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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313675
details
property
value
status
complete
benchmark
div_notCeTermin.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n153.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.604 seconds
cpu usage
1150.59
user time
1141.29
system time
9.29857
max virtual memory
3.817728E7
max residence set size
6663812.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1150.39/291.53 WORST_CASE(Omega(n^1), O(n^2)) 1150.39/291.54 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1150.39/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1150.39/291.54 1150.39/291.54 1150.39/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1150.39/291.54 1150.39/291.54 (0) CpxTRS 1150.39/291.54 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1150.39/291.54 (2) CpxWeightedTrs 1150.39/291.54 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1150.39/291.54 (4) CpxTypedWeightedTrs 1150.39/291.54 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1150.39/291.54 (6) CpxTypedWeightedCompleteTrs 1150.39/291.54 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1150.39/291.54 (8) CpxRNTS 1150.39/291.54 (9) CompleteCoflocoProof [FINISHED, 1860 ms] 1150.39/291.54 (10) BOUNDS(1, n^2) 1150.39/291.54 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1150.39/291.54 (12) TRS for Loop Detection 1150.39/291.54 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1150.39/291.54 (14) BEST 1150.39/291.54 (15) proven lower bound 1150.39/291.54 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1150.39/291.54 (17) BOUNDS(n^1, INF) 1150.39/291.54 (18) TRS for Loop Detection 1150.39/291.54 1150.39/291.54 1150.39/291.54 ---------------------------------------- 1150.39/291.54 1150.39/291.54 (0) 1150.39/291.54 Obligation: 1150.39/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1150.39/291.54 1150.39/291.54 1150.39/291.54 The TRS R consists of the following rules: 1150.39/291.54 1150.39/291.54 ge(0, 0) -> true 1150.39/291.54 ge(s(x), 0) -> ge(x, 0) 1150.39/291.54 ge(0, s(0)) -> false 1150.39/291.54 ge(0, s(s(x))) -> ge(0, s(x)) 1150.39/291.54 ge(s(x), s(y)) -> ge(x, y) 1150.39/291.54 minus(0, 0) -> 0 1150.39/291.54 minus(0, s(x)) -> minus(0, x) 1150.39/291.54 minus(s(x), 0) -> s(minus(x, 0)) 1150.39/291.54 minus(s(x), s(y)) -> minus(x, y) 1150.39/291.54 plus(0, 0) -> 0 1150.39/291.54 plus(0, s(x)) -> s(plus(0, x)) 1150.39/291.54 plus(s(x), y) -> s(plus(x, y)) 1150.39/291.54 div(x, y) -> ify(ge(y, s(0)), x, y) 1150.39/291.54 ify(false, x, y) -> divByZeroError 1150.39/291.54 ify(true, x, y) -> if(ge(x, y), x, y) 1150.39/291.54 if(false, x, y) -> 0 1150.39/291.54 if(true, x, y) -> s(div(minus(x, y), y)) 1150.39/291.54 1150.39/291.54 S is empty. 1150.39/291.54 Rewrite Strategy: INNERMOST 1150.39/291.54 ---------------------------------------- 1150.39/291.54 1150.39/291.54 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1150.39/291.54 Transformed relative TRS to weighted TRS 1150.39/291.54 ---------------------------------------- 1150.39/291.54 1150.39/291.54 (2) 1150.39/291.54 Obligation: 1150.39/291.54 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1150.39/291.55 1150.39/291.55 1150.39/291.55 The TRS R consists of the following rules: 1150.39/291.55 1150.39/291.55 ge(0, 0) -> true [1] 1150.39/291.55 ge(s(x), 0) -> ge(x, 0) [1] 1150.39/291.55 ge(0, s(0)) -> false [1] 1150.39/291.55 ge(0, s(s(x))) -> ge(0, s(x)) [1] 1150.39/291.55 ge(s(x), s(y)) -> ge(x, y) [1] 1150.39/291.55 minus(0, 0) -> 0 [1] 1150.39/291.55 minus(0, s(x)) -> minus(0, x) [1] 1150.39/291.55 minus(s(x), 0) -> s(minus(x, 0)) [1] 1150.39/291.55 minus(s(x), s(y)) -> minus(x, y) [1] 1150.39/291.55 plus(0, 0) -> 0 [1] 1150.39/291.55 plus(0, s(x)) -> s(plus(0, x)) [1] 1150.39/291.55 plus(s(x), y) -> s(plus(x, y)) [1] 1150.39/291.55 div(x, y) -> ify(ge(y, s(0)), x, y) [1] 1150.39/291.55 ify(false, x, y) -> divByZeroError [1] 1150.39/291.55 ify(true, x, y) -> if(ge(x, y), x, y) [1] 1150.39/291.55 if(false, x, y) -> 0 [1] 1150.39/291.55 if(true, x, y) -> s(div(minus(x, y), y)) [1] 1150.39/291.55 1150.39/291.55 Rewrite Strategy: INNERMOST 1150.39/291.55 ---------------------------------------- 1150.39/291.55 1150.39/291.55 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1150.39/291.55 Infered types. 1150.39/291.55 ---------------------------------------- 1150.39/291.55 1150.39/291.55 (4) 1150.39/291.55 Obligation: 1150.39/291.55 Runtime Complexity Weighted TRS with Types. 1150.39/291.55 The TRS R consists of the following rules: 1150.39/291.55
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