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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308035
details
property
value
status
complete
benchmark
MYNAT_nosorts_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n019.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.92709 seconds
cpu usage
20.6104
user time
19.0581
system time
1.55234
max virtual memory
3.7302112E7
max residence set size
3808000.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
20.42/7.87 WORST_CASE(Omega(n^2), O(n^2)) 20.42/7.88 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 20.42/7.88 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.42/7.88 20.42/7.88 20.42/7.88 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 20.42/7.88 20.42/7.88 (0) CpxTRS 20.42/7.88 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 20.42/7.88 (2) CpxTRS 20.42/7.88 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 20.42/7.88 (4) CdtProblem 20.42/7.88 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 20.42/7.88 (6) CdtProblem 20.42/7.88 (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 20.42/7.88 (8) CdtProblem 20.42/7.88 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 41 ms] 20.42/7.88 (10) CdtProblem 20.42/7.88 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 39 ms] 20.42/7.88 (12) CdtProblem 20.42/7.88 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 20.42/7.88 (14) BOUNDS(1, 1) 20.42/7.88 (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 20.42/7.88 (16) CpxTRS 20.42/7.88 (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 20.42/7.88 (18) typed CpxTrs 20.42/7.88 (19) OrderProof [LOWER BOUND(ID), 0 ms] 20.42/7.88 (20) typed CpxTrs 20.42/7.88 (21) RewriteLemmaProof [LOWER BOUND(ID), 292 ms] 20.42/7.88 (22) BEST 20.42/7.88 (23) proven lower bound 20.42/7.88 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 20.42/7.88 (25) BOUNDS(n^1, INF) 20.42/7.88 (26) typed CpxTrs 20.42/7.88 (27) RewriteLemmaProof [LOWER BOUND(ID), 50 ms] 20.42/7.88 (28) proven lower bound 20.42/7.88 (29) LowerBoundPropagationProof [FINISHED, 0 ms] 20.42/7.88 (30) BOUNDS(n^2, INF) 20.42/7.88 20.42/7.88 20.42/7.88 ---------------------------------------- 20.42/7.88 20.42/7.88 (0) 20.42/7.88 Obligation: 20.42/7.88 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 20.42/7.88 20.42/7.88 20.42/7.88 The TRS R consists of the following rules: 20.42/7.88 20.42/7.88 and(tt, X) -> activate(X) 20.42/7.88 plus(N, 0) -> N 20.42/7.88 plus(N, s(M)) -> s(plus(N, M)) 20.42/7.88 x(N, 0) -> 0 20.42/7.88 x(N, s(M)) -> plus(x(N, M), N) 20.42/7.88 activate(X) -> X 20.42/7.88 20.42/7.88 S is empty. 20.42/7.88 Rewrite Strategy: FULL 20.42/7.88 ---------------------------------------- 20.42/7.88 20.42/7.88 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 20.42/7.88 Converted rc-obligation to irc-obligation. 20.42/7.88 20.42/7.88 The duplicating contexts are: 20.42/7.88 x([], s(M)) 20.42/7.88 20.42/7.88 20.42/7.88 The defined contexts are: 20.42/7.88 plus([], x1) 20.42/7.88 20.42/7.88 20.42/7.88 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 20.42/7.88 ---------------------------------------- 20.42/7.88 20.42/7.88 (2) 20.42/7.88 Obligation: 20.42/7.88 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 20.42/7.88 20.42/7.88 20.42/7.88 The TRS R consists of the following rules: 20.42/7.88 20.42/7.88 and(tt, X) -> activate(X) 20.42/7.88 plus(N, 0) -> N 20.42/7.88 plus(N, s(M)) -> s(plus(N, M)) 20.42/7.88 x(N, 0) -> 0 20.42/7.88 x(N, s(M)) -> plus(x(N, M), N) 20.42/7.88 activate(X) -> X 20.42/7.88 20.42/7.88 S is empty. 20.42/7.88 Rewrite Strategy: INNERMOST 20.42/7.88 ---------------------------------------- 20.42/7.88 20.42/7.88 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 20.42/7.88 Converted Cpx (relative) TRS to CDT 20.42/7.88 ---------------------------------------- 20.42/7.88 20.42/7.88 (4) 20.42/7.88 Obligation: 20.42/7.88 Complexity Dependency Tuples Problem 20.42/7.88
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