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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308414
details
property
value
status
complete
benchmark
2.17.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n051.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.94064 seconds
cpu usage
26.2466
user time
24.8893
system time
1.35728
max virtual memory
1.9209568E7
max residence set size
3908996.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
25.45/7.31 WORST_CASE(Omega(n^1), O(n^1)) 25.52/7.33 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 25.52/7.33 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 25.52/7.33 25.52/7.33 25.52/7.33 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 25.52/7.33 25.52/7.33 (0) CpxTRS 25.52/7.33 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 25.52/7.33 (2) CpxTRS 25.52/7.33 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 25.52/7.33 (4) CdtProblem 25.52/7.33 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 25.52/7.33 (6) CdtProblem 25.52/7.33 (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 25.52/7.33 (8) CdtProblem 25.52/7.33 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 21 ms] 25.52/7.33 (10) CdtProblem 25.52/7.33 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms] 25.52/7.33 (12) CdtProblem 25.52/7.33 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 25.52/7.33 (14) BOUNDS(1, 1) 25.52/7.33 (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 25.52/7.33 (16) CpxTRS 25.52/7.33 (17) SlicingProof [LOWER BOUND(ID), 0 ms] 25.52/7.33 (18) CpxTRS 25.52/7.33 (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 25.52/7.33 (20) typed CpxTrs 25.52/7.33 (21) OrderProof [LOWER BOUND(ID), 0 ms] 25.52/7.33 (22) typed CpxTrs 25.52/7.33 (23) RewriteLemmaProof [LOWER BOUND(ID), 1924 ms] 25.52/7.33 (24) BEST 25.52/7.33 (25) proven lower bound 25.52/7.33 (26) LowerBoundPropagationProof [FINISHED, 0 ms] 25.52/7.33 (27) BOUNDS(n^1, INF) 25.52/7.33 (28) typed CpxTrs 25.52/7.33 25.52/7.33 25.52/7.33 ---------------------------------------- 25.52/7.33 25.52/7.33 (0) 25.52/7.33 Obligation: 25.52/7.33 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 25.52/7.33 25.52/7.33 25.52/7.33 The TRS R consists of the following rules: 25.52/7.33 25.52/7.33 sum(0) -> 0 25.52/7.33 sum(s(x)) -> +(sum(x), s(x)) 25.52/7.33 sum1(0) -> 0 25.52/7.33 sum1(s(x)) -> s(+(sum1(x), +(x, x))) 25.52/7.33 25.52/7.33 S is empty. 25.52/7.33 Rewrite Strategy: FULL 25.52/7.33 ---------------------------------------- 25.52/7.33 25.52/7.33 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 25.52/7.33 Converted rc-obligation to irc-obligation. 25.52/7.33 25.52/7.33 As the TRS does not nest defined symbols, we have rc = irc. 25.52/7.33 ---------------------------------------- 25.52/7.33 25.52/7.33 (2) 25.52/7.33 Obligation: 25.52/7.33 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 25.52/7.33 25.52/7.33 25.52/7.33 The TRS R consists of the following rules: 25.52/7.33 25.52/7.33 sum(0) -> 0 25.52/7.33 sum(s(x)) -> +(sum(x), s(x)) 25.52/7.33 sum1(0) -> 0 25.52/7.33 sum1(s(x)) -> s(+(sum1(x), +(x, x))) 25.52/7.33 25.52/7.33 S is empty. 25.52/7.33 Rewrite Strategy: INNERMOST 25.52/7.33 ---------------------------------------- 25.52/7.33 25.52/7.33 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 25.52/7.33 Converted Cpx (relative) TRS to CDT 25.52/7.33 ---------------------------------------- 25.52/7.33 25.52/7.33 (4) 25.52/7.33 Obligation: 25.52/7.33 Complexity Dependency Tuples Problem 25.52/7.33 25.52/7.33 Rules: 25.52/7.33 sum(0) -> 0 25.52/7.33 sum(s(z0)) -> +(sum(z0), s(z0)) 25.52/7.33 sum1(0) -> 0 25.52/7.33 sum1(s(z0)) -> s(+(sum1(z0), +(z0, z0))) 25.52/7.33 Tuples: 25.52/7.33 SUM(0) -> c 25.52/7.33 SUM(s(z0)) -> c1(SUM(z0)) 25.52/7.33 SUM1(0) -> c2 25.52/7.33 SUM1(s(z0)) -> c3(SUM1(z0)) 25.52/7.33 S tuples: 25.52/7.33 SUM(0) -> c 25.52/7.33 SUM(s(z0)) -> c1(SUM(z0)) 25.52/7.33 SUM1(0) -> c2
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