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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307721
details
property
value
status
complete
benchmark
#3.16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.552 seconds
cpu usage
323.808
user time
320.815
system time
2.99322
max virtual memory
1.9276024E7
max residence set size
6139956.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^3))
output
323.64/291.49 WORST_CASE(Omega(n^2), O(n^3)) 323.73/291.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 323.73/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 323.73/291.51 323.73/291.51 323.73/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^3). 323.73/291.51 323.73/291.51 (0) CpxTRS 323.73/291.51 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 323.73/291.51 (2) CpxTRS 323.73/291.51 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 323.73/291.51 (4) CpxWeightedTrs 323.73/291.51 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 323.73/291.51 (6) CpxTypedWeightedTrs 323.73/291.51 (7) CompletionProof [UPPER BOUND(ID), 3 ms] 323.73/291.51 (8) CpxTypedWeightedCompleteTrs 323.73/291.51 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 323.73/291.51 (10) CpxTypedWeightedCompleteTrs 323.73/291.51 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 323.73/291.51 (12) CpxRNTS 323.73/291.51 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 323.73/291.51 (14) CpxRNTS 323.73/291.51 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 323.73/291.51 (16) CpxRNTS 323.73/291.51 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 323.73/291.51 (18) CpxRNTS 323.73/291.51 (19) IntTrsBoundProof [UPPER BOUND(ID), 611 ms] 323.73/291.51 (20) CpxRNTS 323.73/291.51 (21) IntTrsBoundProof [UPPER BOUND(ID), 190 ms] 323.73/291.51 (22) CpxRNTS 323.73/291.51 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 323.73/291.51 (24) CpxRNTS 323.73/291.51 (25) IntTrsBoundProof [UPPER BOUND(ID), 606 ms] 323.73/291.51 (26) CpxRNTS 323.73/291.51 (27) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 323.73/291.51 (28) CpxRNTS 323.73/291.51 (29) FinalProof [FINISHED, 0 ms] 323.73/291.51 (30) BOUNDS(1, n^3) 323.73/291.51 (31) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 323.73/291.51 (32) CpxTRS 323.73/291.51 (33) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 323.73/291.51 (34) typed CpxTrs 323.73/291.51 (35) OrderProof [LOWER BOUND(ID), 0 ms] 323.73/291.51 (36) typed CpxTrs 323.73/291.51 (37) RewriteLemmaProof [LOWER BOUND(ID), 290 ms] 323.73/291.51 (38) BEST 323.73/291.51 (39) proven lower bound 323.73/291.51 (40) LowerBoundPropagationProof [FINISHED, 0 ms] 323.73/291.51 (41) BOUNDS(n^1, INF) 323.73/291.51 (42) typed CpxTrs 323.73/291.51 (43) RewriteLemmaProof [LOWER BOUND(ID), 58 ms] 323.73/291.51 (44) proven lower bound 323.73/291.51 (45) LowerBoundPropagationProof [FINISHED, 0 ms] 323.73/291.51 (46) BOUNDS(n^2, INF) 323.73/291.51 323.73/291.51 323.73/291.51 ---------------------------------------- 323.73/291.51 323.73/291.51 (0) 323.73/291.51 Obligation: 323.73/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^3). 323.73/291.51 323.73/291.51 323.73/291.51 The TRS R consists of the following rules: 323.73/291.51 323.73/291.51 times(x, 0) -> 0 323.73/291.51 times(x, s(y)) -> plus(times(x, y), x) 323.73/291.51 plus(x, 0) -> x 323.73/291.51 plus(0, x) -> x 323.73/291.51 plus(x, s(y)) -> s(plus(x, y)) 323.73/291.51 plus(s(x), y) -> s(plus(x, y)) 323.73/291.51 323.73/291.51 S is empty. 323.73/291.51 Rewrite Strategy: FULL 323.73/291.51 ---------------------------------------- 323.73/291.51 323.73/291.51 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 323.73/291.51 Converted rc-obligation to irc-obligation. 323.73/291.51 323.73/291.51 The duplicating contexts are: 323.73/291.51 times([], s(y)) 323.73/291.51 323.73/291.51 323.73/291.51 The defined contexts are: 323.73/291.51 plus([], x1) 323.73/291.51 323.73/291.51 323.73/291.51 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 323.73/291.51 ---------------------------------------- 323.73/291.51 323.73/291.51 (2) 323.73/291.51 Obligation: 323.73/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^3). 323.73/291.51 323.73/291.51 323.73/291.51 The TRS R consists of the following rules: 323.73/291.51 323.73/291.51 times(x, 0) -> 0 323.73/291.51 times(x, s(y)) -> plus(times(x, y), x) 323.73/291.51 plus(x, 0) -> x
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