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Runtime Complexity: TRS pair #487111230
details
property
value
status
complete
benchmark
z27.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.763 seconds
cpu usage
642.236
user time
635.182
system time
7.05415
max virtual memory
1.9082032E7
max residence set size
1.0589592E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 414 ms] (8) proven lower bound (9) LowerBoundPropagationProof [FINISHED, 0 ms] (10) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: f(0, 1, x) -> f(g(x), g(x), x) f(g(x), y, z) -> g(f(x, y, z)) f(x, g(y), z) -> g(f(x, y, z)) f(x, y, g(z)) -> g(f(x, y, z)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: f(0', 1', x) -> f(g(x), g(x), x) f(g(x), y, z) -> g(f(x, y, z)) f(x, g(y), z) -> g(f(x, y, z)) f(x, y, g(z)) -> g(f(x, y, z)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: f(0', 1', x) -> f(g(x), g(x), x) f(g(x), y, z) -> g(f(x, y, z)) f(x, g(y), z) -> g(f(x, y, z)) f(x, y, g(z)) -> g(f(x, y, z)) Types: f :: 0':1':g -> 0':1':g -> 0':1':g -> 0':1':g 0' :: 0':1':g 1' :: 0':1':g g :: 0':1':g -> 0':1':g hole_0':1':g1_0 :: 0':1':g gen_0':1':g2_0 :: Nat -> 0':1':g ---------------------------------------- (5) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: f ---------------------------------------- (6) Obligation: TRS: Rules: f(0', 1', x) -> f(g(x), g(x), x) f(g(x), y, z) -> g(f(x, y, z)) f(x, g(y), z) -> g(f(x, y, z)) f(x, y, g(z)) -> g(f(x, y, z)) Types: f :: 0':1':g -> 0':1':g -> 0':1':g -> 0':1':g 0' :: 0':1':g 1' :: 0':1':g g :: 0':1':g -> 0':1':g
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