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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313923
details
property
value
status
complete
benchmark
08.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n016.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.74866 seconds
cpu usage
15.3105
user time
14.3122
system time
0.998306
max virtual memory
1.887334E7
max residence set size
2995248.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
14.75/4.66 WORST_CASE(Omega(n^1), O(n^1)) 14.75/4.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 14.75/4.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.75/4.67 14.75/4.67 14.75/4.67 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 14.75/4.67 14.75/4.67 (0) CpxTRS 14.75/4.67 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 14.75/4.67 (2) CpxWeightedTrs 14.75/4.67 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 14.75/4.67 (4) CpxTypedWeightedTrs 14.75/4.67 (5) CompletionProof [UPPER BOUND(ID), 3 ms] 14.75/4.67 (6) CpxTypedWeightedCompleteTrs 14.75/4.67 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 14.75/4.67 (8) CpxRNTS 14.75/4.67 (9) CompleteCoflocoProof [FINISHED, 156 ms] 14.75/4.67 (10) BOUNDS(1, n^1) 14.75/4.67 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 14.75/4.67 (12) TRS for Loop Detection 14.75/4.67 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 14.75/4.67 (14) BEST 14.75/4.67 (15) proven lower bound 14.75/4.67 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 14.75/4.67 (17) BOUNDS(n^1, INF) 14.75/4.67 (18) TRS for Loop Detection 14.75/4.67 14.75/4.67 14.75/4.67 ---------------------------------------- 14.75/4.67 14.75/4.67 (0) 14.75/4.67 Obligation: 14.75/4.67 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 14.75/4.67 14.75/4.67 14.75/4.67 The TRS R consists of the following rules: 14.75/4.67 14.75/4.67 D(t) -> 1 14.75/4.67 D(constant) -> 0 14.75/4.67 D(+(x, y)) -> +(D(x), D(y)) 14.75/4.67 D(*(x, y)) -> +(*(y, D(x)), *(x, D(y))) 14.75/4.67 D(-(x, y)) -> -(D(x), D(y)) 14.75/4.67 14.75/4.67 S is empty. 14.75/4.67 Rewrite Strategy: INNERMOST 14.75/4.67 ---------------------------------------- 14.75/4.67 14.75/4.67 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 14.75/4.67 Transformed relative TRS to weighted TRS 14.75/4.67 ---------------------------------------- 14.75/4.67 14.75/4.67 (2) 14.75/4.67 Obligation: 14.75/4.67 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 14.75/4.67 14.75/4.67 14.75/4.67 The TRS R consists of the following rules: 14.75/4.67 14.75/4.67 D(t) -> 1 [1] 14.75/4.67 D(constant) -> 0 [1] 14.75/4.67 D(+(x, y)) -> +(D(x), D(y)) [1] 14.75/4.67 D(*(x, y)) -> +(*(y, D(x)), *(x, D(y))) [1] 14.75/4.67 D(-(x, y)) -> -(D(x), D(y)) [1] 14.75/4.67 14.75/4.67 Rewrite Strategy: INNERMOST 14.75/4.67 ---------------------------------------- 14.75/4.67 14.75/4.67 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 14.75/4.67 Infered types. 14.75/4.67 ---------------------------------------- 14.75/4.67 14.75/4.67 (4) 14.75/4.67 Obligation: 14.75/4.67 Runtime Complexity Weighted TRS with Types. 14.75/4.67 The TRS R consists of the following rules: 14.75/4.67 14.75/4.67 D(t) -> 1 [1] 14.75/4.67 D(constant) -> 0 [1] 14.75/4.67 D(+(x, y)) -> +(D(x), D(y)) [1] 14.75/4.67 D(*(x, y)) -> +(*(y, D(x)), *(x, D(y))) [1] 14.75/4.67 D(-(x, y)) -> -(D(x), D(y)) [1] 14.75/4.67 14.75/4.67 The TRS has the following type information: 14.75/4.67 D :: t:1:constant:0:+:*:- -> t:1:constant:0:+:*:- 14.75/4.67 t :: t:1:constant:0:+:*:- 14.75/4.67 1 :: t:1:constant:0:+:*:- 14.75/4.67 constant :: t:1:constant:0:+:*:- 14.75/4.67 0 :: t:1:constant:0:+:*:- 14.75/4.67 + :: t:1:constant:0:+:*:- -> t:1:constant:0:+:*:- -> t:1:constant:0:+:*:- 14.75/4.67 * :: t:1:constant:0:+:*:- -> t:1:constant:0:+:*:- -> t:1:constant:0:+:*:- 14.75/4.67 - :: t:1:constant:0:+:*:- -> t:1:constant:0:+:*:- -> t:1:constant:0:+:*:- 14.75/4.67 14.75/4.67 Rewrite Strategy: INNERMOST 14.75/4.67 ---------------------------------------- 14.75/4.67 14.75/4.67 (5) CompletionProof (UPPER BOUND(ID)) 14.75/4.67 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 14.75/4.67 14.75/4.67 D(v0) -> null_D [0] 14.75/4.67
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