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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313819
details
property
value
status
complete
benchmark
select.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n004.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.559 seconds
cpu usage
351.291
user time
348.157
system time
3.13354
max virtual memory
1.9276104E7
max residence set size
5585780.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
351.19/291.50 WORST_CASE(Omega(n^1), O(n^2)) 351.21/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 351.21/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 351.21/291.51 351.21/291.51 351.21/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 351.21/291.51 351.21/291.51 (0) CpxTRS 351.21/291.51 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 351.21/291.51 (2) CpxWeightedTrs 351.21/291.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 351.21/291.51 (4) CpxTypedWeightedTrs 351.21/291.51 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 351.21/291.51 (6) CpxTypedWeightedCompleteTrs 351.21/291.51 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 351.21/291.51 (8) CpxRNTS 351.21/291.51 (9) CompleteCoflocoProof [FINISHED, 278 ms] 351.21/291.51 (10) BOUNDS(1, n^2) 351.21/291.51 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 351.21/291.51 (12) TRS for Loop Detection 351.21/291.51 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 351.21/291.51 (14) BEST 351.21/291.51 (15) proven lower bound 351.21/291.51 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 351.21/291.51 (17) BOUNDS(n^1, INF) 351.21/291.51 (18) TRS for Loop Detection 351.21/291.51 351.21/291.51 351.21/291.51 ---------------------------------------- 351.21/291.51 351.21/291.51 (0) 351.21/291.51 Obligation: 351.21/291.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 351.21/291.51 351.21/291.51 351.21/291.51 The TRS R consists of the following rules: 351.21/291.51 351.21/291.51 selects(x', revprefix, Cons(x, xs)) -> Cons(Cons(x', revapp(revprefix, Cons(x, xs))), selects(x, Cons(x', revprefix), xs)) 351.21/291.51 select(Cons(x, xs)) -> selects(x, Nil, xs) 351.21/291.51 revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) 351.21/291.51 selects(x, revprefix, Nil) -> Cons(Cons(x, revapp(revprefix, Nil)), Nil) 351.21/291.51 select(Nil) -> Nil 351.21/291.51 revapp(Nil, rest) -> rest 351.21/291.51 351.21/291.51 S is empty. 351.21/291.51 Rewrite Strategy: INNERMOST 351.21/291.51 ---------------------------------------- 351.21/291.51 351.21/291.51 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 351.21/291.51 Transformed relative TRS to weighted TRS 351.21/291.51 ---------------------------------------- 351.21/291.51 351.21/291.51 (2) 351.21/291.51 Obligation: 351.21/291.51 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 351.21/291.51 351.21/291.51 351.21/291.51 The TRS R consists of the following rules: 351.21/291.51 351.21/291.51 selects(x', revprefix, Cons(x, xs)) -> Cons(Cons(x', revapp(revprefix, Cons(x, xs))), selects(x, Cons(x', revprefix), xs)) [1] 351.21/291.51 select(Cons(x, xs)) -> selects(x, Nil, xs) [1] 351.21/291.51 revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1] 351.21/291.51 selects(x, revprefix, Nil) -> Cons(Cons(x, revapp(revprefix, Nil)), Nil) [1] 351.21/291.51 select(Nil) -> Nil [1] 351.21/291.51 revapp(Nil, rest) -> rest [1] 351.21/291.51 351.21/291.51 Rewrite Strategy: INNERMOST 351.21/291.51 ---------------------------------------- 351.21/291.51 351.21/291.51 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 351.21/291.51 Infered types. 351.21/291.51 ---------------------------------------- 351.21/291.51 351.21/291.51 (4) 351.21/291.51 Obligation: 351.21/291.51 Runtime Complexity Weighted TRS with Types. 351.21/291.51 The TRS R consists of the following rules: 351.21/291.51 351.21/291.51 selects(x', revprefix, Cons(x, xs)) -> Cons(Cons(x', revapp(revprefix, Cons(x, xs))), selects(x, Cons(x', revprefix), xs)) [1] 351.21/291.51 select(Cons(x, xs)) -> selects(x, Nil, xs) [1] 351.21/291.51 revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1] 351.21/291.51 selects(x, revprefix, Nil) -> Cons(Cons(x, revapp(revprefix, Nil)), Nil) [1] 351.21/291.51 select(Nil) -> Nil [1] 351.21/291.51 revapp(Nil, rest) -> rest [1] 351.21/291.51 351.21/291.51 The TRS has the following type information: 351.21/291.51 selects :: Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil 351.21/291.51 Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil 351.21/291.51 revapp :: Cons:Nil -> Cons:Nil -> Cons:Nil 351.21/291.51 select :: Cons:Nil -> Cons:Nil 351.21/291.51 Nil :: Cons:Nil 351.21/291.51 351.21/291.51 Rewrite Strategy: INNERMOST 351.21/291.51 ---------------------------------------- 351.21/291.51 351.21/291.51 (5) CompletionProof (UPPER BOUND(ID)) 351.21/291.51 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 351.21/291.51 none 351.21/291.51 351.21/291.51 And the following fresh constants: none
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