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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307618
details
property
value
status
complete
benchmark
round.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n052.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.556 seconds
cpu usage
889.034
user time
884.999
system time
4.03491
max virtual memory
3.7046072E7
max residence set size
5416568.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
888.76/291.49 WORST_CASE(Omega(n^1), O(n^1)) 888.92/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 888.92/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 888.92/291.51 888.92/291.51 888.92/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 888.92/291.51 888.92/291.51 (0) CpxTRS 888.92/291.51 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 888.92/291.51 (2) CpxTRS 888.92/291.51 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 888.92/291.51 (4) CpxWeightedTrs 888.92/291.51 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 888.92/291.51 (6) CpxTypedWeightedTrs 888.92/291.51 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 888.92/291.51 (8) CpxTypedWeightedCompleteTrs 888.92/291.51 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 7 ms] 888.92/291.51 (10) CpxRNTS 888.92/291.51 (11) CompleteCoflocoProof [FINISHED, 166 ms] 888.92/291.51 (12) BOUNDS(1, n^1) 888.92/291.51 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 888.92/291.51 (14) TRS for Loop Detection 888.92/291.51 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 888.92/291.51 (16) BEST 888.92/291.51 (17) proven lower bound 888.92/291.51 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 888.92/291.51 (19) BOUNDS(n^1, INF) 888.92/291.51 (20) TRS for Loop Detection 888.92/291.51 888.92/291.51 888.92/291.51 ---------------------------------------- 888.92/291.51 888.92/291.51 (0) 888.92/291.51 Obligation: 888.92/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 888.92/291.51 888.92/291.51 888.92/291.51 The TRS R consists of the following rules: 888.92/291.51 888.92/291.51 f(s(x), x) -> f(s(x), round(s(x))) 888.92/291.51 round(0) -> 0 888.92/291.51 round(0) -> s(0) 888.92/291.51 round(s(0)) -> s(0) 888.92/291.51 round(s(s(x))) -> s(s(round(x))) 888.92/291.51 888.92/291.51 S is empty. 888.92/291.51 Rewrite Strategy: FULL 888.92/291.51 ---------------------------------------- 888.92/291.51 888.92/291.51 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 888.92/291.51 Converted rc-obligation to irc-obligation. 888.92/291.51 888.92/291.51 As the TRS is a non-duplicating overlay system, we have rc = irc. 888.92/291.51 ---------------------------------------- 888.92/291.51 888.92/291.51 (2) 888.92/291.51 Obligation: 888.92/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 888.92/291.51 888.92/291.51 888.92/291.51 The TRS R consists of the following rules: 888.92/291.51 888.92/291.51 f(s(x), x) -> f(s(x), round(s(x))) 888.92/291.51 round(0) -> 0 888.92/291.51 round(0) -> s(0) 888.92/291.51 round(s(0)) -> s(0) 888.92/291.51 round(s(s(x))) -> s(s(round(x))) 888.92/291.51 888.92/291.51 S is empty. 888.92/291.51 Rewrite Strategy: INNERMOST 888.92/291.51 ---------------------------------------- 888.92/291.51 888.92/291.51 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 888.92/291.51 Transformed relative TRS to weighted TRS 888.92/291.51 ---------------------------------------- 888.92/291.51 888.92/291.51 (4) 888.92/291.51 Obligation: 888.92/291.51 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 888.92/291.51 888.92/291.51 888.92/291.51 The TRS R consists of the following rules: 888.92/291.51 888.92/291.51 f(s(x), x) -> f(s(x), round(s(x))) [1] 888.92/291.51 round(0) -> 0 [1] 888.92/291.51 round(0) -> s(0) [1] 888.92/291.51 round(s(0)) -> s(0) [1] 888.92/291.51 round(s(s(x))) -> s(s(round(x))) [1] 888.92/291.51 888.92/291.51 Rewrite Strategy: INNERMOST 888.92/291.51 ---------------------------------------- 888.92/291.51 888.92/291.51 (5) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 888.92/291.51 Infered types. 888.92/291.51 ---------------------------------------- 888.92/291.51 888.92/291.51 (6) 888.92/291.51 Obligation: 888.92/291.51 Runtime Complexity Weighted TRS with Types. 888.92/291.51 The TRS R consists of the following rules:
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