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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313890
details
property
value
status
complete
benchmark
1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n019.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.531 seconds
cpu usage
459.905
user time
456.073
system time
3.83253
max virtual memory
3.8311896E7
max residence set size
5426472.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
459.77/291.47 WORST_CASE(Omega(n^1), O(n^2)) 459.81/291.48 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 459.81/291.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 459.81/291.48 459.81/291.48 459.81/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 459.81/291.48 459.81/291.48 (0) CpxTRS 459.81/291.48 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 459.81/291.48 (2) CpxWeightedTrs 459.81/291.48 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 459.81/291.48 (4) CpxTypedWeightedTrs 459.81/291.48 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 459.81/291.48 (6) CpxTypedWeightedCompleteTrs 459.81/291.48 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 459.81/291.48 (8) CpxRNTS 459.81/291.48 (9) CompleteCoflocoProof [FINISHED, 289 ms] 459.81/291.48 (10) BOUNDS(1, n^2) 459.81/291.48 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 459.81/291.48 (12) CpxTRS 459.81/291.48 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 459.81/291.48 (14) typed CpxTrs 459.81/291.48 (15) OrderProof [LOWER BOUND(ID), 0 ms] 459.81/291.48 (16) typed CpxTrs 459.81/291.48 (17) RewriteLemmaProof [LOWER BOUND(ID), 295 ms] 459.81/291.48 (18) BEST 459.81/291.48 (19) proven lower bound 459.81/291.48 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 459.81/291.48 (21) BOUNDS(n^1, INF) 459.81/291.48 (22) typed CpxTrs 459.81/291.48 459.81/291.48 459.81/291.48 ---------------------------------------- 459.81/291.48 459.81/291.48 (0) 459.81/291.48 Obligation: 459.81/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 459.81/291.48 459.81/291.48 459.81/291.48 The TRS R consists of the following rules: 459.81/291.48 459.81/291.48 cond(true, x, y) -> cond(gr(x, y), p(x), y) 459.81/291.48 gr(0, x) -> false 459.81/291.48 gr(s(x), 0) -> true 459.81/291.48 gr(s(x), s(y)) -> gr(x, y) 459.81/291.48 p(0) -> 0 459.81/291.48 p(s(x)) -> x 459.81/291.48 459.81/291.48 S is empty. 459.81/291.48 Rewrite Strategy: INNERMOST 459.81/291.48 ---------------------------------------- 459.81/291.48 459.81/291.48 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 459.81/291.48 Transformed relative TRS to weighted TRS 459.81/291.48 ---------------------------------------- 459.81/291.48 459.81/291.48 (2) 459.81/291.48 Obligation: 459.81/291.48 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 459.81/291.48 459.81/291.48 459.81/291.48 The TRS R consists of the following rules: 459.81/291.48 459.81/291.48 cond(true, x, y) -> cond(gr(x, y), p(x), y) [1] 459.81/291.48 gr(0, x) -> false [1] 459.81/291.48 gr(s(x), 0) -> true [1] 459.81/291.48 gr(s(x), s(y)) -> gr(x, y) [1] 459.81/291.48 p(0) -> 0 [1] 459.81/291.48 p(s(x)) -> x [1] 459.81/291.48 459.81/291.48 Rewrite Strategy: INNERMOST 459.81/291.48 ---------------------------------------- 459.81/291.48 459.81/291.48 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 459.81/291.48 Infered types. 459.81/291.48 ---------------------------------------- 459.81/291.48 459.81/291.48 (4) 459.81/291.48 Obligation: 459.81/291.48 Runtime Complexity Weighted TRS with Types. 459.81/291.48 The TRS R consists of the following rules: 459.81/291.48 459.81/291.48 cond(true, x, y) -> cond(gr(x, y), p(x), y) [1] 459.81/291.48 gr(0, x) -> false [1] 459.81/291.48 gr(s(x), 0) -> true [1] 459.81/291.48 gr(s(x), s(y)) -> gr(x, y) [1] 459.81/291.48 p(0) -> 0 [1] 459.81/291.48 p(s(x)) -> x [1] 459.81/291.48 459.81/291.48 The TRS has the following type information: 459.81/291.48 cond :: true:false -> 0:s -> 0:s -> cond 459.81/291.48 true :: true:false 459.81/291.48 gr :: 0:s -> 0:s -> true:false 459.81/291.48 p :: 0:s -> 0:s 459.81/291.48 0 :: 0:s 459.81/291.48 false :: true:false 459.81/291.48 s :: 0:s -> 0:s 459.81/291.48 459.81/291.48 Rewrite Strategy: INNERMOST 459.81/291.48 ----------------------------------------
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