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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307732
details
property
value
status
complete
benchmark
#3.42.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n037.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.518 seconds
cpu usage
321.308
user time
319.339
system time
1.96879
max virtual memory
1.8279384E7
max residence set size
5468848.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
321.23/291.47 WORST_CASE(Omega(n^1), ?) 321.23/291.48 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 321.23/291.48 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 321.23/291.48 321.23/291.48 321.23/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 321.23/291.48 321.23/291.48 (0) CpxTRS 321.23/291.48 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 321.23/291.48 (2) CpxTRS 321.23/291.48 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 321.23/291.48 (4) typed CpxTrs 321.23/291.48 (5) OrderProof [LOWER BOUND(ID), 0 ms] 321.23/291.48 (6) typed CpxTrs 321.23/291.48 (7) RewriteLemmaProof [LOWER BOUND(ID), 330 ms] 321.23/291.48 (8) BEST 321.23/291.48 (9) proven lower bound 321.23/291.48 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 321.23/291.48 (11) BOUNDS(n^1, INF) 321.23/291.48 (12) typed CpxTrs 321.23/291.48 (13) RewriteLemmaProof [LOWER BOUND(ID), 34 ms] 321.23/291.48 (14) typed CpxTrs 321.23/291.48 321.23/291.48 321.23/291.48 ---------------------------------------- 321.23/291.48 321.23/291.48 (0) 321.23/291.48 Obligation: 321.23/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 321.23/291.48 321.23/291.48 321.23/291.48 The TRS R consists of the following rules: 321.23/291.48 321.23/291.48 half(0) -> 0 321.23/291.48 half(s(0)) -> 0 321.23/291.48 half(s(s(x))) -> s(half(x)) 321.23/291.48 lastbit(0) -> 0 321.23/291.48 lastbit(s(0)) -> s(0) 321.23/291.48 lastbit(s(s(x))) -> lastbit(x) 321.23/291.48 conv(0) -> cons(nil, 0) 321.23/291.48 conv(s(x)) -> cons(conv(half(s(x))), lastbit(s(x))) 321.23/291.48 321.23/291.48 S is empty. 321.23/291.48 Rewrite Strategy: FULL 321.23/291.48 ---------------------------------------- 321.23/291.48 321.23/291.48 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 321.23/291.48 Renamed function symbols to avoid clashes with predefined symbol. 321.23/291.48 ---------------------------------------- 321.23/291.48 321.23/291.48 (2) 321.23/291.48 Obligation: 321.23/291.48 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 321.23/291.48 321.23/291.48 321.23/291.48 The TRS R consists of the following rules: 321.23/291.48 321.23/291.48 half(0') -> 0' 321.23/291.48 half(s(0')) -> 0' 321.23/291.48 half(s(s(x))) -> s(half(x)) 321.23/291.48 lastbit(0') -> 0' 321.23/291.48 lastbit(s(0')) -> s(0') 321.23/291.48 lastbit(s(s(x))) -> lastbit(x) 321.23/291.48 conv(0') -> cons(nil, 0') 321.23/291.48 conv(s(x)) -> cons(conv(half(s(x))), lastbit(s(x))) 321.23/291.48 321.23/291.48 S is empty. 321.23/291.48 Rewrite Strategy: FULL 321.23/291.48 ---------------------------------------- 321.23/291.48 321.23/291.48 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 321.23/291.48 Infered types. 321.23/291.48 ---------------------------------------- 321.23/291.48 321.23/291.48 (4) 321.23/291.48 Obligation: 321.23/291.48 TRS: 321.23/291.48 Rules: 321.23/291.48 half(0') -> 0' 321.23/291.48 half(s(0')) -> 0' 321.23/291.48 half(s(s(x))) -> s(half(x)) 321.23/291.48 lastbit(0') -> 0' 321.23/291.48 lastbit(s(0')) -> s(0') 321.23/291.48 lastbit(s(s(x))) -> lastbit(x) 321.23/291.48 conv(0') -> cons(nil, 0') 321.23/291.48 conv(s(x)) -> cons(conv(half(s(x))), lastbit(s(x))) 321.23/291.48 321.23/291.48 Types: 321.23/291.48 half :: 0':s -> 0':s 321.23/291.48 0' :: 0':s 321.23/291.48 s :: 0':s -> 0':s 321.23/291.48 lastbit :: 0':s -> 0':s 321.23/291.48 conv :: 0':s -> nil:cons 321.23/291.48 cons :: nil:cons -> 0':s -> nil:cons 321.23/291.48 nil :: nil:cons 321.23/291.48 hole_0':s1_0 :: 0':s 321.23/291.48 hole_nil:cons2_0 :: nil:cons 321.23/291.48 gen_0':s3_0 :: Nat -> 0':s 321.23/291.48 gen_nil:cons4_0 :: Nat -> nil:cons 321.23/291.48
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