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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307720
details
property
value
status
complete
benchmark
#3.48.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n106.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.534 seconds
cpu usage
308.678
user time
306.176
system time
2.50282
max virtual memory
1.8277336E7
max residence set size
5832888.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
308.61/291.48 WORST_CASE(Omega(n^1), ?) 308.61/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 308.61/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 308.61/291.49 308.61/291.49 308.61/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.61/291.49 308.61/291.49 (0) CpxTRS 308.61/291.49 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 308.61/291.49 (2) CpxTRS 308.61/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 308.61/291.49 (4) typed CpxTrs 308.61/291.49 (5) OrderProof [LOWER BOUND(ID), 0 ms] 308.61/291.49 (6) typed CpxTrs 308.61/291.49 (7) RewriteLemmaProof [LOWER BOUND(ID), 211 ms] 308.61/291.49 (8) BEST 308.61/291.49 (9) proven lower bound 308.61/291.49 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 308.61/291.49 (11) BOUNDS(n^1, INF) 308.61/291.49 (12) typed CpxTrs 308.61/291.49 308.61/291.49 308.61/291.49 ---------------------------------------- 308.61/291.49 308.61/291.49 (0) 308.61/291.49 Obligation: 308.61/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.61/291.49 308.61/291.49 308.61/291.49 The TRS R consists of the following rules: 308.61/291.49 308.61/291.49 f(0) -> true 308.61/291.49 f(1) -> false 308.61/291.49 f(s(x)) -> f(x) 308.61/291.49 if(true, s(x), s(y)) -> s(x) 308.61/291.49 if(false, s(x), s(y)) -> s(y) 308.61/291.49 g(x, c(y)) -> c(g(x, y)) 308.61/291.49 g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y))) 308.61/291.49 308.61/291.49 S is empty. 308.61/291.49 Rewrite Strategy: FULL 308.61/291.49 ---------------------------------------- 308.61/291.49 308.61/291.49 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 308.61/291.49 Renamed function symbols to avoid clashes with predefined symbol. 308.61/291.49 ---------------------------------------- 308.61/291.49 308.61/291.49 (2) 308.61/291.49 Obligation: 308.61/291.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 308.61/291.49 308.61/291.49 308.61/291.49 The TRS R consists of the following rules: 308.61/291.49 308.61/291.49 f(0') -> true 308.61/291.49 f(1') -> false 308.61/291.49 f(s(x)) -> f(x) 308.61/291.49 if(true, s(x), s(y)) -> s(x) 308.61/291.49 if(false, s(x), s(y)) -> s(y) 308.61/291.49 g(x, c(y)) -> c(g(x, y)) 308.61/291.49 g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y))) 308.61/291.49 308.61/291.49 S is empty. 308.61/291.49 Rewrite Strategy: FULL 308.61/291.49 ---------------------------------------- 308.61/291.49 308.61/291.49 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 308.61/291.49 Infered types. 308.61/291.49 ---------------------------------------- 308.61/291.49 308.61/291.49 (4) 308.61/291.49 Obligation: 308.61/291.49 TRS: 308.61/291.49 Rules: 308.61/291.49 f(0') -> true 308.61/291.49 f(1') -> false 308.61/291.49 f(s(x)) -> f(x) 308.61/291.49 if(true, s(x), s(y)) -> s(x) 308.61/291.49 if(false, s(x), s(y)) -> s(y) 308.61/291.49 g(x, c(y)) -> c(g(x, y)) 308.61/291.49 g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y))) 308.61/291.49 308.61/291.49 Types: 308.61/291.49 f :: 0':1':s:c -> true:false 308.61/291.49 0' :: 0':1':s:c 308.61/291.49 true :: true:false 308.61/291.49 1' :: 0':1':s:c 308.61/291.49 false :: true:false 308.61/291.49 s :: 0':1':s:c -> 0':1':s:c 308.61/291.49 if :: true:false -> 0':1':s:c -> 0':1':s:c -> 0':1':s:c 308.61/291.49 g :: 0':1':s:c -> 0':1':s:c -> 0':1':s:c 308.61/291.49 c :: 0':1':s:c -> 0':1':s:c 308.61/291.49 hole_true:false1_0 :: true:false 308.61/291.49 hole_0':1':s:c2_0 :: 0':1':s:c 308.61/291.49 gen_0':1':s:c3_0 :: Nat -> 0':1':s:c 308.61/291.49 308.61/291.49 ---------------------------------------- 308.61/291.49 308.61/291.49 (5) OrderProof (LOWER BOUND(ID)) 308.61/291.49 Heuristically decided to analyse the following defined symbols:
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