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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307659
details
property
value
status
complete
benchmark
2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n127.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.535 seconds
cpu usage
303.11
user time
301.36
system time
1.75
max virtual memory
1.8279356E7
max residence set size
5220040.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
303.11/291.48 WORST_CASE(Omega(n^1), ?) 303.11/291.49 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 303.11/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 303.11/291.49 303.11/291.49 303.11/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 303.11/291.49 303.11/291.49 (0) CpxTRS 303.11/291.49 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 303.11/291.49 (2) CpxTRS 303.11/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 303.11/291.49 (4) typed CpxTrs 303.11/291.49 (5) OrderProof [LOWER BOUND(ID), 0 ms] 303.11/291.49 (6) typed CpxTrs 303.11/291.49 (7) RewriteLemmaProof [LOWER BOUND(ID), 255 ms] 303.11/291.49 (8) BEST 303.11/291.49 (9) proven lower bound 303.11/291.49 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 303.11/291.49 (11) BOUNDS(n^1, INF) 303.11/291.49 (12) typed CpxTrs 303.11/291.49 303.11/291.49 303.11/291.49 ---------------------------------------- 303.11/291.49 303.11/291.49 (0) 303.11/291.49 Obligation: 303.11/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 303.11/291.49 303.11/291.49 303.11/291.49 The TRS R consists of the following rules: 303.11/291.49 303.11/291.49 cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) 303.11/291.49 gr(0, x) -> false 303.11/291.49 gr(s(x), 0) -> true 303.11/291.49 gr(s(x), s(y)) -> gr(x, y) 303.11/291.49 p(0) -> 0 303.11/291.49 p(s(x)) -> x 303.11/291.49 303.11/291.49 S is empty. 303.11/291.49 Rewrite Strategy: FULL 303.11/291.49 ---------------------------------------- 303.11/291.49 303.11/291.49 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 303.11/291.49 Renamed function symbols to avoid clashes with predefined symbol. 303.11/291.49 ---------------------------------------- 303.11/291.49 303.11/291.49 (2) 303.11/291.49 Obligation: 303.11/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 303.11/291.49 303.11/291.49 303.11/291.49 The TRS R consists of the following rules: 303.11/291.49 303.11/291.49 cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) 303.11/291.49 gr(0', x) -> false 303.11/291.49 gr(s(x), 0') -> true 303.11/291.49 gr(s(x), s(y)) -> gr(x, y) 303.11/291.49 p(0') -> 0' 303.11/291.49 p(s(x)) -> x 303.11/291.49 303.11/291.49 S is empty. 303.11/291.49 Rewrite Strategy: FULL 303.11/291.49 ---------------------------------------- 303.11/291.49 303.11/291.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 303.11/291.49 Infered types. 303.11/291.49 ---------------------------------------- 303.11/291.49 303.11/291.49 (4) 303.11/291.49 Obligation: 303.11/291.49 TRS: 303.11/291.49 Rules: 303.11/291.49 cond(true, x, y) -> cond(gr(x, y), p(x), s(y)) 303.11/291.49 gr(0', x) -> false 303.11/291.49 gr(s(x), 0') -> true 303.11/291.49 gr(s(x), s(y)) -> gr(x, y) 303.11/291.49 p(0') -> 0' 303.11/291.49 p(s(x)) -> x 303.11/291.49 303.11/291.49 Types: 303.11/291.49 cond :: true:false -> s:0' -> s:0' -> cond 303.11/291.49 true :: true:false 303.11/291.49 gr :: s:0' -> s:0' -> true:false 303.11/291.49 p :: s:0' -> s:0' 303.11/291.49 s :: s:0' -> s:0' 303.11/291.49 0' :: s:0' 303.11/291.49 false :: true:false 303.11/291.49 hole_cond1_0 :: cond 303.11/291.49 hole_true:false2_0 :: true:false 303.11/291.49 hole_s:0'3_0 :: s:0' 303.11/291.49 gen_s:0'4_0 :: Nat -> s:0' 303.11/291.49 303.11/291.49 ---------------------------------------- 303.11/291.49 303.11/291.49 (5) OrderProof (LOWER BOUND(ID)) 303.11/291.49 Heuristically decided to analyse the following defined symbols: 303.11/291.49 cond, gr 303.11/291.49 303.11/291.49 They will be analysed ascendingly in the following order: 303.11/291.49 gr < cond
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