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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313388
details
property
value
status
complete
benchmark
gcd.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n125.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.63 seconds
cpu usage
1131.56
user time
1120.28
system time
11.2773
max virtual memory
3.7781548E7
max residence set size
1.2204976E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1131.02/291.51 WORST_CASE(Omega(n^1), O(n^2)) 1131.40/291.56 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1131.40/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1131.40/291.56 1131.40/291.56 1131.40/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1131.40/291.56 1131.40/291.56 (0) CpxTRS 1131.40/291.56 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.40/291.56 (2) CpxWeightedTrs 1131.40/291.56 (3) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 5 ms] 1131.40/291.56 (4) CpxWeightedTrs 1131.40/291.56 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1131.40/291.56 (6) CpxTypedWeightedTrs 1131.40/291.56 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 1131.40/291.56 (8) CpxTypedWeightedCompleteTrs 1131.40/291.56 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1131.40/291.56 (10) CpxRNTS 1131.40/291.56 (11) CompleteCoflocoProof [FINISHED, 10.2 s] 1131.40/291.56 (12) BOUNDS(1, n^2) 1131.40/291.56 (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1131.40/291.56 (14) TRS for Loop Detection 1131.40/291.56 (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1131.40/291.56 (16) BEST 1131.40/291.56 (17) proven lower bound 1131.40/291.56 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 1131.40/291.56 (19) BOUNDS(n^1, INF) 1131.40/291.56 (20) TRS for Loop Detection 1131.40/291.56 1131.40/291.56 1131.40/291.56 ---------------------------------------- 1131.40/291.56 1131.40/291.56 (0) 1131.40/291.56 Obligation: 1131.40/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1131.40/291.56 1131.40/291.56 1131.40/291.56 The TRS R consists of the following rules: 1131.40/291.56 1131.40/291.56 min(x, 0) -> 0 1131.40/291.56 min(0, y) -> 0 1131.40/291.56 min(s(x), s(y)) -> s(min(x, y)) 1131.40/291.56 max(x, 0) -> x 1131.40/291.56 max(0, y) -> y 1131.40/291.56 max(s(x), s(y)) -> s(max(x, y)) 1131.40/291.56 -(x, 0) -> x 1131.40/291.56 -(s(x), s(y)) -> -(x, y) 1131.40/291.56 gcd(s(x), 0) -> s(x) 1131.40/291.56 gcd(0, s(x)) -> s(x) 1131.40/291.56 gcd(s(x), s(y)) -> gcd(-(max(x, y), min(x, y)), s(min(x, y))) 1131.40/291.56 1131.40/291.56 S is empty. 1131.40/291.56 Rewrite Strategy: INNERMOST 1131.40/291.56 ---------------------------------------- 1131.40/291.56 1131.40/291.56 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1131.40/291.56 Transformed relative TRS to weighted TRS 1131.40/291.56 ---------------------------------------- 1131.40/291.56 1131.40/291.56 (2) 1131.40/291.56 Obligation: 1131.40/291.56 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1131.40/291.56 1131.40/291.56 1131.40/291.56 The TRS R consists of the following rules: 1131.40/291.56 1131.40/291.56 min(x, 0) -> 0 [1] 1131.40/291.56 min(0, y) -> 0 [1] 1131.40/291.56 min(s(x), s(y)) -> s(min(x, y)) [1] 1131.40/291.56 max(x, 0) -> x [1] 1131.40/291.56 max(0, y) -> y [1] 1131.40/291.56 max(s(x), s(y)) -> s(max(x, y)) [1] 1131.40/291.56 -(x, 0) -> x [1] 1131.40/291.56 -(s(x), s(y)) -> -(x, y) [1] 1131.40/291.56 gcd(s(x), 0) -> s(x) [1] 1131.40/291.56 gcd(0, s(x)) -> s(x) [1] 1131.40/291.56 gcd(s(x), s(y)) -> gcd(-(max(x, y), min(x, y)), s(min(x, y))) [1] 1131.40/291.56 1131.40/291.56 Rewrite Strategy: INNERMOST 1131.40/291.56 ---------------------------------------- 1131.40/291.56 1131.40/291.56 (3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) 1131.40/291.56 Renamed defined symbols to avoid conflicts with arithmetic symbols: 1131.40/291.56 1131.40/291.56 - => minus 1131.40/291.56 1131.40/291.56 ---------------------------------------- 1131.40/291.56 1131.40/291.56 (4) 1131.40/291.56 Obligation: 1131.40/291.56 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1131.40/291.56 1131.40/291.56 1131.40/291.56 The TRS R consists of the following rules: 1131.40/291.56 1131.40/291.56 min(x, 0) -> 0 [1] 1131.40/291.56 min(0, y) -> 0 [1] 1131.40/291.56 min(s(x), s(y)) -> s(min(x, y)) [1] 1131.40/291.56 max(x, 0) -> x [1] 1131.40/291.56 max(0, y) -> y [1]
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