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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307610
details
property
value
status
complete
benchmark
gcdhard.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n046.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.572 seconds
cpu usage
302.607
user time
300.54
system time
2.06718
max virtual memory
1.8279384E7
max residence set size
5186044.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
302.40/291.49 WORST_CASE(Omega(n^1), ?) 302.52/291.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 302.52/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 302.52/291.53 302.52/291.53 302.52/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 302.52/291.53 302.52/291.53 (0) CpxTRS 302.52/291.53 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 302.52/291.53 (2) CpxTRS 302.52/291.53 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 302.52/291.53 (4) typed CpxTrs 302.52/291.53 (5) OrderProof [LOWER BOUND(ID), 0 ms] 302.52/291.53 (6) typed CpxTrs 302.52/291.53 (7) RewriteLemmaProof [LOWER BOUND(ID), 294 ms] 302.52/291.53 (8) BEST 302.52/291.53 (9) proven lower bound 302.52/291.53 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 302.52/291.53 (11) BOUNDS(n^1, INF) 302.52/291.53 (12) typed CpxTrs 302.52/291.53 (13) RewriteLemmaProof [LOWER BOUND(ID), 51 ms] 302.52/291.53 (14) typed CpxTrs 302.52/291.53 302.52/291.53 302.52/291.53 ---------------------------------------- 302.52/291.53 302.52/291.53 (0) 302.52/291.53 Obligation: 302.52/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 302.52/291.53 302.52/291.53 302.52/291.53 The TRS R consists of the following rules: 302.52/291.53 302.52/291.53 minus(0, x) -> 0 302.52/291.53 minus(s(x), 0) -> s(x) 302.52/291.53 minus(s(x), s(y)) -> minus(x, y) 302.52/291.53 mod(x, 0) -> 0 302.52/291.53 mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) 302.52/291.53 if(true, x, y) -> x 302.52/291.53 if(false, x, y) -> mod(minus(x, y), y) 302.52/291.53 gcd(x, 0) -> x 302.52/291.53 gcd(0, s(y)) -> s(y) 302.52/291.53 gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) 302.52/291.53 lt(x, 0) -> false 302.52/291.53 lt(0, s(x)) -> true 302.52/291.53 lt(s(x), s(y)) -> lt(x, y) 302.52/291.53 302.52/291.53 S is empty. 302.52/291.53 Rewrite Strategy: FULL 302.52/291.53 ---------------------------------------- 302.52/291.53 302.52/291.53 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 302.52/291.53 Renamed function symbols to avoid clashes with predefined symbol. 302.52/291.53 ---------------------------------------- 302.52/291.53 302.52/291.53 (2) 302.52/291.53 Obligation: 302.52/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 302.52/291.53 302.52/291.53 302.52/291.53 The TRS R consists of the following rules: 302.52/291.53 302.52/291.53 minus(0', x) -> 0' 302.52/291.53 minus(s(x), 0') -> s(x) 302.52/291.53 minus(s(x), s(y)) -> minus(x, y) 302.52/291.53 mod(x, 0') -> 0' 302.52/291.53 mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) 302.52/291.53 if(true, x, y) -> x 302.52/291.53 if(false, x, y) -> mod(minus(x, y), y) 302.52/291.53 gcd(x, 0') -> x 302.52/291.53 gcd(0', s(y)) -> s(y) 302.52/291.53 gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) 302.52/291.53 lt(x, 0') -> false 302.52/291.53 lt(0', s(x)) -> true 302.52/291.53 lt(s(x), s(y)) -> lt(x, y) 302.52/291.53 302.52/291.53 S is empty. 302.52/291.53 Rewrite Strategy: FULL 302.52/291.53 ---------------------------------------- 302.52/291.53 302.52/291.53 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 302.52/291.53 Infered types. 302.52/291.53 ---------------------------------------- 302.52/291.53 302.52/291.53 (4) 302.52/291.53 Obligation: 302.52/291.53 TRS: 302.52/291.53 Rules: 302.52/291.53 minus(0', x) -> 0' 302.52/291.53 minus(s(x), 0') -> s(x) 302.52/291.53 minus(s(x), s(y)) -> minus(x, y) 302.52/291.53 mod(x, 0') -> 0' 302.52/291.53 mod(x, s(y)) -> if(lt(x, s(y)), x, s(y)) 302.52/291.53 if(true, x, y) -> x 302.52/291.53 if(false, x, y) -> mod(minus(x, y), y) 302.52/291.53 gcd(x, 0') -> x 302.52/291.53 gcd(0', s(y)) -> s(y) 302.52/291.53 gcd(s(x), s(y)) -> gcd(mod(s(x), s(y)), mod(s(y), s(x))) 302.52/291.53 lt(x, 0') -> false 302.52/291.53 lt(0', s(x)) -> true
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