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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313326
details
property
value
status
complete
benchmark
tpa08.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.798 seconds
cpu usage
1070.28
user time
1060.99
system time
9.28956
max virtual memory
5.710418E7
max residence set size
1.506594E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1069.26/291.55 WORST_CASE(Omega(n^2), ?) 1070.03/291.72 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1070.03/291.72 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1070.03/291.72 1070.03/291.72 1070.03/291.72 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1070.03/291.72 1070.03/291.72 (0) CpxTRS 1070.03/291.72 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1070.03/291.72 (2) CpxTRS 1070.03/291.72 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1070.03/291.72 (4) typed CpxTrs 1070.03/291.72 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1070.03/291.72 (6) typed CpxTrs 1070.03/291.72 (7) RewriteLemmaProof [LOWER BOUND(ID), 273 ms] 1070.03/291.72 (8) BEST 1070.03/291.72 (9) proven lower bound 1070.03/291.72 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1070.03/291.72 (11) BOUNDS(n^1, INF) 1070.03/291.72 (12) typed CpxTrs 1070.03/291.72 (13) RewriteLemmaProof [LOWER BOUND(ID), 63 ms] 1070.03/291.72 (14) typed CpxTrs 1070.03/291.72 (15) RewriteLemmaProof [LOWER BOUND(ID), 62 ms] 1070.03/291.72 (16) BEST 1070.03/291.72 (17) proven lower bound 1070.03/291.72 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 1070.03/291.72 (19) BOUNDS(n^2, INF) 1070.03/291.72 (20) typed CpxTrs 1070.03/291.72 1070.03/291.72 1070.03/291.72 ---------------------------------------- 1070.03/291.72 1070.03/291.72 (0) 1070.03/291.72 Obligation: 1070.03/291.72 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1070.03/291.72 1070.03/291.72 1070.03/291.72 The TRS R consists of the following rules: 1070.03/291.72 1070.03/291.72 -(x, 0) -> x 1070.03/291.72 -(s(x), s(y)) -> -(x, y) 1070.03/291.72 +(0, y) -> y 1070.03/291.72 +(s(x), y) -> s(+(x, y)) 1070.03/291.72 *(x, 0) -> 0 1070.03/291.72 *(x, s(y)) -> +(x, *(x, y)) 1070.03/291.72 f(s(x)) -> f(-(+(*(s(x), s(x)), *(s(x), s(s(s(0))))), *(s(s(x)), s(s(x))))) 1070.03/291.72 1070.03/291.72 S is empty. 1070.03/291.72 Rewrite Strategy: INNERMOST 1070.03/291.72 ---------------------------------------- 1070.03/291.72 1070.03/291.72 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1070.03/291.72 Renamed function symbols to avoid clashes with predefined symbol. 1070.03/291.72 ---------------------------------------- 1070.03/291.72 1070.03/291.72 (2) 1070.03/291.72 Obligation: 1070.03/291.72 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1070.03/291.72 1070.03/291.72 1070.03/291.72 The TRS R consists of the following rules: 1070.03/291.72 1070.03/291.72 -(x, 0') -> x 1070.03/291.72 -(s(x), s(y)) -> -(x, y) 1070.03/291.72 +'(0', y) -> y 1070.03/291.72 +'(s(x), y) -> s(+'(x, y)) 1070.03/291.72 *'(x, 0') -> 0' 1070.03/291.72 *'(x, s(y)) -> +'(x, *'(x, y)) 1070.03/291.72 f(s(x)) -> f(-(+'(*'(s(x), s(x)), *'(s(x), s(s(s(0'))))), *'(s(s(x)), s(s(x))))) 1070.03/291.72 1070.03/291.72 S is empty. 1070.03/291.72 Rewrite Strategy: INNERMOST 1070.03/291.72 ---------------------------------------- 1070.03/291.72 1070.03/291.72 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1070.03/291.72 Infered types. 1070.03/291.72 ---------------------------------------- 1070.03/291.72 1070.03/291.72 (4) 1070.03/291.72 Obligation: 1070.03/291.72 Innermost TRS: 1070.03/291.72 Rules: 1070.03/291.72 -(x, 0') -> x 1070.03/291.72 -(s(x), s(y)) -> -(x, y) 1070.03/291.72 +'(0', y) -> y 1070.03/291.72 +'(s(x), y) -> s(+'(x, y)) 1070.03/291.72 *'(x, 0') -> 0' 1070.03/291.72 *'(x, s(y)) -> +'(x, *'(x, y)) 1070.03/291.72 f(s(x)) -> f(-(+'(*'(s(x), s(x)), *'(s(x), s(s(s(0'))))), *'(s(s(x)), s(s(x))))) 1070.03/291.72 1070.03/291.72 Types: 1070.03/291.72 - :: 0':s -> 0':s -> 0':s 1070.03/291.72 0' :: 0':s 1070.03/291.72 s :: 0':s -> 0':s 1070.03/291.72 +' :: 0':s -> 0':s -> 0':s 1070.03/291.72 *' :: 0':s -> 0':s -> 0':s 1070.03/291.72 f :: 0':s -> f 1070.03/291.72 hole_0':s1_0 :: 0':s 1070.03/291.72 hole_f2_0 :: f 1070.03/291.72 gen_0':s3_0 :: Nat -> 0':s
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