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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313382
details
property
value
status
complete
benchmark
gcdMinMax.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.625 seconds
cpu usage
1122.24
user time
1107.96
system time
14.2744
max virtual memory
3.8039272E7
max residence set size
1.4868084E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1121.71/291.47 WORST_CASE(Omega(n^1), O(n^2)) 1121.95/291.53 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1121.95/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1121.95/291.53 1121.95/291.53 1121.95/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1121.95/291.53 1121.95/291.53 (0) CpxTRS 1121.95/291.53 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1121.95/291.53 (2) CpxWeightedTrs 1121.95/291.53 (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1121.95/291.53 (4) CpxWeightedTrs 1121.95/291.53 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1121.95/291.53 (6) CpxTypedWeightedTrs 1121.95/291.53 (7) CompletionProof [UPPER BOUND(ID), 3 ms] 1121.95/291.53 (8) CpxTypedWeightedCompleteTrs 1121.95/291.53 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1121.95/291.53 (10) CpxRNTS 1121.95/291.53 (11) CompleteCoflocoProof [FINISHED, 13.8 s] 1121.95/291.53 (12) BOUNDS(1, n^2) 1121.95/291.53 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1121.95/291.53 (14) TRS for Loop Detection 1121.95/291.53 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1121.95/291.53 (16) BEST 1121.95/291.53 (17) proven lower bound 1121.95/291.53 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 1121.95/291.53 (19) BOUNDS(n^1, INF) 1121.95/291.53 (20) TRS for Loop Detection 1121.95/291.53 1121.95/291.53 1121.95/291.53 ---------------------------------------- 1121.95/291.53 1121.95/291.53 (0) 1121.95/291.53 Obligation: 1121.95/291.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1121.95/291.53 1121.95/291.53 1121.95/291.53 The TRS R consists of the following rules: 1121.95/291.53 1121.95/291.53 min(x, 0) -> 0 1121.95/291.53 min(0, y) -> 0 1121.95/291.53 min(s(x), s(y)) -> s(min(x, y)) 1121.95/291.53 max(x, 0) -> x 1121.95/291.53 max(0, y) -> y 1121.95/291.53 max(s(x), s(y)) -> s(max(x, y)) 1121.95/291.53 -(x, 0) -> x 1121.95/291.53 -(s(x), s(y)) -> -(x, y) 1121.95/291.53 gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) 1121.95/291.53 gcd(s(x), 0) -> s(x) 1121.95/291.53 gcd(0, s(y)) -> s(y) 1121.95/291.53 1121.95/291.53 S is empty. 1121.95/291.53 Rewrite Strategy: INNERMOST 1121.95/291.53 ---------------------------------------- 1121.95/291.53 1121.95/291.53 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1121.95/291.53 Transformed relative TRS to weighted TRS 1121.95/291.53 ---------------------------------------- 1121.95/291.53 1121.95/291.53 (2) 1121.95/291.53 Obligation: 1121.95/291.53 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1121.95/291.53 1121.95/291.53 1121.95/291.53 The TRS R consists of the following rules: 1121.95/291.53 1121.95/291.53 min(x, 0) -> 0 [1] 1121.95/291.53 min(0, y) -> 0 [1] 1121.95/291.53 min(s(x), s(y)) -> s(min(x, y)) [1] 1121.95/291.53 max(x, 0) -> x [1] 1121.95/291.53 max(0, y) -> y [1] 1121.95/291.53 max(s(x), s(y)) -> s(max(x, y)) [1] 1121.95/291.53 -(x, 0) -> x [1] 1121.95/291.53 -(s(x), s(y)) -> -(x, y) [1] 1121.95/291.53 gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) [1] 1121.95/291.53 gcd(s(x), 0) -> s(x) [1] 1121.95/291.53 gcd(0, s(y)) -> s(y) [1] 1121.95/291.53 1121.95/291.53 Rewrite Strategy: INNERMOST 1121.95/291.53 ---------------------------------------- 1121.95/291.53 1121.95/291.53 (3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) 1121.95/291.53 Renamed defined symbols to avoid conflicts with arithmetic symbols: 1121.95/291.53 1121.95/291.53 - => minus 1121.95/291.53 1121.95/291.53 ---------------------------------------- 1121.95/291.53 1121.95/291.53 (4) 1121.95/291.53 Obligation: 1121.95/291.53 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1121.95/291.53 1121.95/291.53 1121.95/291.53 The TRS R consists of the following rules: 1121.95/291.53 1121.95/291.53 min(x, 0) -> 0 [1] 1121.95/291.53 min(0, y) -> 0 [1] 1121.95/291.53 min(s(x), s(y)) -> s(min(x, y)) [1] 1121.95/291.53 max(x, 0) -> x [1] 1121.95/291.53 max(0, y) -> y [1]
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