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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308452
details
property
value
status
complete
benchmark
2.19.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.89266 seconds
cpu usage
25.9531
user time
24.175
system time
1.77811
max virtual memory
7.556848E7
max residence set size
3921944.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
25.84/8.83 WORST_CASE(Omega(n^2), O(n^2)) 25.84/8.85 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 25.84/8.85 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 25.84/8.85 25.84/8.85 25.84/8.85 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 25.84/8.85 25.84/8.85 (0) CpxTRS 25.84/8.85 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 25.84/8.85 (2) CpxTRS 25.84/8.85 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 7 ms] 25.84/8.85 (4) CdtProblem 25.84/8.85 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 25.84/8.85 (6) CdtProblem 25.84/8.85 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 94 ms] 25.84/8.85 (8) CdtProblem 25.84/8.85 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 55 ms] 25.84/8.85 (10) CdtProblem 25.84/8.85 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 49 ms] 25.84/8.85 (12) CdtProblem 25.84/8.85 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 25.84/8.85 (14) BOUNDS(1, 1) 25.84/8.85 (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 25.84/8.85 (16) CpxTRS 25.84/8.85 (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 25.84/8.85 (18) typed CpxTrs 25.84/8.85 (19) OrderProof [LOWER BOUND(ID), 0 ms] 25.84/8.85 (20) typed CpxTrs 25.84/8.85 (21) RewriteLemmaProof [LOWER BOUND(ID), 292 ms] 25.84/8.85 (22) BEST 25.84/8.85 (23) proven lower bound 25.84/8.85 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 25.84/8.85 (25) BOUNDS(n^1, INF) 25.84/8.85 (26) typed CpxTrs 25.84/8.85 (27) RewriteLemmaProof [LOWER BOUND(ID), 78 ms] 25.84/8.85 (28) typed CpxTrs 25.84/8.85 (29) RewriteLemmaProof [LOWER BOUND(ID), 134 ms] 25.84/8.85 (30) proven lower bound 25.84/8.85 (31) LowerBoundPropagationProof [FINISHED, 0 ms] 25.84/8.85 (32) BOUNDS(n^2, INF) 25.84/8.85 25.84/8.85 25.84/8.85 ---------------------------------------- 25.84/8.85 25.84/8.85 (0) 25.84/8.85 Obligation: 25.84/8.85 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 25.84/8.85 25.84/8.85 25.84/8.85 The TRS R consists of the following rules: 25.84/8.85 25.84/8.85 sqr(0) -> 0 25.84/8.85 sqr(s(x)) -> +(sqr(x), s(double(x))) 25.84/8.85 double(0) -> 0 25.84/8.85 double(s(x)) -> s(s(double(x))) 25.84/8.85 +(x, 0) -> x 25.84/8.85 +(x, s(y)) -> s(+(x, y)) 25.84/8.85 sqr(s(x)) -> s(+(sqr(x), double(x))) 25.84/8.85 25.84/8.85 S is empty. 25.84/8.85 Rewrite Strategy: FULL 25.84/8.85 ---------------------------------------- 25.84/8.85 25.84/8.85 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 25.84/8.85 Converted rc-obligation to irc-obligation. 25.84/8.85 25.84/8.85 The duplicating contexts are: 25.84/8.85 sqr(s([])) 25.84/8.85 25.84/8.85 25.84/8.85 The defined contexts are: 25.84/8.85 +([], x1) 25.84/8.85 +(x0, []) 25.84/8.85 +([], s(x1)) 25.84/8.85 +(x0, s([])) 25.84/8.85 25.84/8.85 25.84/8.85 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 25.84/8.85 ---------------------------------------- 25.84/8.85 25.84/8.85 (2) 25.84/8.85 Obligation: 25.84/8.85 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 25.84/8.85 25.84/8.85 25.84/8.85 The TRS R consists of the following rules: 25.84/8.85 25.84/8.85 sqr(0) -> 0 25.84/8.85 sqr(s(x)) -> +(sqr(x), s(double(x))) 25.84/8.85 double(0) -> 0 25.84/8.85 double(s(x)) -> s(s(double(x))) 25.84/8.85 +(x, 0) -> x 25.84/8.85 +(x, s(y)) -> s(+(x, y)) 25.84/8.85 sqr(s(x)) -> s(+(sqr(x), double(x))) 25.84/8.85 25.84/8.85 S is empty. 25.84/8.85 Rewrite Strategy: INNERMOST 25.84/8.85 ---------------------------------------- 25.84/8.85 25.84/8.85 (3) CpxTrsToCdtProof (UPPER BOUND(ID))
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