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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313316
details
property
value
status
complete
benchmark
tpa04.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n099.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.863 seconds
cpu usage
1118.1
user time
1109.04
system time
9.06146
max virtual memory
3.81692E7
max residence set size
1.0564144E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1117.62/291.99 WORST_CASE(Omega(n^1), ?) 1117.62/292.04 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1117.62/292.04 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1117.62/292.04 1117.62/292.04 1117.62/292.04 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1117.62/292.04 1117.62/292.04 (0) CpxTRS 1117.62/292.04 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1117.62/292.04 (2) CpxTRS 1117.62/292.04 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1117.62/292.04 (4) typed CpxTrs 1117.62/292.04 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1117.62/292.04 (6) typed CpxTrs 1117.62/292.04 (7) RewriteLemmaProof [LOWER BOUND(ID), 319 ms] 1117.62/292.04 (8) BEST 1117.62/292.04 (9) proven lower bound 1117.62/292.04 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1117.62/292.04 (11) BOUNDS(n^1, INF) 1117.62/292.04 (12) typed CpxTrs 1117.62/292.04 (13) RewriteLemmaProof [LOWER BOUND(ID), 92 ms] 1117.62/292.04 (14) typed CpxTrs 1117.62/292.04 (15) RewriteLemmaProof [LOWER BOUND(ID), 77 ms] 1117.62/292.04 (16) typed CpxTrs 1117.62/292.04 (17) RewriteLemmaProof [LOWER BOUND(ID), 33 ms] 1117.62/292.04 (18) typed CpxTrs 1117.62/292.04 1117.62/292.04 1117.62/292.04 ---------------------------------------- 1117.62/292.04 1117.62/292.04 (0) 1117.62/292.04 Obligation: 1117.62/292.04 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1117.62/292.04 1117.62/292.04 1117.62/292.04 The TRS R consists of the following rules: 1117.62/292.04 1117.62/292.04 min(0, y) -> 0 1117.62/292.04 min(x, 0) -> 0 1117.62/292.04 min(s(x), s(y)) -> s(min(x, y)) 1117.62/292.04 max(0, y) -> y 1117.62/292.04 max(x, 0) -> x 1117.62/292.04 max(s(x), s(y)) -> s(max(x, y)) 1117.62/292.04 twice(0) -> 0 1117.62/292.04 twice(s(x)) -> s(s(twice(x))) 1117.62/292.04 -(x, 0) -> x 1117.62/292.04 -(s(x), s(y)) -> -(x, y) 1117.62/292.04 p(s(x)) -> x 1117.62/292.04 f(s(x), s(y)) -> f(-(max(s(x), s(y)), min(s(x), s(y))), p(twice(min(x, y)))) 1117.62/292.04 1117.62/292.04 S is empty. 1117.62/292.04 Rewrite Strategy: INNERMOST 1117.62/292.04 ---------------------------------------- 1117.62/292.04 1117.62/292.04 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1117.62/292.04 Renamed function symbols to avoid clashes with predefined symbol. 1117.62/292.04 ---------------------------------------- 1117.62/292.04 1117.62/292.04 (2) 1117.62/292.04 Obligation: 1117.62/292.04 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1117.62/292.04 1117.62/292.04 1117.62/292.04 The TRS R consists of the following rules: 1117.62/292.04 1117.62/292.04 min(0', y) -> 0' 1117.62/292.04 min(x, 0') -> 0' 1117.62/292.04 min(s(x), s(y)) -> s(min(x, y)) 1117.62/292.04 max(0', y) -> y 1117.62/292.04 max(x, 0') -> x 1117.62/292.04 max(s(x), s(y)) -> s(max(x, y)) 1117.62/292.04 twice(0') -> 0' 1117.62/292.04 twice(s(x)) -> s(s(twice(x))) 1117.62/292.04 -(x, 0') -> x 1117.62/292.04 -(s(x), s(y)) -> -(x, y) 1117.62/292.04 p(s(x)) -> x 1117.62/292.04 f(s(x), s(y)) -> f(-(max(s(x), s(y)), min(s(x), s(y))), p(twice(min(x, y)))) 1117.62/292.04 1117.62/292.04 S is empty. 1117.62/292.04 Rewrite Strategy: INNERMOST 1117.62/292.04 ---------------------------------------- 1117.62/292.04 1117.62/292.04 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1117.62/292.04 Infered types. 1117.62/292.04 ---------------------------------------- 1117.62/292.04 1117.62/292.04 (4) 1117.62/292.04 Obligation: 1117.62/292.04 Innermost TRS: 1117.62/292.04 Rules: 1117.62/292.04 min(0', y) -> 0' 1117.62/292.04 min(x, 0') -> 0' 1117.62/292.04 min(s(x), s(y)) -> s(min(x, y)) 1117.62/292.04 max(0', y) -> y 1117.62/292.04 max(x, 0') -> x 1117.62/292.04 max(s(x), s(y)) -> s(max(x, y)) 1117.62/292.04 twice(0') -> 0' 1117.62/292.04 twice(s(x)) -> s(s(twice(x))) 1117.62/292.04 -(x, 0') -> x 1117.62/292.04 -(s(x), s(y)) -> -(x, y)
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