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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307802
details
property
value
status
complete
benchmark
thiemann24.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n001.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.608 seconds
cpu usage
999.292
user time
991.338
system time
7.95384
max virtual memory
3.7778776E7
max residence set size
8517148.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
999.10/291.53 WORST_CASE(Omega(n^2), ?) 999.10/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 999.10/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 999.10/291.54 999.10/291.54 999.10/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 999.10/291.54 999.10/291.54 (0) CpxTRS 999.10/291.54 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 999.10/291.54 (2) CpxTRS 999.10/291.54 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 999.10/291.54 (4) typed CpxTrs 999.10/291.54 (5) OrderProof [LOWER BOUND(ID), 0 ms] 999.10/291.54 (6) typed CpxTrs 999.10/291.54 (7) RewriteLemmaProof [LOWER BOUND(ID), 268 ms] 999.10/291.54 (8) BEST 999.10/291.54 (9) proven lower bound 999.10/291.54 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 999.10/291.54 (11) BOUNDS(n^1, INF) 999.10/291.54 (12) typed CpxTrs 999.10/291.54 (13) RewriteLemmaProof [LOWER BOUND(ID), 60 ms] 999.10/291.54 (14) typed CpxTrs 999.10/291.54 (15) RewriteLemmaProof [LOWER BOUND(ID), 63 ms] 999.10/291.54 (16) BEST 999.10/291.54 (17) proven lower bound 999.10/291.54 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 999.10/291.54 (19) BOUNDS(n^2, INF) 999.10/291.54 (20) typed CpxTrs 999.10/291.54 999.10/291.54 999.10/291.54 ---------------------------------------- 999.10/291.54 999.10/291.54 (0) 999.10/291.54 Obligation: 999.10/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 999.10/291.54 999.10/291.54 999.10/291.54 The TRS R consists of the following rules: 999.10/291.54 999.10/291.54 lt(0, s(x)) -> true 999.10/291.54 lt(x, 0) -> false 999.10/291.54 lt(s(x), s(y)) -> lt(x, y) 999.10/291.54 times(0, y) -> 0 999.10/291.54 times(s(x), y) -> plus(y, times(x, y)) 999.10/291.54 plus(0, y) -> y 999.10/291.54 plus(s(x), y) -> s(plus(x, y)) 999.10/291.54 fac(x) -> loop(x, s(0), s(0)) 999.10/291.54 loop(x, c, y) -> if(lt(x, c), x, c, y) 999.10/291.54 if(false, x, c, y) -> loop(x, s(c), times(y, s(c))) 999.10/291.54 if(true, x, c, y) -> y 999.10/291.54 999.10/291.54 S is empty. 999.10/291.54 Rewrite Strategy: FULL 999.10/291.54 ---------------------------------------- 999.10/291.54 999.10/291.54 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 999.10/291.54 Renamed function symbols to avoid clashes with predefined symbol. 999.10/291.54 ---------------------------------------- 999.10/291.54 999.10/291.54 (2) 999.10/291.54 Obligation: 999.10/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 999.10/291.54 999.10/291.54 999.10/291.54 The TRS R consists of the following rules: 999.10/291.54 999.10/291.54 lt(0', s(x)) -> true 999.10/291.54 lt(x, 0') -> false 999.10/291.54 lt(s(x), s(y)) -> lt(x, y) 999.10/291.54 times(0', y) -> 0' 999.10/291.54 times(s(x), y) -> plus(y, times(x, y)) 999.10/291.54 plus(0', y) -> y 999.10/291.54 plus(s(x), y) -> s(plus(x, y)) 999.10/291.54 fac(x) -> loop(x, s(0'), s(0')) 999.10/291.54 loop(x, c, y) -> if(lt(x, c), x, c, y) 999.10/291.54 if(false, x, c, y) -> loop(x, s(c), times(y, s(c))) 999.10/291.54 if(true, x, c, y) -> y 999.10/291.54 999.10/291.54 S is empty. 999.10/291.54 Rewrite Strategy: FULL 999.10/291.54 ---------------------------------------- 999.10/291.54 999.10/291.54 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 999.10/291.54 Infered types. 999.10/291.54 ---------------------------------------- 999.10/291.54 999.10/291.54 (4) 999.10/291.54 Obligation: 999.10/291.54 TRS: 999.10/291.54 Rules: 999.10/291.54 lt(0', s(x)) -> true 999.10/291.54 lt(x, 0') -> false 999.10/291.54 lt(s(x), s(y)) -> lt(x, y) 999.10/291.54 times(0', y) -> 0' 999.10/291.54 times(s(x), y) -> plus(y, times(x, y)) 999.10/291.54 plus(0', y) -> y 999.10/291.54 plus(s(x), y) -> s(plus(x, y)) 999.10/291.54 fac(x) -> loop(x, s(0'), s(0')) 999.10/291.54 loop(x, c, y) -> if(lt(x, c), x, c, y) 999.10/291.54 if(false, x, c, y) -> loop(x, s(c), times(y, s(c)))
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