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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307706
details
property
value
status
complete
benchmark
#3.12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n109.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.52238 seconds
cpu usage
18.486
user time
17.1781
system time
1.30788
max virtual memory
1.9079836E7
max residence set size
3039220.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), O(n^3))
output
18.25/6.46 WORST_CASE(Omega(n^3), O(n^3)) 18.25/6.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 18.25/6.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 18.25/6.48 18.25/6.48 18.25/6.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 18.25/6.48 18.25/6.48 (0) CpxTRS 18.25/6.48 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 18.25/6.48 (2) CpxTRS 18.25/6.48 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 6 ms] 18.25/6.48 (4) CdtProblem 18.25/6.48 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 18.25/6.48 (6) CdtProblem 18.25/6.48 (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 18.25/6.48 (8) CdtProblem 18.25/6.48 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 31 ms] 18.25/6.48 (10) CdtProblem 18.25/6.48 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 40 ms] 18.25/6.48 (12) CdtProblem 18.25/6.48 (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 67 ms] 18.25/6.48 (14) CdtProblem 18.25/6.48 (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 18.25/6.48 (16) BOUNDS(1, 1) 18.25/6.48 (17) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 18.25/6.48 (18) CpxTRS 18.25/6.48 (19) SlicingProof [LOWER BOUND(ID), 0 ms] 18.25/6.48 (20) CpxTRS 18.25/6.48 (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 18.25/6.48 (22) typed CpxTrs 18.25/6.48 (23) OrderProof [LOWER BOUND(ID), 0 ms] 18.25/6.48 (24) typed CpxTrs 18.25/6.48 (25) RewriteLemmaProof [LOWER BOUND(ID), 308 ms] 18.25/6.48 (26) BEST 18.25/6.48 (27) proven lower bound 18.25/6.48 (28) LowerBoundPropagationProof [FINISHED, 0 ms] 18.25/6.48 (29) BOUNDS(n^1, INF) 18.25/6.48 (30) typed CpxTrs 18.25/6.48 (31) RewriteLemmaProof [LOWER BOUND(ID), 14 ms] 18.25/6.48 (32) BEST 18.25/6.48 (33) proven lower bound 18.25/6.48 (34) LowerBoundPropagationProof [FINISHED, 0 ms] 18.25/6.48 (35) BOUNDS(n^2, INF) 18.25/6.48 (36) typed CpxTrs 18.25/6.48 (37) RewriteLemmaProof [LOWER BOUND(ID), 3 ms] 18.25/6.48 (38) proven lower bound 18.25/6.48 (39) LowerBoundPropagationProof [FINISHED, 0 ms] 18.25/6.48 (40) BOUNDS(n^3, INF) 18.25/6.48 18.25/6.48 18.25/6.48 ---------------------------------------- 18.25/6.48 18.25/6.48 (0) 18.25/6.48 Obligation: 18.25/6.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 18.25/6.48 18.25/6.48 18.25/6.48 The TRS R consists of the following rules: 18.25/6.48 18.25/6.48 app(nil, y) -> y 18.25/6.48 app(add(n, x), y) -> add(n, app(x, y)) 18.25/6.48 reverse(nil) -> nil 18.25/6.48 reverse(add(n, x)) -> app(reverse(x), add(n, nil)) 18.25/6.48 shuffle(nil) -> nil 18.25/6.48 shuffle(add(n, x)) -> add(n, shuffle(reverse(x))) 18.25/6.48 18.25/6.48 S is empty. 18.25/6.48 Rewrite Strategy: FULL 18.25/6.48 ---------------------------------------- 18.25/6.48 18.25/6.48 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 18.25/6.48 Converted rc-obligation to irc-obligation. 18.25/6.48 18.25/6.48 As the TRS is a non-duplicating overlay system, we have rc = irc. 18.25/6.48 ---------------------------------------- 18.25/6.48 18.25/6.48 (2) 18.25/6.48 Obligation: 18.25/6.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^3). 18.25/6.48 18.25/6.48 18.25/6.48 The TRS R consists of the following rules: 18.25/6.48 18.25/6.48 app(nil, y) -> y 18.25/6.48 app(add(n, x), y) -> add(n, app(x, y)) 18.25/6.48 reverse(nil) -> nil 18.25/6.48 reverse(add(n, x)) -> app(reverse(x), add(n, nil)) 18.25/6.48 shuffle(nil) -> nil 18.25/6.48 shuffle(add(n, x)) -> add(n, shuffle(reverse(x))) 18.25/6.48 18.25/6.48 S is empty. 18.25/6.48 Rewrite Strategy: INNERMOST 18.25/6.48 ---------------------------------------- 18.25/6.48 18.25/6.48 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 18.25/6.48 Converted Cpx (relative) TRS to CDT 18.25/6.48 ---------------------------------------- 18.25/6.48 18.25/6.48 (4) 18.25/6.48 Obligation:
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