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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313597
details
property
value
status
complete
benchmark
2.20.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n008.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.79469 seconds
cpu usage
24.5775
user time
22.4701
system time
2.10741
max virtual memory
5.5906048E7
max residence set size
5068732.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
24.30/7.70 WORST_CASE(Omega(n^1), O(n^1)) 24.30/7.70 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 24.30/7.70 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 24.30/7.70 24.30/7.70 24.30/7.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 24.30/7.70 24.30/7.70 (0) CpxTRS 24.30/7.70 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 24.30/7.70 (2) CpxWeightedTrs 24.30/7.70 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms] 24.30/7.70 (4) CpxTypedWeightedTrs 24.30/7.70 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 24.30/7.70 (6) CpxTypedWeightedCompleteTrs 24.30/7.70 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 24.30/7.70 (8) CpxRNTS 24.30/7.70 (9) CompleteCoflocoProof [FINISHED, 62 ms] 24.30/7.70 (10) BOUNDS(1, n^1) 24.30/7.70 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 24.30/7.70 (12) TRS for Loop Detection 24.30/7.70 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 24.30/7.70 (14) BEST 24.30/7.70 (15) proven lower bound 24.30/7.70 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 24.30/7.70 (17) BOUNDS(n^1, INF) 24.30/7.70 (18) TRS for Loop Detection 24.30/7.70 24.30/7.70 24.30/7.70 ---------------------------------------- 24.30/7.70 24.30/7.70 (0) 24.30/7.70 Obligation: 24.30/7.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 24.30/7.70 24.30/7.70 24.30/7.70 The TRS R consists of the following rules: 24.30/7.70 24.30/7.70 sum(0) -> 0 24.30/7.70 sum(s(x)) -> +(sqr(s(x)), sum(x)) 24.30/7.70 sqr(x) -> *(x, x) 24.30/7.70 sum(s(x)) -> +(*(s(x), s(x)), sum(x)) 24.30/7.70 24.30/7.70 S is empty. 24.30/7.70 Rewrite Strategy: INNERMOST 24.30/7.70 ---------------------------------------- 24.30/7.70 24.30/7.70 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 24.30/7.70 Transformed relative TRS to weighted TRS 24.30/7.70 ---------------------------------------- 24.30/7.70 24.30/7.70 (2) 24.30/7.70 Obligation: 24.30/7.70 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 24.30/7.70 24.30/7.70 24.30/7.70 The TRS R consists of the following rules: 24.30/7.70 24.30/7.70 sum(0) -> 0 [1] 24.30/7.70 sum(s(x)) -> +(sqr(s(x)), sum(x)) [1] 24.30/7.70 sqr(x) -> *(x, x) [1] 24.30/7.70 sum(s(x)) -> +(*(s(x), s(x)), sum(x)) [1] 24.30/7.70 24.30/7.70 Rewrite Strategy: INNERMOST 24.30/7.70 ---------------------------------------- 24.30/7.70 24.30/7.70 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 24.30/7.70 Infered types. 24.30/7.70 ---------------------------------------- 24.30/7.70 24.30/7.70 (4) 24.30/7.70 Obligation: 24.30/7.70 Runtime Complexity Weighted TRS with Types. 24.30/7.70 The TRS R consists of the following rules: 24.30/7.70 24.30/7.70 sum(0) -> 0 [1] 24.30/7.70 sum(s(x)) -> +(sqr(s(x)), sum(x)) [1] 24.30/7.70 sqr(x) -> *(x, x) [1] 24.30/7.70 sum(s(x)) -> +(*(s(x), s(x)), sum(x)) [1] 24.30/7.70 24.30/7.70 The TRS has the following type information: 24.30/7.70 sum :: 0:s:+ -> 0:s:+ 24.30/7.70 0 :: 0:s:+ 24.30/7.70 s :: 0:s:+ -> 0:s:+ 24.30/7.70 + :: * -> 0:s:+ -> 0:s:+ 24.30/7.70 sqr :: 0:s:+ -> * 24.30/7.70 * :: 0:s:+ -> 0:s:+ -> * 24.30/7.70 24.30/7.70 Rewrite Strategy: INNERMOST 24.30/7.70 ---------------------------------------- 24.30/7.70 24.30/7.70 (5) CompletionProof (UPPER BOUND(ID)) 24.30/7.70 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 24.30/7.70 24.30/7.70 sum(v0) -> null_sum [0] 24.30/7.70 24.30/7.70 And the following fresh constants: null_sum, const 24.30/7.70 24.30/7.70 ---------------------------------------- 24.30/7.70 24.30/7.70 (6)
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