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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307902
details
property
value
status
complete
benchmark
33.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n168.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.527 seconds
cpu usage
329.69
user time
326.412
system time
3.2783
max virtual memory
1.9178656E7
max residence set size
6394332.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
329.61/291.48 WORST_CASE(Omega(n^1), O(n^2)) 329.61/291.49 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 329.61/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 329.61/291.49 329.61/291.49 329.61/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 329.61/291.49 329.61/291.49 (0) CpxTRS 329.61/291.49 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 329.61/291.49 (2) CpxTRS 329.61/291.49 (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 4 ms] 329.61/291.49 (4) CpxTRS 329.61/291.49 (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 329.61/291.49 (6) CdtProblem 329.61/291.49 (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 329.61/291.49 (8) CdtProblem 329.61/291.49 (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 329.61/291.49 (10) CdtProblem 329.61/291.49 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 15 ms] 329.61/291.49 (12) CdtProblem 329.61/291.49 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 329.61/291.49 (14) BOUNDS(1, 1) 329.61/291.49 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 329.61/291.49 (16) TRS for Loop Detection 329.61/291.49 (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 329.61/291.49 (18) BEST 329.61/291.49 (19) proven lower bound 329.61/291.49 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 329.61/291.49 (21) BOUNDS(n^1, INF) 329.61/291.49 (22) TRS for Loop Detection 329.61/291.49 329.61/291.49 329.61/291.49 ---------------------------------------- 329.61/291.49 329.61/291.49 (0) 329.61/291.49 Obligation: 329.61/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 329.61/291.49 329.61/291.49 329.61/291.49 The TRS R consists of the following rules: 329.61/291.49 329.61/291.49 h(z, e(x)) -> h(c(z), d(z, x)) 329.61/291.49 d(z, g(0, 0)) -> e(0) 329.61/291.49 d(z, g(x, y)) -> g(e(x), d(z, y)) 329.61/291.49 d(c(z), g(g(x, y), 0)) -> g(d(c(z), g(x, y)), d(z, g(x, y))) 329.61/291.49 g(e(x), e(y)) -> e(g(x, y)) 329.61/291.49 329.61/291.49 S is empty. 329.61/291.49 Rewrite Strategy: FULL 329.61/291.49 ---------------------------------------- 329.61/291.49 329.61/291.49 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 329.61/291.49 The following defined symbols can occur below the 1th argument of h: d 329.61/291.49 The following defined symbols can occur below the 1th argument of d: d 329.61/291.49 329.61/291.49 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 329.61/291.49 d(z, g(0, 0)) -> e(0) 329.61/291.49 d(z, g(x, y)) -> g(e(x), d(z, y)) 329.61/291.49 d(c(z), g(g(x, y), 0)) -> g(d(c(z), g(x, y)), d(z, g(x, y))) 329.61/291.49 329.61/291.49 ---------------------------------------- 329.61/291.49 329.61/291.49 (2) 329.61/291.49 Obligation: 329.61/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 329.61/291.49 329.61/291.49 329.61/291.49 The TRS R consists of the following rules: 329.61/291.49 329.61/291.49 h(z, e(x)) -> h(c(z), d(z, x)) 329.61/291.49 g(e(x), e(y)) -> e(g(x, y)) 329.61/291.49 329.61/291.49 S is empty. 329.61/291.49 Rewrite Strategy: FULL 329.61/291.49 ---------------------------------------- 329.61/291.49 329.61/291.49 (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) 329.61/291.49 Converted rc-obligation to irc-obligation. 329.61/291.49 329.61/291.49 As the TRS does not nest defined symbols, we have rc = irc. 329.61/291.49 ---------------------------------------- 329.61/291.49 329.61/291.49 (4) 329.61/291.49 Obligation: 329.61/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 329.61/291.49 329.61/291.49 329.61/291.49 The TRS R consists of the following rules: 329.61/291.49 329.61/291.49 h(z, e(x)) -> h(c(z), d(z, x)) 329.61/291.49 g(e(x), e(y)) -> e(g(x, y)) 329.61/291.49 329.61/291.49 S is empty. 329.61/291.49 Rewrite Strategy: INNERMOST 329.61/291.49 ---------------------------------------- 329.61/291.49 329.61/291.49 (5) CpxTrsToCdtProof (UPPER BOUND(ID)) 329.61/291.49 Converted Cpx (relative) TRS to CDT 329.61/291.49 ---------------------------------------- 329.61/291.49
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