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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308436
details
property
value
status
complete
benchmark
4.25.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n133.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.75203 seconds
cpu usage
18.9588
user time
17.9963
system time
0.96252
max virtual memory
1.913914E7
max residence set size
2686524.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
18.78/5.70 WORST_CASE(Omega(n^1), O(n^1)) 18.78/5.71 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 18.78/5.71 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 18.78/5.71 18.78/5.71 18.78/5.71 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.78/5.71 18.78/5.71 (0) CpxTRS 18.78/5.71 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 18.78/5.71 (2) CpxTRS 18.78/5.71 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 18.78/5.71 (4) CpxWeightedTrs 18.78/5.71 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 18.78/5.71 (6) CpxTypedWeightedTrs 18.78/5.71 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 18.78/5.71 (8) CpxTypedWeightedCompleteTrs 18.78/5.71 (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 18.78/5.71 (10) CpxTypedWeightedCompleteTrs 18.78/5.71 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 18.78/5.71 (12) CpxRNTS 18.78/5.71 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 18.78/5.71 (14) CpxRNTS 18.78/5.71 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 18.78/5.71 (16) CpxRNTS 18.78/5.71 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 18.78/5.71 (18) CpxRNTS 18.78/5.71 (19) IntTrsBoundProof [UPPER BOUND(ID), 364 ms] 18.78/5.71 (20) CpxRNTS 18.78/5.71 (21) IntTrsBoundProof [UPPER BOUND(ID), 99 ms] 18.78/5.71 (22) CpxRNTS 18.78/5.71 (23) FinalProof [FINISHED, 0 ms] 18.78/5.71 (24) BOUNDS(1, n^1) 18.78/5.71 (25) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 18.78/5.71 (26) TRS for Loop Detection 18.78/5.71 (27) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 18.78/5.71 (28) BEST 18.78/5.71 (29) proven lower bound 18.78/5.71 (30) LowerBoundPropagationProof [FINISHED, 0 ms] 18.78/5.71 (31) BOUNDS(n^1, INF) 18.78/5.71 (32) TRS for Loop Detection 18.78/5.71 18.78/5.71 18.78/5.71 ---------------------------------------- 18.78/5.71 18.78/5.71 (0) 18.78/5.71 Obligation: 18.78/5.71 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.78/5.71 18.78/5.71 18.78/5.71 The TRS R consists of the following rules: 18.78/5.71 18.78/5.71 rev(a) -> a 18.78/5.71 rev(b) -> b 18.78/5.71 rev(++(x, y)) -> ++(rev(y), rev(x)) 18.78/5.71 rev(++(x, x)) -> rev(x) 18.78/5.71 18.78/5.71 S is empty. 18.78/5.71 Rewrite Strategy: FULL 18.78/5.71 ---------------------------------------- 18.78/5.71 18.78/5.71 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 18.78/5.71 Converted rc-obligation to irc-obligation. 18.78/5.71 18.78/5.71 As the TRS does not nest defined symbols, we have rc = irc. 18.78/5.71 ---------------------------------------- 18.78/5.71 18.78/5.71 (2) 18.78/5.71 Obligation: 18.78/5.71 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 18.78/5.71 18.78/5.71 18.78/5.71 The TRS R consists of the following rules: 18.78/5.71 18.78/5.71 rev(a) -> a 18.78/5.71 rev(b) -> b 18.78/5.71 rev(++(x, y)) -> ++(rev(y), rev(x)) 18.78/5.71 rev(++(x, x)) -> rev(x) 18.78/5.71 18.78/5.71 S is empty. 18.78/5.71 Rewrite Strategy: INNERMOST 18.78/5.71 ---------------------------------------- 18.78/5.71 18.78/5.71 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 18.78/5.71 Transformed relative TRS to weighted TRS 18.78/5.71 ---------------------------------------- 18.78/5.71 18.78/5.71 (4) 18.78/5.71 Obligation: 18.78/5.71 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 18.78/5.71 18.78/5.71 18.78/5.71 The TRS R consists of the following rules: 18.78/5.71 18.78/5.71 rev(a) -> a [1] 18.78/5.71 rev(b) -> b [1] 18.78/5.71 rev(++(x, y)) -> ++(rev(y), rev(x)) [1] 18.78/5.71 rev(++(x, x)) -> rev(x) [1] 18.78/5.71 18.78/5.71 Rewrite Strategy: INNERMOST 18.78/5.71 ----------------------------------------
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