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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308460
details
property
value
status
complete
benchmark
2.18.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)
291.54 seconds
cpu usage
333.875
user time
330.928
system time
2.9474
max virtual memory
1.9218008E7
max residence set size
5865800.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
333.78/291.49 WORST_CASE(Omega(n^1), O(n^2)) 333.78/291.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 333.78/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 333.78/291.50 333.78/291.50 333.78/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 333.78/291.50 333.78/291.50 (0) CpxTRS 333.78/291.50 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 333.78/291.50 (2) CpxTRS 333.78/291.50 (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 333.78/291.50 (4) CdtProblem 333.78/291.50 (5) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 333.78/291.50 (6) CdtProblem 333.78/291.50 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 32 ms] 333.78/291.50 (8) CdtProblem 333.78/291.50 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 37 ms] 333.78/291.50 (10) CdtProblem 333.78/291.50 (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 333.78/291.50 (12) BOUNDS(1, 1) 333.78/291.50 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 333.78/291.50 (14) TRS for Loop Detection 333.78/291.50 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 333.78/291.50 (16) BEST 333.78/291.50 (17) proven lower bound 333.78/291.50 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 333.78/291.50 (19) BOUNDS(n^1, INF) 333.78/291.50 (20) TRS for Loop Detection 333.78/291.50 333.78/291.50 333.78/291.50 ---------------------------------------- 333.78/291.50 333.78/291.50 (0) 333.78/291.50 Obligation: 333.78/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 333.78/291.50 333.78/291.50 333.78/291.50 The TRS R consists of the following rules: 333.78/291.50 333.78/291.50 sum(0) -> 0 333.78/291.50 sum(s(x)) -> +(sum(x), s(x)) 333.78/291.50 +(x, 0) -> x 333.78/291.50 +(x, s(y)) -> s(+(x, y)) 333.78/291.50 333.78/291.50 S is empty. 333.78/291.50 Rewrite Strategy: FULL 333.78/291.50 ---------------------------------------- 333.78/291.50 333.78/291.50 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 333.78/291.50 Converted rc-obligation to irc-obligation. 333.78/291.50 333.78/291.50 The duplicating contexts are: 333.78/291.50 sum(s([])) 333.78/291.50 333.78/291.50 333.78/291.50 The defined contexts are: 333.78/291.50 +([], s(x1)) 333.78/291.50 +([], x1) 333.78/291.50 333.78/291.50 333.78/291.50 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 333.78/291.50 ---------------------------------------- 333.78/291.50 333.78/291.50 (2) 333.78/291.50 Obligation: 333.78/291.50 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 333.78/291.50 333.78/291.50 333.78/291.50 The TRS R consists of the following rules: 333.78/291.50 333.78/291.50 sum(0) -> 0 333.78/291.50 sum(s(x)) -> +(sum(x), s(x)) 333.78/291.50 +(x, 0) -> x 333.78/291.50 +(x, s(y)) -> s(+(x, y)) 333.78/291.50 333.78/291.50 S is empty. 333.78/291.50 Rewrite Strategy: INNERMOST 333.78/291.50 ---------------------------------------- 333.78/291.50 333.78/291.50 (3) CpxTrsToCdtProof (UPPER BOUND(ID)) 333.78/291.50 Converted Cpx (relative) TRS to CDT 333.78/291.50 ---------------------------------------- 333.78/291.50 333.78/291.50 (4) 333.78/291.50 Obligation: 333.78/291.50 Complexity Dependency Tuples Problem 333.78/291.50 333.78/291.50 Rules: 333.78/291.50 sum(0) -> 0 333.78/291.50 sum(s(z0)) -> +(sum(z0), s(z0)) 333.78/291.50 +(z0, 0) -> z0 333.78/291.50 +(z0, s(z1)) -> s(+(z0, z1)) 333.78/291.50 Tuples: 333.78/291.50 SUM(0) -> c 333.78/291.50 SUM(s(z0)) -> c1(+'(sum(z0), s(z0)), SUM(z0)) 333.78/291.50 +'(z0, 0) -> c2 333.78/291.50 +'(z0, s(z1)) -> c3(+'(z0, z1)) 333.78/291.50 S tuples: 333.78/291.50 SUM(0) -> c 333.78/291.50 SUM(s(z0)) -> c1(+'(sum(z0), s(z0)), SUM(z0))
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