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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308531
details
property
value
status
complete
benchmark
#4.30.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n113.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.534 seconds
cpu usage
308.275
user time
306.259
system time
2.01589
max virtual memory
1.8282028E7
max residence set size
5326768.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
308.21/291.48 WORST_CASE(Omega(n^1), ?) 308.21/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 308.21/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 308.21/291.49 308.21/291.49 308.21/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.21/291.49 308.21/291.49 (0) CpxTRS 308.21/291.49 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 308.21/291.49 (2) CpxTRS 308.21/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 308.21/291.49 (4) typed CpxTrs 308.21/291.49 (5) OrderProof [LOWER BOUND(ID), 0 ms] 308.21/291.49 (6) typed CpxTrs 308.21/291.49 (7) RewriteLemmaProof [LOWER BOUND(ID), 269 ms] 308.21/291.49 (8) BEST 308.21/291.49 (9) proven lower bound 308.21/291.49 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 308.21/291.49 (11) BOUNDS(n^1, INF) 308.21/291.49 (12) typed CpxTrs 308.21/291.49 (13) RewriteLemmaProof [LOWER BOUND(ID), 47 ms] 308.21/291.49 (14) typed CpxTrs 308.21/291.49 308.21/291.49 308.21/291.49 ---------------------------------------- 308.21/291.49 308.21/291.49 (0) 308.21/291.49 Obligation: 308.21/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.21/291.49 308.21/291.49 308.21/291.49 The TRS R consists of the following rules: 308.21/291.49 308.21/291.49 minus(x, 0) -> x 308.21/291.49 minus(s(x), s(y)) -> minus(x, y) 308.21/291.49 le(0, y) -> true 308.21/291.49 le(s(x), 0) -> false 308.21/291.49 le(s(x), s(y)) -> le(x, y) 308.21/291.49 quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) 308.21/291.49 if_quot(true, x, y) -> s(quot(minus(x, y), y)) 308.21/291.49 if_quot(false, x, y) -> 0 308.21/291.49 308.21/291.49 S is empty. 308.21/291.49 Rewrite Strategy: FULL 308.21/291.49 ---------------------------------------- 308.21/291.49 308.21/291.49 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 308.21/291.49 Renamed function symbols to avoid clashes with predefined symbol. 308.21/291.49 ---------------------------------------- 308.21/291.49 308.21/291.49 (2) 308.21/291.49 Obligation: 308.21/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.21/291.49 308.21/291.49 308.21/291.49 The TRS R consists of the following rules: 308.21/291.49 308.21/291.49 minus(x, 0') -> x 308.21/291.49 minus(s(x), s(y)) -> minus(x, y) 308.21/291.49 le(0', y) -> true 308.21/291.49 le(s(x), 0') -> false 308.21/291.49 le(s(x), s(y)) -> le(x, y) 308.21/291.49 quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) 308.21/291.49 if_quot(true, x, y) -> s(quot(minus(x, y), y)) 308.21/291.49 if_quot(false, x, y) -> 0' 308.21/291.49 308.21/291.49 S is empty. 308.21/291.49 Rewrite Strategy: FULL 308.21/291.49 ---------------------------------------- 308.21/291.49 308.21/291.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 308.21/291.49 Infered types. 308.21/291.49 ---------------------------------------- 308.21/291.49 308.21/291.49 (4) 308.21/291.49 Obligation: 308.21/291.49 TRS: 308.21/291.49 Rules: 308.21/291.49 minus(x, 0') -> x 308.21/291.49 minus(s(x), s(y)) -> minus(x, y) 308.21/291.49 le(0', y) -> true 308.21/291.49 le(s(x), 0') -> false 308.21/291.49 le(s(x), s(y)) -> le(x, y) 308.21/291.49 quot(x, s(y)) -> if_quot(le(s(y), x), x, s(y)) 308.21/291.49 if_quot(true, x, y) -> s(quot(minus(x, y), y)) 308.21/291.49 if_quot(false, x, y) -> 0' 308.21/291.49 308.21/291.49 Types: 308.21/291.49 minus :: 0':s -> 0':s -> 0':s 308.21/291.49 0' :: 0':s 308.21/291.49 s :: 0':s -> 0':s 308.21/291.49 le :: 0':s -> 0':s -> true:false 308.21/291.49 true :: true:false 308.21/291.49 false :: true:false 308.21/291.49 quot :: 0':s -> 0':s -> 0':s 308.21/291.49 if_quot :: true:false -> 0':s -> 0':s -> 0':s 308.21/291.49 hole_0':s1_0 :: 0':s 308.21/291.49 hole_true:false2_0 :: true:false 308.21/291.49 gen_0':s3_0 :: Nat -> 0':s 308.21/291.49
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