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Runtime Complexity: TRS Innermost pair #487112128
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
n143.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.632 seconds
cpu usage
1128.28
user time
1114.48
system time
13.7984
max virtual memory
3.7980992E7
max residence set size
1.495026E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
WORST_CASE(Omega(n^2), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 280 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 267 ms] (14) proven lower bound (15) LowerBoundPropagationProof [FINISHED, 0 ms] (16) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: isEmpty(empty) -> true isEmpty(node(l, r)) -> false left(empty) -> empty left(node(l, r)) -> l right(empty) -> empty right(node(l, r)) -> r inc(0) -> s(0) inc(s(x)) -> s(inc(x)) count(n, x) -> if(isEmpty(n), isEmpty(left(n)), right(n), node(left(left(n)), node(right(left(n)), right(n))), x, inc(x)) if(true, b, n, m, x, y) -> x if(false, false, n, m, x, y) -> count(m, x) if(false, true, n, m, x, y) -> count(n, y) nrOfNodes(n) -> count(n, 0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: isEmpty(empty) -> true isEmpty(node(l, r)) -> false left(empty) -> empty left(node(l, r)) -> l right(empty) -> empty right(node(l, r)) -> r inc(0') -> s(0') inc(s(x)) -> s(inc(x)) count(n, x) -> if(isEmpty(n), isEmpty(left(n)), right(n), node(left(left(n)), node(right(left(n)), right(n))), x, inc(x)) if(true, b, n, m, x, y) -> x if(false, false, n, m, x, y) -> count(m, x) if(false, true, n, m, x, y) -> count(n, y) nrOfNodes(n) -> count(n, 0') S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules: isEmpty(empty) -> true isEmpty(node(l, r)) -> false left(empty) -> empty left(node(l, r)) -> l right(empty) -> empty right(node(l, r)) -> r inc(0') -> s(0') inc(s(x)) -> s(inc(x)) count(n, x) -> if(isEmpty(n), isEmpty(left(n)), right(n), node(left(left(n)), node(right(left(n)), right(n))), x, inc(x)) if(true, b, n, m, x, y) -> x
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