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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313738
details
property
value
status
complete
benchmark
thiemann12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n078.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.922 seconds
cpu usage
1010.16
user time
1002.61
system time
7.54887
max virtual memory
3.8047872E7
max residence set size
6621396.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1009.80/291.86 WORST_CASE(Omega(n^1), O(n^2)) 1009.80/291.87 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1009.80/291.87 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1009.80/291.87 1009.80/291.87 1009.80/291.87 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1009.80/291.87 1009.80/291.87 (0) CpxTRS 1009.80/291.87 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1009.80/291.87 (2) CpxWeightedTrs 1009.80/291.87 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1009.80/291.87 (4) CpxTypedWeightedTrs 1009.80/291.87 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1009.80/291.87 (6) CpxTypedWeightedCompleteTrs 1009.80/291.87 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1009.80/291.87 (8) CpxRNTS 1009.80/291.87 (9) CompleteCoflocoProof [FINISHED, 531 ms] 1009.80/291.87 (10) BOUNDS(1, n^2) 1009.80/291.87 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1009.80/291.87 (12) TRS for Loop Detection 1009.80/291.87 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1009.80/291.87 (14) BEST 1009.80/291.87 (15) proven lower bound 1009.80/291.87 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1009.80/291.87 (17) BOUNDS(n^1, INF) 1009.80/291.87 (18) TRS for Loop Detection 1009.80/291.87 1009.80/291.87 1009.80/291.87 ---------------------------------------- 1009.80/291.87 1009.80/291.87 (0) 1009.80/291.87 Obligation: 1009.80/291.87 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1009.80/291.87 1009.80/291.87 1009.80/291.87 The TRS R consists of the following rules: 1009.80/291.87 1009.80/291.87 half(0) -> 0 1009.80/291.87 half(s(0)) -> 0 1009.80/291.87 half(s(s(x))) -> s(half(x)) 1009.80/291.87 le(0, y) -> true 1009.80/291.87 le(s(x), 0) -> false 1009.80/291.87 le(s(x), s(y)) -> le(x, y) 1009.80/291.87 inc(0) -> 0 1009.80/291.87 inc(s(x)) -> s(inc(x)) 1009.80/291.87 log(x) -> log2(x, 0) 1009.80/291.87 log2(x, y) -> if(le(x, s(0)), x, inc(y)) 1009.80/291.87 if(true, x, s(y)) -> y 1009.80/291.87 if(false, x, y) -> log2(half(x), y) 1009.80/291.87 1009.80/291.87 S is empty. 1009.80/291.87 Rewrite Strategy: INNERMOST 1009.80/291.87 ---------------------------------------- 1009.80/291.87 1009.80/291.87 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1009.80/291.87 Transformed relative TRS to weighted TRS 1009.80/291.87 ---------------------------------------- 1009.80/291.87 1009.80/291.87 (2) 1009.80/291.87 Obligation: 1009.80/291.87 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1009.80/291.87 1009.80/291.87 1009.80/291.87 The TRS R consists of the following rules: 1009.80/291.87 1009.80/291.87 half(0) -> 0 [1] 1009.80/291.87 half(s(0)) -> 0 [1] 1009.80/291.87 half(s(s(x))) -> s(half(x)) [1] 1009.80/291.87 le(0, y) -> true [1] 1009.80/291.87 le(s(x), 0) -> false [1] 1009.80/291.87 le(s(x), s(y)) -> le(x, y) [1] 1009.80/291.87 inc(0) -> 0 [1] 1009.80/291.87 inc(s(x)) -> s(inc(x)) [1] 1009.80/291.87 log(x) -> log2(x, 0) [1] 1009.80/291.87 log2(x, y) -> if(le(x, s(0)), x, inc(y)) [1] 1009.80/291.87 if(true, x, s(y)) -> y [1] 1009.80/291.87 if(false, x, y) -> log2(half(x), y) [1] 1009.80/291.87 1009.80/291.87 Rewrite Strategy: INNERMOST 1009.80/291.87 ---------------------------------------- 1009.80/291.87 1009.80/291.87 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1009.80/291.87 Infered types. 1009.80/291.87 ---------------------------------------- 1009.80/291.87 1009.80/291.87 (4) 1009.80/291.87 Obligation: 1009.80/291.87 Runtime Complexity Weighted TRS with Types. 1009.80/291.87 The TRS R consists of the following rules: 1009.80/291.87 1009.80/291.87 half(0) -> 0 [1] 1009.80/291.87 half(s(0)) -> 0 [1] 1009.80/291.87 half(s(s(x))) -> s(half(x)) [1] 1009.80/291.87 le(0, y) -> true [1] 1009.80/291.87 le(s(x), 0) -> false [1] 1009.80/291.87 le(s(x), s(y)) -> le(x, y) [1] 1009.80/291.87 inc(0) -> 0 [1] 1009.80/291.87 inc(s(x)) -> s(inc(x)) [1] 1009.80/291.87 log(x) -> log2(x, 0) [1] 1009.80/291.87 log2(x, y) -> if(le(x, s(0)), x, inc(y)) [1]
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