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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307786
details
property
value
status
complete
benchmark
thiemann22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n100.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.595 seconds
cpu usage
312.848
user time
310.772
system time
2.07598
max virtual memory
1.8281756E7
max residence set size
5262716.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
312.77/291.55 WORST_CASE(Omega(n^1), ?) 312.77/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 312.77/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 312.77/291.56 312.77/291.56 312.77/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 312.77/291.56 312.77/291.56 (0) CpxTRS 312.77/291.56 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 312.77/291.56 (2) CpxTRS 312.77/291.56 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 312.77/291.56 (4) typed CpxTrs 312.77/291.56 (5) OrderProof [LOWER BOUND(ID), 0 ms] 312.77/291.56 (6) typed CpxTrs 312.77/291.56 (7) RewriteLemmaProof [LOWER BOUND(ID), 308 ms] 312.77/291.56 (8) BEST 312.77/291.56 (9) proven lower bound 312.77/291.56 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 312.77/291.56 (11) BOUNDS(n^1, INF) 312.77/291.56 (12) typed CpxTrs 312.77/291.56 (13) RewriteLemmaProof [LOWER BOUND(ID), 70 ms] 312.77/291.56 (14) typed CpxTrs 312.77/291.56 312.77/291.56 312.77/291.56 ---------------------------------------- 312.77/291.56 312.77/291.56 (0) 312.77/291.56 Obligation: 312.77/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 312.77/291.56 312.77/291.56 312.77/291.56 The TRS R consists of the following rules: 312.77/291.56 312.77/291.56 le(s(x), 0) -> false 312.77/291.56 le(0, y) -> true 312.77/291.56 le(s(x), s(y)) -> le(x, y) 312.77/291.56 double(0) -> 0 312.77/291.56 double(s(x)) -> s(s(double(x))) 312.77/291.56 log(0) -> logError 312.77/291.56 log(s(x)) -> loop(s(x), s(0), 0) 312.77/291.56 loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) 312.77/291.56 if(true, x, y, z) -> z 312.77/291.56 if(false, x, y, z) -> loop(x, double(y), s(z)) 312.77/291.56 312.77/291.56 S is empty. 312.77/291.56 Rewrite Strategy: FULL 312.77/291.56 ---------------------------------------- 312.77/291.56 312.77/291.56 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 312.77/291.56 Renamed function symbols to avoid clashes with predefined symbol. 312.77/291.56 ---------------------------------------- 312.77/291.56 312.77/291.56 (2) 312.77/291.56 Obligation: 312.77/291.56 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 312.77/291.56 312.77/291.56 312.77/291.56 The TRS R consists of the following rules: 312.77/291.56 312.77/291.56 le(s(x), 0') -> false 312.77/291.56 le(0', y) -> true 312.77/291.56 le(s(x), s(y)) -> le(x, y) 312.77/291.56 double(0') -> 0' 312.77/291.56 double(s(x)) -> s(s(double(x))) 312.77/291.56 log(0') -> logError 312.77/291.56 log(s(x)) -> loop(s(x), s(0'), 0') 312.77/291.56 loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) 312.77/291.56 if(true, x, y, z) -> z 312.77/291.56 if(false, x, y, z) -> loop(x, double(y), s(z)) 312.77/291.56 312.77/291.56 S is empty. 312.77/291.56 Rewrite Strategy: FULL 312.77/291.56 ---------------------------------------- 312.77/291.56 312.77/291.56 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 312.77/291.56 Infered types. 312.77/291.56 ---------------------------------------- 312.77/291.56 312.77/291.56 (4) 312.77/291.56 Obligation: 312.77/291.56 TRS: 312.77/291.56 Rules: 312.77/291.56 le(s(x), 0') -> false 312.77/291.56 le(0', y) -> true 312.77/291.56 le(s(x), s(y)) -> le(x, y) 312.77/291.56 double(0') -> 0' 312.77/291.56 double(s(x)) -> s(s(double(x))) 312.77/291.56 log(0') -> logError 312.77/291.56 log(s(x)) -> loop(s(x), s(0'), 0') 312.77/291.56 loop(x, s(y), z) -> if(le(x, s(y)), x, s(y), z) 312.77/291.56 if(true, x, y, z) -> z 312.77/291.56 if(false, x, y, z) -> loop(x, double(y), s(z)) 312.77/291.56 312.77/291.56 Types: 312.77/291.56 le :: s:0':logError -> s:0':logError -> false:true 312.77/291.56 s :: s:0':logError -> s:0':logError 312.77/291.56 0' :: s:0':logError 312.77/291.56 false :: false:true 312.77/291.56 true :: false:true 312.77/291.56 double :: s:0':logError -> s:0':logError
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