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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313321
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
n159.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.801 seconds
cpu usage
1113.98
user time
1092.68
system time
21.2962
max virtual memory
3.8437056E7
max residence set size
1.4892456E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1113.72/291.71 WORST_CASE(Omega(n^1), O(n^2)) 1113.72/291.73 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1113.72/291.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1113.72/291.73 1113.72/291.73 1113.72/291.73 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1113.72/291.73 1113.72/291.73 (0) CpxTRS 1113.72/291.73 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1113.72/291.73 (2) CpxWeightedTrs 1113.72/291.73 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1113.72/291.73 (4) CpxTypedWeightedTrs 1113.72/291.73 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1113.72/291.73 (6) CpxTypedWeightedCompleteTrs 1113.72/291.73 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms] 1113.72/291.73 (8) CpxRNTS 1113.72/291.73 (9) CompleteCoflocoProof [FINISHED, 1823 ms] 1113.72/291.73 (10) BOUNDS(1, n^2) 1113.72/291.73 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1113.72/291.73 (12) CpxTRS 1113.72/291.73 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1113.72/291.73 (14) typed CpxTrs 1113.72/291.73 (15) OrderProof [LOWER BOUND(ID), 0 ms] 1113.72/291.73 (16) typed CpxTrs 1113.72/291.73 (17) RewriteLemmaProof [LOWER BOUND(ID), 355 ms] 1113.72/291.73 (18) BEST 1113.72/291.73 (19) proven lower bound 1113.72/291.73 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 1113.72/291.73 (21) BOUNDS(n^1, INF) 1113.72/291.73 (22) typed CpxTrs 1113.72/291.73 (23) RewriteLemmaProof [LOWER BOUND(ID), 37 ms] 1113.72/291.73 (24) typed CpxTrs 1113.72/291.73 (25) RewriteLemmaProof [LOWER BOUND(ID), 59 ms] 1113.72/291.73 (26) typed CpxTrs 1113.72/291.73 1113.72/291.73 1113.72/291.73 ---------------------------------------- 1113.72/291.73 1113.72/291.73 (0) 1113.72/291.73 Obligation: 1113.72/291.73 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1113.72/291.73 1113.72/291.73 1113.72/291.73 The TRS R consists of the following rules: 1113.72/291.73 1113.72/291.73 half(0) -> 0 1113.72/291.73 half(s(0)) -> 0 1113.72/291.73 half(s(s(x))) -> s(half(x)) 1113.72/291.73 le(0, y) -> true 1113.72/291.73 le(s(x), 0) -> false 1113.72/291.73 le(s(x), s(y)) -> le(x, y) 1113.72/291.73 inc(s(x)) -> s(inc(x)) 1113.72/291.73 inc(0) -> s(0) 1113.72/291.73 logarithm(x) -> logIter(x, 0) 1113.72/291.73 logIter(x, y) -> if(le(s(0), x), le(s(s(0)), x), half(x), inc(y)) 1113.72/291.73 if(false, b, x, y) -> logZeroError 1113.72/291.73 if(true, false, x, s(y)) -> y 1113.72/291.73 if(true, true, x, y) -> logIter(x, y) 1113.72/291.73 f -> g 1113.72/291.73 f -> h 1113.72/291.73 1113.72/291.73 S is empty. 1113.72/291.73 Rewrite Strategy: INNERMOST 1113.72/291.73 ---------------------------------------- 1113.72/291.73 1113.72/291.73 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1113.72/291.73 Transformed relative TRS to weighted TRS 1113.72/291.73 ---------------------------------------- 1113.72/291.73 1113.72/291.73 (2) 1113.72/291.73 Obligation: 1113.72/291.73 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1113.72/291.73 1113.72/291.73 1113.72/291.73 The TRS R consists of the following rules: 1113.72/291.73 1113.72/291.73 half(0) -> 0 [1] 1113.72/291.73 half(s(0)) -> 0 [1] 1113.72/291.73 half(s(s(x))) -> s(half(x)) [1] 1113.72/291.73 le(0, y) -> true [1] 1113.72/291.73 le(s(x), 0) -> false [1] 1113.72/291.73 le(s(x), s(y)) -> le(x, y) [1] 1113.72/291.73 inc(s(x)) -> s(inc(x)) [1] 1113.72/291.73 inc(0) -> s(0) [1] 1113.72/291.73 logarithm(x) -> logIter(x, 0) [1] 1113.72/291.73 logIter(x, y) -> if(le(s(0), x), le(s(s(0)), x), half(x), inc(y)) [1] 1113.72/291.73 if(false, b, x, y) -> logZeroError [1] 1113.72/291.73 if(true, false, x, s(y)) -> y [1] 1113.72/291.73 if(true, true, x, y) -> logIter(x, y) [1] 1113.72/291.73 f -> g [1] 1113.72/291.73 f -> h [1] 1113.72/291.73 1113.72/291.73 Rewrite Strategy: INNERMOST 1113.72/291.73 ---------------------------------------- 1113.72/291.73 1113.72/291.73 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1113.72/291.73 Infered types. 1113.72/291.73 ---------------------------------------- 1113.72/291.73 1113.72/291.73 (4)
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