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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313924
details
property
value
status
complete
benchmark
11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n133.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.54403 seconds
cpu usage
22.7457
user time
21.5221
system time
1.22363
max virtual memory
1.9210084E7
max residence set size
3683448.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
22.48/7.28 WORST_CASE(Omega(n^1), O(n^1)) 22.48/7.29 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 22.48/7.29 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 22.48/7.29 22.48/7.29 22.48/7.29 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 22.48/7.29 22.48/7.29 (0) CpxTRS 22.48/7.29 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 22.48/7.29 (2) CpxWeightedTrs 22.48/7.29 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 22.48/7.29 (4) CpxTypedWeightedTrs 22.48/7.29 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 22.48/7.29 (6) CpxTypedWeightedCompleteTrs 22.48/7.29 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 22.48/7.29 (8) CpxRNTS 22.48/7.29 (9) CompleteCoflocoProof [FINISHED, 248 ms] 22.48/7.29 (10) BOUNDS(1, n^1) 22.48/7.29 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 22.48/7.29 (12) TRS for Loop Detection 22.48/7.29 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 22.48/7.29 (14) BEST 22.48/7.29 (15) proven lower bound 22.48/7.29 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 22.48/7.29 (17) BOUNDS(n^1, INF) 22.48/7.29 (18) TRS for Loop Detection 22.48/7.29 22.48/7.29 22.48/7.29 ---------------------------------------- 22.48/7.29 22.48/7.29 (0) 22.48/7.29 Obligation: 22.48/7.29 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 22.48/7.29 22.48/7.29 22.48/7.29 The TRS R consists of the following rules: 22.48/7.29 22.48/7.29 D(t) -> 1 22.48/7.29 D(constant) -> 0 22.48/7.29 D(+(x, y)) -> +(D(x), D(y)) 22.48/7.29 D(*(x, y)) -> +(*(y, D(x)), *(x, D(y))) 22.48/7.29 D(-(x, y)) -> -(D(x), D(y)) 22.48/7.29 D(minus(x)) -> minus(D(x)) 22.48/7.29 D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2))) 22.48/7.29 D(ln(x)) -> div(D(x), x) 22.48/7.29 D(pow(x, y)) -> +(*(*(y, pow(x, -(y, 1))), D(x)), *(*(pow(x, y), ln(x)), D(y))) 22.48/7.29 22.48/7.29 S is empty. 22.48/7.29 Rewrite Strategy: INNERMOST 22.48/7.29 ---------------------------------------- 22.48/7.29 22.48/7.29 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 22.48/7.29 Transformed relative TRS to weighted TRS 22.48/7.29 ---------------------------------------- 22.48/7.29 22.48/7.29 (2) 22.48/7.29 Obligation: 22.48/7.29 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 22.48/7.29 22.48/7.29 22.48/7.29 The TRS R consists of the following rules: 22.48/7.29 22.48/7.29 D(t) -> 1 [1] 22.48/7.29 D(constant) -> 0 [1] 22.48/7.29 D(+(x, y)) -> +(D(x), D(y)) [1] 22.48/7.29 D(*(x, y)) -> +(*(y, D(x)), *(x, D(y))) [1] 22.48/7.29 D(-(x, y)) -> -(D(x), D(y)) [1] 22.48/7.29 D(minus(x)) -> minus(D(x)) [1] 22.48/7.29 D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2))) [1] 22.48/7.29 D(ln(x)) -> div(D(x), x) [1] 22.48/7.29 D(pow(x, y)) -> +(*(*(y, pow(x, -(y, 1))), D(x)), *(*(pow(x, y), ln(x)), D(y))) [1] 22.48/7.29 22.48/7.29 Rewrite Strategy: INNERMOST 22.48/7.29 ---------------------------------------- 22.48/7.29 22.48/7.29 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 22.48/7.29 Infered types. 22.48/7.29 ---------------------------------------- 22.48/7.29 22.48/7.29 (4) 22.48/7.29 Obligation: 22.48/7.29 Runtime Complexity Weighted TRS with Types. 22.48/7.29 The TRS R consists of the following rules: 22.48/7.29 22.48/7.29 D(t) -> 1 [1] 22.48/7.29 D(constant) -> 0 [1] 22.48/7.29 D(+(x, y)) -> +(D(x), D(y)) [1] 22.48/7.29 D(*(x, y)) -> +(*(y, D(x)), *(x, D(y))) [1] 22.48/7.29 D(-(x, y)) -> -(D(x), D(y)) [1] 22.48/7.29 D(minus(x)) -> minus(D(x)) [1] 22.48/7.29 D(div(x, y)) -> -(div(D(x), y), div(*(x, D(y)), pow(y, 2))) [1] 22.48/7.29 D(ln(x)) -> div(D(x), x) [1] 22.48/7.29 D(pow(x, y)) -> +(*(*(y, pow(x, -(y, 1))), D(x)), *(*(pow(x, y), ln(x)), D(y))) [1] 22.48/7.29 22.48/7.29 The TRS has the following type information: 22.48/7.29 D :: t:1:constant:0:+:*:-:minus:div:2:pow:ln -> t:1:constant:0:+:*:-:minus:div:2:pow:ln 22.48/7.29 t :: t:1:constant:0:+:*:-:minus:div:2:pow:ln 22.48/7.30 1 :: t:1:constant:0:+:*:-:minus:div:2:pow:ln 22.48/7.30 constant :: t:1:constant:0:+:*:-:minus:div:2:pow:ln 22.48/7.30 0 :: t:1:constant:0:+:*:-:minus:div:2:pow:ln
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