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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307924
details
property
value
status
complete
benchmark
cade01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.549 seconds
cpu usage
878.311
user time
873.577
system time
4.73396
max virtual memory
3.7784436E7
max residence set size
5457620.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
878.07/291.49 WORST_CASE(Omega(n^1), O(n^2)) 878.20/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 878.20/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 878.20/291.51 878.20/291.51 878.20/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 878.20/291.51 878.20/291.51 (0) CpxTRS 878.20/291.51 (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] 878.20/291.51 (2) CpxTRS 878.20/291.51 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 878.20/291.51 (4) CpxWeightedTrs 878.20/291.51 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 878.20/291.51 (6) CpxTypedWeightedTrs 878.20/291.51 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 878.20/291.51 (8) CpxTypedWeightedCompleteTrs 878.20/291.51 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms] 878.20/291.51 (10) CpxRNTS 878.20/291.51 (11) CompleteCoflocoProof [FINISHED, 239 ms] 878.20/291.51 (12) BOUNDS(1, n^2) 878.20/291.51 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 878.20/291.51 (14) TRS for Loop Detection 878.20/291.51 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 878.20/291.51 (16) BEST 878.20/291.51 (17) proven lower bound 878.20/291.51 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 878.20/291.51 (19) BOUNDS(n^1, INF) 878.20/291.51 (20) TRS for Loop Detection 878.20/291.51 878.20/291.51 878.20/291.51 ---------------------------------------- 878.20/291.51 878.20/291.51 (0) 878.20/291.51 Obligation: 878.20/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 878.20/291.51 878.20/291.51 878.20/291.51 The TRS R consists of the following rules: 878.20/291.51 878.20/291.51 minus(x, y) -> cond(gt(x, y), x, y) 878.20/291.51 cond(false, x, y) -> 0 878.20/291.51 cond(true, x, y) -> s(minus(x, s(y))) 878.20/291.51 gt(0, v) -> false 878.20/291.51 gt(s(u), 0) -> true 878.20/291.51 gt(s(u), s(v)) -> gt(u, v) 878.20/291.51 878.20/291.51 S is empty. 878.20/291.51 Rewrite Strategy: FULL 878.20/291.51 ---------------------------------------- 878.20/291.51 878.20/291.51 (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) 878.20/291.51 Converted rc-obligation to irc-obligation. 878.20/291.51 878.20/291.51 The duplicating contexts are: 878.20/291.51 minus([], y) 878.20/291.51 minus(x, []) 878.20/291.51 878.20/291.51 878.20/291.51 The defined contexts are: 878.20/291.51 cond([], x1, x2) 878.20/291.51 878.20/291.51 878.20/291.51 [] just represents basic- or constructor-terms in the following defined contexts: 878.20/291.51 cond([], x1, x2) 878.20/291.51 878.20/291.51 878.20/291.51 As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. 878.20/291.51 ---------------------------------------- 878.20/291.51 878.20/291.51 (2) 878.20/291.51 Obligation: 878.20/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). 878.20/291.51 878.20/291.51 878.20/291.51 The TRS R consists of the following rules: 878.20/291.51 878.20/291.51 minus(x, y) -> cond(gt(x, y), x, y) 878.20/291.51 cond(false, x, y) -> 0 878.20/291.51 cond(true, x, y) -> s(minus(x, s(y))) 878.20/291.51 gt(0, v) -> false 878.20/291.51 gt(s(u), 0) -> true 878.20/291.51 gt(s(u), s(v)) -> gt(u, v) 878.20/291.51 878.20/291.51 S is empty. 878.20/291.51 Rewrite Strategy: INNERMOST 878.20/291.51 ---------------------------------------- 878.20/291.51 878.20/291.51 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 878.20/291.51 Transformed relative TRS to weighted TRS 878.20/291.51 ---------------------------------------- 878.20/291.51 878.20/291.51 (4) 878.20/291.51 Obligation: 878.20/291.51 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 878.20/291.51 878.20/291.51 878.20/291.51 The TRS R consists of the following rules: 878.20/291.51 878.20/291.51 minus(x, y) -> cond(gt(x, y), x, y) [1] 878.20/291.51 cond(false, x, y) -> 0 [1]
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