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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313671
details
property
value
status
complete
benchmark
identity.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n036.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.619 seconds
cpu usage
887.955
user time
876.675
system time
11.28
max virtual memory
3.8308556E7
max residence set size
1.0384408E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
887.61/291.54 WORST_CASE(Omega(n^1), ?) 887.61/291.56 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 887.61/291.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 887.61/291.56 887.61/291.56 887.61/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 887.61/291.56 887.61/291.56 (0) CpxTRS 887.61/291.56 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 887.61/291.56 (2) CpxTRS 887.61/291.56 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 887.61/291.56 (4) typed CpxTrs 887.61/291.56 (5) OrderProof [LOWER BOUND(ID), 0 ms] 887.61/291.56 (6) typed CpxTrs 887.61/291.56 (7) RewriteLemmaProof [LOWER BOUND(ID), 333 ms] 887.61/291.56 (8) BEST 887.61/291.56 (9) proven lower bound 887.61/291.56 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 887.61/291.56 (11) BOUNDS(n^1, INF) 887.61/291.56 (12) typed CpxTrs 887.61/291.56 887.61/291.56 887.61/291.56 ---------------------------------------- 887.61/291.56 887.61/291.56 (0) 887.61/291.56 Obligation: 887.61/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 887.61/291.56 887.61/291.56 887.61/291.56 The TRS R consists of the following rules: 887.61/291.56 887.61/291.56 g(x, 0) -> 0 887.61/291.56 g(d, s(x)) -> s(s(g(d, x))) 887.61/291.56 g(h, s(0)) -> 0 887.61/291.56 g(h, s(s(x))) -> s(g(h, x)) 887.61/291.56 double(x) -> g(d, x) 887.61/291.56 half(x) -> g(h, x) 887.61/291.56 f(s(x), y) -> f(half(s(x)), double(y)) 887.61/291.56 f(s(0), y) -> y 887.61/291.56 id(x) -> f(x, s(0)) 887.61/291.56 887.61/291.56 S is empty. 887.61/291.56 Rewrite Strategy: INNERMOST 887.61/291.56 ---------------------------------------- 887.61/291.56 887.61/291.56 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 887.61/291.56 Renamed function symbols to avoid clashes with predefined symbol. 887.61/291.56 ---------------------------------------- 887.61/291.56 887.61/291.56 (2) 887.61/291.56 Obligation: 887.61/291.56 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 887.61/291.56 887.61/291.56 887.61/291.56 The TRS R consists of the following rules: 887.61/291.56 887.61/291.56 g(x, 0') -> 0' 887.61/291.56 g(d, s(x)) -> s(s(g(d, x))) 887.61/291.56 g(h, s(0')) -> 0' 887.61/291.56 g(h, s(s(x))) -> s(g(h, x)) 887.61/291.56 double(x) -> g(d, x) 887.61/291.56 half(x) -> g(h, x) 887.61/291.56 f(s(x), y) -> f(half(s(x)), double(y)) 887.61/291.56 f(s(0'), y) -> y 887.61/291.56 id(x) -> f(x, s(0')) 887.61/291.56 887.61/291.56 S is empty. 887.61/291.56 Rewrite Strategy: INNERMOST 887.61/291.56 ---------------------------------------- 887.61/291.56 887.61/291.56 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 887.61/291.56 Infered types. 887.61/291.56 ---------------------------------------- 887.61/291.56 887.61/291.56 (4) 887.61/291.56 Obligation: 887.61/291.56 Innermost TRS: 887.61/291.56 Rules: 887.61/291.56 g(x, 0') -> 0' 887.61/291.56 g(d, s(x)) -> s(s(g(d, x))) 887.61/291.56 g(h, s(0')) -> 0' 887.61/291.56 g(h, s(s(x))) -> s(g(h, x)) 887.61/291.56 double(x) -> g(d, x) 887.61/291.56 half(x) -> g(h, x) 887.61/291.56 f(s(x), y) -> f(half(s(x)), double(y)) 887.61/291.56 f(s(0'), y) -> y 887.61/291.56 id(x) -> f(x, s(0')) 887.61/291.56 887.61/291.56 Types: 887.61/291.56 g :: d:h -> 0':s -> 0':s 887.61/291.56 0' :: 0':s 887.61/291.56 d :: d:h 887.61/291.56 s :: 0':s -> 0':s 887.61/291.56 h :: d:h 887.61/291.56 double :: 0':s -> 0':s 887.61/291.56 half :: 0':s -> 0':s 887.61/291.56 f :: 0':s -> 0':s -> 0':s 887.61/291.56 id :: 0':s -> 0':s 887.61/291.56 hole_0':s1_0 :: 0':s 887.61/291.56 hole_d:h2_0 :: d:h
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