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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313672
details
property
value
status
complete
benchmark
logarithm.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n093.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.709 seconds
cpu usage
1115.8
user time
1102.9
system time
12.9031
max virtual memory
3.8312428E7
max residence set size
1.501378E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1115.54/291.62 WORST_CASE(Omega(n^1), O(n^2)) 1115.54/291.63 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1115.54/291.63 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1115.54/291.63 1115.54/291.63 1115.54/291.63 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1115.54/291.63 1115.54/291.63 (0) CpxTRS 1115.54/291.63 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.54/291.63 (2) CpxWeightedTrs 1115.54/291.63 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.54/291.63 (4) CpxTypedWeightedTrs 1115.54/291.63 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1115.54/291.63 (6) CpxTypedWeightedCompleteTrs 1115.54/291.63 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1115.54/291.63 (8) CpxRNTS 1115.54/291.63 (9) CompleteCoflocoProof [FINISHED, 5268 ms] 1115.54/291.63 (10) BOUNDS(1, n^2) 1115.54/291.63 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.54/291.63 (12) CpxTRS 1115.54/291.63 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.54/291.63 (14) typed CpxTrs 1115.54/291.63 (15) OrderProof [LOWER BOUND(ID), 0 ms] 1115.54/291.63 (16) typed CpxTrs 1115.54/291.63 (17) RewriteLemmaProof [LOWER BOUND(ID), 269 ms] 1115.54/291.63 (18) BEST 1115.54/291.63 (19) proven lower bound 1115.54/291.63 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1115.54/291.63 (21) BOUNDS(n^1, INF) 1115.54/291.63 (22) typed CpxTrs 1115.54/291.63 (23) RewriteLemmaProof [LOWER BOUND(ID), 78 ms] 1115.54/291.63 (24) typed CpxTrs 1115.54/291.63 (25) RewriteLemmaProof [LOWER BOUND(ID), 23 ms] 1115.54/291.63 (26) typed CpxTrs 1115.54/291.63 1115.54/291.63 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (0) 1115.54/291.63 Obligation: 1115.54/291.63 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1115.54/291.63 1115.54/291.63 1115.54/291.63 The TRS R consists of the following rules: 1115.54/291.63 1115.54/291.63 minus(x, 0) -> x 1115.54/291.63 minus(s(x), s(y)) -> minus(x, y) 1115.54/291.63 quot(0, s(y)) -> 0 1115.54/291.63 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) 1115.54/291.63 le(0, y) -> true 1115.54/291.63 le(s(x), 0) -> false 1115.54/291.63 le(s(x), s(y)) -> le(x, y) 1115.54/291.63 inc(s(x)) -> s(inc(x)) 1115.54/291.63 inc(0) -> s(0) 1115.54/291.63 log(x) -> logIter(x, 0) 1115.54/291.63 logIter(x, y) -> if(le(s(0), x), le(s(s(0)), x), quot(x, s(s(0))), inc(y)) 1115.54/291.63 if(false, b, x, y) -> logZeroError 1115.54/291.63 if(true, false, x, s(y)) -> y 1115.54/291.63 if(true, true, x, y) -> logIter(x, y) 1115.54/291.63 1115.54/291.63 S is empty. 1115.54/291.63 Rewrite Strategy: INNERMOST 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1115.54/291.63 Transformed relative TRS to weighted TRS 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (2) 1115.54/291.63 Obligation: 1115.54/291.63 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1115.54/291.63 1115.54/291.63 1115.54/291.63 The TRS R consists of the following rules: 1115.54/291.63 1115.54/291.63 minus(x, 0) -> x [1] 1115.54/291.63 minus(s(x), s(y)) -> minus(x, y) [1] 1115.54/291.63 quot(0, s(y)) -> 0 [1] 1115.54/291.63 quot(s(x), s(y)) -> s(quot(minus(x, y), s(y))) [1] 1115.54/291.63 le(0, y) -> true [1] 1115.54/291.63 le(s(x), 0) -> false [1] 1115.54/291.63 le(s(x), s(y)) -> le(x, y) [1] 1115.54/291.63 inc(s(x)) -> s(inc(x)) [1] 1115.54/291.63 inc(0) -> s(0) [1] 1115.54/291.63 log(x) -> logIter(x, 0) [1] 1115.54/291.63 logIter(x, y) -> if(le(s(0), x), le(s(s(0)), x), quot(x, s(s(0))), inc(y)) [1] 1115.54/291.63 if(false, b, x, y) -> logZeroError [1] 1115.54/291.63 if(true, false, x, s(y)) -> y [1] 1115.54/291.63 if(true, true, x, y) -> logIter(x, y) [1] 1115.54/291.63 1115.54/291.63 Rewrite Strategy: INNERMOST 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1115.54/291.63 Infered types. 1115.54/291.63 ---------------------------------------- 1115.54/291.63 1115.54/291.63 (4) 1115.54/291.63 Obligation: 1115.54/291.63 Runtime Complexity Weighted TRS with Types.
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