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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313720
details
property
value
status
complete
benchmark
otto07.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n061.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.594 seconds
cpu usage
893.848
user time
889.317
system time
4.53182
max virtual memory
5.6012996E7
max residence set size
5414220.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
893.53/291.52 WORST_CASE(Omega(n^1), O(n^2)) 893.53/291.55 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 893.53/291.55 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 893.53/291.55 893.53/291.55 893.53/291.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 893.53/291.55 893.53/291.55 (0) CpxTRS 893.53/291.55 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 893.53/291.55 (2) CpxWeightedTrs 893.53/291.55 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 893.53/291.55 (4) CpxTypedWeightedTrs 893.53/291.55 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 893.53/291.55 (6) CpxTypedWeightedCompleteTrs 893.53/291.55 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 893.53/291.55 (8) CpxRNTS 893.53/291.55 (9) CompleteCoflocoProof [FINISHED, 252 ms] 893.53/291.55 (10) BOUNDS(1, n^2) 893.53/291.55 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 893.53/291.55 (12) CpxTRS 893.53/291.55 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 893.53/291.55 (14) typed CpxTrs 893.53/291.55 (15) OrderProof [LOWER BOUND(ID), 0 ms] 893.53/291.55 (16) typed CpxTrs 893.53/291.55 (17) RewriteLemmaProof [LOWER BOUND(ID), 290 ms] 893.53/291.55 (18) BEST 893.53/291.55 (19) proven lower bound 893.53/291.55 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 893.53/291.55 (21) BOUNDS(n^1, INF) 893.53/291.55 (22) typed CpxTrs 893.53/291.55 893.53/291.55 893.53/291.55 ---------------------------------------- 893.53/291.55 893.53/291.55 (0) 893.53/291.55 Obligation: 893.53/291.55 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 893.53/291.55 893.53/291.55 893.53/291.55 The TRS R consists of the following rules: 893.53/291.55 893.53/291.55 lt(0, s(x)) -> true 893.53/291.55 lt(x, 0) -> false 893.53/291.55 lt(s(x), s(y)) -> lt(x, y) 893.53/291.55 minus(x, y) -> help(lt(y, x), x, y) 893.53/291.55 help(true, x, y) -> s(minus(x, s(y))) 893.53/291.55 help(false, x, y) -> 0 893.53/291.55 893.53/291.55 S is empty. 893.53/291.55 Rewrite Strategy: INNERMOST 893.53/291.55 ---------------------------------------- 893.53/291.55 893.53/291.55 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 893.53/291.55 Transformed relative TRS to weighted TRS 893.53/291.55 ---------------------------------------- 893.53/291.55 893.53/291.55 (2) 893.53/291.55 Obligation: 893.53/291.55 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 893.53/291.55 893.53/291.55 893.53/291.55 The TRS R consists of the following rules: 893.53/291.55 893.53/291.55 lt(0, s(x)) -> true [1] 893.53/291.55 lt(x, 0) -> false [1] 893.53/291.55 lt(s(x), s(y)) -> lt(x, y) [1] 893.53/291.55 minus(x, y) -> help(lt(y, x), x, y) [1] 893.53/291.55 help(true, x, y) -> s(minus(x, s(y))) [1] 893.53/291.55 help(false, x, y) -> 0 [1] 893.53/291.55 893.53/291.55 Rewrite Strategy: INNERMOST 893.53/291.55 ---------------------------------------- 893.53/291.55 893.53/291.55 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 893.53/291.55 Infered types. 893.53/291.55 ---------------------------------------- 893.53/291.55 893.53/291.55 (4) 893.53/291.55 Obligation: 893.53/291.55 Runtime Complexity Weighted TRS with Types. 893.53/291.55 The TRS R consists of the following rules: 893.53/291.55 893.53/291.55 lt(0, s(x)) -> true [1] 893.53/291.55 lt(x, 0) -> false [1] 893.53/291.55 lt(s(x), s(y)) -> lt(x, y) [1] 893.53/291.55 minus(x, y) -> help(lt(y, x), x, y) [1] 893.53/291.55 help(true, x, y) -> s(minus(x, s(y))) [1] 893.53/291.55 help(false, x, y) -> 0 [1] 893.53/291.55 893.53/291.55 The TRS has the following type information: 893.53/291.55 lt :: 0:s -> 0:s -> true:false 893.53/291.55 0 :: 0:s 893.53/291.55 s :: 0:s -> 0:s 893.53/291.55 true :: true:false 893.53/291.55 false :: true:false 893.53/291.55 minus :: 0:s -> 0:s -> 0:s 893.53/291.55 help :: true:false -> 0:s -> 0:s -> 0:s 893.53/291.55 893.53/291.55 Rewrite Strategy: INNERMOST 893.53/291.55 ----------------------------------------
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