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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307693
details
property
value
status
complete
benchmark
#3.6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n009.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.554 seconds
cpu usage
310.312
user time
308.647
system time
1.66512
max virtual memory
1.8279384E7
max residence set size
5271300.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
310.20/291.51 WORST_CASE(Omega(n^1), ?) 310.20/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 310.20/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 310.20/291.52 310.20/291.52 310.20/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 310.20/291.52 310.20/291.52 (0) CpxTRS 310.20/291.52 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 310.20/291.52 (2) CpxTRS 310.20/291.52 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 310.20/291.52 (4) typed CpxTrs 310.20/291.52 (5) OrderProof [LOWER BOUND(ID), 0 ms] 310.20/291.52 (6) typed CpxTrs 310.20/291.52 (7) RewriteLemmaProof [LOWER BOUND(ID), 276 ms] 310.20/291.52 (8) BEST 310.20/291.52 (9) proven lower bound 310.20/291.52 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 310.20/291.52 (11) BOUNDS(n^1, INF) 310.20/291.52 (12) typed CpxTrs 310.20/291.52 (13) RewriteLemmaProof [LOWER BOUND(ID), 862 ms] 310.20/291.52 (14) typed CpxTrs 310.20/291.52 310.20/291.52 310.20/291.52 ---------------------------------------- 310.20/291.52 310.20/291.52 (0) 310.20/291.52 Obligation: 310.20/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 310.20/291.52 310.20/291.52 310.20/291.52 The TRS R consists of the following rules: 310.20/291.52 310.20/291.52 le(0, y) -> true 310.20/291.52 le(s(x), 0) -> false 310.20/291.52 le(s(x), s(y)) -> le(x, y) 310.20/291.52 pred(s(x)) -> x 310.20/291.52 minus(x, 0) -> x 310.20/291.52 minus(x, s(y)) -> pred(minus(x, y)) 310.20/291.52 gcd(0, y) -> y 310.20/291.52 gcd(s(x), 0) -> s(x) 310.20/291.52 gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 310.20/291.52 if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) 310.20/291.52 if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) 310.20/291.52 310.20/291.52 S is empty. 310.20/291.52 Rewrite Strategy: FULL 310.20/291.52 ---------------------------------------- 310.20/291.52 310.20/291.52 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 310.20/291.52 Renamed function symbols to avoid clashes with predefined symbol. 310.20/291.52 ---------------------------------------- 310.20/291.52 310.20/291.52 (2) 310.20/291.52 Obligation: 310.20/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 310.20/291.52 310.20/291.52 310.20/291.52 The TRS R consists of the following rules: 310.20/291.52 310.20/291.52 le(0', y) -> true 310.20/291.52 le(s(x), 0') -> false 310.20/291.52 le(s(x), s(y)) -> le(x, y) 310.20/291.52 pred(s(x)) -> x 310.20/291.52 minus(x, 0') -> x 310.20/291.52 minus(x, s(y)) -> pred(minus(x, y)) 310.20/291.52 gcd(0', y) -> y 310.20/291.52 gcd(s(x), 0') -> s(x) 310.20/291.52 gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 310.20/291.52 if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) 310.20/291.52 if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) 310.20/291.52 310.20/291.52 S is empty. 310.20/291.52 Rewrite Strategy: FULL 310.20/291.52 ---------------------------------------- 310.20/291.52 310.20/291.52 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 310.20/291.52 Infered types. 310.20/291.52 ---------------------------------------- 310.20/291.52 310.20/291.52 (4) 310.20/291.52 Obligation: 310.20/291.52 TRS: 310.20/291.52 Rules: 310.20/291.52 le(0', y) -> true 310.20/291.52 le(s(x), 0') -> false 310.20/291.52 le(s(x), s(y)) -> le(x, y) 310.20/291.52 pred(s(x)) -> x 310.20/291.52 minus(x, 0') -> x 310.20/291.52 minus(x, s(y)) -> pred(minus(x, y)) 310.20/291.52 gcd(0', y) -> y 310.20/291.52 gcd(s(x), 0') -> s(x) 310.20/291.52 gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) 310.20/291.52 if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) 310.20/291.52 if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) 310.20/291.52 310.20/291.52 Types: 310.20/291.52 le :: 0':s -> 0':s -> true:false 310.20/291.52 0' :: 0':s 310.20/291.52 true :: true:false
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