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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307753
details
property
value
status
complete
benchmark
otto05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n067.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.625 seconds
cpu usage
315.532
user time
313.662
system time
1.87038
max virtual memory
1.8281472E7
max residence set size
5370068.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
315.42/291.58 WORST_CASE(Omega(n^1), ?) 315.42/291.58 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 315.42/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 315.42/291.58 315.42/291.58 315.42/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 315.42/291.58 315.42/291.58 (0) CpxTRS 315.42/291.58 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 315.42/291.58 (2) CpxTRS 315.42/291.58 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 315.42/291.58 (4) typed CpxTrs 315.42/291.58 (5) OrderProof [LOWER BOUND(ID), 0 ms] 315.42/291.58 (6) typed CpxTrs 315.42/291.58 (7) RewriteLemmaProof [LOWER BOUND(ID), 310 ms] 315.42/291.58 (8) BEST 315.42/291.58 (9) proven lower bound 315.42/291.58 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 315.42/291.58 (11) BOUNDS(n^1, INF) 315.42/291.58 (12) typed CpxTrs 315.42/291.58 (13) RewriteLemmaProof [LOWER BOUND(ID), 78 ms] 315.42/291.58 (14) typed CpxTrs 315.42/291.58 315.42/291.58 315.42/291.58 ---------------------------------------- 315.42/291.58 315.42/291.58 (0) 315.42/291.58 Obligation: 315.42/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 315.42/291.58 315.42/291.58 315.42/291.58 The TRS R consists of the following rules: 315.42/291.58 315.42/291.58 lt(0, s(x)) -> true 315.42/291.58 lt(x, 0) -> false 315.42/291.58 lt(s(x), s(y)) -> lt(x, y) 315.42/291.58 logarithm(x) -> ifa(lt(0, x), x) 315.42/291.58 ifa(true, x) -> help(x, 1) 315.42/291.58 ifa(false, x) -> logZeroError 315.42/291.58 help(x, y) -> ifb(lt(y, x), x, y) 315.42/291.58 ifb(true, x, y) -> help(half(x), s(y)) 315.42/291.58 ifb(false, x, y) -> y 315.42/291.58 half(0) -> 0 315.42/291.58 half(s(0)) -> 0 315.42/291.58 half(s(s(x))) -> s(half(x)) 315.42/291.58 315.42/291.58 S is empty. 315.42/291.58 Rewrite Strategy: FULL 315.42/291.58 ---------------------------------------- 315.42/291.58 315.42/291.58 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 315.42/291.58 Renamed function symbols to avoid clashes with predefined symbol. 315.42/291.58 ---------------------------------------- 315.42/291.58 315.42/291.58 (2) 315.42/291.58 Obligation: 315.42/291.58 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 315.42/291.58 315.42/291.58 315.42/291.58 The TRS R consists of the following rules: 315.42/291.58 315.42/291.58 lt(0', s(x)) -> true 315.42/291.58 lt(x, 0') -> false 315.42/291.58 lt(s(x), s(y)) -> lt(x, y) 315.42/291.58 logarithm(x) -> ifa(lt(0', x), x) 315.42/291.58 ifa(true, x) -> help(x, 1') 315.42/291.58 ifa(false, x) -> logZeroError 315.42/291.58 help(x, y) -> ifb(lt(y, x), x, y) 315.42/291.58 ifb(true, x, y) -> help(half(x), s(y)) 315.42/291.58 ifb(false, x, y) -> y 315.42/291.58 half(0') -> 0' 315.42/291.58 half(s(0')) -> 0' 315.42/291.58 half(s(s(x))) -> s(half(x)) 315.42/291.58 315.42/291.58 S is empty. 315.42/291.58 Rewrite Strategy: FULL 315.42/291.58 ---------------------------------------- 315.42/291.58 315.42/291.58 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 315.42/291.58 Infered types. 315.42/291.58 ---------------------------------------- 315.42/291.58 315.42/291.58 (4) 315.42/291.58 Obligation: 315.42/291.58 TRS: 315.42/291.58 Rules: 315.42/291.58 lt(0', s(x)) -> true 315.42/291.58 lt(x, 0') -> false 315.42/291.58 lt(s(x), s(y)) -> lt(x, y) 315.42/291.58 logarithm(x) -> ifa(lt(0', x), x) 315.42/291.58 ifa(true, x) -> help(x, 1') 315.42/291.58 ifa(false, x) -> logZeroError 315.42/291.58 help(x, y) -> ifb(lt(y, x), x, y) 315.42/291.58 ifb(true, x, y) -> help(half(x), s(y)) 315.42/291.58 ifb(false, x, y) -> y 315.42/291.58 half(0') -> 0' 315.42/291.58 half(s(0')) -> 0' 315.42/291.58 half(s(s(x))) -> s(half(x)) 315.42/291.58 315.42/291.58 Types:
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