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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313308
details
property
value
status
complete
benchmark
aprove09.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.663 seconds
cpu usage
1144.07
user time
1131.18
system time
12.8938
max virtual memory
3.7918076E7
max residence set size
1.5005668E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
1143.50/291.54 WORST_CASE(Omega(n^1), O(n^3)) 1143.88/291.58 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1143.88/291.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1143.88/291.58 1143.88/291.58 1143.88/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1143.88/291.58 1143.88/291.58 (0) CpxTRS 1143.88/291.58 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1143.88/291.58 (2) CpxWeightedTrs 1143.88/291.58 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1143.88/291.58 (4) CpxTypedWeightedTrs 1143.88/291.58 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1143.88/291.58 (6) CpxTypedWeightedCompleteTrs 1143.88/291.58 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1143.88/291.58 (8) CpxRNTS 1143.88/291.58 (9) CompleteCoflocoProof [FINISHED, 8008 ms] 1143.88/291.58 (10) BOUNDS(1, n^3) 1143.88/291.58 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1143.88/291.58 (12) TRS for Loop Detection 1143.88/291.58 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1143.88/291.58 (14) BEST 1143.88/291.58 (15) proven lower bound 1143.88/291.58 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1143.88/291.58 (17) BOUNDS(n^1, INF) 1143.88/291.58 (18) TRS for Loop Detection 1143.88/291.58 1143.88/291.58 1143.88/291.58 ---------------------------------------- 1143.88/291.58 1143.88/291.58 (0) 1143.88/291.58 Obligation: 1143.88/291.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 1143.88/291.58 1143.88/291.58 1143.88/291.58 The TRS R consists of the following rules: 1143.88/291.58 1143.88/291.58 div(x, y) -> div2(x, y, 0) 1143.88/291.58 div2(x, y, i) -> if1(le(y, 0), le(y, x), x, y, plus(i, 0), inc(i)) 1143.88/291.58 if1(true, b, x, y, i, j) -> divZeroError 1143.88/291.58 if1(false, b, x, y, i, j) -> if2(b, x, y, i, j) 1143.88/291.58 if2(true, x, y, i, j) -> div2(minus(x, y), y, j) 1143.88/291.58 if2(false, x, y, i, j) -> i 1143.88/291.58 inc(0) -> 0 1143.88/291.58 inc(s(i)) -> s(inc(i)) 1143.88/291.58 le(s(x), 0) -> false 1143.88/291.58 le(0, y) -> true 1143.88/291.58 le(s(x), s(y)) -> le(x, y) 1143.88/291.58 minus(x, 0) -> x 1143.88/291.58 minus(0, y) -> 0 1143.88/291.58 minus(s(x), s(y)) -> minus(x, y) 1143.88/291.58 plus(x, y) -> plusIter(x, y, 0) 1143.88/291.58 plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z) 1143.88/291.58 ifPlus(true, x, y, z) -> y 1143.88/291.58 ifPlus(false, x, y, z) -> plusIter(x, s(y), s(z)) 1143.88/291.58 a -> c 1143.88/291.58 a -> d 1143.88/291.58 1143.88/291.58 S is empty. 1143.88/291.58 Rewrite Strategy: INNERMOST 1143.88/291.58 ---------------------------------------- 1143.88/291.58 1143.88/291.58 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1143.88/291.58 Transformed relative TRS to weighted TRS 1143.88/291.58 ---------------------------------------- 1143.88/291.58 1143.88/291.58 (2) 1143.88/291.58 Obligation: 1143.88/291.58 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). 1143.88/291.58 1143.88/291.58 1143.88/291.58 The TRS R consists of the following rules: 1143.88/291.58 1143.88/291.58 div(x, y) -> div2(x, y, 0) [1] 1143.88/291.58 div2(x, y, i) -> if1(le(y, 0), le(y, x), x, y, plus(i, 0), inc(i)) [1] 1143.88/291.58 if1(true, b, x, y, i, j) -> divZeroError [1] 1143.88/291.58 if1(false, b, x, y, i, j) -> if2(b, x, y, i, j) [1] 1143.88/291.58 if2(true, x, y, i, j) -> div2(minus(x, y), y, j) [1] 1143.88/291.58 if2(false, x, y, i, j) -> i [1] 1143.88/291.58 inc(0) -> 0 [1] 1143.88/291.58 inc(s(i)) -> s(inc(i)) [1] 1143.88/291.58 le(s(x), 0) -> false [1] 1143.88/291.58 le(0, y) -> true [1] 1143.88/291.58 le(s(x), s(y)) -> le(x, y) [1] 1143.88/291.58 minus(x, 0) -> x [1] 1143.88/291.58 minus(0, y) -> 0 [1] 1143.88/291.58 minus(s(x), s(y)) -> minus(x, y) [1] 1143.88/291.58 plus(x, y) -> plusIter(x, y, 0) [1] 1143.88/291.58 plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z) [1] 1143.88/291.58 ifPlus(true, x, y, z) -> y [1] 1143.88/291.58 ifPlus(false, x, y, z) -> plusIter(x, s(y), s(z)) [1] 1143.88/291.58 a -> c [1] 1143.88/291.58 a -> d [1] 1143.88/291.58 1143.88/291.58 Rewrite Strategy: INNERMOST 1143.88/291.58 ---------------------------------------- 1143.88/291.58 1143.88/291.58 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1143.88/291.58 Infered types. 1143.88/291.58 ----------------------------------------
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