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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313719
details
property
value
status
complete
benchmark
thiemann27.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n048.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.588 seconds
cpu usage
902.289
user time
898.073
system time
4.21569
max virtual memory
3.8174936E7
max residence set size
5428676.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
901.97/291.52 WORST_CASE(Omega(n^1), O(n^2)) 901.97/291.54 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 901.97/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 901.97/291.54 901.97/291.54 901.97/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 901.97/291.54 901.97/291.54 (0) CpxTRS 901.97/291.54 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 901.97/291.54 (2) CpxWeightedTrs 901.97/291.54 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 901.97/291.54 (4) CpxTypedWeightedTrs 901.97/291.54 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 901.97/291.54 (6) CpxTypedWeightedCompleteTrs 901.97/291.54 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 901.97/291.54 (8) CpxRNTS 901.97/291.54 (9) CompleteCoflocoProof [FINISHED, 239 ms] 901.97/291.54 (10) BOUNDS(1, n^2) 901.97/291.54 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 901.97/291.54 (12) TRS for Loop Detection 901.97/291.54 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 901.97/291.54 (14) BEST 901.97/291.54 (15) proven lower bound 901.97/291.54 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 901.97/291.54 (17) BOUNDS(n^1, INF) 901.97/291.54 (18) TRS for Loop Detection 901.97/291.54 901.97/291.54 901.97/291.54 ---------------------------------------- 901.97/291.54 901.97/291.54 (0) 901.97/291.54 Obligation: 901.97/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 901.97/291.54 901.97/291.54 901.97/291.54 The TRS R consists of the following rules: 901.97/291.54 901.97/291.54 le(0, y) -> true 901.97/291.54 le(s(x), 0) -> false 901.97/291.54 le(s(x), s(y)) -> le(x, y) 901.97/291.54 int(x, y) -> if(le(x, y), x, y) 901.97/291.54 if(true, x, y) -> cons(x, int(s(x), y)) 901.97/291.54 if(false, x, y) -> nil 901.97/291.54 901.97/291.54 S is empty. 901.97/291.54 Rewrite Strategy: INNERMOST 901.97/291.54 ---------------------------------------- 901.97/291.54 901.97/291.54 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 901.97/291.54 Transformed relative TRS to weighted TRS 901.97/291.54 ---------------------------------------- 901.97/291.54 901.97/291.54 (2) 901.97/291.54 Obligation: 901.97/291.54 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 901.97/291.54 901.97/291.54 901.97/291.54 The TRS R consists of the following rules: 901.97/291.54 901.97/291.54 le(0, y) -> true [1] 901.97/291.54 le(s(x), 0) -> false [1] 901.97/291.54 le(s(x), s(y)) -> le(x, y) [1] 901.97/291.54 int(x, y) -> if(le(x, y), x, y) [1] 901.97/291.54 if(true, x, y) -> cons(x, int(s(x), y)) [1] 901.97/291.54 if(false, x, y) -> nil [1] 901.97/291.54 901.97/291.54 Rewrite Strategy: INNERMOST 901.97/291.54 ---------------------------------------- 901.97/291.54 901.97/291.54 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 901.97/291.54 Infered types. 901.97/291.54 ---------------------------------------- 901.97/291.54 901.97/291.54 (4) 901.97/291.54 Obligation: 901.97/291.54 Runtime Complexity Weighted TRS with Types. 901.97/291.54 The TRS R consists of the following rules: 901.97/291.54 901.97/291.54 le(0, y) -> true [1] 901.97/291.54 le(s(x), 0) -> false [1] 901.97/291.54 le(s(x), s(y)) -> le(x, y) [1] 901.97/291.54 int(x, y) -> if(le(x, y), x, y) [1] 901.97/291.54 if(true, x, y) -> cons(x, int(s(x), y)) [1] 901.97/291.54 if(false, x, y) -> nil [1] 901.97/291.54 901.97/291.54 The TRS has the following type information: 901.97/291.54 le :: 0:s -> 0:s -> true:false 901.97/291.54 0 :: 0:s 901.97/291.54 true :: true:false 901.97/291.54 s :: 0:s -> 0:s 901.97/291.54 false :: true:false 901.97/291.54 int :: 0:s -> 0:s -> cons:nil 901.97/291.54 if :: true:false -> 0:s -> 0:s -> cons:nil 901.97/291.54 cons :: 0:s -> cons:nil -> cons:nil 901.97/291.54 nil :: cons:nil 901.97/291.54 901.97/291.54 Rewrite Strategy: INNERMOST 901.97/291.54 ---------------------------------------- 901.97/291.54 901.97/291.54 (5) CompletionProof (UPPER BOUND(ID))
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