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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313726
details
property
value
status
complete
benchmark
otto12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.583 seconds
cpu usage
942.755
user time
937.121
system time
5.63396
max virtual memory
3.7906144E7
max residence set size
5938632.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
942.54/291.50 WORST_CASE(Omega(n^2), ?) 942.62/291.52 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 942.62/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 942.62/291.52 942.62/291.52 942.62/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 942.62/291.52 942.62/291.52 (0) CpxTRS 942.62/291.52 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 942.62/291.52 (2) CpxTRS 942.62/291.52 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 942.62/291.52 (4) typed CpxTrs 942.62/291.52 (5) OrderProof [LOWER BOUND(ID), 0 ms] 942.62/291.52 (6) typed CpxTrs 942.62/291.52 (7) RewriteLemmaProof [LOWER BOUND(ID), 304 ms] 942.62/291.52 (8) BEST 942.62/291.52 (9) proven lower bound 942.62/291.52 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 942.62/291.52 (11) BOUNDS(n^1, INF) 942.62/291.52 (12) typed CpxTrs 942.62/291.52 (13) RewriteLemmaProof [LOWER BOUND(ID), 116 ms] 942.62/291.52 (14) BEST 942.62/291.52 (15) proven lower bound 942.62/291.52 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 942.62/291.52 (17) BOUNDS(n^2, INF) 942.62/291.52 (18) typed CpxTrs 942.62/291.52 (19) RewriteLemmaProof [LOWER BOUND(ID), 592 ms] 942.62/291.52 (20) typed CpxTrs 942.62/291.52 (21) RewriteLemmaProof [LOWER BOUND(ID), 43 ms] 942.62/291.52 (22) typed CpxTrs 942.62/291.52 942.62/291.52 942.62/291.52 ---------------------------------------- 942.62/291.52 942.62/291.52 (0) 942.62/291.52 Obligation: 942.62/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 942.62/291.52 942.62/291.52 942.62/291.52 The TRS R consists of the following rules: 942.62/291.52 942.62/291.52 plus(0, x) -> x 942.62/291.52 plus(s(x), y) -> s(plus(x, y)) 942.62/291.52 times(0, y) -> 0 942.62/291.52 times(s(x), y) -> plus(y, times(x, y)) 942.62/291.52 exp(x, 0) -> s(0) 942.62/291.52 exp(x, s(y)) -> times(x, exp(x, y)) 942.62/291.52 ge(x, 0) -> true 942.62/291.52 ge(0, s(x)) -> false 942.62/291.52 ge(s(x), s(y)) -> ge(x, y) 942.62/291.52 tower(x, y) -> towerIter(0, x, y, s(0)) 942.62/291.52 towerIter(c, x, y, z) -> help(ge(c, x), c, x, y, z) 942.62/291.52 help(true, c, x, y, z) -> z 942.62/291.52 help(false, c, x, y, z) -> towerIter(s(c), x, y, exp(y, z)) 942.62/291.52 942.62/291.52 S is empty. 942.62/291.52 Rewrite Strategy: INNERMOST 942.62/291.52 ---------------------------------------- 942.62/291.52 942.62/291.52 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 942.62/291.52 Renamed function symbols to avoid clashes with predefined symbol. 942.62/291.52 ---------------------------------------- 942.62/291.52 942.62/291.52 (2) 942.62/291.52 Obligation: 942.62/291.52 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 942.62/291.52 942.62/291.52 942.62/291.52 The TRS R consists of the following rules: 942.62/291.52 942.62/291.52 plus(0', x) -> x 942.62/291.52 plus(s(x), y) -> s(plus(x, y)) 942.62/291.52 times(0', y) -> 0' 942.62/291.52 times(s(x), y) -> plus(y, times(x, y)) 942.62/291.52 exp(x, 0') -> s(0') 942.62/291.52 exp(x, s(y)) -> times(x, exp(x, y)) 942.62/291.52 ge(x, 0') -> true 942.62/291.52 ge(0', s(x)) -> false 942.62/291.52 ge(s(x), s(y)) -> ge(x, y) 942.62/291.52 tower(x, y) -> towerIter(0', x, y, s(0')) 942.62/291.52 towerIter(c, x, y, z) -> help(ge(c, x), c, x, y, z) 942.62/291.52 help(true, c, x, y, z) -> z 942.62/291.52 help(false, c, x, y, z) -> towerIter(s(c), x, y, exp(y, z)) 942.62/291.52 942.62/291.52 S is empty. 942.62/291.52 Rewrite Strategy: INNERMOST 942.62/291.52 ---------------------------------------- 942.62/291.52 942.62/291.52 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 942.62/291.52 Infered types. 942.62/291.52 ---------------------------------------- 942.62/291.52 942.62/291.52 (4) 942.62/291.52 Obligation: 942.62/291.52 Innermost TRS: 942.62/291.52 Rules: 942.62/291.52 plus(0', x) -> x 942.62/291.52 plus(s(x), y) -> s(plus(x, y)) 942.62/291.52 times(0', y) -> 0' 942.62/291.52 times(s(x), y) -> plus(y, times(x, y))
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