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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313742
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
n102.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.598 seconds
cpu usage
1010.51
user time
1001.9
system time
8.60963
max virtual memory
3.7508816E7
max residence set size
8678348.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1010.25/291.52 WORST_CASE(Omega(n^2), ?) 1010.25/291.53 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1010.25/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1010.25/291.53 1010.25/291.53 1010.25/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1010.25/291.53 1010.25/291.53 (0) CpxTRS 1010.25/291.53 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1010.25/291.53 (2) CpxTRS 1010.25/291.53 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1010.25/291.53 (4) typed CpxTrs 1010.25/291.53 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1010.25/291.53 (6) typed CpxTrs 1010.25/291.53 (7) RewriteLemmaProof [LOWER BOUND(ID), 273 ms] 1010.25/291.53 (8) BEST 1010.25/291.53 (9) proven lower bound 1010.25/291.53 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1010.25/291.53 (11) BOUNDS(n^1, INF) 1010.25/291.53 (12) typed CpxTrs 1010.25/291.53 (13) RewriteLemmaProof [LOWER BOUND(ID), 67 ms] 1010.25/291.53 (14) typed CpxTrs 1010.25/291.53 (15) RewriteLemmaProof [LOWER BOUND(ID), 55 ms] 1010.25/291.53 (16) BEST 1010.25/291.53 (17) proven lower bound 1010.25/291.53 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 1010.25/291.53 (19) BOUNDS(n^2, INF) 1010.25/291.53 (20) typed CpxTrs 1010.25/291.53 1010.25/291.53 1010.25/291.53 ---------------------------------------- 1010.25/291.53 1010.25/291.53 (0) 1010.25/291.53 Obligation: 1010.25/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1010.25/291.53 1010.25/291.53 1010.25/291.53 The TRS R consists of the following rules: 1010.25/291.53 1010.25/291.53 lt(0, s(x)) -> true 1010.25/291.53 lt(x, 0) -> false 1010.25/291.53 lt(s(x), s(y)) -> lt(x, y) 1010.25/291.53 times(0, y) -> 0 1010.25/291.53 times(s(x), y) -> plus(y, times(x, y)) 1010.25/291.53 plus(0, y) -> y 1010.25/291.53 plus(s(x), y) -> s(plus(x, y)) 1010.25/291.53 fac(x) -> loop(x, s(0), s(0)) 1010.25/291.53 loop(x, c, y) -> if(lt(x, c), x, c, y) 1010.25/291.53 if(false, x, c, y) -> loop(x, s(c), times(y, s(c))) 1010.25/291.53 if(true, x, c, y) -> y 1010.25/291.53 1010.25/291.53 S is empty. 1010.25/291.53 Rewrite Strategy: INNERMOST 1010.25/291.53 ---------------------------------------- 1010.25/291.53 1010.25/291.53 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1010.25/291.53 Renamed function symbols to avoid clashes with predefined symbol. 1010.25/291.53 ---------------------------------------- 1010.25/291.53 1010.25/291.53 (2) 1010.25/291.53 Obligation: 1010.25/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1010.25/291.53 1010.25/291.53 1010.25/291.53 The TRS R consists of the following rules: 1010.25/291.53 1010.25/291.53 lt(0', s(x)) -> true 1010.25/291.53 lt(x, 0') -> false 1010.25/291.53 lt(s(x), s(y)) -> lt(x, y) 1010.25/291.53 times(0', y) -> 0' 1010.25/291.53 times(s(x), y) -> plus(y, times(x, y)) 1010.25/291.53 plus(0', y) -> y 1010.25/291.53 plus(s(x), y) -> s(plus(x, y)) 1010.25/291.53 fac(x) -> loop(x, s(0'), s(0')) 1010.25/291.53 loop(x, c, y) -> if(lt(x, c), x, c, y) 1010.25/291.53 if(false, x, c, y) -> loop(x, s(c), times(y, s(c))) 1010.25/291.53 if(true, x, c, y) -> y 1010.25/291.53 1010.25/291.53 S is empty. 1010.25/291.53 Rewrite Strategy: INNERMOST 1010.25/291.53 ---------------------------------------- 1010.25/291.53 1010.25/291.53 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1010.25/291.53 Infered types. 1010.25/291.53 ---------------------------------------- 1010.25/291.53 1010.25/291.53 (4) 1010.25/291.53 Obligation: 1010.25/291.53 Innermost TRS: 1010.25/291.53 Rules: 1010.25/291.53 lt(0', s(x)) -> true 1010.25/291.53 lt(x, 0') -> false 1010.25/291.53 lt(s(x), s(y)) -> lt(x, y) 1010.25/291.53 times(0', y) -> 0' 1010.25/291.53 times(s(x), y) -> plus(y, times(x, y)) 1010.25/291.53 plus(0', y) -> y 1010.25/291.53 plus(s(x), y) -> s(plus(x, y)) 1010.25/291.53 fac(x) -> loop(x, s(0'), s(0')) 1010.25/291.53 loop(x, c, y) -> if(lt(x, c), x, c, y) 1010.25/291.53 if(false, x, c, y) -> loop(x, s(c), times(y, s(c)))
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