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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313739
details
property
value
status
complete
benchmark
otto09.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n171.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.723 seconds
cpu usage
1100.44
user time
1094.58
system time
5.85922
max virtual memory
1.9522508E7
max residence set size
6273232.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1099.67/291.59 WORST_CASE(Omega(n^1), ?) 1100.04/291.67 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1100.04/291.67 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1100.04/291.67 1100.04/291.67 1100.04/291.67 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1100.04/291.67 1100.04/291.67 (0) CpxTRS 1100.04/291.67 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1100.04/291.67 (2) CpxTRS 1100.04/291.67 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1100.04/291.67 (4) typed CpxTrs 1100.04/291.67 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1100.04/291.67 (6) typed CpxTrs 1100.04/291.67 (7) RewriteLemmaProof [LOWER BOUND(ID), 293 ms] 1100.04/291.67 (8) BEST 1100.04/291.67 (9) proven lower bound 1100.04/291.67 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1100.04/291.67 (11) BOUNDS(n^1, INF) 1100.04/291.67 (12) typed CpxTrs 1100.04/291.67 (13) RewriteLemmaProof [LOWER BOUND(ID), 76 ms] 1100.04/291.67 (14) typed CpxTrs 1100.04/291.67 1100.04/291.67 1100.04/291.67 ---------------------------------------- 1100.04/291.67 1100.04/291.67 (0) 1100.04/291.67 Obligation: 1100.04/291.67 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1100.04/291.67 1100.04/291.67 1100.04/291.67 The TRS R consists of the following rules: 1100.04/291.67 1100.04/291.67 lt(x, 0) -> false 1100.04/291.67 lt(0, s(y)) -> true 1100.04/291.67 lt(s(x), s(y)) -> lt(x, y) 1100.04/291.67 plus(x, 0) -> x 1100.04/291.67 plus(x, s(y)) -> s(plus(x, y)) 1100.04/291.67 quot(x, s(y)) -> help(x, s(y), 0) 1100.04/291.67 help(x, s(y), c) -> if(lt(c, x), x, s(y), c) 1100.04/291.67 if(true, x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) 1100.04/291.67 if(false, x, s(y), c) -> 0 1100.04/291.67 1100.04/291.67 S is empty. 1100.04/291.67 Rewrite Strategy: INNERMOST 1100.04/291.67 ---------------------------------------- 1100.04/291.67 1100.04/291.67 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1100.04/291.67 Renamed function symbols to avoid clashes with predefined symbol. 1100.04/291.67 ---------------------------------------- 1100.04/291.67 1100.04/291.67 (2) 1100.04/291.67 Obligation: 1100.04/291.67 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1100.04/291.67 1100.04/291.67 1100.04/291.67 The TRS R consists of the following rules: 1100.04/291.67 1100.04/291.67 lt(x, 0') -> false 1100.04/291.67 lt(0', s(y)) -> true 1100.04/291.67 lt(s(x), s(y)) -> lt(x, y) 1100.04/291.67 plus(x, 0') -> x 1100.04/291.67 plus(x, s(y)) -> s(plus(x, y)) 1100.04/291.67 quot(x, s(y)) -> help(x, s(y), 0') 1100.04/291.67 help(x, s(y), c) -> if(lt(c, x), x, s(y), c) 1100.04/291.67 if(true, x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) 1100.04/291.67 if(false, x, s(y), c) -> 0' 1100.04/291.67 1100.04/291.67 S is empty. 1100.04/291.67 Rewrite Strategy: INNERMOST 1100.04/291.67 ---------------------------------------- 1100.04/291.67 1100.04/291.67 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1100.04/291.67 Infered types. 1100.04/291.67 ---------------------------------------- 1100.04/291.67 1100.04/291.67 (4) 1100.04/291.67 Obligation: 1100.04/291.67 Innermost TRS: 1100.04/291.67 Rules: 1100.04/291.67 lt(x, 0') -> false 1100.04/291.67 lt(0', s(y)) -> true 1100.04/291.67 lt(s(x), s(y)) -> lt(x, y) 1100.04/291.67 plus(x, 0') -> x 1100.04/291.67 plus(x, s(y)) -> s(plus(x, y)) 1100.04/291.67 quot(x, s(y)) -> help(x, s(y), 0') 1100.04/291.67 help(x, s(y), c) -> if(lt(c, x), x, s(y), c) 1100.04/291.67 if(true, x, s(y), c) -> s(help(x, s(y), plus(c, s(y)))) 1100.04/291.67 if(false, x, s(y), c) -> 0' 1100.04/291.67 1100.04/291.67 Types: 1100.04/291.67 lt :: 0':s -> 0':s -> false:true 1100.04/291.67 0' :: 0':s 1100.04/291.67 false :: false:true 1100.04/291.67 s :: 0':s -> 0':s 1100.04/291.67 true :: false:true 1100.04/291.67 plus :: 0':s -> 0':s -> 0':s 1100.04/291.67 quot :: 0':s -> 0':s -> 0':s 1100.04/291.67 help :: 0':s -> 0':s -> 0':s -> 0':s 1100.04/291.67 if :: false:true -> 0':s -> 0':s -> 0':s -> 0':s
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