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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307900
details
property
value
status
complete
benchmark
20.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n128.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.643 seconds
cpu usage
1070.35
user time
1058.43
system time
11.9294
max virtual memory
3.7256832E7
max residence set size
1.4689868E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1069.83/291.49 WORST_CASE(Omega(n^1), ?) 1069.83/291.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1069.83/291.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1069.83/291.50 1069.83/291.50 1069.83/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1069.83/291.50 1069.83/291.50 (0) CpxTRS 1069.83/291.50 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1069.83/291.50 (2) TRS for Loop Detection 1069.83/291.50 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1069.83/291.50 (4) BEST 1069.83/291.50 (5) proven lower bound 1069.83/291.50 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 1069.83/291.50 (7) BOUNDS(n^1, INF) 1069.83/291.50 (8) TRS for Loop Detection 1069.83/291.50 1069.83/291.50 1069.83/291.50 ---------------------------------------- 1069.83/291.50 1069.83/291.50 (0) 1069.83/291.50 Obligation: 1069.83/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1069.83/291.50 1069.83/291.50 1069.83/291.50 The TRS R consists of the following rules: 1069.83/291.50 1069.83/291.50 not(not(x)) -> x 1069.83/291.50 not(or(x, y)) -> and(not(not(not(x))), not(not(not(y)))) 1069.83/291.50 not(and(x, y)) -> or(not(not(not(x))), not(not(not(y)))) 1069.83/291.50 1069.83/291.50 S is empty. 1069.83/291.50 Rewrite Strategy: FULL 1069.83/291.50 ---------------------------------------- 1069.83/291.50 1069.83/291.50 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1069.83/291.50 Transformed a relative TRS into a decreasing-loop problem. 1069.83/291.50 ---------------------------------------- 1069.83/291.50 1069.83/291.50 (2) 1069.83/291.50 Obligation: 1069.83/291.50 Analyzing the following TRS for decreasing loops: 1069.83/291.50 1069.83/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1069.83/291.50 1069.83/291.50 1069.83/291.50 The TRS R consists of the following rules: 1069.83/291.50 1069.83/291.50 not(not(x)) -> x 1069.83/291.50 not(or(x, y)) -> and(not(not(not(x))), not(not(not(y)))) 1069.83/291.50 not(and(x, y)) -> or(not(not(not(x))), not(not(not(y)))) 1069.83/291.50 1069.83/291.50 S is empty. 1069.83/291.50 Rewrite Strategy: FULL 1069.83/291.50 ---------------------------------------- 1069.83/291.50 1069.83/291.50 (3) DecreasingLoopProof (LOWER BOUND(ID)) 1069.83/291.50 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1069.83/291.50 1069.83/291.50 The rewrite sequence 1069.83/291.50 1069.83/291.50 not(or(x, y)) ->^+ and(not(not(not(x))), not(not(not(y)))) 1069.83/291.50 1069.83/291.50 gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0,0]. 1069.83/291.50 1069.83/291.50 The pumping substitution is [x / or(x, y)]. 1069.83/291.50 1069.83/291.50 The result substitution is [ ]. 1069.83/291.50 1069.83/291.50 1069.83/291.50 1069.83/291.50 1069.83/291.50 ---------------------------------------- 1069.83/291.50 1069.83/291.50 (4) 1069.83/291.50 Complex Obligation (BEST) 1069.83/291.50 1069.83/291.50 ---------------------------------------- 1069.83/291.50 1069.83/291.50 (5) 1069.83/291.50 Obligation: 1069.83/291.50 Proved the lower bound n^1 for the following obligation: 1069.83/291.50 1069.83/291.50 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1069.83/291.50 1069.83/291.50 1069.83/291.50 The TRS R consists of the following rules: 1069.83/291.50 1069.83/291.50 not(not(x)) -> x 1069.83/291.50 not(or(x, y)) -> and(not(not(not(x))), not(not(not(y)))) 1069.83/291.50 not(and(x, y)) -> or(not(not(not(x))), not(not(not(y)))) 1069.83/291.50 1069.83/291.50 S is empty. 1069.83/291.50 Rewrite Strategy: FULL 1069.83/291.50 ---------------------------------------- 1069.83/291.50 1069.83/291.50 (6) LowerBoundPropagationProof (FINISHED) 1069.83/291.50 Propagated lower bound. 1069.83/291.50 ---------------------------------------- 1069.83/291.50
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