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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308430
details
property
value
status
complete
benchmark
2.20.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.16067 seconds
cpu usage
19.3498
user time
18.1093
system time
1.24047
max virtual memory
1.8912652E7
max residence set size
3542512.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
18.91/5.94 WORST_CASE(Omega(n^1), O(n^1)) 18.91/5.95 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 18.91/5.95 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 18.91/5.95 18.91/5.95 18.91/5.95 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.91/5.95 18.91/5.95 (0) CpxTRS 18.91/5.95 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 18.91/5.95 (2) CpxTRS 18.91/5.95 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 18.91/5.95 (4) CdtProblem 18.91/5.95 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 18.91/5.95 (6) CdtProblem 18.91/5.95 (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] 18.91/5.95 (8) CdtProblem 18.91/5.95 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 18.91/5.95 (10) CdtProblem 18.91/5.95 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 39 ms] 18.91/5.95 (12) CdtProblem 18.91/5.95 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 18.91/5.95 (14) BOUNDS(1, 1) 18.91/5.95 (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 18.91/5.95 (16) CpxTRS 18.91/5.95 (17) SlicingProof [LOWER BOUND(ID), 0 ms] 18.91/5.95 (18) CpxTRS 18.91/5.95 (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 18.91/5.95 (20) typed CpxTrs 18.91/5.95 (21) OrderProof [LOWER BOUND(ID), 0 ms] 18.91/5.95 (22) typed CpxTrs 18.91/5.95 (23) RewriteLemmaProof [LOWER BOUND(ID), 779 ms] 18.91/5.95 (24) proven lower bound 18.91/5.95 (25) LowerBoundPropagationProof [FINISHED, 0 ms] 18.91/5.95 (26) BOUNDS(n^1, INF) 18.91/5.95 18.91/5.95 18.91/5.95 ---------------------------------------- 18.91/5.95 18.91/5.95 (0) 18.91/5.95 Obligation: 18.91/5.95 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.91/5.95 18.91/5.95 18.91/5.95 The TRS R consists of the following rules: 18.91/5.95 18.91/5.95 sum(0) -> 0 18.91/5.95 sum(s(x)) -> +(sqr(s(x)), sum(x)) 18.91/5.95 sqr(x) -> *(x, x) 18.91/5.95 sum(s(x)) -> +(*(s(x), s(x)), sum(x)) 18.91/5.95 18.91/5.95 S is empty. 18.91/5.95 Rewrite Strategy: FULL 18.91/5.95 ---------------------------------------- 18.91/5.95 18.91/5.95 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 18.91/5.95 Converted rc-obligation to irc-obligation. 18.91/5.95 18.91/5.95 As the TRS does not nest defined symbols, we have rc = irc. 18.91/5.95 ---------------------------------------- 18.91/5.95 18.91/5.95 (2) 18.91/5.95 Obligation: 18.91/5.95 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 18.91/5.95 18.91/5.95 18.91/5.95 The TRS R consists of the following rules: 18.91/5.95 18.91/5.95 sum(0) -> 0 18.91/5.95 sum(s(x)) -> +(sqr(s(x)), sum(x)) 18.91/5.95 sqr(x) -> *(x, x) 18.91/5.95 sum(s(x)) -> +(*(s(x), s(x)), sum(x)) 18.91/5.95 18.91/5.95 S is empty. 18.91/5.95 Rewrite Strategy: INNERMOST 18.91/5.95 ---------------------------------------- 18.91/5.95 18.91/5.95 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 18.91/5.95 Converted Cpx (relative) TRS to CDT 18.91/5.95 ---------------------------------------- 18.91/5.95 18.91/5.95 (4) 18.91/5.95 Obligation: 18.91/5.95 Complexity Dependency Tuples Problem 18.91/5.95 18.91/5.95 Rules: 18.91/5.95 sum(0) -> 0 18.91/5.95 sum(s(z0)) -> +(sqr(s(z0)), sum(z0)) 18.91/5.95 sum(s(z0)) -> +(*(s(z0), s(z0)), sum(z0)) 18.91/5.95 sqr(z0) -> *(z0, z0) 18.91/5.95 Tuples: 18.91/5.95 SUM(0) -> c 18.91/5.95 SUM(s(z0)) -> c1(SQR(s(z0)), SUM(z0)) 18.91/5.95 SUM(s(z0)) -> c2(SUM(z0)) 18.91/5.95 SQR(z0) -> c3 18.91/5.95 S tuples: 18.91/5.95 SUM(0) -> c 18.91/5.95 SUM(s(z0)) -> c1(SQR(s(z0)), SUM(z0)) 18.91/5.95 SUM(s(z0)) -> c2(SUM(z0)) 18.91/5.95 SQR(z0) -> c3 18.91/5.95 K tuples:none
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