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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307872
details
property
value
status
complete
benchmark
nrOfNodes.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n133.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.521 seconds
cpu usage
304.528
user time
302.901
system time
1.62703
max virtual memory
1.8279384E7
max residence set size
5184384.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
304.44/291.48 WORST_CASE(Omega(n^2), ?) 304.44/291.49 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 304.44/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 304.44/291.49 304.44/291.49 304.44/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 304.44/291.49 304.44/291.49 (0) CpxTRS 304.44/291.49 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 304.44/291.49 (2) CpxTRS 304.44/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 304.44/291.49 (4) typed CpxTrs 304.44/291.49 (5) OrderProof [LOWER BOUND(ID), 0 ms] 304.44/291.49 (6) typed CpxTrs 304.44/291.49 (7) RewriteLemmaProof [LOWER BOUND(ID), 265 ms] 304.44/291.49 (8) BEST 304.44/291.49 (9) proven lower bound 304.44/291.49 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 304.44/291.49 (11) BOUNDS(n^1, INF) 304.44/291.49 (12) typed CpxTrs 304.44/291.49 (13) RewriteLemmaProof [LOWER BOUND(ID), 151 ms] 304.44/291.49 (14) proven lower bound 304.44/291.49 (15) LowerBoundPropagationProof [FINISHED, 0 ms] 304.44/291.49 (16) BOUNDS(n^2, INF) 304.44/291.49 304.44/291.49 304.44/291.49 ---------------------------------------- 304.44/291.49 304.44/291.49 (0) 304.44/291.49 Obligation: 304.44/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 304.44/291.49 304.44/291.49 304.44/291.49 The TRS R consists of the following rules: 304.44/291.49 304.44/291.49 isEmpty(empty) -> true 304.44/291.49 isEmpty(node(l, r)) -> false 304.44/291.49 left(empty) -> empty 304.44/291.49 left(node(l, r)) -> l 304.44/291.49 right(empty) -> empty 304.44/291.49 right(node(l, r)) -> r 304.44/291.49 inc(0) -> s(0) 304.44/291.49 inc(s(x)) -> s(inc(x)) 304.44/291.49 count(n, x) -> if(isEmpty(n), isEmpty(left(n)), right(n), node(left(left(n)), node(right(left(n)), right(n))), x, inc(x)) 304.44/291.49 if(true, b, n, m, x, y) -> x 304.44/291.49 if(false, false, n, m, x, y) -> count(m, x) 304.44/291.49 if(false, true, n, m, x, y) -> count(n, y) 304.44/291.49 nrOfNodes(n) -> count(n, 0) 304.44/291.49 304.44/291.49 S is empty. 304.44/291.49 Rewrite Strategy: FULL 304.44/291.49 ---------------------------------------- 304.44/291.49 304.44/291.49 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 304.44/291.49 Renamed function symbols to avoid clashes with predefined symbol. 304.44/291.49 ---------------------------------------- 304.44/291.49 304.44/291.49 (2) 304.44/291.49 Obligation: 304.44/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 304.44/291.49 304.44/291.49 304.44/291.49 The TRS R consists of the following rules: 304.44/291.49 304.44/291.49 isEmpty(empty) -> true 304.44/291.49 isEmpty(node(l, r)) -> false 304.44/291.49 left(empty) -> empty 304.44/291.49 left(node(l, r)) -> l 304.44/291.49 right(empty) -> empty 304.44/291.49 right(node(l, r)) -> r 304.44/291.49 inc(0') -> s(0') 304.44/291.49 inc(s(x)) -> s(inc(x)) 304.44/291.49 count(n, x) -> if(isEmpty(n), isEmpty(left(n)), right(n), node(left(left(n)), node(right(left(n)), right(n))), x, inc(x)) 304.44/291.49 if(true, b, n, m, x, y) -> x 304.44/291.49 if(false, false, n, m, x, y) -> count(m, x) 304.44/291.49 if(false, true, n, m, x, y) -> count(n, y) 304.44/291.49 nrOfNodes(n) -> count(n, 0') 304.44/291.49 304.44/291.49 S is empty. 304.44/291.49 Rewrite Strategy: FULL 304.44/291.49 ---------------------------------------- 304.44/291.49 304.44/291.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 304.44/291.49 Infered types. 304.44/291.49 ---------------------------------------- 304.44/291.49 304.44/291.49 (4) 304.44/291.49 Obligation: 304.44/291.49 TRS: 304.44/291.49 Rules: 304.44/291.49 isEmpty(empty) -> true 304.44/291.49 isEmpty(node(l, r)) -> false 304.44/291.49 left(empty) -> empty 304.44/291.49 left(node(l, r)) -> l 304.44/291.49 right(empty) -> empty 304.44/291.49 right(node(l, r)) -> r 304.44/291.49 inc(0') -> s(0') 304.44/291.49 inc(s(x)) -> s(inc(x)) 304.44/291.49 count(n, x) -> if(isEmpty(n), isEmpty(left(n)), right(n), node(left(left(n)), node(right(left(n)), right(n))), x, inc(x)) 304.44/291.49 if(true, b, n, m, x, y) -> x
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