, y) 22.50/6.83 quot(0, s(y)) -> 0 22.50/6.83 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 22.50/6.83 22.50/6.83 S is empty. 22.50/6.83 Rewrite Strategy: INNERMOST 22.50/6.83 ---------------------------------------- 22.50/6.83 22.50/6.83 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 22.50/6.83 Transformed relative TRS to weighted TRS 22.50/6.83 ---------------------------------------- 22.50/6.83 22.50/6.83 (4) 22.50/6.83 Obligation: 22.50/6.83 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 22.50/6.83 22.50/6.83 22.50/6.83 The TRS R consists of the following rules: 22.50/6.83 22.50/6.83 minus(x, 0) -> x [1] 22.50/6.83 minus(s(x), s(y)) -> minus(x, y) [1]
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