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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307915
details
property
value
status
complete
benchmark
t013.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.569 seconds
cpu usage
313.888
user time
312.157
system time
1.73057
max virtual memory
1.8282176E7
max residence set size
5112940.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
313.79/291.52 WORST_CASE(Omega(n^1), ?) 313.79/291.52 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 313.79/291.52 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 313.79/291.52 313.79/291.52 313.79/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 313.79/291.52 313.79/291.52 (0) CpxTRS 313.79/291.52 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 313.79/291.52 (2) CpxTRS 313.79/291.52 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 313.79/291.52 (4) typed CpxTrs 313.79/291.52 (5) OrderProof [LOWER BOUND(ID), 0 ms] 313.79/291.52 (6) typed CpxTrs 313.79/291.52 (7) RewriteLemmaProof [LOWER BOUND(ID), 323 ms] 313.79/291.52 (8) BEST 313.79/291.52 (9) proven lower bound 313.79/291.52 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 313.79/291.52 (11) BOUNDS(n^1, INF) 313.79/291.52 (12) typed CpxTrs 313.79/291.52 (13) RewriteLemmaProof [LOWER BOUND(ID), 1252 ms] 313.79/291.52 (14) typed CpxTrs 313.79/291.52 (15) RewriteLemmaProof [LOWER BOUND(ID), 2034 ms] 313.79/291.52 (16) typed CpxTrs 313.79/291.52 (17) RewriteLemmaProof [LOWER BOUND(ID), 2530 ms] 313.79/291.52 (18) BOUNDS(1, INF) 313.79/291.52 313.79/291.52 313.79/291.52 ---------------------------------------- 313.79/291.52 313.79/291.52 (0) 313.79/291.52 Obligation: 313.79/291.52 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 313.79/291.53 313.79/291.53 313.79/291.53 The TRS R consists of the following rules: 313.79/291.53 313.79/291.53 -(x, 0) -> x 313.79/291.53 -(0, s(y)) -> 0 313.79/291.53 -(s(x), s(y)) -> -(x, y) 313.79/291.53 f(0) -> 0 313.79/291.53 f(s(x)) -> -(s(x), g(f(x))) 313.79/291.53 g(0) -> s(0) 313.79/291.53 g(s(x)) -> -(s(x), f(g(x))) 313.79/291.53 313.79/291.53 S is empty. 313.79/291.53 Rewrite Strategy: FULL 313.79/291.53 ---------------------------------------- 313.79/291.53 313.79/291.53 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 313.79/291.53 Renamed function symbols to avoid clashes with predefined symbol. 313.79/291.53 ---------------------------------------- 313.79/291.53 313.79/291.53 (2) 313.79/291.53 Obligation: 313.79/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 313.79/291.53 313.79/291.53 313.79/291.53 The TRS R consists of the following rules: 313.79/291.53 313.79/291.53 -(x, 0') -> x 313.79/291.53 -(0', s(y)) -> 0' 313.79/291.53 -(s(x), s(y)) -> -(x, y) 313.79/291.53 f(0') -> 0' 313.79/291.53 f(s(x)) -> -(s(x), g(f(x))) 313.79/291.53 g(0') -> s(0') 313.79/291.53 g(s(x)) -> -(s(x), f(g(x))) 313.79/291.53 313.79/291.53 S is empty. 313.79/291.53 Rewrite Strategy: FULL 313.79/291.53 ---------------------------------------- 313.79/291.53 313.79/291.53 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 313.79/291.53 Infered types. 313.79/291.53 ---------------------------------------- 313.79/291.53 313.79/291.53 (4) 313.79/291.53 Obligation: 313.79/291.53 TRS: 313.79/291.53 Rules: 313.79/291.53 -(x, 0') -> x 313.79/291.53 -(0', s(y)) -> 0' 313.79/291.53 -(s(x), s(y)) -> -(x, y) 313.79/291.53 f(0') -> 0' 313.79/291.53 f(s(x)) -> -(s(x), g(f(x))) 313.79/291.53 g(0') -> s(0') 313.79/291.53 g(s(x)) -> -(s(x), f(g(x))) 313.79/291.53 313.79/291.53 Types: 313.79/291.53 - :: 0':s -> 0':s -> 0':s 313.79/291.53 0' :: 0':s 313.79/291.53 s :: 0':s -> 0':s 313.79/291.53 f :: 0':s -> 0':s 313.79/291.53 g :: 0':s -> 0':s 313.79/291.53 hole_0':s1_0 :: 0':s 313.79/291.53 gen_0':s2_0 :: Nat -> 0':s 313.79/291.53 313.79/291.53 ---------------------------------------- 313.79/291.53 313.79/291.53 (5) OrderProof (LOWER BOUND(ID))
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