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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313781
details
property
value
status
complete
benchmark
naiverev.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n041.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.88555 seconds
cpu usage
11.9536
user time
11.2632
system time
0.690345
max virtual memory
1.8612904E7
max residence set size
1947988.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
11.71/3.82 WORST_CASE(Omega(n^2), O(n^2)) 11.88/3.83 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 11.88/3.83 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 11.88/3.83 11.88/3.83 11.88/3.83 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 11.88/3.83 11.88/3.83 (0) CpxTRS 11.88/3.83 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 11.88/3.83 (2) CpxWeightedTrs 11.88/3.83 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 11.88/3.83 (4) CpxTypedWeightedTrs 11.88/3.83 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 11.88/3.83 (6) CpxTypedWeightedCompleteTrs 11.88/3.83 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 11.88/3.83 (8) CpxRNTS 11.88/3.83 (9) CompleteCoflocoProof [FINISHED, 162 ms] 11.88/3.83 (10) BOUNDS(1, n^2) 11.88/3.83 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 11.88/3.83 (12) CpxTRS 11.88/3.83 (13) SlicingProof [LOWER BOUND(ID), 0 ms] 11.88/3.83 (14) CpxTRS 11.88/3.83 (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 11.88/3.83 (16) typed CpxTrs 11.88/3.83 (17) OrderProof [LOWER BOUND(ID), 0 ms] 11.88/3.83 (18) typed CpxTrs 11.88/3.83 (19) RewriteLemmaProof [LOWER BOUND(ID), 301 ms] 11.88/3.83 (20) BEST 11.88/3.83 (21) proven lower bound 11.88/3.83 (22) LowerBoundPropagationProof [FINISHED, 0 ms] 11.88/3.83 (23) BOUNDS(n^1, INF) 11.88/3.83 (24) typed CpxTrs 11.88/3.83 (25) RewriteLemmaProof [LOWER BOUND(ID), 8 ms] 11.88/3.83 (26) proven lower bound 11.88/3.83 (27) LowerBoundPropagationProof [FINISHED, 0 ms] 11.88/3.83 (28) BOUNDS(n^2, INF) 11.88/3.83 11.88/3.83 11.88/3.83 ---------------------------------------- 11.88/3.83 11.88/3.83 (0) 11.88/3.83 Obligation: 11.88/3.83 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). 11.88/3.83 11.88/3.83 11.88/3.83 The TRS R consists of the following rules: 11.88/3.83 11.88/3.83 naiverev(Cons(x, xs)) -> app(naiverev(xs), Cons(x, Nil)) 11.88/3.83 app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) 11.88/3.83 notEmpty(Cons(x, xs)) -> True 11.88/3.83 notEmpty(Nil) -> False 11.88/3.83 naiverev(Nil) -> Nil 11.88/3.83 app(Nil, ys) -> ys 11.88/3.83 goal(xs) -> naiverev(xs) 11.88/3.83 11.88/3.83 S is empty. 11.88/3.83 Rewrite Strategy: INNERMOST 11.88/3.83 ---------------------------------------- 11.88/3.83 11.88/3.83 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 11.88/3.83 Transformed relative TRS to weighted TRS 11.88/3.83 ---------------------------------------- 11.88/3.83 11.88/3.83 (2) 11.88/3.83 Obligation: 11.88/3.83 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 11.88/3.83 11.88/3.83 11.88/3.83 The TRS R consists of the following rules: 11.88/3.83 11.88/3.83 naiverev(Cons(x, xs)) -> app(naiverev(xs), Cons(x, Nil)) [1] 11.88/3.83 app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) [1] 11.88/3.83 notEmpty(Cons(x, xs)) -> True [1] 11.88/3.83 notEmpty(Nil) -> False [1] 11.88/3.83 naiverev(Nil) -> Nil [1] 11.88/3.83 app(Nil, ys) -> ys [1] 11.88/3.83 goal(xs) -> naiverev(xs) [1] 11.88/3.83 11.88/3.83 Rewrite Strategy: INNERMOST 11.88/3.83 ---------------------------------------- 11.88/3.83 11.88/3.83 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 11.88/3.83 Infered types. 11.88/3.83 ---------------------------------------- 11.88/3.83 11.88/3.83 (4) 11.88/3.83 Obligation: 11.88/3.83 Runtime Complexity Weighted TRS with Types. 11.88/3.83 The TRS R consists of the following rules: 11.88/3.83 11.88/3.83 naiverev(Cons(x, xs)) -> app(naiverev(xs), Cons(x, Nil)) [1] 11.88/3.83 app(Cons(x, xs), ys) -> Cons(x, app(xs, ys)) [1] 11.88/3.83 notEmpty(Cons(x, xs)) -> True [1] 11.88/3.83 notEmpty(Nil) -> False [1] 11.88/3.83 naiverev(Nil) -> Nil [1] 11.88/3.83 app(Nil, ys) -> ys [1] 11.88/3.83 goal(xs) -> naiverev(xs) [1] 11.88/3.83 11.88/3.83 The TRS has the following type information: 11.88/3.83 naiverev :: Cons:Nil -> Cons:Nil
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