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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308533
details
property
value
status
complete
benchmark
#4.34.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n058.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.671 seconds
cpu usage
300.931
user time
299.317
system time
1.61458
max virtual memory
1.8277336E7
max residence set size
5091464.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
300.85/291.62 WORST_CASE(Omega(n^1), ?) 300.85/291.63 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 300.85/291.63 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 300.85/291.63 300.85/291.63 300.85/291.63 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 300.85/291.63 300.85/291.63 (0) CpxTRS 300.85/291.63 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 300.85/291.63 (2) CpxTRS 300.85/291.63 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 300.85/291.63 (4) typed CpxTrs 300.85/291.63 (5) OrderProof [LOWER BOUND(ID), 0 ms] 300.85/291.63 (6) typed CpxTrs 300.85/291.63 (7) RewriteLemmaProof [LOWER BOUND(ID), 162 ms] 300.85/291.63 (8) BEST 300.85/291.63 (9) proven lower bound 300.85/291.63 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 300.85/291.63 (11) BOUNDS(n^1, INF) 300.85/291.63 (12) typed CpxTrs 300.85/291.63 300.85/291.63 300.85/291.63 ---------------------------------------- 300.85/291.63 300.85/291.63 (0) 300.85/291.63 Obligation: 300.85/291.63 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 300.85/291.63 300.85/291.63 300.85/291.63 The TRS R consists of the following rules: 300.85/291.63 300.85/291.63 f(0) -> true 300.85/291.63 f(1) -> false 300.85/291.63 f(s(x)) -> f(x) 300.85/291.63 if(true, x, y) -> x 300.85/291.63 if(false, x, y) -> y 300.85/291.63 g(s(x), s(y)) -> if(f(x), s(x), s(y)) 300.85/291.63 g(x, c(y)) -> g(x, g(s(c(y)), y)) 300.85/291.63 300.85/291.63 S is empty. 300.85/291.63 Rewrite Strategy: FULL 300.85/291.63 ---------------------------------------- 300.85/291.63 300.85/291.63 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 300.85/291.63 Renamed function symbols to avoid clashes with predefined symbol. 300.85/291.63 ---------------------------------------- 300.85/291.63 300.85/291.63 (2) 300.85/291.63 Obligation: 300.85/291.63 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 300.85/291.63 300.85/291.63 300.85/291.63 The TRS R consists of the following rules: 300.85/291.63 300.85/291.63 f(0') -> true 300.85/291.63 f(1') -> false 300.85/291.63 f(s(x)) -> f(x) 300.85/291.63 if(true, x, y) -> x 300.85/291.63 if(false, x, y) -> y 300.85/291.63 g(s(x), s(y)) -> if(f(x), s(x), s(y)) 300.85/291.63 g(x, c(y)) -> g(x, g(s(c(y)), y)) 300.85/291.63 300.85/291.63 S is empty. 300.85/291.63 Rewrite Strategy: FULL 300.85/291.63 ---------------------------------------- 300.85/291.63 300.85/291.63 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 300.85/291.63 Infered types. 300.85/291.63 ---------------------------------------- 300.85/291.63 300.85/291.63 (4) 300.85/291.63 Obligation: 300.85/291.63 TRS: 300.85/291.63 Rules: 300.85/291.63 f(0') -> true 300.85/291.63 f(1') -> false 300.85/291.63 f(s(x)) -> f(x) 300.85/291.63 if(true, x, y) -> x 300.85/291.63 if(false, x, y) -> y 300.85/291.63 g(s(x), s(y)) -> if(f(x), s(x), s(y)) 300.85/291.63 g(x, c(y)) -> g(x, g(s(c(y)), y)) 300.85/291.63 300.85/291.63 Types: 300.85/291.63 f :: 0':1':s:c -> true:false 300.85/291.63 0' :: 0':1':s:c 300.85/291.63 true :: true:false 300.85/291.63 1' :: 0':1':s:c 300.85/291.63 false :: true:false 300.85/291.63 s :: 0':1':s:c -> 0':1':s:c 300.85/291.63 if :: true:false -> 0':1':s:c -> 0':1':s:c -> 0':1':s:c 300.85/291.63 g :: 0':1':s:c -> 0':1':s:c -> 0':1':s:c 300.85/291.63 c :: 0':1':s:c -> 0':1':s:c 300.85/291.63 hole_true:false1_0 :: true:false 300.85/291.63 hole_0':1':s:c2_0 :: 0':1':s:c 300.85/291.63 gen_0':1':s:c3_0 :: Nat -> 0':1':s:c 300.85/291.63 300.85/291.63 ---------------------------------------- 300.85/291.63 300.85/291.63 (5) OrderProof (LOWER BOUND(ID)) 300.85/291.63 Heuristically decided to analyse the following defined symbols:
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